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astro-ph0001259

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we found that even if new high resolution images show that most of the so - called tidal dwarf galaxies are clusters of young compact massive star clusters they are likely to merge within a short time - scale . the properties of the merger - objects differ with the scale - length of their initial distribution . we found large fluffy objects with similar properties as the local dsph - galaxies as well as very compact and massive spheroidal objects , which , however , may be similar to the progenitors of some of the local present - day dsph satellites . + in the course of future work we intend to investigate the influence of the choice of orbit around the parent galaxy and how this alters the results . we will focus on the transition between bound and unbound objects , and look for a region in the space of parameters where 2 merger - objects ( binary system ) are more likely to form . our further research will also address the future fate of the merger - objects and their possible counterparts in reality . fellhauer , m. , et al . 2000 , submitted to newa hunsberger , s. d. 1997 , , 29 , 1406 kroupa , p. 1997 , newa , 2 , 139 - 164 kroupa , p. 1998 , , 300 , 200 - 204 theis , c. 1996 astron.soc.pac.conf.ser . , 112 , 35 - 44 whitmore , b. c. , schweizer , f. 1995 , , 109 , 960 - 980 , 1412 - 1416 : it would be interesting to try and see if the age distribution among clusters that are clustered is different ( younger ) from that of yscs distributed more homogeneously . what do you expect to happen with the merged clusters that you compared to a dsph . is nt it bound to sink into the core of the merger remnant by dynamical friction ? the bulk of the yscs is at @xmath18 kpc from the nucleus of ngc 4038 , i.e. not further away than ngc 4039 ( nucleus ) ! + * answer * : we assume that at least some of the tidal - tail dwarfs seen to form in outer ( @xmath19 kpc ) tidal arms are composed of clusters of young massive star clusters . for our models we use an analytic galactic potential , because in the mass range of the merger - object of about @xmath20 m@xmath21 , dynamical friction does not play a significant role . + * e. grebel * : could you comment on how the merged clusters will resemble a dsph galaxy in their properties ( e.g. dsph do nt show rotation , have very low density and surface brightness , etc . ) ? + * answer * : it is too early to quantify the reply in detail , but we expect the merged object to show properties that could make it look similar to the progenitors of some of the dsph satellites . the merged object is spheroidal , and has a high specific frequency of globular clusters , and low angular momentum , which however depends on the initial conditions . it s stellar population contains stars from the mother galaxy , as well as stars formed during the star burst , and maybe stars ( and clusters ) formed during a possible later accretion event of a co - moving gas cloud . many of these issues are discussed in kroupa ( 1998 ) . + * j. gallagher * ( comment ) : since super - star - clusters are often born in groups the luminous clumps destruction via cluster merging is of general interest . for example , if this process reduces the survival rate of massive - star - clusters , it might help to explain why intermediate age examples seem to be rare . + * d. mclaughlin * : what evidence is there that the clustered clusters in the antennae will actually merge ? there are @xmath22 m@xmath21 clouds of gas in this system , so it may be that young clusters are clustered because several form in any given cloud , but they disperse after gas - loss . with no information on either the cluster - cluster velocity dispersion or the time when the parent cloud was disrupted , it would be difficult to rule out this possibility . + * answer * : this is an important issue , and very similar to the problem of forming bound star clusters . while not disproving rapid dispersal entirely , the argument which makes rapid dispersal less likely is as follows : the cluster - cluster velocity dispersion , @xmath23 is either small , which will lead to a bound merger object . if @xmath23 is near to virial for the _ stellar _ mass in the super - cluster , then our models take care of that . if , however , @xmath23 is virial for the stars and a much larger mass in gas , then @xmath24 km / s assuming a star - formation efficiency of 20 per cent and a pre - gas removal super - cluster configuration as in run5 here . thus , within 10 myr , the object will have expanded to a radius of at least 350 pc . since many of the super - clusters are still very concentrated , and about 10 myr old , rapid expansion does not appear to be taking place , especially so since there are at least about 10 observed super clusters and they would have had to start in unrealistically concentrated configurations for them to appear with the sizes they have now . this is further discussed in ( kroupa 1998 ) .

we investigate the behaviour of a cluster of young massive star clusters ( hereafter super - cluster ) in the tidal field of a host galaxy with a high - resolution particle - mesh code , _ superbox_. specifically we want to establish if and how such super star - clusters merge and carry out a detailed study of the resulting merger - object . this merger - object shows either the properties of a compact spherical object or the elongated ( ` fluffy ' ) shape of dsph - galaxies depending on the initial concentration of the super - cluster .

we investigate the behaviour of a cluster of young massive star clusters ( hereafter super - cluster ) in the tidal field of a host galaxy with a high - resolution particle - mesh code , _ superbox_. specifically we want to establish if and how such super star - clusters merge and carry out a detailed study of the resulting merger - object . this merger - object shows either the properties of a compact spherical object or the elongated ( ` fluffy ' ) shape of dsph - galaxies depending on the initial concentration of the super - cluster .

astro-ph0212078

r

although the galaxies in our sample were selected as a fairly homogeneous group with respect to hubble type , distance , and inclination , the sbps show a wide range of shapes . to address this quantitatively , we started by fitting for each galaxy an exponential profile to the i - band sbps inside the pc field . we will refer to this as the ` inner exponential fit ' . in this fit we always excluded the nuclear cluster , as well as any ` central excess emission ' ( the definition and nature of which is discussed below ) , if present . the fits are shown as solid lines in the left panel of each plot . we show the same exponential fit also in the right panel of each plot ( so the solid line in the right panel is _ not _ a fit to the panbg data , but only the continuation of the fit in the left panel ) . the extent to which the inner exponential fit describes the data at the different radii differs considerably for the different galaxies . to illustrate this point , we have ordered the galaxies in figure [ fig : baghst ] in a rough sequence , according to the following scheme . the sequence starts with galaxies for which there is no evidence for a bulge of other inner component in the sbp , except for the nuclear star cluster ( which has a typical hwhm radius of @xmath19 ; paper i ) . this group itself is somewhat heterogeneous . for some galaxies the inner exponential fit yields a good description of the large - scale stellar disk as measured by the panbg profiles ( e.g. , ngc428 ) . these galaxies are fairly well described by a single exponential . for other galaxies ( e.g. , ngc4299 ) , the outer disk falls below the inner exponential fit , which implies that the sbp at small radii falls _ below _ the inward extrapolation of the outer disk . this is exactly opposite to what one would expect if a bulge were present ( see [ subsec : really ] below ) . we interpret both types of galaxy as pure disk systems . interestingly , these pure disks have sbps that can differ from a single exponential . progressing along the sequence , the profiles show an increasing amount of light in excess of the inner exponential fit on radial scales of a few hundred pc ( the affected radii were excluded from the inner exponential fit ) . we refer to this light as ` central excess emission ' . this emission has a distinct profile shape : while the overall galaxy profile steepens towards the center , the excess component flattens towards the center ( see , e.g. , ngc275 , ngc2139 , or ngc3346 ) . this is different from what one would expect for a bulge . bulges tend to have @xmath0 profiles with @xmath20 @xcite . such profiles steepen towards the center , when plotted as a function of ( linear ) @xmath21 . consequently , we interpret the central excess emission as a phenomenon that is different from a central bulge . we discuss this component further in [ subsec : exc ] . approximately halfway along the sequence the outward extrapolation of the inner exponential fit begins to underpredict considerably the true brightness of the outer disk ( e.g. , ngc5068 ) . conversely , this implies that there is excess light in the central few kpc over the inward extrapolation of the outer disk . this is the component that is traditionally called a bulge . we discuss the nature of this component further in [ subsec : really ] . given the narrow range of hubble types of our sample ( between scd and sm ) , and the uniformity in inclination ( less than @xmath22 from face - on ) , the variety of profile shapes is somewhat surprising . in addition , there seems to be no clear trend of position along our sequence with either hubble type or galaxy luminosity . for example , the profiles of ngc275 and ngc1042 are very different , even though both galaxies have nearly identical hubble type ( sb(rs)cd vs. sab(rs)cd ) and total blue magnitude ( @xmath23 ) . clearly , late - type spirals are not simple systems , their morphologies ( and possibly evolutionary states ) can differ drastically . a considerable source of confusion in discussions of bulges is that different definitions are often used when referring to a bulge . modern theorists tend to think of a bulge as a kinematically hot component with an extended three - dimensional structure . however , the observational definition of a bulge is often a different one , and relies on the assumption that bulges have different sbps than disks . the standard wisdom is that a disk can be well fit by an exponential profile , @xmath24 . by contrast , bulges can be described empirically with either a second exponential with different scale length ( e.g. * ? ? ? * ) , a de vaucouleurs @xmath1 profile ( e.g. * ? ? ? * ; * ? ? ? * ) , or most generally , a srsic @xmath0 profile ( e.g. * ? ? ? * ) . if one defines a bulge as ` the central concentration of mass [ or light ] in excess of the inward extrapolation of the outer , constant scale - length , exponential disk ' @xcite , one must make sure that exponential profiles indeed provide a highly accurate description of galaxy disks . here one is on shaky ground . the exponential model has been widely used to describe galaxy disks because it provides a fairly good fit to many observed galaxy profiles ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? however , the fits are generally restricted to the region outside the central few kpc , so that it is actually very hard to know whether disks remain exponential all the way into the center . the disks of many late - type spirals in fact show sharp , well - defined `` breaks '' in their brightness profiles , which separate sections of the disk that follow exponential profiles with different scale lengths @xcite . so observationally , it is not at all clear how photometry alone can distinguish between an exponential bulge and a somewhat steeper disk section in the inner part of the galaxy . theoretical considerations also do not clinch the argument . there is no theory that unequivocally predicts that disks must be exponential . as an ` a posteriori ' explanation , ( semi-)analytical models that invoke angular momentum redistribution via viscosity - driven radial gas flows can provide a plausible mechanism for building profile shapes close ( but not identical ) to an exponential . this has been demonstrated in the initial work by @xcite and @xcite , and recently confirmed by the refined study of @xcite . an alternative scenario which invokes self - propagating stochastic star formation in a disk of constant density atomic hydrogen gas @xcite also results in brightness profiles that approximate the exponential shape . however , all these models are dependent on a number of parameters , which can be fine - tuned to reproduce a range of profile shapes . in fact , most model profiles presented by @xcite show significant curvature at all radii . it is therefore not obvious that a simple exponential is a good analytic model for disks to begin with . in order to demonstrate the ambiguity of profile decompositions , and the ensuing interpretation of the derived `` bulge '' properties , we have compared two different fits to the combined ( wfpc2 plus panbg ) datasets , excluding again the nuclear cluster . the two models are : ( a ) a single srsic profile ; and ( b ) the sum of two exponentials of different scale lengths . interestingly , we find that most galaxies in the second half of our sequence are equally well fit with either model , thus questioning the need for a `` bulge '' component . this is demonstrated in figure [ fig : comps ] which compares these two fits for five galaxies with apparent disk - bulge transitions . in most cases the two profiles provide equally adequate fits , and for one galaxy , ngc5668 , the srsic profile provides an obviously better fit . only for one galaxy , ngc1042 , does a sum of two exponentials provide the better fit . overall , we find that roughly half of our sample galaxies show excess light ( over the inward extrapolation of the outer exponential disk ) that can be fit by a second exponential . this is similar to the ` pseudo bulges ' or ` exponential bulges ' that have been reported by other authors , mostly in earlier type spirals . however , the extent to which this excess light is associated with a bona - fide bulge component remains an open question . the sbps of these galaxies are generally well fit with srsic profiles with @xmath25@xmath26 ( as listed in the panels of figure [ fig : comps ] ) . in the absence of information on kinematics or three - dimensional structure it is difficult to rule out that we are dealing merely with non - exponential disks , or possibly small - scale stellar bars which are known to also have exponential - like sbps ( e.g. * ? ? ? as described in [ subsec : seq ] , several galaxies of our sample show evidence for central excess emission on scales of a few hundred pc which does not show the steepening characteristic of bulges . in order to investigate the nature of this emission , we have measured the amount of excess light for four example cases ( ngc275 , ngc2139 , ngc3346 and ngc5584 ) . we first determined by eye the radius @xmath27 at which the sbp starts to deviate from the inward extrapolation of the exponential fit . we then analyzed the wfpc2 i - band images presented in paper i with the _ iraf _ photometry package _ apphot _ in order to measure the total flux within a circular aperture of radius @xmath27 , centered on the nuclear star cluster . to give a better visual impression of the four case studies , figure [ fig : four ] reproduces their images presented in paper i. here , we have overlaid circles with radius @xmath27 to indicate the aperture over which we measure the excess emission . also , we have slightly modified the grey scale stretch to emphasize the disk structure rather than the nuclear cluster . from the total flux inside @xmath27 , we subtract the contribution of the galaxy disk which is calculated by integrating the exponential fit ( the solid lines in figure [ fig : baghst ] ) inside @xmath27 . we also subtract the light from the nuclear cluster as listed in paper i , which usually constitutes only a small correction . table [ tab : excess ] summarizes the results of this analysis . for the four galaxies of figure [ fig : four ] , the apparent magnitude of the excess emission is in the range @xmath28 which corresponds to luminosities between @xmath29 and @xmath30 . this is between 10 and 100 times brighter than the median luminosity of the nuclear star cluster in our sample ( @xmath31 or @xmath32 , paper i ) , but constitutes only between 1% and 5% of the total galaxy luminosity . it is interesting that with absolute luminosities of @xmath33 ( using the distances in table [ tab : excess ] ) , this excess emission appears to be a faint end continuation of the distribution of spiral bulge luminosities shown in figure14 of @xcite , if one assumes a mean color of @xmath34 . the images in figure [ fig : four ] reveal a variety of morphologies for the excess emission . for ngc275 , ngc5584 , and ngc3346 , the emission appears fairly smooth and follows the larger scale disk structure . however , this is clearly not the case for ngc2139 , for which the observed excess emission ( which is also by far the brightest in our sample ) is due to a prominent , bright star forming region which is elongated in the e - w direction . inspection of the wf chips shows that this structure is the inward continuation of at least one spiral arm ( the other direction is off the wfpc2 field of view ) . this underlines the danger of relying solely on one - dimensional surface brightness data for evaluating galaxy morphology .

we have sorted our sample in a sequence , starting with `` pure '' disk galaxies ( approximately 30% of the sample ) . they appear to be truly bulge - less systems . progressing along the sequence , the galaxies show increasingly prominent deviations from a simple exponential disk model on kpc scales .

we investigate the stellar disk properties of a sample of 19 nearby spiral galaxies with low inclination and late hubble type ( scd or later ) . we combine our high - resolution _ hubble space telescope _ i - band observations with existing ground - based optical images to obtain surface brightness profiles that cover a high dynamic range of galactic radius . most of these galaxies contain a nuclear star cluster , as discussed in a separate paper . the main goal of the present work is to constrain the properties of stellar bulges at these extremely late hubble types . we find that the surface brightness profiles of the latest - type spirals are complex , with a wide range in shapes . we have sorted our sample in a sequence , starting with `` pure '' disk galaxies ( approximately 30% of the sample ) . these galaxies have exponential stellar disks that extend inwards to within a few tens of pc from the nucleus , where the light from the nuclear cluster starts to dominate . they appear to be truly bulge - less systems . progressing along the sequence , the galaxies show increasingly prominent deviations from a simple exponential disk model on kpc scales . traditionally , such deviations have prompted `` bulge - disk '' decompositions . indeed , the surface brightness profiles of these galaxies are generally well fit by adding a second ( exponential ) bulge component . however , we find that most surface brightness profiles can be fit equally well ( or better ) with a single srsic - type @xmath0 profile over the entire radial range of the galaxy , without requiring a separate `` bulge '' component . we warn in a general sense against identification of bulges solely on the basis of single - band surface brightness profiles . despite the narrow range of hubble types in our sample , the surface brightness profiles are far from uniform . the differences between the various galaxies appear unrelated to their hubble - types , thus questioning the usefulness of the hubble - sequence for the sub - categorization of the latest - type spirals . a number of galaxies show central excess emission on spatial scales of a few hundred parsec that can be attributed neither to the nuclear cluster , nor to the srsic - type description of the stellar disk , nor to what one would generally consider to be a bulge component . the origin of this light component remains unclear .

astro-ph0212078

c

we have presented an investigation into the structural properties of 19 spiral galaxies with hubble type between scd and sm . from a combination of our high - resolution hst data and wide - field ground - based images , we obtain surface brightness profiles ( sbps ) for the sample galaxies that cover a large dynamic range in galactic radius . we use these profiles to study quantitatively the presence and properties of bulges in spiral galaxies of the very latest hubble types . of course , by the very definition of the hubble sequence , one does not expect very prominent bulges in these galaxies . however , it has been somewhat of an open question whether bulges are present at all in these galaxies . it has been realized only recently that space - based resolution is required to properly address this question . the nuclear morphologies of most spiral galaxies are complex , and a large fraction of spiral galaxies has a nuclear star cluster . these clusters are easily mistaken for `` compact bulges '' when observed with ground - based resolution . previous studies with the hst have focused in majority on earlier hubble types , and the present study is the first to focus exclusively on the very latest hubble types . approximately 30% of the sample galaxies seem to be more - or - less `` pure '' exponential disks , without any type of a central bulge . our sample was selected to focus on face - on galaxies , but studies of edge - on galaxies support the view that disk galaxies can indeed be completely bulgeless . @xcite and @xcite have studied edge - on `` super - thin '' galaxies such as ugc7321 , and have demonstrated that in these galaxies there is no evidence for a spheroidal component . despite being disk - dominated systems , most galaxies in our sample have sbps that can not be well fit by a single exponential , in the sense that the surface brightness in the central few kpc exceeds the inward extrapolation of the outer exponential disk . this has generally been found for other samples of spirals as well , and has generally prompted the addition of a bulge component to analytic models of the sbp . in particular , numerous studies have shown that the sbps of intermediate- to late - type spirals can be well fit by a sum of two exponentials . the inner exponential has traditionally been interpreted as an ` exponential ' bulge or ` pseudo ' bulge . such bulges can be ( qualitatively ) explained theoretically as a result of secular evolution of the disk . while this may be correct , we point out that this is not an unambiguous interpretation . in the absence of information on three - dimensional structure or dynamics there is no guarantee that one is dealing with a bona - fide bulge component . we explicitly illustrate this point for the galaxies in our sample that are not well fit by a single exponential . indeed , the sbps of these galaxies are generally well fit by a sum of two exponentials . however , most profiles can be described at least equally well with a srsic - type @xmath0 model over the entire radial range ( outside the nuclear star cluster ) . the shape parameter @xmath3 is in the range @xmath35 , which is not unrealistically large . as we have discussed in [ subsec : really ] , there is no a priori theoretical reason for the sbps of disk galaxies to be pure exponentials ; srsic - type profiles are in some sense equally arbitrary as the model of choice . so it may well be that we are simply dealing with non - exponential disks in most of our sample galaxies , and that bona - fide bulges are rare at these hubble types . we have found that a number of late - type galaxies show central excess emission on spatial scales of a few hundred parsec that can be attributed neither to the nuclear cluster , nor to the srsic - type description of the stellar disk , nor to what one would generally consider to be a bulge component . the origin of this light component remains unclear . one of the interesting findings from our work is that , despite the narrow range in hubble type , the sbps of the sample galaxies are far from uniform . our study finds no systematic trends in the structural properties with morphological type . the exact hubble type of spirals between scd and sm appears somewhat arbitrary , in the sense that it provides little information about the presence and relative importance of galaxy bulges . it is quite possible that this may be due to the presence of nuclear clusters , which may have played an important role in the morphological classification in photographic catalogs . in general our results fit in well with the picture that emerged from a ground - based imaging study of 49 late - type spirals by @xcite . they found that late - type spirals exhibit a diverse array of structural properties and morphologies , even in galaxies with otherwise similar parameters , and they concluded that bulges are often very weak or non - existent . in studies of this kind one does need to be concerned about selection effects and observational bias . the @xcite sample was selected for low galaxy luminosity ( @xmath36 ) , and one might worry that it did not provide a representative view of the family of very late - type spirals . our galaxy sample , on the other hand , has been selected only for hubble type , distance , and inclination . it thus includes more luminous ( and presumably more massive ) galaxies than the @xcite sample . the blue absolute luminosity of the galaxies in our sample ranges from @xmath37 ( ngc2552 , ngc4701 ) to @xmath38 ( ngc2805 ) . however , we find no systematic correlation between absolute luminosity and position along the sequence of sbp shapes discussed in [ subsec : seq ] . this suggests that more luminous late - type spirals are not systematically different from their faint - end relatives , and that presumably the @xcite results are valid for most late - type spirals . late type spiral galaxies are in most ways `` normal '' spiral galaxies . their angular momenta and rotation velocities are not atypical , as demonstrated by a recent survey of optical rotation curves @xcite . they are in some sense the dynamically simplest type of disk galaxies . they are ( mostly ) disk - dominated and often have only faint spiral arm structure or even no detectable density perturbations at all . yet , we are clearly a long way from understanding their formation and evolution . the latest - type disk galaxies provide the most stringent observational constraints on the well - known angular momentum problem in cold dark matter ( cdm ) galaxy formation models ( e.g. * ? ? ? * ) . because of their unevolved disks and apparent history of only modest star formation , they are a challenge for proposed solutions for the angular momentum problem which rely on energy feedback from supernova explosions @xcite . to gain a better understanding of these issues it will be important to continue to improve our knowledge of the structure of late - type spiral galaxies . observational studies such as the one presented here will continue to be essential . we are grateful to m. hamabe for providing us with the digital surface brightness data from the panbg , to roelof de jong for helpful discussions , and to the anonymous referee for useful comments . r. s. acknowledges a grant from the stsci summer student program . support for proposal # 8599 was provided by nasa through a grant from the space telescope science institute , which is operated by the association for research in astronomy , inc . , under nasa contract no . nas 5 - 26555 . this research has made use of the nasa / ipac extragalactic database ( ned ) which is operated by the jet propulsion laboratory , california institute of technology , under contract with nasa . it has also benefited greatly from use of the lyon - meudon extragalactic database ( leda , http://leda.univ-lyon1.fr ) . aguerri , j. a. l. , balcells , m. , & peletier 2001 , , 367 , 428 andredakis , y. c. , & sanders , r. h. 1994 , , 267 , 283 andredakis , y. c. , peletier , r. f. , & balcells , m. 1995 , mnras , 275 , 874 baggett , w. e. , baggett , s. m. , & anderson , k. s. j. 1998 , aj , 116 , 1626 bker , t. , laine , s. , van der marel , r. p. , sarzi , m. , rix , h .- w . , ho , l. c. , & shields , j. c. 2002 , aj , 123 , 1389 ( paper i ) boroson , t. a. 1981 , apjs , 46 , 177 bosma , a. , & freeman , k. c. 1993 , aj , 106 , 1394 carollo , c. m. , stiavelli , m. , & mack , j. 1998 , aj , 116 , 68 carollo , c. m. , ferguson , h. c. , & wyse , r. f. g. 1999 , eds . , the formation of galactic bulges . cambridge : cambridge university press de jong , r. s. 1996a , a&as , 118 , 557 de jong , r. s. 1996b , a&a , 313 , 377 de vaucouleurs , g. 1948 , ann . dastrophysique , 11 , 247 eggen , o. , lynden - bell , d. , & sandage , a. 1962 , apj , 136 , 748 elmegreen , b. g. , & elmegreen , d. m. 1985 , apj , 288 , 438 ferguson , a. m. n. , & clarke , c. j. 2001 , , 325 , 781 freeman , k. c. 1970 , apj , 160 , 811 graham , a. w. 2001 , aj , 121 , 820 hubble , e. 1926 , apj , 64 , 321 hubble , e. 1936 , the realm of the nebulae ( new haven : yale univ . press ) kent , m. s. 1984 , apjs , 56 , 105 kodaira , k. , okamura , s. , & ichikawa , s. 1990 , _ photometric atlas of northern bright galaxies _ ( tokyo : univ . of tokyo press ) ( panbg ) kormendy j. 1993 , in _ galactic bulges _ , iau symp . 153 , ( dordrecht : kluwer ) , p. 209 kormendy j. , & bender , r. 1996 , apj , 464 , 119 lin , d. n. c. , & pringle , j. e. 1987 , , 320 , l87 matthews , l. d. , & gallagher , j. s. 1997 , aj , 114 , 1899 matthews , l. d. , gallagher , j. s. & van driel , w. 1999 , aj , 118 , 2751 matthews , l. d. 2000 , aj , 120 , 1764 matthews , l. d. & gallagher , j. s. 2002 , apjs , in press [ astro - ph/0203188 ] navarro , j. f. , & steinmetz , m. 2000 , apj , 538 , 477 norman , c. a. , sellwood , j. a. , & hasan , h. 1996 , apj , 462 , 114 raha , n. , sellwood , j. a. , james , r. a. , & kahn , f. d. 1991 , nature , 352 , 411 sandage a. , & tammann , g. 1990 , apj , 365 , 1 seiden , p. e. , schulman , l. s. , & elmegreen , b. g. 1984 , apj , 282 , 95 srsic , j .- l . 1968 , atlas de galaxias australes ( cordoba : obs . astron . ) silk , j. 2001 , mnras , 324 , 313 wyse , r. f. g. , gilmore , g. , & franx , m. 1997 , , 35 , 637 yoshii , y. , & sommer - larsen , j. 1989 , , 236 , 779 lcccccc ngc275 & 00 51 04.20 & -07 04 00.0 & 1681 & sb(rs)cd pec & 13.16 & 1.5 + ngc428 & 01 12 55.60 & -00 58 54.4 & 1130 & sab(s)m & 11.91 & 4.1 + ngc1042 & 02 40 23.63 & -08 25 59.8 & 1271 & sab(rs)cd & 12.50 & 4.7 + ngc2139 & 06 01 07.90 & -23 40 21.3 & 1649 & sab(rs)cd & 11.99 & 2.6 + ngc2552 & 08 19 20.14 & + 50 00 25.2 & 695 & sa(s)m ? & 12.56 & 3.5 + ngc2805 & 09 20 24.56 & + 64 05 55.2 & 1968 & sab(rs)d & 11.52 & 6.3 + ngc3346 & 10 43 38.90 & + 14 52 18.0 & 1315 & sb(rs)cd & 12.41 & 2.9 + ngc3423 & 10 51 14.30 & + 05 50 24.0 & 1025 & sa(s)cd & 11.59 & 3.8 + ngc3445 & 10 54 35.87 & + 56 59 24.4 & 2245 & sab(s)m & 12.90 & 1.6 + ngc4027 & 11 59 30.50 & -19 15 44.0 & 1588 & sb(s)dm & 11.66 & 3.2 + ngc4299 & 12 21 40.90 & + 11 30 03.0 & 306 & sab(s)dm : & 12.88 & 1.7 + ngc4540 & 12 34 50.90 & + 15 33 06.9 & 1383 & sab(rs)cd & 12.44 & 1.9 + ngc4701 & 12 49 11.71 & + 03 23 21.8 & 768 & sa(s)cd & 12.80 & 2.8 + ngc4775 & 12 53 45.79 & -06 37 20.1 & 1565 & sa(s)d & 12.24 & 2.1 + ngc4904 & 13 00 56.97 & -00 01 31.9 & 1204 & sb(s)cd & 12.60 & 2.2 + ngc5068 & 13 18 54.60 & -21 02 19.7 & 607 & sb(s)d & 10.52 & 7.2 + ngc5585 & 14 19 48.08 & + 56 43 43.8 & 571 & sab(s)d & 11.20 & 5.8 + ngc5584 & 14 22 23.65 & -00 23 09.2 & 1695 & sab(rs)cd & 12.63 & 3.4 + ngc5668 & 14 33 24.30 & + 04 27 02.0 & 1665 & sa(s)d & 12.2 & 3.3 + lcccccccc ngc275 & 24.0 & 2.5 & 290 & 15.33 & 15.54 & 19.47 & 17.38 & 2.9 + ngc5584 & 24.2 & 3.5 & 410 & 15.11 & 15.36 & 22.53 & 16.83 & 5.2 + ngc3346 & 18.8 & 5.0 & 460 & 14.61 & 14.73 & 19.64 & 17.21 & 2.0 + ngc2139 & 23.6 & 7.0 & 800 & 12.98 & 13.13 & 19.28 & 15.24 & 19.2 +

we investigate the stellar disk properties of a sample of 19 nearby spiral galaxies with low inclination and late hubble type ( scd or later ) . we combine our high - resolution _ hubble space telescope _ i - band observations with existing ground - based optical images to obtain surface brightness profiles that cover a high dynamic range of galactic radius . traditionally , such deviations have prompted `` bulge - disk '' decompositions . indeed , the surface brightness profiles of these galaxies are generally well fit by adding a second ( exponential ) bulge component . however , we find that most surface brightness profiles can be fit equally well ( or better ) with a single srsic - type @xmath0 profile over the entire radial range of the galaxy , without requiring a separate `` bulge '' component . we warn in a general sense against identification of bulges solely on the basis of single - band surface brightness profiles . despite the narrow range of hubble types in our sample , the surface brightness profiles are far from uniform . a number of galaxies show central excess emission on spatial scales of a few hundred parsec that can be attributed neither to the nuclear cluster , nor to the srsic - type description of the stellar disk , nor to what one would generally consider to be a bulge component . the origin of this light component remains unclear .

we investigate the stellar disk properties of a sample of 19 nearby spiral galaxies with low inclination and late hubble type ( scd or later ) . we combine our high - resolution _ hubble space telescope _ i - band observations with existing ground - based optical images to obtain surface brightness profiles that cover a high dynamic range of galactic radius . most of these galaxies contain a nuclear star cluster , as discussed in a separate paper . the main goal of the present work is to constrain the properties of stellar bulges at these extremely late hubble types . we find that the surface brightness profiles of the latest - type spirals are complex , with a wide range in shapes . we have sorted our sample in a sequence , starting with `` pure '' disk galaxies ( approximately 30% of the sample ) . these galaxies have exponential stellar disks that extend inwards to within a few tens of pc from the nucleus , where the light from the nuclear cluster starts to dominate . they appear to be truly bulge - less systems . progressing along the sequence , the galaxies show increasingly prominent deviations from a simple exponential disk model on kpc scales . traditionally , such deviations have prompted `` bulge - disk '' decompositions . indeed , the surface brightness profiles of these galaxies are generally well fit by adding a second ( exponential ) bulge component . however , we find that most surface brightness profiles can be fit equally well ( or better ) with a single srsic - type @xmath0 profile over the entire radial range of the galaxy , without requiring a separate `` bulge '' component . we warn in a general sense against identification of bulges solely on the basis of single - band surface brightness profiles . despite the narrow range of hubble types in our sample , the surface brightness profiles are far from uniform . the differences between the various galaxies appear unrelated to their hubble - types , thus questioning the usefulness of the hubble - sequence for the sub - categorization of the latest - type spirals . a number of galaxies show central excess emission on spatial scales of a few hundred parsec that can be attributed neither to the nuclear cluster , nor to the srsic - type description of the stellar disk , nor to what one would generally consider to be a bulge component . the origin of this light component remains unclear .

1108.1949

i

in this paper we consider the ginzburg - landau energy posed on a @xmath0-manifold . we will present two results , one for critical points of the ginzburg - landau energy and one for the ginzburg - landau heat flow , both showing the non - existence of stable vortex solutions under certain geometric assumptions on the manifold . we say a critical point is unstable if there is a direction in which the second variation of the energy is negative . for the heat flow , we will show that all initial data , even those containing vortices , will eventually converge to a vortex - free solution . let @xmath1 be ginzburg - landau energy on an orientable manifold @xmath2 equipped with a metric @xmath3 for @xmath4 , @xmath5 there is a vast literature on ginzburg - landau , but we review here just a few of the results most closely related to our investigation . when @xmath2 is a bounded domain @xmath6 , and under an @xmath7-valued dirichlet condition , bethuel , brezis and hlein establish in @xcite that vortices of minimizers converge as @xmath8 to a finite set of points or limiting vortices @xmath9 . here vortices refer to zeros of the order parameter @xmath10 carrying nonzero degree . moreover , the limiting vortex locations @xmath9 will minimize a renormalized energy @xmath11 . another important result comes in @xcite where for @xmath12 , jimbo and morita prove that under homogeneous neumann boundary conditions , if @xmath13 is convex , the only stable critical points are constants for any @xmath14 . most important to our work on stability of critical points is the work of serfaty in @xcite on ginzburg - landau in simply connected planar domains . here she shows that there is no nonconstant stable critical point of @xmath1 with homogeneous neumann boundary conditions for @xmath15 small . to achieve this , she shows that the renormalized energy has no stable critical points . then using her theory of @xmath16-gamma convergence , " she argues that there must be unstable directions for the hessian of @xmath17 as well for @xmath15 small . our first main result ( theorem [ main ] ) in this paper is that for compact , simply connected @xmath0-manifolds without boundary , any critical points must be unstable when @xmath15 is small if at least one limiting vortex is located at a point of positive gauss curvature . furthermore , if one additionally assumes that @xmath18 is a surface of revolution with non - zero gauss curvature at at least one of the poles , then we argue that all critical points are unstable for @xmath15 small , regardless of the curvature of the manifold at the limiting vortex locations ( theorem [ thm3 ] ) . to prove this , we will apply serfaty s abstract result in @xcite ( see theorem [ s ] below ) , showing again that the renormalized energy has no stable critical points on such manifolds . for ginzburg - landau posed on a @xmath0-manifold , baraket generalizes the work of @xcite to identify the renormalized energy on compact @xmath0-manifolds without boundary in @xcite . we should perhaps note that for ginzburg - landau in @xmath19-dimensional domains , there do exist stable vortex solutions ( @xcite ) . this analysis will be presented in section 2 . the second setting we consider is the heat flow for the ginzburg - landau energy , with @xmath20 , on surfaces of revolution @xmath18 with boundary : @xmath21 here @xmath22@xmath23 , and @xmath24 is any constant unit vector . we allow the compatible initial data @xmath25 to have any number of vortices though necessarily the total degree @xmath26 in light of the dirichlet condition . we want to find conditions on @xmath2 such that as @xmath27 , all vortices are annihilated . when @xmath28 , it has been shown in @xcite that if @xmath25 is close to @xmath24 at infinity in some sense , all vortices of @xmath29 disappear after a finite time . as in @xcite , we will derive a pohozaev - type inequality on surfaces ( lemma [ pohozaev ] ) to prove a similar result when @xmath2 is a simply connected surface of revolution satisfying an extra geometric assumption that is unrelated to curvature , see theorem [ koshin ] . this work is presented in section 3 .

we investigate two settings of ginzburg - landau posed on a manifold where vortices are unstable . the first is an instability result for critical points with vortices of the ginzburg - landau energy posed on a simply connected , compact , closed @xmath0-manifold . the second is a vortex annihilation result for the ginzburg - landau heat flow posed on certain surfaces of revolution with boundary .

we investigate two settings of ginzburg - landau posed on a manifold where vortices are unstable . the first is an instability result for critical points with vortices of the ginzburg - landau energy posed on a simply connected , compact , closed @xmath0-manifold . the second is a vortex annihilation result for the ginzburg - landau heat flow posed on certain surfaces of revolution with boundary .

1509.04858

i

in the early 1996s , grover search algorithm ( ga ) has attracted much interest , since it could work in quantum computer . the quantum search , from computational point of view , is proved to get approximately @xmath0 operations ( in comparison with the @xmath1 classical operations ) , which indicates a quadratic speedup @xcite . many efforts have been devoted to achievement of this algorithm theoretically and experimentally by using superconducting qubits @xcite , trapped ions @xcite , atom cavity qed systems @xcite and nuclear magnetic resonance @xcite . also , most previous studies for improving the quantum ga were general and do not depend on a physical system . further , all previous implementations of quantum ga have been developed depending on grover visualizations , where the control phase parameter for the controlled phase gates or oracle is switched to @xmath2 or @xmath3 @xcite . however , an interesting work by long et al @xcite has replaced the grover s arbitrary phase by @xmath4 . the combination of strong resonant interactions with tight subwavelength traps gives an excellent opportunity to implement much faster quantum gates . however , there is no way to achieve single site addressability in those systems . existing proposals circumventing this problem @xcite do not consider an arbitrary controlled phase parameter or dispassion effect , as the interaction need not to be restricted by certain values of the phase control . + in this article , we propose to add new factors allowing for significant speedup . by combining a multi - qubit system with dissipation taking into account an arbitrary phase control , we can achieve a fast search in a realistic setting . we assume that the control phase is time - dependent to realize the dynamical quantum controlled phase gates . it is shown that the involved time is the crucial factor for controlling and searching of any marked state regardless the number of qubits . consequently , we define a new algorithm called a dynamical quantum search algorithm ( dqsa ) . the proposed algorithm is a generalization of grover algorithm and ( i ) gives a higher probability of finding any marked state in shorter time , ( ii ) there is no restriction on the controlled phase parameter and ( iii ) the presence of qubits dissipation is allowed .

we invoke an efficient search algorithms as a key challenge in multi - qubit quantum systems . an original algorithm called dynamical quantum search algorithm from which grover algorithm is obtained at a specified time this algorithm is distinguished by accuracy in obtaining high probability of finding any marked state in a shorter time than grover algorithm time .

we invoke an efficient search algorithms as a key challenge in multi - qubit quantum systems . an original algorithm called dynamical quantum search algorithm from which grover algorithm is obtained at a specified time is presented . this algorithm is distinguished by accuracy in obtaining high probability of finding any marked state in a shorter time than grover algorithm time . the algorithm performance can be improved with respect to the different values of the controlled phase . a new technique is used to generate the dynamical quantum gates in the presence of dissipation effect that helps in implementing the current algorithm .

0710.5649

i

the proton structure has been widely explored in inclusive measurements , mainly in deeply inelastic lepton - proton scattering ( dis ) . here the scattering essentially occurs due to the exchange of a virtual boson ( photon ) between lepton and a single parton , and so one can access _ parton distribution functions _ ( pdfs ) . these universal , however , convention - dependent functions @xmath3 are interpreted as probabilities that partons of certain flavour @xmath4 will be found with given longitudinal momentum fraction @xmath5 . since the pdfs are naturally defined in a translation invariant manner , they do not carry information about the transversal distribution of partons . some information about transversal degrees of freedom can be obtained from elastic lepton - proton scattering . namely , the electromagnetic form factors @xmath6 are fourier transforms of the electric and magnetic charge distribution in nucleon , and can be , e.g. , in the infinite momentum frame , interpreted as probability that partons are found at some transversal distance @xmath7 from the center - of - mass . however , one should not assume that a realistic probability distribution of partons , given by a two - variable function @xmath8 is simply a direct product , i.e. , @xmath9 , of two probability functions . rather it is anticipated that longitudinal and transversal degrees of freedom have a cross talk , e.g. , as @xmath5 gets bigger partons carry more of the nucleon longitudinal momentum and are expected to be closer to the proton center , and thus the @xmath7 dependence in @xmath10 should become narrower with increasing @xmath5 . the three dimensional distribution of partons in the nucleon can be addressed within more general objects , called _ generalized parton distributions _ ( gpds ) @xcite . such distributions can be revealed by analyzing hard exclusive leptoproduction of mesons or photon . the theoretical description of the former processes is perhaps more problematic , but they offer a direct view into individual flavour gpds . to the latter one the _ deeply virtual compton scattering _ ( dvcs ) process contributes , where one photon has a large virtuality . dvcs is theoretically considered as the cleanest probe of gpds , however , here only certain flavour combinations of gpds appear . the non - forward compton scattering process is described by the compton tensor @xmath11 where @xmath12 , @xmath13 and @xmath14 . the generalized bjorken limit corresponds to @xmath15 with the scaling variables @xmath16 and the momentum transfer squared @xmath17 being fixed . note that in the forward case , i.e. , @xmath18 , the hadronic dis tensor @xmath19 is related to the _ forward _ compton scattering tensor by the optical theorem @xmath20 where @xmath21 and @xmath22 . [ cols="^,^,^ " , ]

we outline the twist - two analysis of deeply virtual compton scattering ( dvcs ) within the conformal partial wave expansion of the amplitude , represented as a mellin the radiative corrections are evaluated up to next - to - next - to - leading order . using a new proposed parameterization for gpds , we study the convergence of perturbation theory and demonstrate for h1 and zeus measurements that our formalism is suitable for a fitting procedure of dvcs observables .

we outline the twist - two analysis of deeply virtual compton scattering ( dvcs ) within the conformal partial wave expansion of the amplitude , represented as a mellin barnes integral . the complete next - to - leading order results , including evolution , are obtained in the @xmath0 and a conformal factorization scheme . within the latter , exploiting conformal symmetry , the radiative corrections are evaluated up to next - to - next - to - leading order . using a new proposed parameterization for gpds , we study the convergence of perturbation theory and demonstrate for h1 and zeus measurements that our formalism is suitable for a fitting procedure of dvcs observables . we comment on a recent claim of a breakdown of collinear factorization and show that a regge - inspired @xmath1 scaling law is ruled out by small @xmath2 dvcs data .

0710.5649

i

gpds encode a unified description of the proton structure and they are experimentally accessible via the hard leptoproduction of photon or mesons . we have shown that the representation of compton form factors as mellin - barnes integrals offers a useful tool in analyzing dvcs : the inclusion of evolution is simple , numerical treatment is stable and fast . although the motivation for this representation originated from manifest conformal symmetry at lo , we have shown here that this mellin barnes integral representation can be used within the standard @xmath23 scheme beyond lo . such a representation can be straightforwardly obtained from the momentum fraction representation and , therefore , also other gpd related processes , e.g. , the hard electroproduction of mesons , can be given in terms of mellin barnes integrals . this opens a new road for the ` global ' analysis of experimental data within the perturbative gpd formalism to nlo accuracy . furthermore , the use of conformal symmetry enables elegant approach to higher - order radiative corrections to the dvcs amplitude . we have shown that although nlo corrections can be sizable , and are strongly dependent on the gluonic input , the nnlo corrections are small to moderate , supporting perturbative framework of dvcs . the observed change in the scale dependence is not so conclusive : similarly as in dis we encounter large nnlo effects for @xmath24 , which signal a breakdown of naive perturbation series expansion of the evolution operator . nevertheless , this breakdown is universal and if we precisely define the treatment of this operator , perturbative qcd can be employed as a tool for analyzing data even in the small @xmath25 region . we expect that within increasing accuracy in the perturbative approximation the gpd formalism improves . finally , fits to available dvcs and dis data in collider kinematics work well in the collinear factorization approach beyond lo and give access to transversal distribution of partons . the lesson learned from the failure of lo fits can be extended to ( oversimplified ) gpd models used for phenomenology in fixed target kinematics . they do not possess a flexible skewness dependence parameterization and so the normalization of the amplitude for fixed @xmath26 is mostly determined . ironically , this non - flexibility originates from the implementation of pdf and form factor constraints in the most convenient manner . this can be repaired in the mellin - barnes representation by a model dependent resummation of so(3 ) partial waves or in the momentum fraction representation by a more flexible double distribution ansatz , in which also the correlation of @xmath26- and skewness dependence is improved @xcite . additionally , we have observed that the off - shell regge - exchange amplitudes@xcite , having the generic @xmath27-dependence of high - energy on - shell amplitudes , are ruled out . repairing this failure yields the well - known dilemma of regge - phenomenology . namely , when extended to off - shell processes it fails to describe high energy data and must be improved , thereby loosing its predictive power @xcite . this loss of predictive power appears also in description of deeply exclusive leptoproduction data in the valence quark region within regge inspired _ models _ , often outside of the accepted validity region @xmath28 in classical regge phenomenology , see e.g. @xcite . certainly , these approaches offer an easy and economical possibility to fit data and to interpret them in terms of mesonic exchanges and numerous couplings ( unknown form factors ) . in our opinion the gpd formalism offers a new perspective for our qcd understanding , including a handle on the dynamical sources of regge behavior . in this formalism one extracts information about non - perturbative quantities from experimental observables and interprets it in terms of partonic degrees of freedom . we consider regge - inspired interpretations of data @xcite as valuable tool for building realistic gpd models . this gives one handle more on the challenging task to understand hadron physics from qcd dynamics . non - perturbative gpd aspects , in particular regge behavior , might be studied within ( partial ) resummation of @xmath26-channel ladders ( in the language of light - cone wave functions of higher partonic fock states ) , e.g. , ref . @xcite , lattice simulations , and model building . this might lead to clues to improved understanding of hadron physics in terms of the underlying theory . for illuminating discussions on regge , bfkl , and collinear factorization approaches and their interplay as well as on gpd modelling we like to thank s. brodsky , m. diehl , b. ermolaev , v. fadin , d. ivanov , l.l . jenkovszky , p. kroll , m. polyakov , and a. radyushkin . in particular , we are grateful to a. szczepaniak for discussions on the work presented in ref . is indebted to a. miller , a.v . efremov and o. teryaev for invitation and support , allowing him to participate on _ the 6th circum - pan - pacific symposium on high energy spin physics _ and the _ xii workshop on high energy spin physics _ , k. p - k . would like to thank the organizers of the _ 12th international conference on elastic and diffractive scattering _ , desy hamburg , for invitation and support .

barnes integral . the complete next - to - leading order results , including evolution , are obtained in the @xmath0 and a conformal factorization scheme . within the latter , exploiting conformal symmetry , we comment on a recent claim of a breakdown of collinear factorization and show that a regge - inspired @xmath1 scaling law is ruled out by small @xmath2 dvcs data .

we outline the twist - two analysis of deeply virtual compton scattering ( dvcs ) within the conformal partial wave expansion of the amplitude , represented as a mellin barnes integral . the complete next - to - leading order results , including evolution , are obtained in the @xmath0 and a conformal factorization scheme . within the latter , exploiting conformal symmetry , the radiative corrections are evaluated up to next - to - next - to - leading order . using a new proposed parameterization for gpds , we study the convergence of perturbation theory and demonstrate for h1 and zeus measurements that our formalism is suitable for a fitting procedure of dvcs observables . we comment on a recent claim of a breakdown of collinear factorization and show that a regge - inspired @xmath1 scaling law is ruled out by small @xmath2 dvcs data .

1107.3347

i

while quantum physics is expected to play an important role near the big bang when the universe was small , there are a number of differing opinions on how to quantise the classical universe , see reviews in @xcite , leading to different approaches to quantum cosmology . one issue of interest in quantum cosmology is whether classical singularities are resolved @xcite . in our previous study @xcite we found the answer to be affirmative in the information - theoretic approach , as is the case also in many other approaches @xcite . the philosophy of the information - theoretic approach , also known as the maximum uncertainty ( entropy ) method " , is that one should minimise any bias when choosing probability distributions , while still satisfying relevant constraints @xcite . while this approach originated in statistical mechanics , it has wider applicability such as motivating the structure of the usual schrodinger equation @xcite and its potential nonlinear modifications to model new short distance effects@xcite . in our previous study @xcite , which we briefly review in the next section , we treated the nonlinearity of the modified wdw equation ( [ nl1 ] ) perturbatively and studied a truncated linearised equation with an effective potential . in this paper we present a full investigation for the case of a de sitter universe . the de sitter universe is a reasonable model for early stages of inflation and furthermore , if the current accelerating phase of our universe continues , then at late times it can again be well approximated as a de sitter universe . treating the universe as an isolated system , one may apply quantum mechanics to the whole de sitter universe regardless of its size ; in other words , study the wavefunction of the universe . our main intent in this paper is to see how the classical de sitter dynamics is modified by information - theoretically motivated corrections to the wdw equation , extending the previous @xcite approximate investigation . consider the einstein - hilbert action for a frw universe with the cosmological constant @xmath0 modeling inflationary sources in the early universe , @xmath1 \label{frw1 } \ , .\ ] ] where @xmath2 is the dimensionless , where @xmath3 , the planck length . ] scale factor , @xmath4 the lapse function , @xmath5 , and we have taken @xmath6 . varying with respect to @xmath4 and choosing the @xmath7 gauge gives us the friedmann equation @xmath8 we have set @xmath9 as the results for other values can be obtained by scaling . the flat , @xmath10 , geometry has the expanding classical solution @xmath11 which implies an arbitrarily small universe , @xmath12 , at early times @xmath13 . expected quantum effects are studied in standard minisuperspace quantisation by promoting the canonical momentum @xmath14 to an operator , @xmath15 , leading to the wdw equation @xcite , @xmath16 \psi(a ) = 0 \ , . \label{wdw1}\ ] ] the solution of ( [ wdw1 ] ) representing an expanding universe is given by the hankel function @xmath17 } \,\,\ , \mbox{as } \ ; \ ; a \to \infty \ , , \label{asymp}\end{aligned}\ ] ] as one can verify by noting that the negative value for the momentum @xmath18 of the asymptotic form corresponds to @xmath19 . notice that the , solution ( [ out ] ) of the linear wdw gives a nonzero probability for a universe of size @xmath20 , and hence for a big bang . in a previous perturbative study @xcite we showed that a modified wdw dynamics screened the @xmath20 region , leading to the quantum creation of a universe through tunneling @xcite . we postulated in ref.@xcite that if there is some new physics at quantum gravity scales , it may be modeled , within the information theory framework , by a modified wdw equation @xcite which can be derived by extremising the usual wdw lagrangian while also maximising the relevant uncertainty measure . we state and explain first the equation before motivating it further below : @xmath21 \psi(a ) = 0 \label{nl1}\ ] ] where @xmath22 with @xmath23 \ , \label{q2}\ ] ] and @xmath24 here @xmath25 is the probability density and @xmath26 , where the dimensionless parameter @xmath27 is the nonlinearity scale . the linear theory is recovered as @xmath28 while the other parameter @xmath29 labels a family of nonlinearisations . notice that the modified wdw equation is still invariant under a scaling of the wavefunction , @xmath30 , and so the solutions of the equation do not depend on the normalisation of the probability density . the appearance of @xmath31 in ( [ nl1 ] ) implies a nonlocality of the modified wdw equation which takes the form of a difference - differential equation . while the equation itself looks complicated , it follows from a relatively simple lagrangian involving the kullback - leibler ( kl ) information measure @xcite : the nonlinear piece @xmath32 in eq.([nl1 ] ) arises from maximising , in the spirit of the maximum uncertainty method , the following term in the action @xmath33 the kullback - leibler measure is clearly a relative uncertainty measure which generalises the usual gibbs - shannon entropy of statistical mechanics , and which reduces , as @xmath28 , to the fisher " information measure used in ref.@xcite for motivating the usual schrodinger equation within the information - theoretic framework . indeed , as discussed in @xcite , the ( @xmath34-regularised ) kl measure is probably the simplest nonsingular measure which interpolates between the shannon and fisher measures and which keeps some desirable properties such as the scale invariance mentioned above . in physical terms , the nonlinearity scale @xmath35 may be interpreted as a kinematic implementation of the resolution at which the coordinates become distinguishable @xcite . clearly for @xmath36 the dynamics given by eq.([nl1 ] ) will be modified from the usual case . the nonlinearity in ( [ nl1 ] ) was originally explored in quantum mechanical systems @xcite , and its various perturbative and non - perturbative properties studied in refs.@xcite . however as experimental constraints simply place limits on the size of the nonlinearity for simple quantum mechanical systems @xcite , we then applied the modified quantum equation to cosmology in ref.@xcite and found encouraging results for singularity resolution . in this paper we continue our study of the consequences of the information - theoretically motivated nonlinear wdw equation ( [ nl1 ] ) . the outline of this paper is as follows . in the next section we review the perturbative results of ref.@xcite on how the nonlinearly corrected quantum dynamics can avoid the @xmath20 possibility that is present in eq.([out ] ) . then in section(3 ) we show how to transform ( [ nl1 ] ) into a purely difference equation for @xmath37 which is solved numerically in section(4 ) and studied analytically in section(5 ) . in section(6 ) we discuss the effective classical dynamics suggested by the nonlinear wdw equation and elucidate the physical meaning of the nodes of the wavefunction . in section(7 ) we discuss the @xmath38 case and conclude in section(8 ) .

we perform a minisuperspace analysis of an information - theoretic nonlinear wheeler - dewitt ( wdw ) equation for de sitter universes . the studied model suggests implications for the early universe , and plausibly also for the future of an ongoing accelerating phase of the universe . * nonlinear quantum cosmology of de sitter space * rajesh r. parwani and siti nursaba tarih department of physics , + national university of singapore , + kent ridge , + singapore .

we perform a minisuperspace analysis of an information - theoretic nonlinear wheeler - dewitt ( wdw ) equation for de sitter universes . the nonlinear wdw equation , which is in the form of a difference - differential equation , is transformed into a pure difference equation for the probability density by using the current conservation constraint . in the present study we observe some new features not seen in our previous approximate investigation , such as a nonzero minimum and maximum allowable size to the quantum universe : an examination of the effective classical dynamics supports the interpretation of a bouncing universe . the studied model suggests implications for the early universe , and plausibly also for the future of an ongoing accelerating phase of the universe . * nonlinear quantum cosmology of de sitter space * rajesh r. parwani and siti nursaba tarih department of physics , + national university of singapore , + kent ridge , + singapore .

1309.3907

c

we have performed full two - dimensional numerical relaxations of isospinning soliton solutions in the standard baby skyrme model where the potential is given by the 2d analogue of the pion mass term of the full three - dimensional skyrme model . we find that completely analogous to the recent work on internally rotating soliton solutions @xcite in the 3d skyrme - faddeev model @xcite , there exist two types of critical frequencies : if the mass parameter @xmath2 is smaller than @xmath118 , the isospinning configurations become unstable when the angular frequency @xmath4 approaches @xmath2 . if the mass parameter @xmath2 is taken to be larger than @xmath118 , the energy of the isospinning solution becomes unbounded from below as @xmath4 increases above @xmath118 . hence , a stable isospinning soliton solution can only exist for frequencies @xmath1 . however , isospinning multi - skyrmion solutions can break up into their constituent charge-1 skyrmions before reaching this upper frequency limit . for @xmath2 sufficiently large there exists a third critical angular frequency value @xmath99 at which the total energy per unit charge is larger than the one of a single baby skyrmion and the breakup into charge-1 baby skyrmions is energetically favorable . this pattern of critical behaviour has been unobserved in previous work @xcite on isospinning charge-1 and -2 baby skyrme solitons ; mainly because the authors did not take into account deformations which break the rotational symmetry and only investigated relatively low mass values . our numerical calculations clearly show that stable , rotationally symmetric skyme solitons with mass parameter @xmath119 for angular frequencies @xmath55 are simply an artefact of the hedgehog approximation . even for lower mass values ( @xmath120 ) we find that the hedgehog ansatz can be a very poor approximation ; the charge-2 baby skyrmion solution can spontaneously break its rotational symmetry when isospinning . further , we observe that for the conventional mass parameter choice ( @xmath65 ) the symmetries of the static , nonspinning soliton solutions are not significantly modified when isospin is added . this is in contrast to recent results on internally rotating soliton solutions @xcite in the 3d skyrme - faddeev model , where it was found that the model allows for transmutations , formation of new solution types and a rearrangement of the spectrum of minimal - energy solitons in a given topological sector when isospin is added . however , although the soliton s geometrical shape is largely independent of the rotation frequency @xmath4 , the soliton s size increases monotonically with increasing @xmath4 . in general , the rigid - body formula predicts for the solutions considered here total energies which for large angular momenta are roughly @xmath121 larger than those obtained for the deformed , isospinning solutions . naturally , the accuracy of the rigid rotator approximation improves with increasing soliton mass and topological charge @xmath3 .

we perform full two - dimensional ( 2d ) numerical relaxations of isospinning soliton solutions in the baby skyrme model in which the global @xmath0 symmetry is broken by the 2d analogue of the pion mass term in the skyrme model . in our calculations we find that stable isospinning baby skyrme solutions can be constructed numerically for all angular frequencies @xmath1 , where @xmath2 is the mass parameter of the model . stable , rotationally - symmetric baby skyrmion solutions for higher angular velocities are simply an artefact of the hedgehog approximation . isospinning multisoliton solutions of topological charge @xmath3 turn out to be unstable to break up into their @xmath3 charge-1 constituents at some critical breakup frequency value . furthermore , we find that for @xmath2 sufficiently large the rotational symmetry of charge-2 baby skyrmions becomes broken at a critical angular frequency @xmath4 .

we perform full two - dimensional ( 2d ) numerical relaxations of isospinning soliton solutions in the baby skyrme model in which the global @xmath0 symmetry is broken by the 2d analogue of the pion mass term in the skyrme model . in our calculations we explicitely allow the isospinning solitons to deform and to break the symmetries of the static configurations . we find that stable isospinning baby skyrme solutions can be constructed numerically for all angular frequencies @xmath1 , where @xmath2 is the mass parameter of the model . stable , rotationally - symmetric baby skyrmion solutions for higher angular velocities are simply an artefact of the hedgehog approximation . isospinning multisoliton solutions of topological charge @xmath3 turn out to be unstable to break up into their @xmath3 charge-1 constituents at some critical breakup frequency value . furthermore , we find that for @xmath2 sufficiently large the rotational symmetry of charge-2 baby skyrmions becomes broken at a critical angular frequency @xmath4 .

1104.4836

c

in this paper , we have reported a detailed study of hess j1745 - 303 with _ fermi _ lat data which provides a missing piece in understanding the nature of this dark accelerator . in view of the putative variability of 3eg j1744 - 3011 , aharonian et al . ( 2008 ) argued that the gev counterpart is unlikely to be associated with hess j1745 - 303 . however , we do not find any evidence for the spectral / flux variability from the lat data . the discrepancy of the lat result and that inferred from egret is most likely due to the differences between their instrumental performance . with the improved angular resolution and sensitivity of lat , many previously unknown sources in the proximity of hess j1745 - 303 are now detected . as several sources within @xmath70 are found to be variable , including 1fgl j1747.2 - 2958 which is the @xmath0ray counterpart of psr j1747 - 2958 ( abdo et al . 2010 ) , the source confusion in the egret data can possibly lead to the apparent variability . it is interesting to compare the spectral properties inferred in the gev regime with those obtained by h.e.s.s .. first , the photon index inferred from the lat data ( i.e. @xmath34 ) is similar to that inferred in tev ( cf . tab . 2 of aharonian et al . furthermore , the extrapolated photon flux in @xmath7 tev with the best - fit pl model is found to be @xmath71 @xmath24 s@xmath25 which is consistent with any individual spatial component observed by h.e.s.s . within @xmath62 uncertainties ( cf . tab . 2 of aharonian et al . 2008 ) . since the tev spectral data of region a is avaliable ( cf . fig . 2 of aharonian et al . 2008 ) , we further compare this particular region with the gev spectrum by constructing a spectral energy distribution ( sed ) which is display in figure [ sed ] . both data can be simultaneously fitted with a single pl of @xmath72 . this clearly demonstrates that the tev spectrum of this spatial component can be smoothly connected to the gev spectrum . for regions b and c , despite that no tev spectral data is currently available , we note that their spectral shapes reported by aharonian et al . ( 2008 ) are similar to that of region a. within the statistical uncertainties of the spectral properties inferred in both gev and tev regimes , the tev spectra of these regions can also be possibly connected to that of gev . further investigation by h.e.s.s . is strongly encouraged , particularly for region c as most of the @xmath0ray emission in @xmath5 gev apparently coincides with this spatial component . as both pl and ple model can describe the gev spectrum equally well , we can not discriminate these competing models based on the current data . in view of the exponential cut - off , the spectral connection between the gev and tev regimes can not be established with the ple model . however , we would like to point out that the best - fit cut - off energy , @xmath37 gev , falls in the highest energy bin of the lat spectrum ( cf . [ spec ] and fig . [ sed ] ) . owing to the small photon statistics in the hard band , the statistical uncertainty of the highest energy bin is rather large . in view of this , it remains unclear whether the inferred cut - off is genuine as this particular data point is sensitive to the systematic uncertainty of the background . analysis of the lat data in higher energies ( e.g. @xmath73 gev ) with sufficient photon statistic in the future can help to discriminate these two models . the detection of @xmath0rays provides a strong evidence for the particle acceleration . it should be noted that there are two snrs and two pulsars around hess j1745 - 303 which can be the potential high energy particle injector ( cf . fig . 1 of aharonian et al . based on the small distances of g359.0 - 0.9 and psr b1742 - 30 , bamba et al . ( 2009 ) argued that these two sources are foreground objects which are unrelated to hess j1745 - 303 . with the gev counterpart revealed by lat , we can now safely rule out the possibility that psr b1742 - 30 is the major contributor as its spin - down flux , @xmath74 erg @xmath24 s@xmath25 , is lower than the energy flux observed in the gev regime ( cf . manchester et al . on the other hand , for psr j1747 - 2958 , the sum of @xmath0ray flux of 1fgl j1747.2 - 2958 and hess j1745 - 303 observed by lat only consumes @xmath75 of its spin - down flux ( @xmath76 erg @xmath24 s@xmath25 ) . therefore , it is energetically possible to be the source for the high energy particles . nevertheless , with its eastward proper - motion ( hales et al . 2009 ) , its backward extrapolated position by its spin - down age is found to have an offset of @xmath77 and @xmath30 from the best - fit positions inferred in @xmath4 gev and @xmath5 gev respectively . if the feature found by h.e.s.s . and lat is indeed a pwn , then it is one of the most peculiar system because of its large positional offset with respect to the pulsar position . while the contribution of psr j1747 - 2958 is uncertain , the interaction between the shock from g359.1 - 0.5 and a molecular cloud in its neighbourhood is considered to be a more viable means to produce the observed @xmath0rays . for both hadronic and leptonic scenarios , bamba et al . ( 2009 ) have modeled the broadband spectrum of the region a of hess j1745 - 303 . however , comparing fig . [ spec ] in this paper and fig . 5 & 6 in bamba et al . ( 2009 ) , the gev flux predicted in all the scenarios considered in their work are at least an order of magnitude lower than that observed by lat . revised theoretical investigation with constraints provided by lat is therefore required . moreover , while the other known systems of snrs interacting with molecular clouds have their remnant shells found in other wavelengths coincided with the @xmath0ray emission ( e.g. castro & slane 2010 ; abdo et al . 2010c ) , there is no such evidence for hess j1745 - 303 . we should point out that all the previous multiwavelength campaign were targeted only at the bright component of hess j1745 - 303 , namely the region a. since the lat observation suggested that the gev emission can possibly be originated from the regions c / b , observational investigations aim at these regions are encouraged for a further understanding of this mysterious object . based on the above discussion , we have to admit that the energy injection source of hess j1745 - 303 remains unclear . it is instructive to compare it with other nearby high energy sources . aharonian et al . ( 2006b ) have reported observations of an extended region of very high energy ( vhe , @xmath18 gev ) @xmath78-ray emission correlated spatially with a complex of giant molecular clouds in the central 200 pc of the milky way . it appears that tev emissions from the molecular clouds in the vicinity of the galactic center are quite common phenomena . in addition , similar to the case of hess j1745 - 303 , 6.4 kev lines have been commonly detected from many molecular clouds near the galactic center , e.g. sgr b2 ( koyama et al . 1996 ; murakami et al . 2000 ) , sgr c ( murakami et al . 2001 ) and others ( bamba et al . 2002 ; predehl et al . 2003 ; nobukawa et al . 2008 ; nakajima et al . 2009 ; koyama et al . it has been speculated that these neutral iron lines arise from the reflection by the dense molecular clouds which are irradiated by the nearby x - ray sources ( e.g. koyama et al . 2007 ; inui et al . on the other hand , dogiel et al . ( 2009 ) argued that these 6.4 kev lines from the molecular clouds are excited by a background intensity of subrelativistic protons coming from the escaped part of a past captured star by the galactic supermassive black hole sgr a*. the periodic stellar capture events may explain the recent observed _ fermi _ bubble ( cheng et al . this subrelativistic proton wind can also form shock by hitting the clouds and produce relativistic protons . it is shown that the decay of neutral pions produced by hadronic collisions between the accelerated relativistic protons in the clouds can emit a power - law @xmath0ray spectrum from 30 mev to 10 tev without any spectral break ( cheng et al . 2011b in preparation ) . if this is true , then the high energy emission from various molecular clouds in the vicinity of the galactic center are correlated to the past activities of the galactic center and their intensity might be correlated with the propagation history of the injection of these subrelativistic protons escaped from the capture past events . abdo , a. a. , et al . 2011 , apjs , 193 , 22 abdo , a. a. , et al . 2010 , apjs , 188 , 405 abdo , a. a. , et al . 2010b , apjs , 187 , 460 abdo , a. a. , et al . 2010c , science , 327 , 1103 aharonian , f. , et al . 2002 , a&a , 393 , l37 aharonian , f. , et al . 2005a , science , 307 , 1938 aharonian , f. , et al . 2005b , a&a , 439 , 1013 aharonian , f. , et al . 2006a , apj , 636 , 777 aharonian , f. , et al . 2006b , nature , 439 , 695 aharonian , f. , et al . 2008 , a&a , 483 , 509 bamba , a. , et al . 2009 , apj , 691 , 1854 bamba , a. , et al . 2007 , pasj , 59 , s209 bamba , a. , et al . 2002 , proceedings of the symposium new visions of the x - ray universe in the xmm - newton and chandra era " , noordwijk - nl bamba , a. , et al . 2000 , pasj , 52 , 259 castro , d. , & slane , p. 2010 , apj , 717 , 372 cheng , k. s. , et al . 2011 , apj , 731 , l17 chernyakova , m. , malyshev , d. , aharonian , f. a. , crocker , r. m. , & jones , d. i. 2011 , apj , 726 , 60 dogiel , v. , et al . 2009 , pasj , 61 , 901 hales , c. a. , gaensler , b. m. , chatterjee , s. , van der swaluw , e. , & camilo , f. 2009 , apj , 706 , 1316 hartman , r. c. , et al . 1999 , apjs , 123 , 79 inui et al . 2009 , pasj , 61 , s241 koyama , k , et al . 2009 , pasj , 61 , 255 koyama , k , et al . 2007 , pasj , 59 , s221 koyama , k , et al . 1996 , pasj , 48 , 249 lazendic , j. s , et al . 2002 , mnras , 331 , 537 manchester , r. n. , hobbs , g. b. , teoh , a. , & hobbs , m. 2005 , aj , 129 , 1993 matsumoto , h. , et al . 2007 , pasj , 59 , s199 murakami , h. , et al . 2001 , apj , 550 , 297 murakami , h. , et al . 2000 , apj , 534 , 283 nakajima , h. , et al . 2009 , pasj , 61 , 233 nobukawa , m. , et al . 2008 , pasj , 60 , 191 ohnishi , t et al . 2011 , pasj in press ( arxiv:1103.0348 ) predehl , p. , costantini , e. , hasinger , g. , & tanaka , y. 2003 , an , 324 , 73 torres , d. f. , et al . 2001 , a&a , 370 , 468

we present a detailed analysis of the @xmath0ray emission from hess j1745 - 303 with the data obtained by the _ fermi _ gamma - ray space telescope in the first @xmath1 months observation . the source can be clearly detected at the level of @xmath2 and @xmath3 in @xmath4 gev and @xmath5 gev respectively . gamma - ray observatory , we do not find any evidence of variability . most of emission in @xmath5 gev is found to coincide with the region c of hess j1745 - 303 . the power - law spectrum inferred in the gev regime can be connected to that of a particular spatial component of hess j1745 - 303 in @xmath7 tev without any spectral break . these properties impose independent constraints for understanding the nature of this dark particle accelerator " .

we present a detailed analysis of the @xmath0ray emission from hess j1745 - 303 with the data obtained by the _ fermi _ gamma - ray space telescope in the first @xmath1 months observation . the source can be clearly detected at the level of @xmath2 and @xmath3 in @xmath4 gev and @xmath5 gev respectively . different from the results obtained by the _ compton _ gamma - ray observatory , we do not find any evidence of variability . most of emission in @xmath5 gev is found to coincide with the region c of hess j1745 - 303 . a simple power - law is sufficient to describe the gev spectrum with a photon index of @xmath6 . the power - law spectrum inferred in the gev regime can be connected to that of a particular spatial component of hess j1745 - 303 in @xmath7 tev without any spectral break . these properties impose independent constraints for understanding the nature of this dark particle accelerator " .

cond-mat9806238

c

in this paper we have presented a comprehensive analysis of the low - lying spectrum of the electrons in the quantum hall effect , in the regime of hierarchical hall states @xmath200 . we have gone beyond previous works along these lines : regarding the studies of the composite - fermion correspondence @xcite @xcite , we have done the first detailed analysis of the edge state structure , which was overlooked by the studies on the spherical geometry @xcite@xcite . we have shown that the jain composite - fermion theory describes very well the low - lying spectrum ; but we also revealed the dynamical mechanism which takes place when two jain states are allowed : the electrons tend to `` pile up '' , if they are let to freely fill the effective landau levels . moreover , we improved and reviewed previous analyses on the disk geometry @xcite@xcite@xcite . we introduced two new criteria for the analysis of the exact states : i ) the plot of their density profiles for distinguishing quasi - particle excitations from new incompressible ground states , and for identifying the real edge excitations within the low - lying states ; ii ) the interpretation of their overlaps with the jain states in the language of conformal field theory , with concrete relations among the states and projections thereof . we have presented a consistent analysis of the low - lying spectrum . we have shown that the edge excitations form specific subset of the low - lying states , by applying the previous criteria and by checking that the laughlin quasi - particles are described by the well - understood one - component abelian conformal theory . while all the low - lying states are nicely described by the jain theory , i.e. by the multi - component abelian conformal theory @xcite@xcite@xcite , the real edge excitations of the hierarchical hall states match the predictions of the @xmath0 minimal theory @xcite ( and those of the laughlin quasi - particles naturally match the one - component abelian theory ) . although the numerical data show some blurs and some finite - size limitations , the general picture seems firmly established ; we found four neat positive evidences out of the six hierarchical states with @xmath30 and @xmath12 electrons . in conclusion , we hope that this work will stimulate further analyses of the hierarchical hall states . a. c. and g. r. z. would like to thank the c.e.r.n . theory division and the theory group at l.a.p.p . , annecy , for hospitality . a. c. also thanks the theory group of the centro atmico bariloche for hospitality and acknowledges the partial support of the european community program fmrx - ct96 - 0012 . g. r. z. is grateful to i.n.f.n . sezione di firenze for hospitality . the work of g. r. z. is supported by a grant of the antorchas foundation ( argentina ) . for a review see : r. a. prange , s. m. girvin , _ the quantum hall effect _ , springer verlag , new york ( 1990 ) . for a review see : s. das sarma and a. pinczuk , _ perspectives in quantum hall effects _ , wiley , new york ( 1996 ) . r. b. laughlin , ( 1983 ) 1395 ; for a review see : r. b. laughlin , _ elementary theory : the incompressible quantum fluid _ , in @xcite . j. k. jain , ( 1989 ) 199 ; ( 1990 ) 7653 ; for reviews see : j. k. jain , _ adv . in phys . _ * 41 * ( 1992 ) 105 , and _ composite fermions _ , in @xcite . for a review see : h. l. stormer and d. c. tsui , _ composite fermions in the fractional quantum hall effect _ , in @xcite for a review see : e. fradkin and a. lopez , ( 1993 ) 67 . x. g. wu and j. k. jain , ( 1995 ) 1752 . j. k. jain and r. k. kamilla , ( 1997 ) 2621 . for a review , see : x. g. wen , ( 1992 ) 1711 , _ adv . in phys . _ * 44 * ( 1995 ) 405 . r. c. ashoori , h. l. stormer , l. n. pfeiffer , k. w. baldwin and k. west , ( 1992 ) 3894 ; f. p. milliken , c. p. umbach and r. a. webb , _ solid state commun . _ * 97 * ( 1996 ) 309 ; p. fendley , a. w. w. ludwig and h. saleur , ( 1995 ) 8934 ; for a review , see : c. l. kane and m. p. a. fisher , _ edge - state transport _ , in @xcite . v. j. goldman and b. su , _ science _ * 267 * ( 1995 ) 1010 ; r. de - picciotto et al . , cond - mat/9707289 ; l. saminadayar et al . , cond - mat/9706307 . j. frhlich and a. zee , ( 1991 ) 517 ; x .- g . wen and a. zee , ( 1993 ) 2290 . j. frhlich and e. thiran , _ j. stat . * 76 * ( 1994 ) 209 ; j. frlich , t. kerler , u. m. studer and e. thiran , ( 1995 ) 670 . a. a. belavin , a. m. polyakov and a. b. zamolodchikov , ( 1984 ) 333 ; for a review see : p. ginsparg , _ applied conformal field theory _ , in _ fields , strings and critical phenomena _ , les houches school 1988 , e. brezin and j. zinn - justin eds . , north - holland , amsterdam ( 1990 ) . m. stone , ( ny ) * 207 * ( 1991 ) 38 . a. cappelli , g. v. dunne , c. a. trugenberger and g. r. zemba , ( 1993 ) 531 . n. read , ( 1990 ) 1502 . a. cappelli , c. a. trugenberger and g. r. zemba , ( 1995 ) 470 ; for a review , see : ( 1996 ) 112 . s. iso , d. karabali and b. sakita , ( 1992 ) 700 , ( 1992 ) 143 . a. cappelli , c. a. trugenberger and g. r. zemba , ( 1993 ) 465 , ( 1993 ) 100 ; for a review , see : a.cappelli , g.v.dunne , c.a.trugenberger and g.r.zemba , ( 1993 ) 21 . a. cappelli , c. a. trugenberger and g. r. zemba , ( 1994 ) 1902 . f. d. m. haldane , _ the hierarchy of fractional states and numerical studies _ , in @xcite . g. dev and j. k. jain , _ phys . _ * 45 b * ( 1992 ) 1223 . m. kasner and w. apel , _ phys . rev . _ * 48 b * ( 1993 ) 11435 ; _ ann . physik _ * 3 * ( 1994 ) 433 . a. cappelli and g. r. zemba , _ hamiltonian formulation for the minimal models of the incompressible quantum hall fluids _ , to appear . v. kac and a. radul , _ comm . * 157 * ( 1993 ) 429 ; h. awata , m. fukuma , y. matsuo and s. odake , _ prog . ( supp . ) _ * 118 * ( 1995 ) 343 ; e. frenkel , v. kac , a. radul and w. wang , ( 1995 ) 337 . a. m. polyakov , ( 1990 ) 833 ; m. bershadsky and h. ooguri , ( 1989 ) 49 . f. d. m. haldane ( 1983 ) 605 ; b. i. halperin , 91984 ) 1583 ; m. greiter , ( 1994 ) 48 . .bottom states of the jain theory for @xmath30 , ordered by the decreasing angular momentum @xmath223 , and the corresponding approximated energies @xmath178 , in units of @xmath44 . [ cols="^,^,^",options="header " , ]

we study the edge excitations of the hierarchical plateaus and check the predictions of two relevant conformal field theories : the multi - component abelian theory and the @xmath0 minimal theory of the incompressible fluids . we introduce two new criteria for identifying the edge excitations within the low - lying states : the plot of their density profiles and the study of their overlaps with the jain wave functions in a meaningful basis . we find that the exact bulk and edge excitations are very well reproduced by the jain states ; these , in turn , can be described by the multi - component abelian conformal theory . most notably , we observe that the edge excitations form sub - families of the low - lying states with a definite pattern , which is explained by the @xmath0 minimal conformal theory . actually , the two conformal theories are related by a projection mechanism whose effects are observed in the spectrum .

we present a detailed analysis of the exact numerical spectrum of up to ten interacting electrons in the first landau level on the disk geometry . we study the edge excitations of the hierarchical plateaus and check the predictions of two relevant conformal field theories : the multi - component abelian theory and the @xmath0 minimal theory of the incompressible fluids . we introduce two new criteria for identifying the edge excitations within the low - lying states : the plot of their density profiles and the study of their overlaps with the jain wave functions in a meaningful basis . we find that the exact bulk and edge excitations are very well reproduced by the jain states ; these , in turn , can be described by the multi - component abelian conformal theory . most notably , we observe that the edge excitations form sub - families of the low - lying states with a definite pattern , which is explained by the @xmath0 minimal conformal theory . actually , the two conformal theories are related by a projection mechanism whose effects are observed in the spectrum . therefore , the edge excitations of the hierarchical hall states are consistently described by the @xmath0 minimal theory , within the finite - size limitations . 200 1 2_1

1008.4127

c

the existence of ultra - compact , massive ( @xmath65 ) quiescent galaxies already in place merely 3 billion years after the big bang has been one of the great surprises of galaxy evolution studies in the last few years . their discovery has triggered questions regarding their origin and fate , as well as the reliability with which their properties such as mass and size are characterized . in this paper , we address the formation and nature of such systems in the context of ( gas - rich ) merger scenarios . as such , this study is part of a larger effort that couples hydrodynamic simulations with radiative transfer in order to investigate how different types of observed high - redshift galaxies may tie together as stages of one evolutionary sequence . figure [ summary.fig ] illustrates a typical star formation history of a gas - rich merger simulation . gas - rich star - forming galaxies ( _ blue _ ) are abundantly present at high redshift ( erb et al . 2006 ; tacconi et al . when in the process of merging ( _ yellow _ ) , the morphology of such systems may ( but will not always ) appear disturbed . the timescales of a morphological merger signature depend on mass ratio ( lotz et al . 2010a ) and gas fraction ( lotz et al . 2010b ) of the merger . narayanan et al . ( 2010 ) describe how during a relatively short ( @xmath137 myr ) period at final coalescence ( _ orange _ ) a peak in emission at sub - millimeter wavelengths is reached . continuing over a somewhat longer ( @xmath138 myr ) timespan , the system may be identified as a so - called dust - obscured galaxy ( dog ) , characterized by its large 24 @xmath139 m to optical flux ratio , although not every dog , and particularly those with low 24 @xmath139 m luminosity , is a gas - rich merger ( narayanan et al . 2009 ) . shortly after the peak in star formation rate ( at @xmath140 myr for the particular simulation shown ) , the accretion rate onto the central supermassive black hole peaks . the role of merging in galaxy - black hole coevolution has been discussed extensively by hopkins et al . ( 2006 , 2008a ) . finally , wuyts et al . ( 2009b ) investigated the role major mergers may have played in producing the above mentioned compact systems , in terms of their number and mass densities as well as their integrated stellar population properties . iterating on the latter aspect , the inset panel in figure[summary.fig ] contrasts the distribution of rest - frame uv to near - infrared seds of merger remnants computed from our simulations ( _ median , 50th and 100th percentiles are displayed in red _ ) to the mean rest - frame sed of quiescent galaxies from the vd08 sample ( muzzin et al . 2009b , _ black data points , with error bars representing the error on the mean _ ) . the model and observations show an excellent agreement over the full wavelength range probed , boosting confidence that the modeled stellar populations reflect reality at least in an integrated sense . in this paper , we focussed on the structure and resolved stellar populations of merger remnants . we used the sample of massive quiescent galaxies from vd08 as reference sample . their near - infrared spectra are characterized by a balmer/4000 break ( kriek et al . deep nic2 observations ( vd08 ) have revealed their compact nature at the highest resolution currently available . analyzing a suite of binary merger simulations of varying mass , gas fraction , progenitor scaling , and orbital configuration , we confirm the idea originally proposed by khochfar & silk ( 2006a ) that major mergers can explain their location in the size - mass diagram provided they are gas - rich . merging galaxies scaled to represent high - redshift star - forming disks , we find that systems of @xmath65 with half - mass radius @xmath2 kpc can be formed when the gas fraction by the time of final coalescence is about @xmath3% . observational evidence for gas fractions of this magnitude has been accumulating in recent years ( e.g. , tacconi et al . the corresponding velocity dispersions of these simulated massive compact galaxies are of order 300 - 400 km s@xmath79 . they show considerable rotation ( @xmath141 of up to unity ) compared to the majority of lower redshift early - type galaxies , a result that has yet to be confirmed observationally . running radiative transfer on the output of our sph simulations , we find that the merger remnants have a radially dependent mass - to - light ratio . typically , when observing the remnant 500 myr to 1 gyr after the peak in star formation rate , the half - mass radius is a factor @xmath7 smaller than the rest - frame @xmath6-band half - light radius . this implies that the high effective densities inferred from nicmos and wfc3 observations of high - redshift quiescent galaxies may in fact only be lower limits . in the rest - frame @xmath66-band , the typical light - to - mass size ratio increases to a factor 3 - 4 . the ratio @xmath142 shows a significant sightline - dependence , with a tail to high values ( @xmath143 ) . our conclusions are robust to the choice of radiative transfer code , input stellar population synthesis models , dust attenuation law , and whether or not the progenitor disks had stellar population gradients . the @xmath5 ratio gradient is expressed as a color gradient that correlates with the integrated color of the system ( redder galaxies hosting a more pronounced red core ) . we caution that the presence of a red core can not unambiguously be interpreted as evidence for inside - out growth . in fact , in the simulations studied in this paper , the central stellar population formed last , rather than first . the effect of the negative age gradient is compensated by the fact that the stars inside the half - mass radius are more metal - rich , and suffer more extinction . finally , we perform two - dimensional parametric fitting with the galfit code ( peng et al . 2002 ) on real and mock nic2 observations with the same limitations of resolution and depth . we find that our simulated merger remnants occupy a different region in ( @xmath93 , @xmath12)-space than the vd08 quiescent galaxies . so do simulations of disk galaxies that are left to evolve in isolation . the high sersic indices ( @xmath8 ) inferred from the mock observations are driven by both the central cusp ( consisting of young stars ) and the extended wings ( consisting of old stars ) . we explored a number of variations in progenitor properties that influence the amplitude of the central cusp , but have little effect on the outskirts . subsequent ( minor ) merging tends to build up the profile wings even further while leaving the central cusp in the mass distribution relatively unaffected . by lack of cosmological context , the binary merger simulations start with large amounts of gas in the progenitor disks ( up to 80% of the baryonic mass content ) in order to have a sufficiently large gas fraction by final coalescence to model the dissipational merger event . given this large gas reservoir at the start of the simulation , it is hard to prevent it from forming stars and ending up forming the extended wings of the remnant profiles ( wings that are not seen to that degree in the observations ) . as a consequence , while gas - rich mergers as simulated in this paper reproduce the basic structural diagnostic ( the size - mass diagram ) , second order structural properties such as profile shape may differ because too many stars are formed at early times . this could be prevented if the gas was not all present initially but instead accreted more gradually over time , or if star formation and/or stellar mass loss and its feedback operated in such a way that the efficiency of converting gas into stars was lower at low densities than assumed here ( i.e. , in the progenitor disks and particularly their outer parts ) . one could speculate that a low gas - phase metallicity , turbulence from accretion ( bournaud et al . 2010 ) , or the elevated intensity of the ionizing background radiation at @xmath0 inhibit the formation of molecular gas and thus stars during this early phase , especially at low densities where the gas may still be pristine . we demonstrate that , in addition to spatial resolution , timestep resolution is important in modeling the detailed structure of such extreme systems properly . therefore , running spheroid evolution simulations in a full cosmological context is computationally very expensive . pioneering efforts to simulate spheroid formation in a cosmological context ( without agn feedback ) have recently been carried out by naab et al . ( 2007 ; 2009 ) . these authors apply a resimulation technique on three target halos extracted from a low - resolution dark matter simulation to follow the formation and evolution of spheroids within those halos from high redshift to the present day . in agreement with our findings , naab et al . ( 2007 ; 2009 ) argue that at high redshift dissipational processes on short timescales are a plausible mechanism to produce the compact galaxies observed at @xmath58 . at later times , they find that minor and gas - poor merging forms an efficient means to build up an envelope around this core ( see also section [ subsequent.sec ] of this paper , and hopkins et al . 2009a ) . in the scenario investigated in this paper , the initial dissipational event occurs in the form of a major merger . such a scenario connects three types of galaxies observed at high redshift in one evolutionary sequence : gas - rich disks , dusty starbursts with star formation rates peaking to @xmath144 , and quiescent remnants . the dissipational event modeled by naab et al . ( 2007 ; 2009 ) is driven by efficient radiative cooling and collapsing of gas , not necessarily involving major merging . it remains to be seen whether such a model can account for the peak star formation rates observed in , e.g. , sub - millimeter galaxies , and the post - starburst nature of the stellar populations of compact galaxies . observationally , measurements of clustering , from large scales to pair counts , based on wide and deep cosmological surveys could potentially provide support for a merger - driven evolutionary scenario . baker , a. j. , tacconi , l. j. , genzel , r. , lehnert , m. d. , & lutz , d. 2004 , apj , 604 , 125 barnes , j. e. , hernquist , l. 1991 , apj , 370 , l65 barnes , j. e. 1992 , apj , 393 , 484 barnes , j. e. , hernquist , l. 1996 , apj , 471 , 115 bezanson , r. , van dokkum , p. g. , tal , t. , marchesini , d. , kriek , m. , franx , m. , & coppi , p. 2009 , apj , 697 , 1290 binney , j. 1978 , mnras , 183 , 501 binney , j. , & merrifield , m. 1998 , galactic astronomy , princeton university press , princeton bournaud , f. , et al . 2010 , submitted to apjl ( astro - 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we find that major merging is a viable mechanism to produce systems of @xmath1 and @xmath2 kpc size , provided the gas fraction at the time of final coalescence is high ( @xmath3% ) , and provided that the progenitors are compact star - forming galaxies , as expected at high redshift . this is typically expressed by a negative color gradient ( i.e. , red core ) , which we expect to correlate with the integrated color of the system . finally , the simulations differ from the observations in their surface brightness profile shape .

we present a detailed analysis of the structure and resolved stellar populations of simulated merger remnants , and compare them to observations of compact quiescent galaxies at @xmath0 . we find that major merging is a viable mechanism to produce systems of @xmath1 and @xmath2 kpc size , provided the gas fraction at the time of final coalescence is high ( @xmath3% ) , and provided that the progenitors are compact star - forming galaxies , as expected at high redshift . their integrated spectral energy distributions and velocity dispersions are in good agreement with the observations , and their position in the @xmath4 diagram traces the upper envelope of the distribution of lower redshift early - type galaxies . the simulated merger remnants show time- and sightline - dependent @xmath5 ratio gradients that result from a superposition of radially dependent stellar age , stellar metallicity , and extinction . the median ratio of effective radius in rest - frame @xmath6-band light to that in mass surface density is @xmath7 during the quiescent remnant phase . this is typically expressed by a negative color gradient ( i.e. , red core ) , which we expect to correlate with the integrated color of the system . finally , the simulations differ from the observations in their surface brightness profile shape . the simulated remnants are typically best fit by high ( @xmath8 ) sersic indices , whereas observed quiescent galaxies at @xmath0 tend to be less cuspy ( @xmath9 ) . limiting early star formation in the progenitors may be required to prevent the simulated merger remnants from having extended wings .

hep-ph9709253

i

the minimal supersymmetric standard model ( mssm ) @xcite implies the existence of five physical higgs bosons @xmath11 , @xmath1 , @xmath2 , and @xmath12 @xcite . for the search of these particles a precise knowledge of all possible decay modes is necessary . the higgs boson decays to supersymmetric ( susy ) particles could be very important if they are kinematically allowed . this can be the case for the charged higgs boson @xmath0 , and the neutral higgs bosons @xmath1 and @xmath2 . if all susy particles are very heavy , the @xmath0 decays dominantly into @xmath13 ; the decays @xmath14 and/or @xmath15 are dominant below the @xmath13 threshold @xcite . if all decay modes into susy particles are kinematically forbidden the @xmath1 and @xmath2 decay dominantly into a fermion pair of the third generation . in the case that the susy particles are relatively light , the branching ratios of the @xmath0 , @xmath1 and @xmath2 decays at tree level were studied in @xcite and @xcite . the susy qcd corrections in @xmath16 were calculated in the on shell scheme for the processes @xmath17 in @xcite , @xmath18 in @xcite , and for the decays of all higgs particles into squark pairs in @xcite , including squark mixing and a proper renormalization of the mixing angle @xmath19 @xcite . + within this work we will discuss the branching ratios of the higgs decays including all susy qcd corrections in @xmath16 . we will see that the decay modes into susy particles ( squarks of the third generation , charginos and neutralinos ) become more important when the qcd corrections are taken into account .

we present a detailed study of the decays of the higgs bosons @xmath0 , @xmath1 , and @xmath2 within the minimal supersymmetric standard model including susy qcd corrections . we find that the supersymmetric modes @xmath3 ( @xmath4 , and for large @xmath5 @xmath6 ) can dominate the @xmath0 ( @xmath1 , @xmath2 ) decays in a wide range of the model parameters due to the large yukawa couplings and mixings of @xmath7 and @xmath8 . = -1 cm = 13.9 cm 0.0 in 0.0 in _ _ hep - ph/9709253 * higgs particle decays in supersymmetry * +

we present a detailed study of the decays of the higgs bosons @xmath0 , @xmath1 , and @xmath2 within the minimal supersymmetric standard model including susy qcd corrections . we find that the supersymmetric modes @xmath3 ( @xmath4 , and for large @xmath5 @xmath6 ) can dominate the @xmath0 ( @xmath1 , @xmath2 ) decays in a wide range of the model parameters due to the large yukawa couplings and mixings of @xmath7 and @xmath8 . compared to the conventional modes @xmath9 , and @xmath10 , the supersymmetric modes can have an important impact on the higgs boson searches at future colliders . = -1 cm = 13.9 cm 0.0 in 0.0 in _ _ hep - ph/9709253 * higgs particle decays in supersymmetry * +

1702.05280

c

the x - ray emission from pulsars is typically attributed to a magnetospheric and/or a thermal origin . because of the small separation between the two neutron stars , a strong interaction is expected between the wind of pulsar a and the magnetosphere of pulsar b , inducing possibly more complex mechanisms of the x - ray emission . in the following , we discuss the origin of the soft x - ray emission ( up to 4 kev ) and hard x - ray emission , including the detection of the spectral feature at @xmath54 kev . the spectral analysis of the observations performed in 2011 , as well as combining 2006 + 2011 data , provides results comparable with those related to 2006 data alone . different two - component ( black body plus power law or double black body ) or three - component spectral models ( double black - body plus power law ) can fit the whole dataset . however , scenarios involving only thermal emission components are disfavoured , since the flux is most likely dominated by non - thermal pulsar a s magnetosphere emission . a double black - body model implies that the x - ray flux of pulsar b would be about half of pulsar a s flux ( looking at black - body normalizations ) and this is inconsistent with x - ray fluxes derived from timing analysis by @xcite for which x - ray emission from pulsar a is over three times higher with respect to pulsar b. furthermore , pulsar phase - resolved analysis demonstrated that a non - thermal component clearly correlate with pulsar a s light curve peaks @xcite . no significant spectral variability in soft x - rays is evident over 5 years . in particular , despite a significant relativistic spin precession occurred in the considered time span ( @xmath0 ) , no significant long - term variation of the soft pulsar a s spectral component is observed . this further supports the hypothesis of a small misalignment between the spin axis and the orbital momentum axis as suggested by timing analysis of the same data @xcite . the non - thermal x - ray emission of psr j0737 - 3039 is likely attributed to relativistic charged particles accelerated in the magnetosphere of pulsar a , via synchrotron emission in the outer gap model @xcite and/or via inverse compton scattering of the thermal x - ray photons in the polar cap model ( * ? ? ? * and references therein ) . no signature of a bow shock component ( power law with @xmath55 as suggested by canonical shock models ; see @xcite and references therein ) between the wind from pulsar a and pulsar b s magnetosphere is present in our soft spectral data , nor evidence of spectral variability as a function of the orbital phase . a weak orbital flux variability ( @xmath567% ) was detected in the timing analysis @xcite and it was possibly attributed to bow - shock emission . in the spectral analysis , the corresponding bow - shock flux could be concealed by the strong pulsar a s luminosity . as for the thermal emission , it is expected to originate from hot spots around the magnetic poles ( polar caps ) of pulsar a and/or pulsar b , heated up to x - ray temperatures by relativistic particles streaming down onto the surface from the magnetosphere of the pulsar(s ) . indeed , considering the characteristic ages of pulsar a ( @xmath57 myr ) and pulsar b ( @xmath58 myr ) , and the cooling evolution of such objects ( tsuruta 1998 ) , these pulsars are too old to have an intrinsic thermal radiation from their entire surface or from the atmosphere @xcite . the radio pulsar models @xcite predict polar cap radii @xmath59s@xmath60 km for a neutron star of radius @xmath61 km . hence , theoretically , the polar cap radii associated with pulsar a and pulsar b are @xmath62 km and @xmath63 m , respectively . these values are in agreement with black - body emission radii derived from our spectral results . either assuming the presence of one or two black - body components in our spectral scenario , the expected luminosity of each component is @xmath6410@xmath65 erg / s , a value higher than pulsar b s spin - down luminosity . this means that the black - body component luminosity would be @xmath66 @xmath67 . thus , we can confirm that pulsar b s emission can only be powered by an external source ( i.e. pulsar a s spin - down energy ) . for any applicable spectral scenario in the @xmath68 kev range , the data above 4 kev are not correctly described by the two or three - component models ( see figure 2 ) . the complementarity of the independent spatial and spectral approaches allows us to claim for the first time hard x - ray emission from the double pulsar . this hard emission is well fitted by a gaussian line at @xmath69 kev in the 2006 data . no other simple model , such as a power law or a black body , is able to fit the high - energy excess . emission at these energies indicates the likely presence of iron line emission . the firm detection of hard x - ray emission in the @xmath48 kev range coupled with no source detection @xmath70 kev through spatial analysis , strengthen the reliability of our spectral feature detection . the presence of such a feature has major importance since it represents the first evidence of an x - ray spectral line around a supposedly `` non - accreting system '' . as for the second long - observation performed in 2011 , we can not claim evidence of a high - energy spectral line , because of a poorer signal - to - noise ratio in hard x - rays mostly due to the use of the thin epic - pn filter . in any case , the detection of high - energy photons from the double pulsar is also confirmed in these data through spatial analysis , though spectral parameters can not be precisely constrained in the 2011 data alone . as described in section 3 , line variability is compatible with our data , though not required . associated with emission at @xmath3 kev , the fe k@xmath2 line is widely considered as a particular property of accretion - powered sources in which accreting matter forms a disk . it has been detected in the x - ray spectra of many supermassive black holes and stellar - mass - black - hole and neutron - star x - ray binaries @xcite , and in magnetic cataclysmic variables @xcite . the emission line is thought to originate in the innermost parts of the accretion disk , where strong relativistic effects broaden and distort its shape . the production of such a line is fairly simple requiring a source of thermal or non - thermal hard x - rays to illuminate the disk . in this context our detection of the fe k@xmath2 line in the double pulsar may indicate that at least one of the system components is surrounded by a gaseous disk . however , what could be the origin of such a disk ? the double pulsar , as the other few confirmed double neutron star binaries , is the descendant of a high - mass binary system that has survived two supernova explosions @xcite . the two stars under - filled their roche lobes and lose matter at a relatively low rate through winds of relativistic particles . the conventional scenario of accretion disk formation based on intensive mass - exchange between the system components in this case is not applicable . however , a relic disk of matter captured from ejecta of the second supernova explosion could be present . the disk could be formed in two ways . the first is a so - called fall - back accretion scenario in which the inner parts of the ejecta return towards the newly - formed neutron star forming a disk around its magnetosphere @xcite . the mass of the remnant disk in this case is about @xmath71 m@xmath72 . the second scenario suggests the disk to form around the magnetosphere of the old neutron star born during the first supernova explosion as it moves through the supernova ejecta of its exploded companion . as recently pointed out @xcite , the mass of the remnant disk within this scenario can reach @xmath73 m@xmath72 . thus , current views of the process of supernova explosions do not exclude that one or even both neutron stars could be surrounded by relic disks . observations give no direct evidence that the neutron stars in the double pulsar are accreting material from a disk ( no radio pulsar timing noise reported by @xcite and @xcite ) . it is plausible that the relic disk is currently in a dead state @xcite in which mass - transfer towards the star is suppressed by the centrifugal barrier at the boundary of the stellar magnetosphere . the interaction between the disk and the magnetic field of the radio pulsar in this case results in generation of electrical currents , which connect the inner parts of the disk with polar cap regions at the surface of the neutron star @xcite . as the currents dissipate in small areas of the polar caps the temperature increases dramatically , enhancing the hot spots visible in x - rays . in contrast , the temperature of the disk increases little since current dissipation occurs over a much larger area . the disk in this case could contribute to the pulsar emission at lower frequencies by a significant fraction of the pulsar spin - down power . our spectral analysis of the xmm - newton data demonstrates that the thermal x - ray emission is indeed incompatible with a disk origin , since the disk radius would be too small ( even assuming a disk black - body model _ diskbb _ ) . the surface area associated with the black bodies at 0.1 and 0.3 kev is of the order of 600 and 100 m@xmath74 , respectively , indicating most likely thermal emission from the polar cap(s ) . the putative disk is most likely colder and thus invisible in x - rays . it manifests itself only through the iron line that requires external heating . this could be by illumination by a hard continuum x - rays from pulsar a , although this might be too weak or anisotropic to be observed . alternatively , unlike accretion - powered pulsars , the disk could be illuminated by high - energy particles from pulsar a s wind . in this case , about @xmath75 of spin - down energy of pulsar a could power the k@xmath2 line . interestingly enough , this is the same amount of energy powering pulsar b s x - ray emission . iron line emission could also be in principle associated with an accumulation of matter trapped in the shock layer foreseen between pulsar a s wind and the magnetosphere of pulsar b. a hypothetical spectral line from the surface or atmosphere of the neutron star is not favored , since the gravitational redshift would induce a line at @xmath76 kev accordingly to the lower limit on the neutron stars mass - radius ratio @xcite . an idea about a relic disk to surrounding a radio pulsar has been invoked by a discovery of two planet - mass companions around the millisecond pulsar psr 1257 + 12 @xcite . further studies eventually confirmed that the components are likely to originate from a durable remnant disk , which in a previous epoch could be in an accretion or dead state . the presence of remnant disks around isolated neutron stars has later been suspected in studies of anomalous x - ray pulsars ( axps ) and soft gamma - ray repeaters ( sgrs ) @xcite . iron line emission at 6.4 kev was detected during a gamma - ray burst in sgr 1900 + 14 @xcite . the presence of a relic disk was also been invoked to explain the ir / optical radiation discovered from two axps @xcite . only upper limits to the optical flux were derived for the double pulsar @xcite , which was instead detected in the fuv @xcite . although the thermal or non - thermal nature of this emission is still unclear , it is not related to magnetospheric or surface x - ray pulsar emission since it does not match with extrapolated x - ray spectra . it is in principle compatible with a relic disk of luminosity l@xmath77 erg / s . the possible weakening or even disappearance of the spectral feature at @xmath54 kev in the data obtained in 2011 could be related to actual variability of the fe line because of changes in the geometry or precession of the disk , which is not illuminated in the same way over time . the parameters of interaction between the wind of pulsar a and the magnetosphere of pulsar b are expected to be different between 2006 and 2011 , as manifested by radio disappearance of pulsar b in 2008 . as the orbit is seen edge - on , changes on the disk could in principle also affect radio pulsar timing ( e.g. observed dispersion measure , pulse shapes and eclipses ) when it crosses the line - of - sight to the pulsars . a multi - messenger approach is then required to probe the putative relic disk and its time - dependent geometry .

spectral variability of pulsar emission in soft x - rays is not evident over 5 years , despite the significant relativistic spin precession in the considered time span ( @xmath0 ) . the existence of a relic disk in this system reinforces speculation about the presence of similar structures around other peculiar classes of isolated neutron stars .

we present a long - term spectral monitoring of the unique double pulsar binary psr j0737 - 3039 corresponding to two `` large programs '' performed by xmm - newton in 2006 and 2011 . spectral variability of pulsar emission in soft x - rays is not evident over 5 years , despite the significant relativistic spin precession in the considered time span ( @xmath0 ) . we provide , for the first time , evidence of hard x - ray emission from the system in the @xmath1 kev energy band . the standard spectral analysis was coupled to the energy dependent spatial analysis to confirm this excess , most likely ascribed to iron line emission . the fe k@xmath2 emission line at @xmath3 kev was previously unheard - of in non - accreting binary systems and could testify to the presence of a relic disk that survived the supernova explosions that terminated the lives of the double pulsar s stellar progenitors . the existence of a relic disk in this system reinforces speculation about the presence of similar structures around other peculiar classes of isolated neutron stars .

1702.05280

c

two large programs of observations of the relativistic double pulsar were performed by xmm - newton in 2006 and 2011 . the total observing time of about 600 ks offers the opportunity to investigate the low luminosity source with a high number of @xmath78 source photon events . no significant spectral variations in soft x - rays can be claimed in the 5 years between 2006 and 2011 , substantially confirming the previously reported results based on the analysis of the 2006 data alone . two - component ( black body plus power law ) or three - component spectral models ( double black - body plus power law ) can in principle fit the whole dataset , although the latter models seem better suited according to phase - resolved spectral analysis @xcite . however , for any applicable spectral scenario in the @xmath68 kev range , the data above 4 kev are not correctly described by the models . we investigated for the first time the high - energy part of the spectrum of the double pulsar . an intriguing emission feature , possibly variable , is detected at about @xmath54 kev . spatial analysis confirms the emission of hard energy photons between 4 and 8 kev ascribed to the source . this feature is most likely attributed to iron line emission , testifying the presence of a relic disk that survived the supernova explosions that terminated the lives of the double pulsar s stellar progenitors . we acknowledge the referee for his / her constructive suggestions that have helped to improve the content of this paper . this work is based on observations obtained with _ xmm - newton _ , an esa science mission with instruments and contributions directly funded by esa member states and the usa ( nasa ) . the authors thank the members of the _ xmm - newton _ user support group . e. egron and m. marongiu acknowledge financial support from the autonomous region of sardinia through a research grant under the program crp-25399 po sardegna fse 2007 - 2013 , l.r . 7/2007 , promoting scientific research and innovation technology in sardinia . ikhsanov acknowledges support of the russian scientific foundation under the grant no . 14 - 50 - 00043 . arnaud , k. a. 1996 , in asp conf . astronomical data analysis software and systems v , ed . g. h. jacoby & j. barnes , 101 , 17 arons , j. 1981 , , 248 , 1099 beskin , v. s. , gurevich , a. v. , & istomin , y. n. 1993 , physics of pulsar magnetosphere ( cambridge : cambridge univ.press ) bisnovatyi - kogan , g. s. & ikhsanov , n. r. 2015 , astronomy reports , 59 , 503 breton , r. p. , kaspi , v. m. , kramer , m. et al . 2008 , science , 321 , 5885 , 104 burgay , m. , damico , n. , possenti , a. , et al . 2003 , , 426 , 531 cackett , e. m. , miller , j. m. , ballantyne , d. r. 2010 , , 720 , 205 campana , s. , possenti , a. , & burgay , m. 2004 , , 613 , l53 cash , w. 1979 , , 228 , 939 chatterjee , s. , gaensler , b. m. , melatos , a. , et al . 2007 , , 670 , 1301 chatterjee , p. , hernquist , l. , narayan , r. 2000 , , 534 , 373 cheng , a. f. & ruderman , m. a. 1980 , , 235 , 576 cheng , k. s. & zhang , l. 1999 , , 515 , 337 chevalier , r. a. 1989 , , 346 , 847 colgate , s. a. 1971 , , 163 , 221 de luca , a. & molendi , s. 2004 , , 419 , 837 durant , m. , kargaltsev , o. & pavlov , g. g. , 2014 , , 783 , 22 ezuka , m. 1999 , , 120 , 277 ferraro , f. r. , mignani , r. p. , pallanca , c. et al . 2012 , , 749 , 84 granot , j. & mszros , p. 2004 , , 609 , l17 iacolina m. n. , pellizzoni , a. , egron , e. et al . 2016 , , 824 , 87 kaplan , d. l. , chakrabarty , d. , wang , z. & wachter , s. 2009 , , 700 , 149 kaspi , v. m. , ransom , s. m. , backer , d. c. , et al . 2004 , , 613 , l137 kramer , m. , stairs , i. h. , manchester , r. n. , et al . 2006 , science , 314 , 97 kramer , m. & stairs , i. h. 2008 , , 46 , 541 kramer , m. & wex , n. 2009 , classical and quantum gravity , 26 , 7 lyne , a. g. , burgay , m. , kramer , et al . 2004 , science , 303 , 1153 lyutikov , m. 2004 , , 353 , 1095 mclaughlin , m. a. , lyne , a. g. , lorimer , d. r. , et al . 2004 , , 616 , l131 michel f. c. , & dessler , a. j. 1981 , , 251 , 654 michel f. c. , & dessler , a. j.1983 , , 303 , 48 michel f. c. , & dessler , a. j. 1985 , sience , 228 , 1015 michel f. c. 1985 , , 290 , 721 michel f. c. 1988 , , 333 , 644 miller , j. m. 2007 , , 45 , 441 pellizzoni , a. , de luca , a. , mereghetti , s. , et al . 2004 , , 612 , l49 pellizzoni , a. , tiengo , a. , de luca , a. , et al . 2008 , , 679 , 664 perera , b. b. p. , mclaughlin , m. a. , kramer , et al . 2010 , , 721 , 1193 pollock , a. m. t. 1987 , , 320 , 283 possenti , a. , rea , n. , mclaughlin , m. a. , et al . 2008 , , 680 , 654 protassov , r. , van dyk , d. a. , connors , a. et al . 2002 , , 571 , 545 stairs , i. h. 2004 , science , 304 , 547 strohmayer , t. e. & ibrahim a. i. 2000 , , 537,111 strder , l. , briel , u. , dennerl , k. , et al . 2001 , , 365 , l18 sturner , s. j. , skibo , j. g. , dermer , c. d. , mattox , j. r. 1997 , , 490 , 619 sunyaev , r. a. & shakura , n. i. 1977 , soviet astronomy letters 3 , 138 verbiest , j. p. w. , weisberg , j. m. , chael , a. a. , et al . 2012 , , 755 , 39 tsuruta , s. 1998 , , 292 , 1 turner , m. j. l. , abbey , a. , arnaud , m. , et al . 2001 , , 365 , l27 wang , z. , chakrabarty , d. & kaplan , d. l. , 2006 , , 440 , 772 wilms , j. , allen , a. , & mccray , r. 2000 , , 542 , 914 wolszczan , a. & frail , d. a. 1992 , , 355 , 145 zavlin , v. e. 2009 , theory of radiative transfer in neutron star atmospheres and its applications , astrophysics and space science library , ed . becker w. , 357 , 181 zeldovich , y. b. , ivanova , l. n. & nadezhin , d. k. 1972 , soviet astronomy 16 , 209 zhang , b. & harding , a. k. 2000 , , 532 , 1150 zhao , h. h. & song , l. m. 2012 , proceedings iau symposium n.290 , 8 , pp 369 - 37

we present a long - term spectral monitoring of the unique double pulsar binary psr j0737 - 3039 corresponding to two `` large programs '' performed by xmm - newton in 2006 and 2011 . the fe k@xmath2 emission line at @xmath3 kev was previously unheard - of in non - accreting binary systems and could testify to the presence of a relic disk that survived the supernova explosions that terminated the lives of the double pulsar s stellar progenitors .

we present a long - term spectral monitoring of the unique double pulsar binary psr j0737 - 3039 corresponding to two `` large programs '' performed by xmm - newton in 2006 and 2011 . spectral variability of pulsar emission in soft x - rays is not evident over 5 years , despite the significant relativistic spin precession in the considered time span ( @xmath0 ) . we provide , for the first time , evidence of hard x - ray emission from the system in the @xmath1 kev energy band . the standard spectral analysis was coupled to the energy dependent spatial analysis to confirm this excess , most likely ascribed to iron line emission . the fe k@xmath2 emission line at @xmath3 kev was previously unheard - of in non - accreting binary systems and could testify to the presence of a relic disk that survived the supernova explosions that terminated the lives of the double pulsar s stellar progenitors . the existence of a relic disk in this system reinforces speculation about the presence of similar structures around other peculiar classes of isolated neutron stars .

1503.05629

i

we develop new entropy based statistics @xmath2 called _ slide statistics _ which can be computed from any sample data in a metric space . as an application , we use these statistics to test whether financial returns are independent observations from a particular distribution . for example , figure [ fig : fig1 ] shows plots of @xmath3 against @xmath14 for data @xmath15 consisting of n - tuples of consecutive returns regarded as a subset of the metric space @xmath16 with the usual metric . as can be seen , the lower curve corresponding to the s@xmath0p @xmath1 is very different from the ones obtained for either the normal or laplace distributions . any potential model for the returns of the s@xmath0p @xmath1 must be able simulate the @xmath3 curve in figure [ fig : fig1 ] which is a new requirement that is apparently difficult to meet . the statistics @xmath17 contain information about the interplay between the dimension of a space and distributions on that space and provide a new way of describing continuous random variables and stochastic processes in general . the @xmath17 will take some time to define but we will provide explicit formulas for slide statistics @xmath3 and @xmath4 that are easily computed for any sample in a metric space . against @xmath14 for the s@xmath0p @xmath1 for the @xmath18 trading days ending december 31 , 2014 . the middle cluster of five graphs are the corresponding plots obtained from five different simulated sequences of returns with the laplace distribution . the upper cluster of five graphs are the corresponding plots obtained from five different simulated sequences of normally distributed returns . , width=384 ] our applications will focus on financial returns but many other important processes in science and mathematics also yield data in the form of a set of points in a metric space that must be quantified and interpreted . fields like fractal analysis have developed in order to obtain dimensional information from a wide range of real world data using quantities like the hausdorff , information and correlation dimensions @xcite . one of the problems with these traditional measures of dimension is that they tend to concentrate on the geometric properties of a set while ignoring the statistical origins of the data . we will give examples where @xmath19 appears to converge to the reciprocal of the hausdorff dimension when @xmath20 is taken to be a a larger and larger random sample from a fractal . it is not clear in general how to assign a dimension to a point process but our theory and simulations suggest a purely statistical way to identify a class of them for which it does make sense to assign a dimension . specifically , we think the dimension of a point process @xmath21 should be defined to be @xmath22 provided @xmath23 and @xmath24 for @xmath25 in which case we say the process is tangible with dimension @xmath22 . in the case of a tangible process , the values of @xmath26 are entirely determined by the number @xmath22 but this relationship does not hold in general . a possible example of a tangible process is the random generation of points @xmath27 in @xmath8^d$ ] , where the @xmath28 are chosen independently and uniformly at random from @xmath8 $ ] , for which we provide evidence that @xmath29 and @xmath30 . in particular , @xmath3 and @xmath4 are new spatial statistics for testing hypotheses concerning the distribution of points in @xmath8^d$ ] . although we will sometimes use fractals as examples , these statistics can be applied to any random variable with values in a metric space . in particular , the slide statistics appear to describe continuous random variables @xmath7 in an entirely new way that has nothing to do with mean and standard deviation since @xmath31 for @xmath32 . for example , the first two slide statistics for any normal variable @xmath11 appear to converge to @xmath12 and @xmath13 which provide the basis for a new goodness of fit test for normality . for any exponential random variable @xmath33 , simulation gives that @xmath34 and @xmath35 and we conjecture from these and other simulations that @xmath36 for any continuous real - valued random variable @xmath7 . if we think of @xmath37 as the _ dimension _ of the random variable @xmath7 , then this last conjecture says the uniform distribution on @xmath8 $ ] has the maximum dimension of any continuous real - valued random variable . the second slide statistic @xmath4 is negative for the examples given so far but @xmath4 is positive for the cauchy distribution and is often found to be positive for the log daily returns of the standard and poor 500 index which is yet another demonstration of the non - normality of these returns . the construction of @xmath38 requires several ideas working in concert and can be summarized as follows . in section [ s:2 ] , we introduce a variant of the differential entropy called the genial entropy which is the starting point for defining the slide statistics . unlike the differential entropy , the genial entropy is scale invariant and in section [ s : inequality ] we prove it is never negative which will give a new lower bound for the differential entropy . given a finite set of distinct points @xmath20 in a metric space , we find the distance from each point to its nearest neighbour and arrange these distances in descending order so @xmath39 . let @xmath40 be the function on @xmath41 whose value on @xmath42 is @xmath43 . let @xmath44 be the area under @xmath45 and let @xmath46 denote the genial entropy of the density @xmath47 which turns out to be @xmath48 at @xmath49 . we then define @xmath50 to be the @xmath14th derivative from the right at @xmath48 of the function @xmath46 which is developed in section [ s : calculus ] . in section [ s : calculus ] , we derive an explicit formula for @xmath19 and state a conjectured formula for @xmath51 . the fact that @xmath3 and @xmath4 are easily evaluated using a computer makes them particularly suitable for practical applications . the results obtained from the simulation of @xmath3 and @xmath4 in a variety of contexts are summarized in section [ s : slide ] and demonstrate the interplay between dimension and distribution that is captured by these statistics . as applications in section [ s : returns ] , we consider a variety of possible distributions as models for financial returns and use the slide statistics to illustrate how poorly these models fit the empirical data .

we present a new approach to financial returns based on an infinite family of statistics called _ slide statistics _ that we introduce . the evidence these statistics provide suggests that certain distributions such as the stable distributions are not good models for the financial returns from various securities or indexes like the s@xmath0p @xmath1 and the dow jones . formally , we associate with any finite subset of a metric space an infinite sequence of scale invariant numbers @xmath2 derived from a variant of differential entropy called the genial entropy . we give explicit formulas for @xmath3 and @xmath4 that are easily evaluated by a computer and make this theory particularly suitable for applications . as statistics for point processes , these numbers often appear to converge in simulations and we give examples where @xmath5 converges to the hausdorff dimension and we prove that @xmath6 . for a uniform random variable @xmath7 on @xmath8^n$ ] , the evidence from simulations suggests that @xmath9 and @xmath10 which yields new tests for spatial randomness . the slide statistics describe continuous random variables in an entirely new way . for example , if @xmath11 is any normal variable then simulations suggest that @xmath12 and @xmath13 which provides new goodness of fit tests for normality .

we present a new approach to financial returns based on an infinite family of statistics called _ slide statistics _ that we introduce . the evidence these statistics provide suggests that certain distributions such as the stable distributions are not good models for the financial returns from various securities or indexes like the s@xmath0p @xmath1 and the dow jones . formally , we associate with any finite subset of a metric space an infinite sequence of scale invariant numbers @xmath2 derived from a variant of differential entropy called the genial entropy . we give explicit formulas for @xmath3 and @xmath4 that are easily evaluated by a computer and make this theory particularly suitable for applications . as statistics for point processes , these numbers often appear to converge in simulations and we give examples where @xmath5 converges to the hausdorff dimension and we prove that @xmath6 . for a uniform random variable @xmath7 on @xmath8^n$ ] , the evidence from simulations suggests that @xmath9 and @xmath10 which yields new tests for spatial randomness . the slide statistics describe continuous random variables in an entirely new way . for example , if @xmath11 is any normal variable then simulations suggest that @xmath12 and @xmath13 which provides new goodness of fit tests for normality .

astro-ph0101447

i

fly is the tree n - body code we design , develop and use to run very big simulations of the large scale structure of the universe using parallel systems mpp and smp . fly uses the leapfrog numerical integration scheme for performance reasons , and incorporates fully periodic boundary conditions using the ewald method . the i / o data format is integrated with the astromd package . + astromd is an analysis and visualization tool specifically designed to deal with the visualization and analysis of astrophysical data . astromd can find structures having a not well defined shape or symmetries , and performs quantitative calculations on a selected region or structure . astromd makes use of virtual reality techniques which are particularly effective for understanding the three dimensional distribution of the fields , their geometry , topology and specific patterns . the display of data gives the illusion of a surrounding medium into which the user is immersed . the result is that the user has the impression of travelling through a computer - based multi - dimensional model which could be directly hand - manipulated .

fly * ( fast level - based n - body code ) is a fully parallel code based on a tree algorithm . it adopts periodic boundary conditions implemented by means of the ewald summation technique . version 1.1 is an open source _ freely available code_. + fly data output can be analysed with astromd , an analysis and visualization tool specifically designed to deal with the visualization and analysis of astrophysical data . astromd can manage different physical quantities . it can find out structures without well defined shape or symmetries , and perform quantitative calculations on selected regions .

we present a new code allowing to evolve three - dimensional self - gravitating collisionless systems with a large number of particles @xmath0 . * fly * ( fast level - based n - body code ) is a fully parallel code based on a tree algorithm . it adopts periodic boundary conditions implemented by means of the ewald summation technique . fly is based on the one - side communication paradigm to share data among the processors that access remote private data avoiding any kind of synchronism . the code was originally developed on a cray t3e system using the _ shmem _ library and it was ported on sgi origin 2000 and on ibm sp ( on the latter making use of the _ lapi _ library ) . version 1.1 is an open source _ freely available code_. + fly data output can be analysed with astromd , an analysis and visualization tool specifically designed to deal with the visualization and analysis of astrophysical data . astromd can manage different physical quantities . it can find out structures without well defined shape or symmetries , and perform quantitative calculations on selected regions . is a _ freely available _ code .

1105.1248

i

facility location is one of the most studied optimization problems in operations research and captures a large variety of applications . a classical motivation is placing facilities ( e.g , warehouses ) in such a way that the combined costs of customer satisfaction and warehouse construction are minimized . however , there are also plenty of applications in distributed scenarios . for instance , in wireless networks a set of nodes has to be chosen to provide some services ( e.g , a distributed database ) . making such services available incurs costs at those _ facility _ nodes , while all remaining nodes act as _ clients_. they use the services of the nearest facility node , and are charged a cost proportional to the corresponding distance . the objective is to determine a set of facility nodes such that the costs caused by the facilities and the clients is as low as possible . [ [ formal - problem - definition . ] ] formal problem definition . + + + + + + + + + + + + + + + + + + + + + + + + + + we consider the _ metric uncapacitated facility location _ problem in a distributed setting . here , we are given a complete bipartite graph @xmath5 consisting of a set of _ facilities _ @xmath6 and a set of _ clients _ @xmath7 . to each facility @xmath8 an opening cost @xmath9 is assigned . each edge @xmath10 in @xmath11 is weighted with the value @xmath12 that represents the costs of connecting client @xmath13 with facility @xmath14 . the objective is to determine a subset of the facilities to be opened and connect every client to at least one open facility in such a way that the sum of the opening costs and connection costs is minimized . the linear program representation of the facility location problem and its dual program are as follows : @xmath15 @xmath16 the variable @xmath17 indicates whether facility @xmath14 is open ( @xmath18 ) or closed ( @xmath19 ) . the other indicator variable @xmath20 has the value @xmath21 if the client @xmath13 is connected to facility @xmath14 , and @xmath22 otherwise . the constraints ( @xmath21 ) guarantee that each client is connected to at least one facility , while the constraints ( @xmath23 ) make sure that a client can only be connected to an open facility . the problem we consider is _ metric _ , since the values @xmath24 are required to satisfy the triangle inequality ( i.e , @xmath25 ) , and _ uncapacitated _ , since an arbitrary number of clients can be connected to an open facility . furthermore , for the sake of presentation we assume all @xmath26 to be normalized such that the smallest non - zero value is @xmath21 . the dual program will be used in the description of our approximation algorithm . intuitively , a @xmath27 variable can be seen as the amount the client @xmath13 is willing to pay for being connected to a facility . from the point of view of a facility @xmath14 , @xmath27 is the sum of @xmath24 ( the amount @xmath13 pays for a connection to @xmath14 ) and @xmath28 ( the amount it pays for opening @xmath14 ) . our algorithm is executed in the @xmath0 model , which was introduced by peleg @xcite and is commonly used to model the execution of distributed algorithms on graphs : algorithms are executed in synchronous send - receive - compute rounds . in a single round , each node sends a message to each of its neighbors in the graph . note that the messages sent to each neighbor by a single node are not required to contain the same information . once all nodes have sent their messages , they receive a single message from each of their neighbors . after all the messages have been received , every node is allowed to spend an arbitrary amount of time for computation ( i.e , computation is for free and we are only interested in the number of communication rounds ) . the end of the computation by all nodes marks the start of a new send - receive - compute round . the message size in the @xmath0 model is bounded . we will limit the size of the messages used in our algorithm to @xmath29 bits . the same limitations were also used in @xcite , @xcite and @xcite . this bound is reasonable , because it allows the nodes to send their i d in a single message . due to this constraint on message size , we restrict the values @xmath30 and @xmath24 in such a way that it is possible to represent them with @xmath29 bits ( i.e. to be able to send them in a single message ) . the graph our algorithm is executed on is the complete bipartite graph of clients and facilities . this means that within a single round each client can communicate with all facilities and each facility can communicate with all clients . since nodes of the same partition can not communicate directly with each other , but instead have to use nodes of the other partition as relays , gathering all information about the graph requires @xmath31 rounds note that without a limit on the message size our problem could be trivially solved in four rounds ( all information about the graph is gathered at a single node in two rounds , an optimal solution is computed and distributed in two more rounds ) . we want to stress that , although in our algorithm the nodes communicate with all their neighbors in each round , it is possible to restate the algorithm such that nodes @xmath14 and @xmath13 where @xmath24 is `` large '' ( more than @xmath32 ) never communicate with each other . [ [ our - contribution . ] ] our contribution . + + + + + + + + + + + + + + + + + we present a distributed approximation algorithm for the metric uncapacitated facility location problem . it is based on a greedy algorithm by jain et al@xcite ( from here on referred to as ) and yields a guaranteed ( not in expectation ) @xmath33-approximation in @xmath3 rounds ( with high probability ) . our algorithm is executed in the @xmath0 model on a complete bipartite graph . although it is strongly related to the _ greedyfl _ algorithm , there are ( due to the parallel execution ) new challenges regarding the selection process that occurs when multiple facilities are eligible for opening . the difficulty is that we require the cost of the solution computed by our algorithm to be always at most @xmath33 times worse than an optimal solution ( in contrast to similar work by blelloch et al@xcite , where the approximation factor is increased by factor @xmath23 ) . moreover , unlike other work ( e.g , @xcite , where the approximation factor is given `` in expectation '' ) , our algorithm provides a worst - case guarantee on the approximation factor . [ [ related - work . ] ] related work . + + + + + + + + + + + + + during the last two decades , the uncapacitated metric facility location problem was of great interest , and a lot of progress has been made concerning the running time and approximation factor of sequential algorithms solving it . aardal et alintroduced the first polynomial time algorithm yielding a @xmath34-approximation @xcite . improving this approximation factor was the topic of a multitude of research papers . for example , chudak et alimproved the approximation factor to @xmath35 @xcite . the factor has been improved , until eventually byrka designed a @xmath36-approximation algorithm @xcite , which , at this point in time , yields the best known approximation . although both last mentioned algorithms yield very good approximation factors , they have , due to applying lp - rounding , high running times . thus , the design of algorithms with slightly worse approximation factors , but better running times , was also of interest in the past . jain and vazirani used the primal - dual approach to develop and analyze an algorithm with approximation factor @xmath37 and a running time of @xmath38 @xcite . a simplified and faster @xmath39 version of this algorithm was introduced by mettu and plaxton @xcite . later on , jain et alimproved the former results by presenting two algorithms in @xcite : one with running time @xmath40 and an approximation factor of @xmath41 ( which we refer to as ) and another one with running time @xmath42 and an approximation factor of @xmath43 ( @xmath4 denoting the number of nodes and @xmath44 the number of edges in the complete bipartite graph of facilities and clients ) . later on , building upon @xcite , mahdian et alimproved the factor to @xmath45 @xcite . under the assumption that @xmath46 , guha et alshowed in @xcite that no polynomial time algorithm with an approximation factor better than @xmath47 exists . thus , an improvement of either the lower or the upper bound for the approximation factor , even in the @xmath37rd or higher fractional digit , is of great interest . the following results concerning the facility location problem can be found in the distributed scenario : in @xcite pandit et alpresent an algorithm yielding a @xmath48-approximation and a running time of @xmath29 . their algorithm is a parallel version of the primal - dual algorithm by jain et al@xcite and is like our algorithm executed in the @xmath0 model on a complete bipartite graph with message size limited to @xmath29 bits . pandit et alassume that the difference between the opening costs of the cheapest and the most expensive facility can be arbitrary large . it is reasonable to drop this assumption , since they ( as well as we ) require that the facility opening costs and distances between clients and facilities are encoded with @xmath29 bits . by dropping this assumption and modifying the algorithm and analysis by pandit et alin a small way ( changing a factor from @xmath23 to @xmath49 ) , it is possible to achieve a @xmath50 approximation factor in @xmath51 rounds . further improvement of the factor with this approach is not possible , since the approximation factor of @xcite , which pandit et alparallelized , is @xmath37 . this means that their algorithm , while faster than ours , has a worse approximation factor . recently , in @xcite pandit et alall presented a technique that can be used to execute greedy facility location algorithms ( like ) in parallel in polylogarithmic time . although they consider a similar problem as we do , their results are quite different from ours : their approximation factor is @xmath52 in expectation ( their algorithm can produce an arbitrary bad solution , even though this is very unlikely ) , while we can guarantee an approximation factor of @xmath33 in the worst case . also , although they do not state their exact approximation factor , the expected approximation factor achieved with their technique can not , to the best of our knowledge , be decreased below @xmath53 , where @xmath54 is the approximation factor of the sequential algorithm ( i.e , @xmath55 if used with ) . a similar result to @xcite was presented by blelloch et alin @xcite . instead of the @xmath0 they use a pram model and achieve a @xmath56 approximation with running time @xmath57 by parallelizing the algorithm . in order to choose which facilities to open , they use a technique introduced by rajagopalan and vazirani @xcite . this technique can also be used to execute greedy facility location algorithms ( in a distributed manner and polylogarithmic time ) and yields a guaranteed approximation factor of @xmath58 , where @xmath54 is again the approximation factor of the corresponding sequential algorithm ( i.e@xmath59 if used with ) . other results that also use the bound of @xmath29 on the message complexity are @xcite and @xcite . in @xcite moscibroda et alshow that in @xmath60 communication rounds a @xmath61 approximation in @xmath60 communication rounds ( @xmath62 and @xmath63 are the number of facilities , respectably clients , and @xmath64 a coefficient dependent on instance parameters ) can be achieved in the more general _ non - metric _ facility location problem . gehweiler et alshow in @xcite that @xmath37 rounds are sufficient to compute a @xmath52-approximation for the uniform facility location problem ( opening each facility incurs the same costs ) . @xcite applies the approach of mettu and plaxton @xcite , which has been successful in a lot of other settings as well : in the kinetic setting @xcite , in game theoretic settings @xcite , for algorithms working in sublinear time @xcite , and when confronted with perpetual changes to the problem instance @xcite . [ [ structure - of - the - paper . ] ] structure of the paper . + + + + + + + + + + + + + + + + + + + + + + + in section 2 we give a detailed description of our approximation algorithm and prove its approximation factor by generalizing the techniques and results of @xcite . our main contribution is section 3 . here , we deal with the problem of selecting facilities to be opened that arises due to the parallel execution of the _ greedyfl _ algorithm by jain et aland show that our distributed algorithm presented in section 2 terminates in sublinear time .

we present a randomized distributed approximation algorithm for the metric uncapacitated facility location problem . the algorithm is executed on a bipartite graph in the @xmath0 model yielding a @xmath1 approximation factor , where @xmath2 is an arbitrary small positive constant . it needs @xmath3 communication rounds with high probability ( @xmath4 denoting the number of facilities and clients ) . to the best of our knowledge , our algorithm currently has the best approximation factor for the facility location problem in a distributed setting . it is based on a greedy sequential approximation algorithm by jain et al(j . the main difficulty in executing this sequential algorithm lies in dealing with situations , where multiple facilities are eligible for opening , but ( in order to preserve the approximation factor of the sequential algorithm ) only a subset of them can actually be opened . note that while the presented runtime bound of our algorithm is `` with high probability '' , the approximation factor is not `` in expectation '' but always guaranteed to be @xmath1 . thus , our main contribution is a sublinear time selection mechanism that , while increasing the approximation factor by an arbitrary small additive term , allows us to decide which of the eligible facilities to open .

we present a randomized distributed approximation algorithm for the metric uncapacitated facility location problem . the algorithm is executed on a bipartite graph in the @xmath0 model yielding a @xmath1 approximation factor , where @xmath2 is an arbitrary small positive constant . it needs @xmath3 communication rounds with high probability ( @xmath4 denoting the number of facilities and clients ) . to the best of our knowledge , our algorithm currently has the best approximation factor for the facility location problem in a distributed setting . it is based on a greedy sequential approximation algorithm by jain et al(j . acm 50(6 ) , pages : 795 - 824 , 2003 ) . the main difficulty in executing this sequential algorithm lies in dealing with situations , where multiple facilities are eligible for opening , but ( in order to preserve the approximation factor of the sequential algorithm ) only a subset of them can actually be opened . note that while the presented runtime bound of our algorithm is `` with high probability '' , the approximation factor is not `` in expectation '' but always guaranteed to be @xmath1 . thus , our main contribution is a sublinear time selection mechanism that , while increasing the approximation factor by an arbitrary small additive term , allows us to decide which of the eligible facilities to open .

hep-ph0702120

c

the expansion of the dense matter ( sqgp ) produced in high - energy heavy - ion collisions at rhic may be unstable . the initial transverse density may also be highly fluctuation . the unstable expansion and fluctuating initial transverse density may lead to a fragmentation of the system and the formation of a granular source of qgp droplets . although a granular structure was suggested earlier as the signature of first - order phase transitions@xcite , the occurrence of granular structure may not be limited to the occurrence of first - order phase transitions . there are additional effects which may lead to the dynamical formation of granular droplets@xcite . for a granular source of the droplets , the average particle emission time scales with the initial radius of the droplet . pions will be emitted earlier if the radius is smaller . an earlier emission time will lead to a smaller extracted hbt radius @xmath1 , while the extracted hbt radius @xmath42 is determined by the scale of the distribution of the droplets . a collective expansion of the droplets can further decrease @xmath1 and the value of @xmath94 can be close to , or even less than 1 for an expanding granular source of qgp droplets . in an event - mixing experimental analysis , some signals of the granular source such as the correlation function fluctuations may likely be suppressed after averaging over many events@xcite . however , the property of an earlier average emission time of the granular source will remain as it is common to all events and not averaged out by event mixing . this property leads to a smaller @xmath43 in mixed - event hbt analysis . in conclusion , a granular source model can explain the rhic hbt puzzle and reproduce the data of pion hbt radii , as well as the data of pion transverse momentum spectra and elliptic flow@xcite in @xmath61 gev au + au collisions at rhic . it is of great interest to find direct evidences of the granular structure and to study the mechanics of granular source formation@xcite .

pions will be emitted earlier if the droplet radius is smaller . an earlier emission time will lead to a smaller extracted hbt radius @xmath1 , while the extracted hbt radius @xmath2 is determined by the scale of the distribution of the droplet centers . however , a collective expansion of the droplets can further decrease @xmath1 . as a result , the value of @xmath3 can be close to , or even less than 1 for the granular source of qgp droplets .

we present a review on the explanation of the rhic hbt puzzle by a granular pion - emitting source of quark - gluon plasma droplets . the evolution of the droplet is described by relativistic hydrodynamics with an equation of state suggested by lattice gauge results . the granular source evolution is obtained by superposing all of the evolutions of individual droplets . pions are assumed to be emitted thermally from the droplets at the freeze - out configuration characterized by a freeze - out temperature @xmath0 . we find that the average particle emission time scales with the initial radius of the droplet . pions will be emitted earlier if the droplet radius is smaller . an earlier emission time will lead to a smaller extracted hbt radius @xmath1 , while the extracted hbt radius @xmath2 is determined by the scale of the distribution of the droplet centers . however , a collective expansion of the droplets can further decrease @xmath1 . as a result , the value of @xmath3 can be close to , or even less than 1 for the granular source of qgp droplets .

1612.02597

i

an accurate first - principles description of excited - state properties in crystalline materials requires a high - level treatment of electron correlation . green s function - based many - body perturbation theory ( mbpt ) @xcite , including the @xmath5 approximation @xcite and the solution of the bethe - salpeter equation ( bse ) @xcite , represents the state of the art for calculating charged and neutral excitations in the optical region , respectively @xcite . while the former yields quasi - particle energies , accounting for electron - electron correlation , the latter gives excitation energies of the electron - hole pairs . these methods are routinely applied on top of a mean - field description of the ground state obtained from density - functional theory ( dft ) @xcite . correlation effects enter the description of core excitations differently . as such , several approaches are adopted , often with good results , depending on the range of the transition energies @xcite . excitations from deep - lying core states , which are highly localized and decoupled from the surrounding electron cloud , are dominated by the long - range electron - hole ( @xmath6-@xmath7 ) attraction . as such , these excitations have been successfully described by a constrained dft - based scheme , the so - called _ core - hole _ or the _ final - state rule _ approximation @xcite . with the core - hole potential directly included in the calculation of the electronic states , this method is well suited for extended systems @xcite , although requiring _ supercell _ calculations to avoid spurious interactions between core holes of neigbouring unit cells . for shallower core states , however , the overlap between the initial core state and the conduction bands is usually more relevant and the local treatment of the electron - hole correlation becomes problematic @xcite . indeed , the core - hole approximation is known to fail in case of excitations involving shallow core or even semi - core states , that may interact with the surrounding electrons @xcite . other mean - field methodologies , such as multiple scattering calculations @xcite , are often successfully adopted for finite systems , but are hardly applicable to solids . bse - based approaches to core excitations have proven to overcome these issues and to be reliable for many crystalline materials . however , most of the schemes proposed so far are either based on pseudo - potential approximation @xcite , or , in an all - electron framework , on the description of the core states in terms of local orbitals as part of the valence region , neglecting spin - orbit coupling . while the latter choice turned out to be effective in many cases @xcite , this approximate treatment of core states is limited to a specific energy window and initial states . in particular , excitations from core levels with a non - negligible spin - orbit splitting need a relativistic treatment , even for low transition energies . excitations from @xmath8 and @xmath9 states in transition - metal oxides are an exemplary case that requires an enhanced spinorial treatment of the core electrons @xcite . in such systems local - fields effects are crucial for the spectra , and an accurate description of the @xmath6-@xmath7 exchange interaction is essential to achieve reliable results . in this work , we aim at addressing correlation effects in core excitations of solids , by exploring the spectra of different edges of several materials , spanning a broad range of transition energies . to do so , we adopt an _ ab initio _ approach based on the solution of the bse in an all - electron framework . after presenting the formalism and the essence of its implementation into the ` exciting ` code @xcite , we show x - ray absorption spectra of three materials , focussing on excitations from the ti @xmath0 edge in rutile and anatase @xmath1 , from the @xmath2 edge in lead iodide , and from the ca @xmath4 edge in cao . we discuss the role of the @xmath6-@xmath7 attraction and exchange , and analyze our results to gain insight into the nature of these excitations .

we investigate three different absorption edges of three materials , spanning a broad energy window , with transition energies between a few hundred to thousands of ev . specifically , we consider excitations from the ti @xmath0 edge in rutile and anatase @xmath1 , from the pb @xmath2 edge in @xmath3 , and from the ca @xmath4 edge in cao . we show that the electron - hole attraction rules x - ray absorption for deep core states , when local fields play a minor role . on the other hand , the local - field effects introduced by the exchange interaction between the excited electron and the hole dominate excitation processes from shallower core levels , separated by a spin - orbit splitting of a few ev .

we present an _ ab initio _ study of core excitations of solid - state materials focussing on the role of electron - hole correlation . in the framework of an all - electron implementation of many - body perturbation theory into the ` exciting ` code , we investigate three different absorption edges of three materials , spanning a broad energy window , with transition energies between a few hundred to thousands of ev . specifically , we consider excitations from the ti @xmath0 edge in rutile and anatase @xmath1 , from the pb @xmath2 edge in @xmath3 , and from the ca @xmath4 edge in cao . we show that the electron - hole attraction rules x - ray absorption for deep core states , when local fields play a minor role . on the other hand , the local - field effects introduced by the exchange interaction between the excited electron and the hole dominate excitation processes from shallower core levels , separated by a spin - orbit splitting of a few ev . our approach yields absorption spectra in good agreement with available experimental data , and allows for an in - depth analysis of the results , revealing the electronic contributions to the excitations , as well as their spatial distribution .

astro-ph0504503

i

deep x - ray surveys have progressively resolved an increasing fraction of the soft x - ray background ( xrb ) , into faint point - like sources . most recently , the ultra - deep _ chandra _ surveys ( @xcite , @xcite ) , have resolved over @xmath8 of the 0.52 kev xrb . source counts have been measured in these fields to limiting fluxes of a few times @xmath9erg s@xmath10 @xmath11 , with corresponding sky densities of over @xmath12 sources deg@xmath13 , @xcite . optical identification of faint x - ray sources reveals a heterogeneous mixture of objects , with the dominant class being active galactic nuclei ( agn ) , ( @xcite , @xcite ) . these x - ray selected agn have a range of luminosities spanning several orders of magnitude , are found at redshifts up to 5 , and exhibit a wide range of observational properties . the unification scheme of @xcite attributes the wide variety of radio , optical and x - ray characteristics seen between agn classes , to the geometry and relative orientation of a dusty torus surrounding the central black hole . the dusty torus model is used to to explain both the absence of broadened optical lines , and the strong x - ray absorption seen in many agn . the simplest version of the unified scheme is one in which the geometry of the inner regions , and hence the distribution of absorbing column densities ( @xmath1 ) , is independent of all other agn properties . a number of refinements to this model have been suggested , in order to explain recent observations which are at odds with the simple unified scheme . the demographics of the 0.52 kev agn population have been well measured , albeit to relatively bright flux limits , using _ rosat _ /_einstein _ samples , for example by @xcite , @xcite , @xcite and @xcite . each of these studies indicates strong evolution of the agn x - ray luminosity function ( xlf ) , with a peak in agn activity at @xmath14 , although the best description of this evolution is disputed . the soft xlf is characterised by a double power - law with a knee at @xmath15 erg s@xmath10 . the bulk of the xrb is the result of the integrated emission of agn having luminosities in the vicinity of this knee . the spectral slope of the 0.11 kev xrb is @xmath16 @xcite , approximately matching that of a typical soft band detected agn , @xmath17 , ( @xcite , @xcite , @xcite ) . however , at harder x - ray energies the xrb flattens dramatically , and has @xmath18 in the 110 kev band ( e.g. @xcite , @xcite , @xcite ) , and can not be produced by a simple superposition of canonical @xmath19 agn spectra . clearly , some additional sources of hard x - rays must exist , and a large population of heavily absorbed agn is postulated to fill this role . population synthesis models have been formulated , such as those of @xcite , @xcite , and @xcite , and have been successful in reproducing both the broad band spectrum of the xrb , as well as the agn source counts observed below 10 kev . @xcite predict that the majority ( @xmath20 ) , of the agn population is heavily absorbed . a number of deep surveys of the 210 kev sky have been performed with _ chandra _ and xmm-_newton _ ( e.g. @xcite , @xcite , @xcite ) . in the 2ms observations of the _ chandra _ deep field - north ( cdf - north ) , sources have been detected to a limiting flux of @xmath21 erg s@xmath10 @xmath11 in the 210 kev band @xcite . the 1ms observations of the _ chandra _ deep field - south ( cdf - south ) , are estimated to have resolved more than @xmath22 of the 210 kev xrb @xcite . however , due to the relatively large uncertainty ( @xmath23 ) in the total intensity of the 210 kev cosmic xrb , the precise resolved fraction is still somewhat unknown @xcite . it has also been shown that extrapolating the source counts seen in the chandra deep fields to much lower fluxes does not reproduce fully the total level of the cosmic xrb , suggesting the existence of an additional very faint x - ray population ( e.g. @xcite , @xcite ) . the luminosity function of agn that are selected in the 210 kev band , has been measured by several studies . @xcite demonstrated that strong evolution of the hard xlf has occurred between the @xmath24 and @xmath25 epochs . @xcite used a sample of 247 agn , including some from the cdf - north , to show that the xlf is best represented by a complex luminosity dependent density evolution ( ldde ) model . it should be noted that this sample does not reach to the limiting flux of the cdf - n data , but to @xmath26 erg s@xmath10 @xmath11 , where the optical identifications are reasonably complete . the major stumbling block in understanding the nature of the faint , hard x - ray selected agn population , is the difficulty of obtaining optical spectroscopic identifications . the soft x - ray selected samples used for xlf determinations , for example @xcite and @xcite , are primarily , or wholly , composed of bright ( @xmath27 ) , broad - line agn counterparts , which are relatively easy to optically identify . at fainter x - ray fluxes , such as those probed in the cdf - north , agn without broad lines , together with normal galaxies , make up a large fraction of the identified objects @xcite . those non - broad - line agn having spectroscopic identifications are almost all found with @xmath28 , in contrast to the peak of the broad - line sample , which lies at @xmath29 . the large numbers of @xmath30 type - ii quasars ( having log@xmath31 , log@xmath32 ) , predicted by synthesis models have not been detected in these surveys . the obvious conclusion to be drawn is that the absorbed and unabsorbed agn are taken from separate populations , a direct contradiction of the simplest unified scheme . however , the optical follow up programs in these deep _ chandra _ fields are by no means complete to the faint x - ray limit . for example , in the cdf - north , only 55% of the x - ray detections have optical counterparts with @xmath33 @xcite . objects fainter than this limit are practically unidentifiable with current optical spectroscopic techniques . there is a wide range of x - ray to optical flux ratios , @xmath34 in these samples , and so the unidentifiable objects are not necessarily the faintest x - ray sources , and produce a significant fraction of the xrb . the nature of these optically faint , hard x - ray objects is still not well understood . they could be narrow line agn at @xmath35 , with their strongest emission lines shifted out of the optical band . a number of optically - faint _ chandra _ sources have been identified from their near ir properties to be agn located in luminous , evolved host galaxies at high redshifts ( e.g. @xcite ) . alternatively , the unidentifiable sources may be agn embedded in optically thick dusty galaxies at moderate redshifts , the faintness of the hosts precluding identification @xcite . optical studies of nearby seyfert galaxies have found that the ratio , r , of type 2 to type 1 seyferts , is approximately 4 @xcite . the hard x - ray study of these type 2 seyferts by @xcite discovered a wide distribution of absorbing columns , but with @xmath36 of the agn having @xmath37 @xmath7 . however , this study was limited to the very local universe , @xmath38 mpc , and to low nuclear luminosities , @xmath39 ; the behaviour in the rest of the redshift - luminosity plane is less well understood . the distribution of absorption in x - ray selected agn is poorly constrained , the prime difficulty being that the greater an object s @xmath1 , the lower is its chance of being detected , or optically identified . there have been several published cases of agn in which the absorbing columns inferred by optical and x - ray measurements differ significantly ( e.g. @xcite , @xcite , @xcite ) . despite these limitations , the @xmath1 distribution , for hard x - ray selected agn , has been estimated , for relatively bright samples , by @xcite . these authors have primarily determined @xmath1 in their optically identified sample by examination of x - ray hardness ratio between the 0.52 and 210 kev bands . the distribution of absorption within the sample is described with a luminosity dependent @xmath1 model , in which high intrinsic luminosity agn are less likely to be heavily absorbed . this model does require some additional compton thick agn to reproduce fully the xrb when extrapolated to harder energies . so , despite the progress made in resolving , and to some extent optically identifying , the hard x - ray population , it has still not been possible to delimit the distribution of absorption in agn . this problem is particularly acute for the heavily absorbed , high-@xmath40 agn ; few of which have been detected and identified . however , by better constraining the @xmath41 in faint agn , we can hope to answer many questions about the geometry , composition and evolution of the dusty torus . for example , the strength of the luminosity dependence of @xmath41 can tell us about how the radiation from the accretion disk influences the surrounding torus , and/or how the torus geometry scales with black hole mass . if some redshift evolution of @xmath41 is detected , is it related to the overall evolution of the agn luminosity function ? does the dusty torus form coevally with the black hole , and is the amount of absorbing material related to the black hole mass ? in this study we use x - ray hardness ratios as an indicator of absorption in the spectra of the sources in our sample . many authors ( e.g. @xcite , @xcite , and @xcite ) have shown that colour based analyses are effective in deriving the properties of xmm-_newton _ sources which are detected with too few counts to permit full spectral fitting . in these optically identified samples , the agn with and without broad emission lines are seen to occupy separate regions in x - ray colour - colour plots . we present in this paper an analysis of the x - ray properties of sources detected by xmm-_newton _ in the @xmath0deep field . in section [ section_observations ] we describe the xmm-_newton _ observations . in order to escape the possible biases introduced by the incompleteness of optical identification programmes , we have devised a method to probe the @xmath41 of our sample . our technique does not depend on optical identification of the sample , permitting the inclusion of the optically faint x - ray detections . the simulations use a model xlf to describe the intrinsic distribution of all agn in redshift and ( de - absorbed ) luminosity space ; this is coupled to a model @xmath1 function , to generate a synthetic agn population ( described in section [ section_simulation_method ] ) . we simulate how this model population would be seen with xmm-_newton _ , accounting for both the selection function caused by the complex epic detector imaging characteristics , and the nuances of the source detection process ( see section [ section_capabilities ] ) . the output products of the simulation allow direct comparison of each of the model @xmath1 distributions with the @xmath0sample . we then compare the predictions of several simple unified scheme models of the @xmath1 distribution , by using a statistical comparison of the x - ray colour distributions found in the data and models ( section [ section_colour_stats ] ) . furthermore , we test two examples of more complex @xmath1 distribution models taken from the literature , and compare them to the @xmath0sample . in section [ section_source_counts ] we compare the source counts found in the @xmath0field and those predicted by the model simulations . finally , in section [ section_discussion ] we discuss our results and their implications for agn torus models , and for the evolving xlf model of @xcite . throughout the paper we use a lambda - dominated flat cosmology with @xmath42 km s@xmath10mpc@xmath10 , @xmath43 . @xmath44 refers to an object s de - absorbed x - ray luminosity in the observed @xmath45 band . @xmath1 is the equivalent hydrogen column density in units of @xmath7 . we refer to the @xmath1 distribution function as @xmath41 , and define it to be the fraction of all agn , per unit log@xmath1 , which have absorbing column @xmath1 . we define a power - law spectrum to be @xmath46 , where @xmath47 is the flux in units of photons kev@xmath10 s@xmath10 @xmath7 , @xmath48 is the photon energy in kev , and @xmath49 is the photon index .

we present an analysis of the x - ray properties of sources detected in the @xmath0xmm-_newton _ deep ( 200ks ) field . in order to constrain the absorbed agn population , we have tested the simplest form of the unified scheme , whereby the intrinsic luminosity function of absorbed agn is set to be the same as that of their unabsorbed brethren , coupled with various model distributions of absorption . we have also tested two extensions to the unified scheme : an evolving absorption scenario , in which the fraction of absorbed sources is larger at higher redshifts , and a luminosity dependent model in which high luminosity agn are less likely to be absorbed . both of these models provide poorer matches to the observed x - ray colour distributions than the best fitting simple unified model . field to field variations could be the cause of this disparity . [ firstpage ] surveys galaxies : active x - rays : galaxies quasars : general

we present an analysis of the x - ray properties of sources detected in the @xmath0xmm-_newton _ deep ( 200ks ) field . in order to constrain the absorbed agn population , we use extensive monte carlo simulations to directly compare the x - ray colours of observed sources with those predicted by several model distributions . in particular , we have carried out our comparisons over the entire 0.210 kev energy range of the xmm-_newton _ cameras , making our analysis sensitive to a large range of absorbing column densities . we have tested the simplest form of the unified scheme , whereby the intrinsic luminosity function of absorbed agn is set to be the same as that of their unabsorbed brethren , coupled with various model distributions of absorption . of the tested distributions , the best fitting model has the fraction of agn with absorbing column @xmath1 , proportional to ( log@xmath1)@xmath2 . we have also tested two extensions to the unified scheme : an evolving absorption scenario , in which the fraction of absorbed sources is larger at higher redshifts , and a luminosity dependent model in which high luminosity agn are less likely to be absorbed . both of these models provide poorer matches to the observed x - ray colour distributions than the best fitting simple unified model . we find that a luminosity dependent density evolution luminosity function reproduces poorly the 0.52 kev source counts seen in the @xmath0field . field to field variations could be the cause of this disparity . computing the x - ray colours with a simple absorbed power - law spectral model is found to over - predict , by a factor of two , the fraction of hard sources that are completely absorbed below 0.5 kev , implying that an additional source of soft - band flux must be present in a number of the absorbed sources . the tested synthesis models predict that around 16% of the detections in the @xmath0field are due to agn at @xmath3 . however , so far , only a single agn with @xmath4 has been identified in our approximately @xmath5 complete optical spectroscopy follow up program . finally , we use our simulations to demonstrate the efficacy of a hardness ratio selection scheme at selecting absorbed sources for further study . using this selection scheme , we show that around 40% of the @xmath0sample are expected to be agn with @xmath6 @xmath7 . [ firstpage ] surveys galaxies : active x - rays : galaxies quasars : general

astro-ph0504503

m

we have devised a monte carlo simulation technique which allows direct comparison of the pattern of x - ray colours produced by agn absorption models , with the pattern seen in the @xmath0sample . for this , we have extended the xmm-_newton _ imaging simulation method of @xcite , to a multi - band approach . we model the epic point spread function , vignetting and diffuse background in the same way as before . this method accounts for observational biases and the complex selection function at work in the sample . each iteration of the simulation method consists of four steps . i ) we generate an input source population , with each member having a set of randomly distributed parameters @xmath92 and @xmath49 , from the xlf , @xmath41 , and @xmath79 models . ii ) multi - band count rates are calculated for each simulated source according to , @xmath93 , and the chosen spectral model . iii ) random source positions are assigned , and the sourcelist is folded through a model of the epic imaging response to create multi - band images for each epic detector . iv ) a source - detection chain is carried out on the resulting multi - band images to create an output sourcelist . we repeat these steps for 100 simulated fields for each @xmath41 model , and for two agn spectral models . simulated images are produced separately for the mos1 , mos2 and pn cameras , then combined to produce a single image in each of the four energy bands for source searching purposes . to generate the catalogue for the @xmath0field , @xcite used model @xmath94 curves to represent the agn population independently in each of four energy bands . while valid for monochromatic studies , this technique is not suitable for colour analyses , since it takes no account of the multi - band properties of individual sources . we assume that there exists a single _ intrinsic _ xlf which describes all agn , which is modified by some distribution of absorption to produce the observed xrb , source counts and source colours . of the various models for the soft xlf ( e.g. @xcite , @xcite , @xcite , @xcite ) , we have chosen to use the luminosity dependent density evolution ( ldde1 ) xlf model of @xcite . this was primarily because it is based on a large sample of agn , and its model parameters have been determined for the currently preferred lambda - dominated cosmology . the sample used to fit this xlf model contains a mixture of agn both with , and without , broad lines , suggesting that it contains a subset of absorbed agn . we adopt the best fitting parameter values presented in table 3 of @xcite , and where appropriate , have corrected for the @xmath42 km s@xmath10 mpc@xmath10 used in this study . we integrate the xlf over the range @xmath95 log@xmath96 , @xmath97 to calculate the total number of agn expected in the field . a 1d cumulative probability distribution is generated by integrating the 2d xlf via an arbitrary path in @xmath40 , @xmath71 space . it is then possible to build a list of agn which are randomly distributed in @xmath40 , @xmath71 according to the model xlf . each of these agn are assigned a random value of @xmath1 according to the @xmath41 model being tested , and a spectral slope taken from @xmath79 . the absolute normalisation of the xlf is iteratively adjusted , so that the simulated fields contain the same source counts as the @xmath0sample at @xmath98 erg s@xmath10 @xmath11 . we determine the x - ray colours of the simulated agn by using a simple absorbed power - law ( apl ) model , which also includes a correction for the small galactic absorbing column ( @xmath99@xmath7 ) found in the @xmath0field . in order to compare simulated images with the observations , we must convert from the simulated agn parameters to multi - band epic count rates . we use the spectral fitting package xspec to generate fake spectra , incorporating both the instrumental response ( for the mos1 , mos2 and pn cameras ) , and the agn parameters @xmath40 , @xmath1 and @xmath49 . these spectra are summed over the appropriate energy bands , to derive the relevant conversion factors . the cost in processing time would be prohibitive if we were to individually recalculate these conversion factors for each of the thousands of simulated agn . hence , we have built lookup tables of conversion ratios , which finely sample @xmath100 parameter space , covering the range @xmath101 , @xmath102 log@xmath103 , @xmath81 . the conversion ratios are calculated for a single luminosity , but then scaled according to the luminosity of each simulated agn . these tables are used to convert rapidly from any set of simulated agn parameters @xmath93 to count rates , for each epic detector , and energy band . we have also examined the effect of including a small reflection component in the spectral model . this has the net effect of hardening the spectrum at higher energies , making simulated agn slightly more detectable above 5 kev . we use the pexrav model of @xcite , with the reflecting material covering @xmath104 steradians , a viewing angle of @xmath105 , and solar abundances . we call this the apl+r spectral model . it is beyond the scope of this study to include more complex agn spectral features , such as @xmath106 lines , or scattered soft x - ray emission . we expect the effect of these features on agn colours to be small relative to the effects of continuum obscuration . however , some of our results suggest that a number of detected sources in the @xmath0field have an additional soft component , as discussed later . we expect to be able to detect very few ( if any ) very heavily absorbed agn having log@xmath65 , and so have not included such objects in the simulated populations . in fact , the simulations show us that we expect agn having log@xmath107 to account for only @xmath108 of the detections in the @xmath0sample . therefore , any additional attenuation due to compton scattering within the dusty torus is ignored , since it has little effect for agn with log@xmath75 . the simulation method incorporates the effects of the epic response function , effective area , point spread function ( psf ) , vignetting , and background to produce multi - band images . we use the energy and off - axis angle dependent `` medium '' accuracy psf model , taken from the xmm-_newton _ calibration library . this psf model has been measured to be accurate to better than @xmath109 at @xmath110kev @xcite . the effective exposure time and vignetting are calculated from the sas generated exposure maps for the @xmath0field . a synthetic background is added to the simulated images to reproduce the level observed in the observations . the correct level of this additional background was determined through an iterative process to account for the contribution from the faint unresolved simulated sources . we use the simultaneous , multi - band source detection process on the combined simulated mos1+mos2+pn images in the same fashion as described for the @xmath0data @xcite . however , only one iteration of the background determination process is carried out , in order to conserve computation time . we have searched for sources over the entire useful field of view of the combined epic detectors , giving a total sky area of 0.185 deg@xmath111 .

we use extensive monte carlo simulations to directly compare the x - ray colours of observed sources with those predicted by several model distributions . in particular , we have carried out our comparisons over the entire 0.210 kev energy range of the xmm-_newton _ cameras , making our analysis sensitive to a large range of absorbing column densities . computing the x - ray colours with a simple absorbed power - law spectral model is found to over - predict , by a factor of two , the fraction of hard sources that are completely absorbed below 0.5 kev , implying that an additional source of soft - band flux must be present in a number of the absorbed sources .

we present an analysis of the x - ray properties of sources detected in the @xmath0xmm-_newton _ deep ( 200ks ) field . in order to constrain the absorbed agn population , we use extensive monte carlo simulations to directly compare the x - ray colours of observed sources with those predicted by several model distributions . in particular , we have carried out our comparisons over the entire 0.210 kev energy range of the xmm-_newton _ cameras , making our analysis sensitive to a large range of absorbing column densities . we have tested the simplest form of the unified scheme , whereby the intrinsic luminosity function of absorbed agn is set to be the same as that of their unabsorbed brethren , coupled with various model distributions of absorption . of the tested distributions , the best fitting model has the fraction of agn with absorbing column @xmath1 , proportional to ( log@xmath1)@xmath2 . we have also tested two extensions to the unified scheme : an evolving absorption scenario , in which the fraction of absorbed sources is larger at higher redshifts , and a luminosity dependent model in which high luminosity agn are less likely to be absorbed . both of these models provide poorer matches to the observed x - ray colour distributions than the best fitting simple unified model . we find that a luminosity dependent density evolution luminosity function reproduces poorly the 0.52 kev source counts seen in the @xmath0field . field to field variations could be the cause of this disparity . computing the x - ray colours with a simple absorbed power - law spectral model is found to over - predict , by a factor of two , the fraction of hard sources that are completely absorbed below 0.5 kev , implying that an additional source of soft - band flux must be present in a number of the absorbed sources . the tested synthesis models predict that around 16% of the detections in the @xmath0field are due to agn at @xmath3 . however , so far , only a single agn with @xmath4 has been identified in our approximately @xmath5 complete optical spectroscopy follow up program . finally , we use our simulations to demonstrate the efficacy of a hardness ratio selection scheme at selecting absorbed sources for further study . using this selection scheme , we show that around 40% of the @xmath0sample are expected to be agn with @xmath6 @xmath7 . [ firstpage ] surveys galaxies : active x - rays : galaxies quasars : general

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sample . the levels of the contours are set such that they include @xmath5 ( short dash ) , @xmath158 ( long dash ) , and @xmath8 ( solid line ) of the smoothed source distribution , and were generated in the same way as for fig . [ colour_nh_ranges ] . typical sizes of @xmath137 , @xmath138 , and @xmath139 are shown with boxes , for sources having `` two - band '' fluxes of @xmath159 and @xmath160 erg s@xmath10 @xmath11 , where the `` two - band '' flux is the flux measured over the two energy bands used to calculate the hardness ratio.,title="fig:",width=302 ] sample . the levels of the contours are set such that they include @xmath5 ( short dash ) , @xmath158 ( long dash ) , and @xmath8 ( solid line ) of the smoothed source distribution , and were generated in the same way as for fig . [ colour_nh_ranges ] . typical sizes of @xmath137 , @xmath138 , and @xmath139 are shown with boxes , for sources having `` two - band '' fluxes of @xmath159 and @xmath160 erg s@xmath10 @xmath11 , where the `` two - band '' flux is the flux measured over the two energy bands used to calculate the hardness ratio.,title="fig:",width=302 ] the two left - most panels of fig . [ colours_sims_models ] show the colour - colour distributions of the @xmath0sample , with grey - scale and contours generated in the same way as for fig [ colour_nh_ranges ] . [ colours_13hr ] shows the same contours , but with the individual data points overlaid [ colours_sims_models ] and [ colours_13hr ] show that there is a strong concentration of sources in the @xmath161 = ( 0.4,-0.5,-0.5 ) region , slightly harder in @xmath141 than the nominal position of an unabsorbed agn with log@xmath162 , @xmath19 . a large number of sources have much harder values of @xmath141 and @xmath142 than the nominal unabsorbed position , indicating that strong absorption is present in a significant fraction of the population . however , the majority of the sources in the @xmath163 , @xmath164 region are actually faint soft sources having large @xmath143 measurement uncertainties . the bimodality apparent either side of @xmath157 is probably due to the fast increase in @xmath141 over the range @xmath165 log@xmath166 , which limits the number of sources in this region . a similarly sparse region occurs at @xmath167 and again , this is probably related to the fast increase in @xmath142 over the range @xmath168 log@xmath169 . curves measured in the @xmath0sample ( filled circles ) , compared to those produced by the @xmath170 ( solid line ) , @xmath59 ( long dash ) , @xmath61 ( short dash ) , @xmath70 ( dotted ) , and @xmath171 ( dot - dash ) , @xmath41 models . these results are for the absorbed power - law spectral model and are normalised to the euclidean - slope . the equivalent points for the sample of @xcite ( taken from fig . 6 ) , are also shown ( open symbols with errorbars ) , and have been normalised assuming a sky area of 0.185 deg@xmath111 . , width=340 ] we have compared the 0.52 kev band integral source counts , @xmath90 , measured in the @xmath0sample with those produced by the simulated model distributions . we make no correction for sky coverage , since the @xmath0sample and the simulated fields have an identical survey - depth / sky area relation . we find a large disparity between the @xmath0and simulated fields , especially around the knee of the observed @xmath172 at @xmath173 erg s@xmath10 @xmath11 , as can be seen in fig . [ source_counts_soft ] . each of the @xmath41 models produced similar @xmath90 curves , especially at faint fluxes , where the statistical errors are better . thus we deduce that the data - model disparity is primarily caused by differences between the data and the model xlf ( and/or its evolution ) . we discuss this later . the primary purpose of this study is to compare the @xmath41 models , so it is important that we minimise the effect on the statistical analysis caused by the disparity between the data and xlf / evolution model . therefore , we have examined the x - ray colour distribution of sources , rather than the distributions of their absolute fluxes . we expect the colour - colour distributions to be more sensitive to @xmath41 than to the xlf , because a small change of the position of an absorbed agn in the @xmath40-@xmath112 plane , has a strong effect on its overall brightness , but only a small effect on its x - ray colours . for example , if the peak of agn space density is actually at @xmath174 , ( rather than at @xmath175 as predicted by the xlf / evolution model ) , then the resulting change in hardness ratios for an agn , having an absorbed power - law spectrum , log@xmath176 , at this peak redshift , would be @xmath177 = + 0.07(+0.03 ) . however , an increase of 0.5 dex in the absorption of the same agn , would result in @xmath177 = + 0.23(+0.17 ) . therefore , a colour analysis of the @xmath41 models is more strongly dependent on the tested @xmath41 , than on differences between the data and xlf / evolution model . we have used the kolmogorov - smirnov test ( ks ) , to determine how well the simulated data reproduce the x - ray colour distribution measured in the @xmath0sample . the ks test has the advantage that it requires no rebinning of data , utilising the full information content of the data set . however , it does not take into account the relative errors on data points , meaning that low signal to noise measurements can , to some extent , `` wash out '' the signal from the more precise measurements . a three dimensional extension of the ks test ( 3d - ks ) , as devised by @xcite , was used to compare the sample with the simulation results in the full ( hr1,hr2,hr3 ) variable space . in order to examine more closely how the models reproduce the sample distribution , we have carried out one dimensional ks tests separately on @xmath141 , @xmath142 and @xmath143 . the conversion from the 3d - ks test statistic , @xmath178 , to the probability that two samples were taken from the same underlying population , @xmath179 , is strongly dependent on the number of sources in the tested samples , and the degree of correlation between the tested variables . @xcite numerically generated lookup tables to allow this conversion at a number of confidence levels , for a range of sample sizes , and values of the correlation parameter . however , these tables give only a relatively small number of conversion values , at discrete confidence levels , sample sizes , and values of the correlation parameter . therefore , we have run a set of simulations , the results of which permit conversion from @xmath178 directly into @xmath179 conversion using the precise sample sizes and correlations seen in the @xmath0sample . we calculated the three - dimensional probability density map ( 3d - pdm ) , of the @xmath0sample in ( hr1,hr2,hr3 ) space . the contribution from each source to the 3d - pdm is calculated from a 3d - gaussian that has widths equivalent to @xmath137,@xmath138 , and @xmath139 . the normalisation of the 3d - gaussian is set such that the total contribution of each source is unity . this 3d - pdm is used to generate pairs of random populations , having 217 and 25000 members respectively , for which @xmath178 is calculated . the latter step is repeated for 100000 iterations . the equivalent probability for any particular value of the 3d - ks statistic , is equal to the fraction of these iterations having @xmath178 greater than this value . the absolute lower limit at which we can evaluate the probability is given by the reciprocal of the number of simulation iterations , i.e. 0.001% , although the errors are large at this level . this limit is determined by the processing time available . table [ ks_results ] shows @xmath179 , for the eight @xmath41 models , and for both of the tested spectral models . in order to determine where the biggest differences arise between the data and models , we have calculated the ks probabilities ( @xmath180 ) , separately for each of @xmath141 , @xmath142 and @xmath143 , the results of which are also shown in table [ ks_results ] . [ cols= " < , > , > , > , > , > , > , > , > " , ] for the simplest toy model of a torus with uniformly density , and a typical opening angle , @xmath181 , the fraction of agn that are heavily absorbed is approximately @xmath182 . so , if we use the size of the `` hard '' fraction of the @xmath0sample as a measure of the number of absorbed agn , we can infer a rather wide opening angle of @xmath183 . however , this estimate does not take into account the effect of the drop in the selection function toward high @xmath1 , and can only be seen as an upper limit on @xmath181 . we estimate the relative selection function for hard sources by counting the fraction of simulated `` hard '' input sources that have output counterparts relative to that for all input sources . applying this correction to the @xmath0sample , we predict an _ intrinsic _ `` hard '' fraction of @xmath184 , implying an opening angle of @xmath185 . if in our correction for the relative selection function , we exclude those sources with absorbing column above log@xmath186 , where our sample constrains the models only weakly , then we find @xmath187 . we are also able to examine the range of torus parameters that would best match the @xmath41 models . for the best fitting @xmath188 model , where the fraction of input sources with log@xmath32 is @xmath189 , the predicted opening angle is @xmath190 . as fig . [ colour_nh_ranges ] shows , @xmath141 and @xmath142 are sensitive to the shape of the distribution over a wide range of @xmath1 , particularly for intermediately absorbed sources . we have seen that the @xmath188 is strongly favoured over the @xmath61 @xmath41 model ( see table [ ks_results ] ) . these two models are very similar in the range @xmath191 log@xmath75 , contain similar numbers of unabsorbed agn ( log @xmath162 ) , and produce comparable numbers of `` hard '' sources . therefore , the difference must lie primarily in the @xmath64 log@xmath63 range , in which the @xmath188 model contains many more agn . a major problem with the uniformly dense torus model is that it predicts that nearly all agn will be either heavily absorbed or completely unabsorbed . however , more complex models , incorporating a wide distribution of torus densities , predict larger numbers of intermediately absorbed agn . for example , a model in which the density falls off exponentially with angle away from the plane of the torus , predicts a much flatter @xmath41 ( e.g. @xcite ) . it is possible , with some tuning of such a model s parameters , to approximately match the best fitting @xmath188 distribution . since absorption in the @xmath64 log@xmath63 range has only a significant effect on @xmath141 , it would not have been detectable in the colour distributions if the @xmath192 kev band had not been considered . a number of studies of absorption in faint agn have based their estimates of @xmath1 on hardness ratios between the @xmath193 and @xmath194 kev bands , and therefore may have underestimated the number of intermediately absorbed agn ( e.g. @xcite,@xcite ) . a better determination of mean torus properties will be possible when the @xmath0field is covered by _ spitzer _ , and we are able to correlate x - ray colours with mid / far - ir data . each of the simulated @xmath41 models produced similar 0.52.0 kev source count - flux relations , @xmath90 . however , these are seen to reproduce poorly the @xmath90 relation observed in the @xmath0sample ( see fig . [ source_counts_soft ] ) . the models under - produce the @xmath90 above the normalisation flux ( @xmath195 erg s@xmath10 @xmath11 ) , and over - produce the @xmath90 below this flux ( see fig . [ source_counts_soft ] ) . in fact , at @xmath160 erg s@xmath10 @xmath11the models under - produce the source counts seen in the @xmath0sample by a factor of about two . this disparity is seen to a similar degree in each of the @xmath41 models , suggesting that it is related to the difference between the data and xlf / evolution model . the @xmath90 of the @xcite sample , is also shown in fig . [ source_counts_soft ] , plotted assuming our field has a uniform sky area of 0.185 deg@xmath111 . this illustrates that in the flux range @xmath196 erg s@xmath10 @xmath11 , the ldde1 xlf also under - produces the source counts of the sample from which it was derived . the shape of the @xmath90 relation of the @xcite sample is closer to that seen in the @xmath0sample than to the models . the faintest agn in the @xcite sample are from the deepest _ rosat _ observations of the lockman hole field , where the flux limit of the data was @xmath197 erg s@xmath10 @xmath11 . our significantly deeper flux limit means that we are using part of @xmath198 space outside that constrained by the sample of @xcite . a previous comparison of source counts from _ rosat _ observations in the lockman hole and @xmath0fields , revealed a @xmath199 over - abundance near @xmath200 erg s@xmath10 @xmath11 in the @xmath0field with respect to the lockman hole @xcite . in addition , @xcite found that the @xmath0field is slightly over - dense in the 0.52 kev band with respect to both of the chandra deep fields . therefore we conclude that the differences between model and sample are caused by a combination of these factors . in particular , our extrapolation of the ldde1 xlf / evolution model to faint fluxes , suggests that this complex scheme requires some revision . the shape of the xlf at high redshift is poorly known because of the difficulties in obtaining a large spectroscopically identified sample of these objects . we can use the simulated source population to make predictions about the number of high-@xmath40 agn in the @xmath0sample . each of the @xmath41 models predict that around 16% of the total number of x - ray detections are due to agn with @xmath201 . therefore , it can be inferred that the fraction of agn with @xmath3 in the x - ray population is primarily dependent on the shape of the underlying xlf and its evolution , rather than the @xmath1 distribution within the high-@xmath40 population . the model predictions suggest that we should expect around 35 high-@xmath40 agn in the @xmath0field . however , only a single agn has been identified having @xmath3 by our follow up optical spectroscopy program ( which has secure ids for over 100 sources ) . this disparity is maybe due to the over - production of faint sources by the xlf / evolution model ; these are more likely to be at high @xmath40 . the x - ray detection probability of the @xmath3 agn is much less dependent on @xmath1 than for the low-@xmath40 agn , since most absorption is redshifted below 2 kev . therefore , most of the @xmath41 models predict that absorbed agn make up the majority of the _ detected _ high-@xmath40 population , the precise fraction being dependent on the particular @xmath41 model . however , the absorption of optical and uv spectral features does severely affect the probability of identification for these objects . we have recently obtained further deep optical imaging of the @xmath0field in several bands , which will permit us to make photometric redshift estimates for some of the optically faint sources . the forthcoming deep coverage of the @xmath0field in the infrared with _ spitzer _ will further constrain the nature of the high-@xmath40 population .

of the tested distributions , the best fitting model has the fraction of agn with absorbing column @xmath1 , proportional to ( log@xmath1)@xmath2 . we find that a luminosity dependent density evolution luminosity function reproduces poorly the 0.52 kev source counts seen in the @xmath0field . the tested synthesis models predict that around 16% of the detections in the @xmath0field are due to agn at @xmath3 . however , so far , only a single agn with @xmath4 has been identified in our approximately @xmath5 complete optical spectroscopy follow up program . we show that around 40% of the @xmath0sample are expected to be agn with @xmath6 @xmath7 .

we present an analysis of the x - ray properties of sources detected in the @xmath0xmm-_newton _ deep ( 200ks ) field . in order to constrain the absorbed agn population , we use extensive monte carlo simulations to directly compare the x - ray colours of observed sources with those predicted by several model distributions . in particular , we have carried out our comparisons over the entire 0.210 kev energy range of the xmm-_newton _ cameras , making our analysis sensitive to a large range of absorbing column densities . we have tested the simplest form of the unified scheme , whereby the intrinsic luminosity function of absorbed agn is set to be the same as that of their unabsorbed brethren , coupled with various model distributions of absorption . of the tested distributions , the best fitting model has the fraction of agn with absorbing column @xmath1 , proportional to ( log@xmath1)@xmath2 . we have also tested two extensions to the unified scheme : an evolving absorption scenario , in which the fraction of absorbed sources is larger at higher redshifts , and a luminosity dependent model in which high luminosity agn are less likely to be absorbed . both of these models provide poorer matches to the observed x - ray colour distributions than the best fitting simple unified model . we find that a luminosity dependent density evolution luminosity function reproduces poorly the 0.52 kev source counts seen in the @xmath0field . field to field variations could be the cause of this disparity . computing the x - ray colours with a simple absorbed power - law spectral model is found to over - predict , by a factor of two , the fraction of hard sources that are completely absorbed below 0.5 kev , implying that an additional source of soft - band flux must be present in a number of the absorbed sources . the tested synthesis models predict that around 16% of the detections in the @xmath0field are due to agn at @xmath3 . however , so far , only a single agn with @xmath4 has been identified in our approximately @xmath5 complete optical spectroscopy follow up program . finally , we use our simulations to demonstrate the efficacy of a hardness ratio selection scheme at selecting absorbed sources for further study . using this selection scheme , we show that around 40% of the @xmath0sample are expected to be agn with @xmath6 @xmath7 . [ firstpage ] surveys galaxies : active x - rays : galaxies quasars : general

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as the instrumentation for millimeter - wave telescopes improves , it becomes progressively more straightforward to study individual molecular clouds in other galaxies . recent studies of local group galaxies have surveyed large numbers of molecular clouds in the large magellanic cloud @xcite , the small magellanic cloud @xcite , m33 @xcite , and a bevy of local group dwarf galaxies ( e.g. * ? ? ? * ; * ? ? ? these recent studies explore the nature of star formation on galactic scales by studying the properties of giant molecular clouds ( gmcs , @xmath1 ) throughout their host galaxies . such gmcs contain the majority of the molecular mass in the milky way s ism and are responsible for most of the star formation in the galaxy @xcite . the andromeda galaxy ( m31 ) is the second largest disk galaxy in the local group , after the milky way , and it subtends over 2 deg@xmath2 on the sky . its proximity ( 770 kpc , * ? ? ? * ) makes it an excellent target for studying extragalactic molecular clouds . numerous surveys of co emission have been conducted over a portion of m31 and a comprehensive list of the 24 co studies published up to 1999 is given in @xcite . this extensive list of surveys can be supplemented with a few major studies that have occurred since then . @xcite used the bima millimeter interferometer to study a @xmath3 field in the outer region of the galaxy ( @xmath4 kpc ) and find 6 molecular complexes similar to those found in the milky way . an extensive survey covering the entirety of the star - forming disk of m31 has been completed using the iram 30-m by ( * ? ? ? * see also references therein ) . finally , @xcite used the plateau de burre interferometer to examine the properties of molecular clouds in 9 fields . using the gaussclumps @xcite algorithm , they decompose the emission into 30 individual molecular clouds . previous high - resolution observations of co in m31 indicate that a large fraction of the molecular gas is found in gmcs . identifying individual gmcs requires a telescope beam with a projected size @xmath5 pc , the typical size of a gmc in the milky way @xcite , which requires an angular resolution of @xmath6 at the distance of m31 . there have been seven observational campaigns that observed co @xmath7 emission from m31 at sufficient resolution to distinguish molecular clouds : @xcite . with the exception of @xcite , all of these studies have found gmcs with properties similar to those found in the inner milky way and @xcite have argued that the differences observed by @xcite can be attributed to observational errors . indeed , @xcite presented the first direct observations of gmcs in any external galaxy using interferometric observations . subsequent studies with interferometers and single - dish telescopes confirmed that most co emission in m31 comes from gmcs and that the gmcs properties were similar to those found in the milky way @xcite . although the molecular gas in m31 has been extensively studied , there remains a gap connecting the large - scale , single - dish observations and the small - scale , interferometer observations . to address this gap , we completed co(@xmath8 ) observations of a large ( 20 kpc@xmath9 region ) along a spiral arm of m31 with high resolution ( @xmath10 pc ) . we then followed up on these observations using a more extended configuration of the interferometer yielding data with a resolution of @xmath11 pc . this paper presents the observational data of the both the survey and the follow - up observations ( [ obs ] ) . using only the follow - up data , we present the first results , namely a confirmation of previous studies that find gmcs in m31 are similar to those in the milky way ( [ analysis],[larson - sec ] ) . notably , this paper utilizes the techniques described in @xcite to correct the observational biases that plague extragalactic co observations , thereby placing derived cloud properties on a common scale that can be rigorously compared with gmc data from other galaxies . the follow - up observations are also used to examine the velocity gradients and angular momentum of the gmcs , which are then compared to the remainder of gas in the galaxy for insight into the gmc formation problem ( [ spang ] ) . we conclude the paper by examining the larger galactic environment of m31 to explore connections between the gmcs and the larger ism ( [ environment ] ) . subsequent work will explore the star formation properties of these gmcs and the formation of such clouds along the spiral arm using the data from the spiral arm survey .

the data are processed using an analysis algorithm designed to extract gmcs and correct their derived properties for observational biases thereby facilitating comparison with milky way data . the velocity gradients and angular momenta of the gmcs are comparable to the values measured in m33 and the milky way ; and , in all cases , are below expected values based on the local galactic shear .

we present berkeley illinois maryland association ( bima ) millimeter interferometer observations of giant molecular clouds ( gmcs ) along a spiral arm in m31 . the observations consist of a survey using the compact configuration of the interferometer and follow - up , higher - resolution observations on a subset of the detections in the survey . the data are processed using an analysis algorithm designed to extract gmcs and correct their derived properties for observational biases thereby facilitating comparison with milky way data . the algorithm identifies 67 gmcs of which 19 have sufficient signal - to - noise to accurately measure their properties . the gmcs in this portion of m31 are indistinguishable from those found in the milky way , having a similar size - line width relationship and distribution of virial parameters , confirming the results of previous , smaller studies . the velocity gradients and angular momenta of the gmcs are comparable to the values measured in m33 and the milky way ; and , in all cases , are below expected values based on the local galactic shear . the studied region of m31 has a similar interstellar radiation field , metallicity , toomre @xmath0 parameter , and midplane volume density as the inner milky way , so the similarity of gmc populations between the two systems is not surprising .

astro-ph0609421

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this paper has presented bima millimeter interferometer observations of @xmath12co(@xmath8 ) emission from giant molecular clouds ( gmcs ) along a spiral arm at @xmath275 kpc in m31 . the observations were conducted in two parts : a low - resolution survey using the compact ( d ) configuration of the array and a high - resolution , follow - up study using a more extended ( c ) configuration of the array . all data from the study were segmented and analyzed with the analysis algorithms of @xcite , which correct the observational biases imprinted on the data by having relatively low signal - to - noise and marginally resolving the gmcs . the c - array follow - up spans 7.4 kpc@xmath276 finding 67 clouds . we report the following conclusions : \1 . the gmc population is very similar to that found in the inner milky way . both the size - line width relationship and distribution of virial parameters are statistically indistinguishable from those derived from the population of clouds in the inner milky way . this confirms the work of several authors @xcite while using techniques that correct for the biases imprinted by using interferometric observations . we measured the velocity gradients and angular momenta across the gmcs . like the milky way and m33 , there is significantly more angular momentum in possible progenitor material than in the resulting gmcs , though the discrepancy is smallest in m31 owing to the relatively low galactic shear at large galactocentric radii . all three systems suggest braking mechanisms act during the process of cloud formation to dissipate angular momentum . \3 . the galactic environment in m31 where the gmcs are found is similar in most respects that of the solar neighborhood and inner milky way . that gmcs in both environments are similar is consistent with the idea that the galactic environment regulates gmc properties . in systems where the galactic environment differs significantly from those studied here , the gmc properties are found to be different ( e.g. , * ? ? ? this work was supported by a nasa gsrp fellowship and an nsf postdoctoral fellowship ( ast-0502605 ) . i am extremely grateful to rainer beck , leo blitz , michel gulin , adam leroy , chris mckee , eve ostriker and an anonymous referee for carefully reading the manuscript and offering in - depth commentary . kartik sheth kindly discussed his current and future work on m31 , allowing me to read a preprint of a forthcoming paper . this work made extensive use of the nasa extragalactic database , the nasa abstract data service , and the mast archive . the molecular line observations used the bima millimeter array which was supported , in part , by nsf grant ast-0228963 to the radio astronomy laboratory at u.c . berkeley . , k. , vogel , s. n. , wilson , c. d. , & dame , t. m. 2000 , in the interstellar medium in m31 and m33 . proceedings 232 . we - heraeus seminar , 22 - 25 may 2000 , bad honnef , germany . edited by elly m. berkhuijsen , rainer beck , and rene a. m. walterbos . shaker , aachen , 2000 , p. 37 - 40 , 3740 , w. j. , thornton , d. d. , plambeck , r. l. , wright , m. c. h. , lugten , j. , urry , l. , fleming , m. , hoffman , w. , hudson , j. , lum , w. t. , forster , j. . r. , thatte , n. , zhang , x. , zivanovic , s. , snyder , l. , crutcher , r. , lo , k. y. , wakker , b. , stupar , m. , sault , r. , miao , y. , rao , r. , wan , k. , dickel , h. r. , blitz , l. , vogel , s. n. , mundy , l. , erickson , w. , teuben , p. j. , morgan , j. , helfer , t. , looney , l. , de gues , e. , grossman , a. , howe , j. e. , pound , m. , & regan , m. 1996 , , 108 , 93

we present berkeley illinois maryland association ( bima ) millimeter interferometer observations of giant molecular clouds ( gmcs ) along a spiral arm in m31 . the observations consist of a survey using the compact configuration of the interferometer and follow - up , higher - resolution observations on a subset of the detections in the survey .

we present berkeley illinois maryland association ( bima ) millimeter interferometer observations of giant molecular clouds ( gmcs ) along a spiral arm in m31 . the observations consist of a survey using the compact configuration of the interferometer and follow - up , higher - resolution observations on a subset of the detections in the survey . the data are processed using an analysis algorithm designed to extract gmcs and correct their derived properties for observational biases thereby facilitating comparison with milky way data . the algorithm identifies 67 gmcs of which 19 have sufficient signal - to - noise to accurately measure their properties . the gmcs in this portion of m31 are indistinguishable from those found in the milky way , having a similar size - line width relationship and distribution of virial parameters , confirming the results of previous , smaller studies . the velocity gradients and angular momenta of the gmcs are comparable to the values measured in m33 and the milky way ; and , in all cases , are below expected values based on the local galactic shear . the studied region of m31 has a similar interstellar radiation field , metallicity , toomre @xmath0 parameter , and midplane volume density as the inner milky way , so the similarity of gmc populations between the two systems is not surprising .

0810.4336

c

there are only a few deep cluster lfs having comparable depth to our own . in general , we are in good agreement with previous work , based on smaller and shallower samples @xcite . the @xmath15 point we measure gets steadily brighter with increasing wavelength , tracking the color of old , passively evolving stellar populations that are the main component of bright elliptical galaxies @xcite . the value we find is also consistent with the local sdss value by @xcite : this is not surprising , as it is well known that massive galaxies evolve passively since high redshift . the main interest of this investigation is in the evolution of the lf slope . the lf is well fitted by a single schechter function , with a slope @xmath55 which is essentially the same in all bands . this suggests that the cluster lf is dominated by galaxies on the red sequence to a luminosity of @xmath56 in all bands , and that therefore the red sequence continues at least to 6 magnitudes below the @xmath10 point even at @xmath11 . this can be clearly seen in fig . 7 where we show the @xmath57 vs. @xmath5 color - magnitude relation for abell 1703 . the relation can be clearly followed at least to @xmath58 with little scatter . a more detailed analysis of the color - magnitude relation is deferred to a future paper ( harsono & de propris 2008 , in preparation ) . the red sequence appears to be well established and contain the majority of cluster populations even at a lookback time of @xmath59 gyrs ( cf . @xcite for a similarly deep relation in local clusters ) . the slope is very similar to the local value for @xmath22 derived by @xcite and @xcite . this argues that even galaxies to @xmath56 have formed their stellar populations and assembled the majority of their mass at least at @xmath11 . we can therefore place a significant lower limit to the assembly epoch of galaxies down to 1/600@xmath60 of the mass of the milky way . given the evidence for truncation of the red sequence at @xmath61 @xcite , our data point to the @xmath62 interval as a crucial epoch to investigate the formation of the fainter galaxy populations . the other issue we wish to address is the faint end upturn . this has been a controversial subject , ever since its original discovery by @xcite and @xcite . there have been a series of claims and counterclaims regarding the faint end slope and the existence of an upward inflection , sometimes even in the same cluster . for instance , @xcite and @xcite observe a steep lf at the faint end for the coma cluster , while @xcite and @xcite quote much flatter slopes . in virgo , @xcite claim a slope as steep as @xmath63 , while @xcite derive @xmath64 . @xcite review the existence of the upturn and the shape of the faint end of the lf and conclude that there is a steep mass function . the observation of the upturn in two composite lfs , derived by two different groups @xcite , suggests that the upward inflection of the lf is real ( however , cf . , @xcite ) . unlike @xcite and @xcite we do not find a steepening of the lf at @xmath13 . however , we must consider that the lf upturn is more pronounced at large clustercentric radii , while our fields generally cover only the central region of each cluster . the size of the acs fields used in this study covers between 350 and 750 @xmath65 kpc on the side . in terms of @xmath66 ( the radius at which @xcite and @xcite normalize their lfs ) , the areas imaged by acs cover between 20% and 40% of the area of the cluster out to @xmath29 . we therefore only derive lfs for the cluster cores . this should not affect our comparisons with the bright end of the lf ( @xmath22 ) , as this does not seem to vary significantly with radius . however , the steep upturn claimed by @xcite and @xcite is much more pronounced at large clustercentric radii , i.e. , in the cluster outskirts . on the other hand it is possible to see the upturn even in the more central regions of the sample studied by @xcite , inside @xmath67 ( see fig . 10 of @xcite ) , so our data should exhibit an upturn at faint magnitudes , although of course more clusters would be welcome to bolster the argument . as we do not detect a steepening in the lf , we suggest that , if the steepening is real , the faint galaxies contributing to the upturn consist of a population of recently infalling objects ( e.g. , @xcite ) whose star formation is curtailed by the cluster environment . this would be consistent with the observation that about 1/2 of the fainter cluster dwarfs in virgo and elsewhere have been forming stars until relatively recently @xcite , until their star formation stopped and their colors moved to the red sequence . the newly infalling population may be the one now contributing to the steep upturn . in a ` downsizing ' model , it may be expected that objects undergoing star formation suppression and cluster infall at the present epoch would indeed tend to be among the fainter and less massive galaxies and to have the steep lf characteristic of ` pristine ' cdm power spectra . our observations imply that the passive evolution of bright galaxies can be extended to faint dwarfs , at least to @xmath11 and suggest that the majority of galaxy evolution may have taken place at surprisingly early epochs even for the least massive objects . all of the data presented in this paper were obtained from the multimission archive at the space telescope science institute ( mast ) . stsci is operated by the association of universities for research in astronomy , inc . , under nasa contract nas5 - 26555 . support for mast for non - hst data is provided by the nasa office of space science via grant nag5 - 7584 and by other grants and contracts . adami , c. , nichol , r. c. , mazure , a. , durret , f. , holden , b. & lobo , c. 1998 , , 334 , 765 adami , c. , picat , j. p. , durret , f. , mazure , a. , pell , r. & west , m. 2007 , , 472 , 749 andreon , s. , punzi , g. , grado , a. 2005 , , 360 , 727 andreon , s. 2006a , , 448 , 447 andreon , s. 2006b , , 369 , 969 andreon , s. , cuillandre , j .- c . , puddu , e. & mellier , y. 2006 , , 372 , 60 baldry , i. k. , glazebrook , k. & driver , s. p. 2008 , , 388 , 945 barkhouse , w. a. , yee , h. k. c. & lopez - cruz o. 2007 , , 671 , 1471 beijersbergen , m. , hoekstra , h. , van dokkum , p. g. & van der hulst , t. 2002 , , 329 , 385 bernstein , g. m. , nichol , r. c. , tyson , j. a. , ulmer , m. p. & wittman , d. 1995 , , 110 , 1507 bertin e. , arnouts s. 1996 , , 117 , 393 boyce , p. j. , phillipps , s. , jones , j. b. , driver , s. p. , smith , r. m. , & couch , w. j. 2001 , , 328 , 277 bruzual , g. & charlot , s. 2003 , , 344 , 1000 capak , p. et al . 2007 , , 172 , 99 carlberg , r. g. , yee , h. k. c. & ellingson , e. 1997 , , 478 , 462 crawford , s. m. , bershady , j. a. & hoessel , j. g. 2008 , astro.ph 0809.1661 colless , m. m. 1989 , , 237 , 799 colless , m. m. et al . 2001 , , 328 , 1039 conselice , c. j. , gallagher , j. s. & wyse , r. f. g. 2001 , , 559 . 791 conselice , c. j. , gallagher , j. s. & wyse , r. f. g. 2003 , , 125 , 66 cool , r. j. , eisenstein , d. j. , scranton , r. , brinkmann , j. , schneider , d. p. & zehavi , i. 2006 , , 131 , 736 cross , n. j. g. & driver , s. p. 2002 , , 329 , 579 croton , d. et al . 2006 , , 365 , 11 de lucia , g. et al . 2007 , , 374 , 809 de propris , r. , pritchet , c. j. , hartwick , f. d. a. & mcclure , r. d. 1995 , , 450 , 534 de propris , r. , eisenhardt , p. r. , stanford , s. a. & dickinson , m. 1998 , , 503 , l45 de propris , r. , stanford , s. a. , eisenhardt , p. r. , holden , b. p. & rosati , p. 2007 , , 133 , 2207 dressler , a. 1980 , , 236 , 351 driver , s. p. , phillipps , s. , davies , j. i. , morgan , i. , disney , m. j. 1994 , , 268 , 393 eisenhardt , p. r. , de propris , r. , gonzalez , a. h. , stanford , s. a. , wang , m. & dickinson , m. 2007 , , 169 , 225 garilli , b. , maccagni , d. & andreon , s. 1999 , , 353 , 479 giavalisco , m. et al . 2004 , , 600 , l93 gomez , p. l. et al . 2003 , , 584 , 210 harsono d. & de propris r. 2007 , , 380 , 1036 hilker , m. , mieske , s. & infante , l. 2003 , , 397 , l9 holberg , j. b. & bergeron p. 2006 , , 132 , 1221 huang j .- s . , cowie l. l. , gardner j. p. , hu e. m. , songaila a. , wainscoat r. j. 1997 , , 476 , 12 jenkins , l. p. , hornschemeier , a. e. , mobasher , b. , alexander , d. m. & bauer , f. e. 2007 , , 666 , 846 koekemoer , a. , fruchter , a. s. , hook , r. n. & hack , w. 2002 , in _ the 2002 hst calibration workshop : hubble after the installation of acs and the nicmos cooling system _ ed . by s. arribas , a. koekemoer , b. whitmore ( baltimore : space telescope science institute ) , p. 337 khochfar , s. , silk , j. , windhorst , r. a. & ryan , r. e. 2007 , , 668 , l115 krick , j. e. , surace , j. a. , thompson , d. , ashby , m. l. n. , hora , j. l. , gorjian , v. & yan , l. 2008 , astro - ph 0807.1565 lewis , i. j. et al . 2002 , , 334 , 673 macdonald , e. c. et al . 2004 , , 352 , 1255 mercurio , a. , massarotti , m. , merluzzi , p. , girardi , m. , la barbera , f. & busarello , g. 2003 , , 408 , 57 milne , m. l. , pritchet , c. j. , poole , g. b. , gwyn , s. d. j. , kavelaars , j. j. , harris , w. e. & hanes , d. a. 2007 , , 133 , 177 muzzin , a. , wilson , g. , lacy , m. , yee , h. k. c. & stanford , s. a. 2008 , astro - ph 0807.0227 penny , s. j. & conselice , c. j. 2008 , , 383 , 247 pointecouteau , e. , arnaud , m. & pratt , g. w. 2005 , , 435 , 1 popesso , p. , biviano , a. , bhringer , h. & romaniello , m. 2006 , , 445 , 29 pracy , m. , de propris , r. , driver , s. p. , couch , w. j. & nulsen , p. e. j. 2004 , , 352 , 1135 rines , k. & geller , m. j. 2008 , , 135 , 1837 sabatini , s. , davies , j. i. , scaramella , r. , smith , r. , baes , m. , linder , s. m. , roberts , s. & testa , m. 2005 , , 357 , 819 schechter , p. 1976 , , 203 , 297 smith , r. j. et al . 2008 , , 386 , l96 stott , j. p. , smail , i. , edge , a. c. , ebeling , h. , smith , g. p. , kneib , j .- & pimbblet , k. a. 2007 , , 661 , 95 trentham , n. 1998a , , 295 , 360 trentham , n. 1998b , , 293 , 71 valotto , c. , moore , b. & lambas , d. g. 2001 , , 546 , 157 wright , e. l. 2006 , , 118 , 1711 wu , x .- , xue , y .- j . & fang , l .- z . 1999 , , 524 , 22 yasuda , n. et al . 2001 , , 122 , 1104 york , d. g. et al . 2000 , , 120 , 1579 lcccccccl abell 1413 & 0.143 & & & & & 2440 & 2560 & 9292 + abell 2218 & 0.171 & 7048 & 5640 & 7048 & 8386 & 10732 & 5640 & 9452 , 9717 , 10325 + abell 1689 & 0.183 & & 9500 & & 9500 & 11800 & 16600 & 9289 + abell 1703 & 0.258 & 7050 & 5564 & 5564 & 9834 & 11128 & 17800 & 10325 + ms 1358.4 + 6245 & 0.328 & 7928 & 5470 & 5482 & 9196 & 10952 & 15017 & 9292 , 9717 , 10325 + cl 0024.0 + 1652 & 0.395 & 6435 & 5072 & 5072 & 8971 & 10144 & 16328 & 10325 + lcccccc abell 1413 & 0.143 & & @xmath68 & @xmath69 & 1.71 & 21 + abell 2218 & 0.171 & @xmath70 & @xmath71 & @xmath72 & 2.94 & 14 + abell 1689 & 0.183 & @xmath73 & @xmath74 & @xmath75 & 2.24 & 19 + abell 1703 & 0.258 & & & & & + ms 1358.4 + 6245 & 0.328 & @xmath76 & @xmath77 & @xmath78 & 2.40 & 28 + cl 0024.0 + 1652 & 0.395 & @xmath79 & & @xmath80 & 1.95 & 39 + cccc @xmath0 ( f435w ) & @xmath89 & @xmath90 & @xmath91 + @xmath1 ( f475w ) & @xmath92 & @xmath93 & @xmath94 + @xmath2 ( f555w ) & @xmath95 & @xmath96 & @xmath97 + @xmath3 ( f625w ) & @xmath98 & @xmath99 & @xmath100 + @xmath4 ( f775w ) & @xmath101 & @xmath102 & @xmath103 + @xmath5 ( f850lp ) & @xmath104 & @xmath105 & @xmath106 +

are well fitted by a single schechter function with @xmath8 mag . and @xmath9 ( in all bands ) . the observations suggest that the galaxy luminosity function is dominated by objects on the red sequence to at least 6 mags . below the @xmath10 point . we do not detect a steepening of the luminosity function at @xmath13 as is observed locally .

we present deep composite luminosity functions in @xmath0 , @xmath1 , @xmath2 , @xmath3 , @xmath4 and @xmath5 for six clusters at @xmath6 observed with the hubble space telescope advanced camera for surveys . the luminosity functions reach to absolute magnitude of @xmath7 mag . and are well fitted by a single schechter function with @xmath8 mag . and @xmath9 ( in all bands ) . the observations suggest that the galaxy luminosity function is dominated by objects on the red sequence to at least 6 mags . below the @xmath10 point . comparison with local data shows that the red sequence is well established at least at @xmath11 down to @xmath12 of the luminosity of the milky way and that galaxies down to the regime of dwarf spheroidals have been completely assembled in clusters at this redshift . we do not detect a steepening of the luminosity function at @xmath13 as is observed locally . if the faint end upturn is real , the steepening of the luminosity function must be due to a newly infalling population of faint dwarf galaxies .

quant-ph0410136

i

according to quantum electrodynamics , quantum fluctuations of electric and magnetic fields give rise to a zero - point energy that never vanishes , even in the absence of electromagnetic sources@xcite . in 1948 , h. b. g. casimir predicted that , as a consequence , two electrically neutral metallic parallel plates in vacuum , assumed to be perfect conductors , should attract each other with a force inversely proportional to the fourth power of separation@xcite . the plates act as a cavity where only the electromagnetic modes that have nodes on both the walls can exist . the zero - point energy ( per unit area ) when the plates are kept at close distance is smaller than when the plates are at infinite separation . the plates thus attract each other to reduce the energy associated with the fluctuations of the electromagnetic field . e. m. lifshitz , i. e. dzyaloshinskii , and l. p. pitaevskii generalized casimir s theory to isotropic dielectrics @xcite . in their theory the force between two uncharged parallel plates with arbitrary dielectric functions can be derived according to an analytical formula that relates the helmholtz free energy associated with the fluctuations of the electromagnetic field to the dielectric functions of the interacting materials and of the medium in which they are immersed@xcite . at very short distances ( typically smaller than a few nanometers ) , lifshitz s theory provides a complete description of the non - retarded van der waals force . at larger separations , retardation effects give rise to a long - range interaction that in the case of two ideal metals in vacuum reduces to casimir s result . lifshitz s equation also shows that two plates made out of the same material always attract , regardless of the choice of the intervening medium . for slabs of different materials , on the contrary , the sign of the force depends on the dielectric properties of the medium in which they are immersed@xcite . while the force is always attractive in vacuum , there are situations for which a properly chosen liquid will cause the two plates to repel each other@xcite . as mentioned above , one of the limitations of lifshitz s theory@xcite is the assumption that the dielectric properties of the interacting materials are isotropic . in 1972 v. a. parsegian and g. h. weiss derived an equation for the non - retarded van der waals interaction energy between two dielectrically anisotropic plates immersed in a third anisotropic material@xcite . one of the authors of the present paper ( y. b. ) analyzed a similar problem and found an equation for the helmholtz free energy ( per unit area ) of the electromagnetic field in which retardation effects are included@xcite . in the non - retarded limit , the two results are in agreement . both articles also show that a torque develops between two parallel birefringent slabs ( with in plane optical anisotropy , as shown in figure [ barash_config ] ) placed in a isotropic medium , causing them to spontaneously rotate towards the configuration in which their principal axes are aligned . this effect can be qualitatively understood by noting that the relative rotation of the two plates will result in a modification of the zero - point energy , because the reflection , transmission , and absorption coefficients of these materials depend on the angle between the wave vector of the virtual photons , responsible for the zero - point energy , and the optical axis . the anisotropy of the zero - point energy between the plates then generates the torque that makes them rotate toward configurations of smaller energy . the casimir - lifshitz force between isotropic dielectrics is receiving considerable attention in the modern literature . the theory has been verified in several high precision experiments , and although the investigation has been mainly focused on the interaction between metallic surfaces in vacuum , there are no doubts about its general validity@xcite ( for a review of previous measurements , see @xcite ; for a critical discussion on the precision of the most recent experiments , see @xcite ) . less precise measurements in liquids have been reported@xcite , and experimental evidence for repulsive van der waals forces between dielectric surfaces in different fluids has also been reported@xcite . finally , it has been pointed out that the casimir - lifshitz force might be a potentially relevant issue for the development of micro- and nanoelectromechanical systems@xcite . on the other hand , essentially no attention has been devoted to the torque between anisotropic materials predicted by parsegian , weiss and barash , with the exception of a theoretical derivation of a more simplified equation of the torque between two plates in a one dimension calculation@xcite and between engineered anisotropic surfaces ( two ellipsoids with anisotropic dielectric function@xcite and two dielectric slabs with different directions of conductivity@xcite ) . no experimental attempts to demonstrate the effect have ever been reported , and so far no numerical calculations to estimate its magnitude have been presented@xcite . in this paper we calculate the magnitude of the torque induced by quantum fluctuations for specific materials and discuss possible experimental validations of the effect . we consider a small birefringent disk ( diameter 40 @xmath3 m , thickness 20 @xmath3 m ) made out of either quartz or calcite placed parallel to a birefringent barium titanate ( batio@xmath8 ) plate in vacuum . using the dielectric properties for the materials reported in the literature , we show that the magnitude of the torque is within the sensitivity of available instrumentation , provided that the plate and the disk are kept at sub - micron distances . unfortunately , at such short separations the tendency of the two surfaces to stick together represents a major technical difficulty . therefore , the measurement of the rotation of the disk may seem to be an extremely challenging problem , which can be only addressed with the design of sophisticated mechanical systems . in this paper we propose a much simpler experimental approach , where the batio@xmath8 plate is immersed in liquid ethanol and the quartz or calcite disk is placed on top of it . in this case the retarded van der waals force between the two birefringent slabs is repulsive . the disk is thus expected to float on top of the plate at a distance of approximately 100 nm , where its weight is counterbalanced by the van der waals repulsion . because there is no contact between the two birefringent surfaces , the disk would be free to rotate in a sort of _ frictionless bearing _ , sensitive to even very small driving torques .

we propose an experiment to observe this torque when the barium titanate plate is immersed in ethanol and the other birefringent disk is placed on top of it . in this case the retarded van der waals ( or casimir - lifshitz ) force between the two birefringent slabs is repulsive . the disk would float parallel to the plate at a distance where its net weight is counterbalanced by the retarded van der waals repulsion , free to rotate in response to very small driving torques . pacs numbers : 12.20.-m,07.10.pz,46.55.+d

we present detailed numerical calculations of the mechanical torque induced by quantum fluctuations on two parallel birefringent plates with in plane optical anisotropy , separated by either vacuum or a liquid ( ethanol ) . the torque is found to vary as @xmath0 , where @xmath1 represents the angle between the two optical axes , and its magnitude rapidly increases with decreasing plate separation @xmath2 . for a 40 @xmath3 m diameter disk , made out of either quartz or calcite , kept parallel to a barium titanate plate at @xmath4 nm , the maximum torque ( at @xmath5 ) is of the order of @xmath6 n@xmath7 m . we propose an experiment to observe this torque when the barium titanate plate is immersed in ethanol and the other birefringent disk is placed on top of it . in this case the retarded van der waals ( or casimir - lifshitz ) force between the two birefringent slabs is repulsive . the disk would float parallel to the plate at a distance where its net weight is counterbalanced by the retarded van der waals repulsion , free to rotate in response to very small driving torques . pacs numbers : 12.20.-m,07.10.pz,46.55.+d

quant-ph0410136

c

we have performed detailed numerical calculations of the mechanical torque between a 40 @xmath3 m diameter birefringent disk , made of quartz or calcite , and a batio@xmath8 birefringent plate . at separations of the order of a few hundreds of nanometers , the magnitude of the torque is of the order of @xmath133 n@xmath7 m . we have shown that a demonstration of the effect could be readily obtained if the birefringent slabs were immersed in liquid ethanol . in this case the disk would float on top of the plate at a distance where the repulsive retarded van der waals force balances gravity , giving rise to a mechanical bearing with ultra - low static friction . the disk , initially set in motion via transfer of angular momentum of light from a laser beam , would return to its equilibrium position solely driven by the torque arising from quantum fluctuations .

we present detailed numerical calculations of the mechanical torque induced by quantum fluctuations on two parallel birefringent plates with in plane optical anisotropy , separated by either vacuum or a liquid ( ethanol ) . for a 40 @xmath3 m diameter disk , made out of either quartz or calcite , kept parallel to a barium titanate plate at @xmath4 nm , the maximum torque ( at @xmath5 ) is of the order of @xmath6 n@xmath7 m .

we present detailed numerical calculations of the mechanical torque induced by quantum fluctuations on two parallel birefringent plates with in plane optical anisotropy , separated by either vacuum or a liquid ( ethanol ) . the torque is found to vary as @xmath0 , where @xmath1 represents the angle between the two optical axes , and its magnitude rapidly increases with decreasing plate separation @xmath2 . for a 40 @xmath3 m diameter disk , made out of either quartz or calcite , kept parallel to a barium titanate plate at @xmath4 nm , the maximum torque ( at @xmath5 ) is of the order of @xmath6 n@xmath7 m . we propose an experiment to observe this torque when the barium titanate plate is immersed in ethanol and the other birefringent disk is placed on top of it . in this case the retarded van der waals ( or casimir - lifshitz ) force between the two birefringent slabs is repulsive . the disk would float parallel to the plate at a distance where its net weight is counterbalanced by the retarded van der waals repulsion , free to rotate in response to very small driving torques . pacs numbers : 12.20.-m,07.10.pz,46.55.+d

1409.3523

i

numerically computed magnetohydrodynamic ( mhd ) equilibria are the starting point of a wide class of numerical solvers that are used to study mhd stability , transport , and heating and current drive in magnetic fusion devices @xcite . static mhd equilibria of toroidally axisymmetric configurations are described by the grad - shafranov ( g - s ) equation @xcite , a nonlinear , second - order elliptic partial differential equation . stationary equilibria with purely toroidal flows are determined by solving a close variant of the g - s equation @xcite , the only difference being that for the latter the pressure term does not only depend on the poloidal flux function @xmath0 , but also on the radial variable @xmath1 . numerical codes to solve the g - s equation have been developed since the early days of the magnetic fusion program @xcite . nevertheless , the development of optimized g - s codes remains a topic of active research , for three main reasons . first , g - s solvers must be able to properly resolve complex two - dimensional geometries @xcite , with boundaries that may have a corner , corresponding to a magnetic field x - point @xcite . second , g - s solvers must be fast . this criterion is particularly relevant in the context of multiphysics integrated simulations @xcite . several of these multiscale , multiphysics solvers already include , or will eventually include , in their iterative procedure a step in which the equilibrium configuration is self - consistently updated . a reasonable requirement is that the calculation of the updated equilibrium takes a negligible amount of time and computing resources as compared to the computationally intensive transport , mhd stability and plasma heating solvers . third , g - s solvers must be accurate . the solution of the g - s equation is the poloidal flux @xmath0 , but the physical quantities of interest , such as the magnetic field , the safety factor , the magnetic shear , the magnetic curvature , and the current density are all functions of partial derivatives of @xmath0 . since there always is some loss of accuracy when computing derivatives , a high level of accuracy for @xmath0 is desired . in this article , we present the new grad - shafranov code ecom ( equilibrium solver via conformal mapping ) . ecom is a fixed boundary , direct solver written in fortran 77/90 that is based on three key elements : 1 ) the formulation of the g - s equation as a nonlinear poisson problem ; 2 ) a spectrally accurate numerical method to compute the conformal map from the smooth plasma cross section of interest to the unit disk ; 3 ) a fast , high order poisson solver on the unit disk @xcite . its main novelty lies in the last two aspects discussed in the paragraph above , namely accuracy and speed . regarding the first point , we demonstrate in this article that ecom has better convergence properties than popular g - s solvers based on finite elements @xcite . in the finite element approach the numerical error of the solution decays as a power of grid size , i.e. @xmath2 where @xmath3 is an integer and @xmath4 is the number of grid points in one direction . often , for magnetic fusion applications @xmath5 @xcite , although @xmath6 was recently demonstrated @xcite . in contrast , convergence in ecom is exponential : the error decays as @xmath7 for some real number @xmath8 . just as importantly , in ecom the rate of convergence for the derivatives of @xmath0 is the same as that of @xmath0 , whereas in the finite element approach the derivatives of @xmath0 converge more slowly than @xmath0 @xcite . remarkably , in ecom numerical accuracy is not obtained at the expense of computational complexity and speed . for a given grid size , our solver is faster than finite element solvers and less demanding in terms of memory . we will show that a drawback of relying on conformal mapping is that ecom often requires a denser grid than fem based solvers to achieve a desired accuracy . yet despite this , we find that for tokamak geometries and medium to high number of grid points , ecom is more accurate than fem based equilibrium codes at equal run time . this article follows an earlier article @xcite , in which we gave a detailed description of our new numerical algorithm for solving the g - s equation . the focus here is different . one of the main motivations is to present extensions recently added to our g - s solver that make it a practical tool readily usable in fusion applications . the new capabilities of our equilibrium solver include the possibility of computing equilibria with arbitrary toroidal flow profiles , the possibility of specifying current and pressure profiles in various ways , as well as the evaluation of the key physical quantities that are required as inputs in stability , transport and heating codes . since ecom is a direct solver that calculates @xmath0 on a prescribed grid for the poloidal cross section @xcite , we put a particular emphasis on the accurate computation of the contours of constant flux , and of flux surface quantities such as the safety factor and the magnetic shear . a second motivation for this article is to perform detailed comparisons between the popular g - s code chease @xcite and ecom , and to assess the merits of each solver . the structure of the article is as follows . in section [ sec : gs ] we briefly review the numerical algorithm we use to solve the g - s equation @xcite . in section [ sec : post ] , we give a detailed presentation of the equilibrium quantities ecom computes during the postprocessing phase , and of the numerical methods we implemented to calculate these quantitites with high accuracy . in section [ sec : accuracy ] we evaluate the speed , accuracy , and convergence properties of our solver , and compare them to those of chease @xcite . in section [ sec : torflow ] we explain how ecom computes stationary equilibria with toroidal flows , and in section [ sec : dis ] we summarize our main findings , discuss the current limitations of ecom and future plans . appendix [ sec : miller ] presents our method to calculate the miller parametrization @xcite of a numerically computed flux contour , and appendix [ sec : namelist ] contains a table with all the important variables in ecom , along with a short description for each of them .

we present ecom ( equilibrium solver via conformal mapping ) , a fast and accurate fixed boundary solver for toroidally axisymmetric magnetohydrodynamic equilibria with or without a toroidal flow . ecom combines conformal mapping and fourier and integral equation methods on the unit disk to achieve exponential convergence for the poloidal flux function as well as its first and second partial derivatives . as a consequence of its high order accuracy , for dense grids and tokamak - like elongations ecom computes key quantities such as the safety factor and the magnetic shear with higher accuracy than the finite element based code chease [ h. ltjens _ et al . ecom has been developed to provide equilibrium quantities and details of the flux contour geometry as inputs to stability , wave propagation and transport codes .

we present ecom ( equilibrium solver via conformal mapping ) , a fast and accurate fixed boundary solver for toroidally axisymmetric magnetohydrodynamic equilibria with or without a toroidal flow . ecom combines conformal mapping and fourier and integral equation methods on the unit disk to achieve exponential convergence for the poloidal flux function as well as its first and second partial derivatives . as a consequence of its high order accuracy , for dense grids and tokamak - like elongations ecom computes key quantities such as the safety factor and the magnetic shear with higher accuracy than the finite element based code chease [ h. ltjens _ et al . _ , computer physics communications 97 , 219 ( 1996 ) ] at equal run time . ecom has been developed to provide equilibrium quantities and details of the flux contour geometry as inputs to stability , wave propagation and transport codes .

astro-ph0611135

c

our spectrum of 2005 fy9 exhibits strong ch@xmath0-ice bands in agreement with the spectrum of @xcite . from a comparison of our spectrum and a hapke model , we find the 2005 fy9 ch@xmath0-ice bands are shifted 3.25 @xmath1 2.25 blueward relative to the positions of pure ch@xmath0-ice bands . the shift could be due to the presence of another ice - component , possibly n@xmath2-ice , co - ice , or ar . future higher resolution spectra of the individual ch@xmath0 bands should determine if the weaker bands which penetrate deeper into the surface exhibit different shifts than the stronger bands which do not penetrate as deep into the surface . such observations could provide a technique to measure the ch@xmath0 concentration relative to the other ice component as a function of depth below the surface of 2005 fy9 . in addition , it is highly desirable to obtain a measure of the shift as a function of rotational longitude on 2005 fy9 for a particular ch@xmath0-ice band . such a technique could provide a measure of inhomogeneity on the surface of 2005 fy9 . @xcite made such measurements for the 8897 band on pluto and found that the blueshift varied from 0 to 10 over the surface . on pluto , it appears n@xmath2 is sufficiently mobile to form textures that allow incoming photons to travel several centimeters through the very transparent , polycrystalline n@xmath2-ice before the photons are scattered off inclusions or grain boundaries . the long pathlengths make it possible for a small amount of ch@xmath0 relative to n@xmath2 to give deep ch@xmath0 absorption bands . the mobility of co is only a little less than n@xmath2 , and the mobility of ar is only a little less than co. therefore , it is possible that co - ice or ar - ice could provide the host matrix for long optical pathlengths . it is also possible the host matrix is a combination of n@xmath2 , co , and ar . a suite of laboratory experiments that measure the shifts of ch@xmath0 absorption maxima for different concentrations of ch@xmath0 relative to n@xmath2 , co , and ar would be highly valuable for the future interpretation of observational data . our spectrum of 2003 el61 is remarkably featureless . there is a hint of a band at 5773 possibly due to o@xmath2-ice . future work will attempt to double the signal precision of the continuum to at least 300 , which is the level that appears to be required for any possible detection of the weaker o@xmath2-ice band at 6275 . the detection of o@xmath2-ice in significant quantities on kbos could be of considerable interest in the distant future as a source of spacecraft fuel . sct , wr , and km gratefully acknowledge support from nasa planetary astronomy grant nng06g138 g to northern arizona university and the university of oklahoma . wmg gratefully acknowledges support from nasa planetary geology and geophysics grant nng04 g172 g to lowell observatory . gjc gratefully acknowledges support from fordham university . we thank steward observatory for the allocation of telescope time on the mmt . we thank dr . j. licandro for providing us with his spectrum of 2005 fy9 . we thank an anonymous referee for a careful review of our manuscript . barkume , k. m. , brown , m. e. , and schaller , e. l. 2006 , , 640 , l87 . brown , m. e. , barkume , k. m. , blake , g. a. , schaller , e. l. , rabinowitz , d. l. , roe , h. g. , & trujillo , c. a. 2006 , , submitted . brown , m. e. , trujillo , c. a. , & rabinowitz , d. l. 2005 , , 635 , l97 brown , r. h. , cruikshank , d. p. , & pendleton , y. 1999 , , 519 , l101 calvin , w. m. , & spencer , j. r. 1997 , icarus , 130 , 505 . cruikshank , d. p. , pilcher , c. b. , & morrison , d. 1976 , science , 194 , 835 cruikshank , d. p. , roush , t. l. , owen , t. c. , geballe , t. r. , de bergh , c. , schmitt , b. , brown , r. h. and bartholomew , m. j. 1993 , science , 261 , 742 delitsky , m. l. , & lane , a. l. 1997 , j. geophys . res . , 102 , 16385 doressoundiram , a. , tozzi , g. p. , barucci , m. a. , boehnhardt , h. , fornasier , s. & romon j. 2003 , , 125 , 2721 elliot , j. l. , kern , s. d. , clancy , k. b. , gulbis , a. a. s. , millis , r. l. , buie , m. w. , wasserman , l. h. , chiang , e. i. , jordan , a. b. , trilling , d. e. , and meech , k. j. 2005 , , 129 , 1117 fink , u. , smith , b. a. , johnson , j. r. , reitsema , h. j. , benner , d. c. , & westphal , j. a. 1980 , icarus , 44 , 62 fornasier , s. , dotto , e. , barucci , m. a. , & barbieri , c. 2004a , a&a , 422 , 43 fornasier , s. , doressoundiram , a. , tozzi , g. p. , barucci , m. a. , boehnhardt , h. , de bergh , c. , delsanti , a. , davies , j. , & dotto , e. 2004b , a&a , 421 , 353 grundy , w. m. , & buie , m. w. 2001 , icarus , 153 , 248 grundy , w. m. , & fink , u. 1993 , pluto & charon conference , flagstaff , az , july 6 - 9 , 1993 grundy , w. m. & fink , u. 1996 , icarus , 124 , 329 . grundy , w. m. , schmitt , b. , and quirico , e. 2002 , icarus , 155 , 486 . hapke , b. 1981 , j. geophys . res . , 86 , 4571 . hapke , b. 1993 , combined theory of reflectance and emittance spectroscopy ( new york : cambridge univ . press ) hardorp , j. 1982 , a&a , 105 , 120 jewitt , d. c. , & luu , j. 2004 , nature , 432 , 731 johnson , r. e. 1990 , energetic charged - particle interactions with atmospheres and surfaces . ( new york : springer - verlag ) johnson , r. e. , & quickenden , t. i. 1997 , j. geophys . res . , 102 , 10985 landau , a. , allin , e. j. , & welsh , h. l. 1962 , spectrochimica acta , 18 , 1 . licandro , j. , oliva , e. , & di martino , m. 2001 , a&a , 373 , l29 licandro , j. , pinilla - alonso , n. , pedani , m. , oliva , e. , tozzi , g. p. , and grundy , w. m. 2006 , a&a , 445 , l35 . luu , j. & jewitt , d. 1996 , , 112 , 2310 massey , p. , valdes , f. , & barnes , j. 1992 , in a user s guide to reducing slit spectra with iraf quirico , e. , & schmitt , b. 1997 , icarus , 127 , 354 rabinowitz , d. l. , barkume , k. , brown , m. e. , roe , h. , schwartz , m. , tourtellotte , s. , and trujillo , c. 2006 , , 639 , 1238 . -ice bands , see table 1 . the middle spectrum is also of 2005 fy9 @xcite . the top spectrum is of pluto @xcite . all spectra are normalized to 1 at 6500 . the @xcite and pluto spectra are offset by 0.4 and 0.8 , respectively . clearly , 2005 fy9 has deeper ch@xmath0-ice bands than pluto . previously unreported ch@xmath0-ice bands appear near 5400 , 5800 , and 6200 in our spectrum of 2005 fy9 . ] -ice grain size of 0.55 cm ( red line ) . we assume an albedo at 6500 of 0.8 . the model fits the core of the 8897 band , but has too little absorption at all other bands . there are no laboratory absorption coefficients to fit ch@xmath0 bands with @xmath28 @xmath19 7000 . ] -ice grain sizes , 6 cm and 0.1 cm ( red line ) . we assume an albedo at 6500 of 0.8 . grains sizes larger than a cm probably provide a measure of the spacing between fractures or voids in the surface rather than indicating a surface covered with golf - ball sized particles . there are no laboratory absorption coefficients to fit ch@xmath0 bands with @xmath28 @xmath19 7000 ] -ice band in 2005 fy9 ( black line ) is blueshifted relative to the minimum of the pure ch@xmath0-ice hapke model ( red line ) . the other bands in 2005 fy9 show a similar shift . the shift may be due to the presence of another ice component on the surface of 2005 fy9 . ] -ice bands at 5773 and 6275 ( red line ) . there is a tantalizing dip in the spectrum of 2003 el61 at the position of the 5773 band ; however , a much higher continuum signal precision is necessary to test for the presence of the weaker 6275 band . ] lcc 3@xmath29 @xmath13 4@xmath30 & 7296 & 13706 + 3@xmath31 @xmath13 3@xmath30 & 7862 & 12719 + 3@xmath29 @xmath13 3@xmath32 & 7993 & 12511 + 4@xmath31 & 8415 & 11884 + @xmath29 @xmath13 3@xmath31 & 8442 & 11846 + 3@xmath31 @xmath13 2@xmath30 & 8691 & 11506 + 2@xmath29 @xmath13 @xmath31 @xmath13 2@xmath30 & 8897 & 11240 + 3@xmath29 @xmath13 2@xmath30 & 8968 & 11151 + 2@xmath31 @xmath13 4@xmath30 & 9019 & 11088 +

the spectrum of 2005 fy9 exhibits strong ch@xmath0-ice bands . a comparison between the spectrum and a hapke model indicates the ch@xmath0 bands are shifted 3.25 @xmath1 2.25 relative to pure ch@xmath0-ice , suggesting the presence of another ice component on the surface of 2005 fy9 , possibly n@xmath2-ice , co - ice , or ar . the spectrum of 2003 el61 is remarkably featureless . there is a hint of an o@xmath2-ice band at 5773 ; however , this feature needs to be confirmed by future spectroscopic observations of 2003 el61 with a higher continuum signal precision , sufficient to detect a second weaker o@xmath2-ice band at 6275 .

we present high signal precision optical reflectance spectra of the large kuiper belt objects 2005 fy9 and 2003 el61 . the spectrum of 2005 fy9 exhibits strong ch@xmath0-ice bands . a comparison between the spectrum and a hapke model indicates the ch@xmath0 bands are shifted 3.25 @xmath1 2.25 relative to pure ch@xmath0-ice , suggesting the presence of another ice component on the surface of 2005 fy9 , possibly n@xmath2-ice , co - ice , or ar . the spectrum of 2003 el61 is remarkably featureless . there is a hint of an o@xmath2-ice band at 5773 ; however , this feature needs to be confirmed by future spectroscopic observations of 2003 el61 with a higher continuum signal precision , sufficient to detect a second weaker o@xmath2-ice band at 6275 .

astro-ph0004371

i

* a new color - based screening technique , using deep @xmath1 photometry obtained with the kpno 4-meter telescope , is combined with traditional morphological star - galaxy separation based on high resolution @xmath14-band images obtained with the keck 10-meter / lris . this enables us to isolate m31 halo red giant stars in a field located at a projected distance of 19 kpc from the galaxy s center along the minor axis . after screening for stars , this field displays a clear excess population relative to a well - matched comparison field , plausibly red giants at the distance of m31 . * these data , taken together with _ hubble space telescope _ studies of the inner halo , suggest that the density of m31 s stellar halo is about @xmath73 higher than that of the milky way halo at comparable radii . * follow - up keck lris spectra are presented for 99 m31 halo red giant candidates and a control sample of 12 foreground galactic dwarf stars . kinematical information derived from the spectra allow elimination of residual contaminants : foreground galactic dwarfs , m31 disk giants , background galaxies . * metallicity measurements are made on a star - by - star basis using two independent methods : the strength of the ca ii absorption lines and the location in the @xmath51 vs @xmath14 color - magnitude diagram . various calibration schemes are tried in deriving spectroscopic [ fe / h ] estimates . the photometric and spectroscopic [ fe / h ] estimates are in reasonable agreement with each other . * the mean metallicity of m31 field halo giants , @xmath53\rangle$ ] , is in the range @xmath54 to @xmath55 depending on the metallicity measurement method , in rough agreement with the mean value of the milky way halo . there does not appear to be a strong radial abundance gradient in m31 s halo : the mean [ fe / h ] in this @xmath0 kpc halo field is similar to ( possibly slightly lower than ) _ findings for the inner parts of the halo ( @xmath811kpc ) . * there is a spread of at least 2 dex in [ fe / h ] even for the spectroscopically - selected sample of secure m31 halo red giants , independent of the method used to measure [ fe / h ] . this is comparable to the [ fe / h ] spread among m31 globular clusters and local group dwarf satellite galaxies . * the velocity distribution in the @xmath0 kpc minor axis halo field is well fit by an equal mix of foreground dwarfs ( drawn from a standard galactic model ) and giants in m31 s halo represented by a gaussian of width @xmath74 km s@xmath26 centered on its systemic velocity ( @xmath75 km s@xmath26 ) . * we present spectra of about 100 red giant candidates in five m31 dsph companions : andi , andiii , andv , andvi ( pegdsph ) , and andvii ( casdsph ) . the first four have been observed with lris and the last one with hires . this fall , we plan to carry out observations with esi , the new , intermediate - resolution , high - throughput spectrograph on keck . * the mean stellar radial velocities of the dsphs are compared to recent velocity measurements of neutral hydrogen clouds seen in the direction of some of these dwarfs@xcite . the stellar and hi velocities are in good agreement in the case of andiii , indicating a physical association , but not in the case of andv ( probably a chance superposition ) . * color - magnitude diagrams of spectroscopically - confirmed dsph member giants suggests the presence of a significant metallicity spread in andvi and possibly in andi , but little or no spread in andiii and andv . spectroscopic estimates of the metallicity distribution in these four dsph galaxies , based on the strength of the ca ii triplet in member red giant stars , appear to be consistent with this finding . * the andvii observations are based on a novel multislit ( 56 stars at a time ) , echelle spectroscopy technique using hires . accurate radial velocity measurements have been obtained for a total of 1520 member giants . the observed rms velocity dispersion is about @xmath76 km s@xmath26 ( uncorrected for measurement error ) . * using our new radial velocity measurements of these outer dsph satellites in combination with other dynamical tracers , the total mass of m31 s extended halo is estimated to be a little under @xmath3 , comparable to or smaller than that of the milky way halo . p.g . would like to thank his collaborators on various ongoing projects from which the data and results in this paper are drawn : steve majewski , jamie ostheimer , drew phillips , mark wilkinson , and especially wyn evans , linda pittroff , and steve vogt . he is grateful to the organizers of the spie meeting in munich for their generous hospitality . e.k.g . acknowledges support by nasa through grant hf-01108.01 - 98a from the space telescope science institute . j. couture , r. racine , w. e. harris , and s. holland , `` stellar populations in m31 : resolved v , i photometry of five halo globular clusters and surrounding fields , '' _ astron . j. _ * 109 * , pp . 20502060 , 1995 . e. k. grebel , `` evolutionary histories of dwarf galaxies in the local group , '' in _ the stellar content of the local group _ , p. whitelock and r. cannon , ed . 192 _ , pp . 1738 , asp , san francisco , 1999 . p. guhathakurta , e. k. grebel , and l. c. pittroff , `` keck spectroscopy of red giants in m31 dwarf spheroidal galaxies . metallicity distribution of andi , andiii , andv , and andvi , '' _ astron . j. _ in preparation , 2000 . p. guhathakurta , e. k. grebel , l. c. pittroff , d. b. reitzel , a. c. phillips , s. s. vogt , j. c. ostheimer , and s. r. majewski , `` keck spectroscopy of red giants in m31 dwarf spheroidal galaxies . i. integrated velocities from a survey of andi , andiii , andv , andvi , and andvii , '' _ astron . j. _ submitted , 2000 . p. guhathakurta , e. k. grebel , s. s. vogt , n. w. evans , and m. i. wilkinson , `` keck spectroscopy of red giants in m31 dwarf spheroidal galaxies . ii . internal dynamics of andvii from multislit hires observations , '' _ astron . j. _ in preparation , 2000 . j. b. oke , j. g. cohen , m. carr , j. cromer , a. dingizian , f. h. harris , s. labrecque , r. lucinio , w. schall , h. epps , and j. miller , `` the keck low - resolution imaging spectrometer , '' _ pub . pacific _ * 107 * , pp . 375385 , 1995 . e. w. olszewski , r. a. schommer , n. b. suntzeff , and h. c. harris , `` spectroscopy of giants in lmc clusters . i - velocities , abundances , and the age - metallicity relation , '' _ astron . j. _ * 101 * , pp . 515537 , 1991 . g. a. rutledge , j. e. hesser , p. b. stetson , m. mateo , l. simard , m. bolte , e. friel , and y. copin , `` galactic globular cluster metallicity scale from the ca ii triplet i. catalog , '' _ pub . pacific _ * 109 * , pp . 883906 , 1997 . g. a. rutledge , j. e. hesser , and p. b. stetson , `` galactic globular cluster metallicity scale from the ca ii triplet ii . rankings , comparisons , and puzzles , '' _ pub . pacific _ * 109 * , pp . 907919 , 1997 . r. zinn , and m. j. west , `` the globular cluster system of the galaxy . iii - measurements of radial velocity and metallicity for 60 clusters and a compilation of metallicities for 121 clusters , '' _ astrophys . _ * 55 * , pp . 4566 , 1984 .

we present keck 10-meter / lris spectra of candidate red giants in the halo of m31 , located at a projected radius of @xmath0 kpc on the minor axis . the various [ fe / h ] estimates are in rough agreement with one another . the data reveal a large spread ( @xmath2 dex ) in [ fe / h ] in m31 s halo ; there is no strong radial [ fe / h ] gradient . lris and hires spectra are also presented for red giants in five dwarf spheroidal satellites of m31 : andi , andiii , andv , andvi , and andvii . there appears to be a significant metallicity spread in andvi and possibly in andi .

we present keck 10-meter / lris spectra of candidate red giants in the halo of m31 , located at a projected radius of @xmath0 kpc on the minor axis . these spectroscopic targets have been selected using a combination of @xmath1-based and morphological screening to eliminate background galaxies . radial velocity measurements are used to separate m31 halo giants from foreground milky way dwarf stars , m31 disk stars , and residual background galaxies . the metallicity of each m31 halo giant is measured using standard photometric and spectroscopic techniques , the latter based on the strength of the ca ii triplet . the various [ fe / h ] estimates are in rough agreement with one another . the data reveal a large spread ( @xmath2 dex ) in [ fe / h ] in m31 s halo ; there is no strong radial [ fe / h ] gradient . lris and hires spectra are also presented for red giants in five dwarf spheroidal satellites of m31 : andi , andiii , andv , andvi , and andvii . there appears to be a significant metallicity spread in andvi and possibly in andi . the new radial velocity data on these outer dwarfs are used to constrain the total mass of m31 : the best estimate is under @xmath3 , somewhat less than the best estimate for the milky way .

hep-th0511092

c

we have presented new results for interaction casimir energies , giving rise to casimir forces between rigid bodies , induced by a fluctuating real scalar field that obeys dirichlet boundary conditions . we have used worldline numerics as a universal tool for dealing with quantum fluctuations in inhomogeneous backgrounds . for the experimentally relevant sphere - plate configuration , we have performed extensive numerical studies , confirming earlier findings @xcite with a significantly higher precision and narrowing the validity bounds of the proximity force approximation even further . moreover , our results for small spheres for the dirichlet scalar shows no sign of a casimir - polder law , as it would be expected for the em field . this provides clear evidence for a different role of casimir curvature effects for these two different field theories , leaving the sphere - plate configuration with a fluctuating em field as a pressing open problem . furthermore , we have investigated a new geometry of two perpendicular plates which has been inaccessible so far for other approximation techniques . the configuration is representative for a whole new class of casimir systems involving sharp edges , where diffractive portions of the fluctuating field will play a major role . it is a pleasure to thank emilio elizalde and his team for the organization of this workshop and for creating such a stimulating atmosphere . acknowledges useful discussions with g.v . dunne , t. emig , a. scardicchio , o. schrder , a. wirzba , and h. weigel . this work was supported by the deutsche forschungsgemeinschaft ( dfg ) under contract gi 328/1 - 3 ( emmy - noether program ) and gi 328/3 - 2 .

we present new results for casimir forces between rigid bodies which impose dirichlet boundary conditions on a fluctuating scalar field . as a universal computational tool worldline numerics is not only particularly powerful for inhomogeneous background configurations such as involved casimir geometries , it also provides for an intuitive picture of quantum - fluctuation - induced phenomena .

we present new results for casimir forces between rigid bodies which impose dirichlet boundary conditions on a fluctuating scalar field . as a universal computational tool , we employ worldline numerics which builds on a combination of the string - inspired worldline approach with monte - carlo techniques . worldline numerics is not only particularly powerful for inhomogeneous background configurations such as involved casimir geometries , it also provides for an intuitive picture of quantum - fluctuation - induced phenomena . results for the casimir geometries of a sphere above a plate and a new perpendicular - plates configuration are presented .

1501.05296

i

sparse polynomials are a fundamental object in computer algebra . computer algebra programs including maple , mathematica , sage , and singular use a sparse representation by default for multivariate polynomials , and there has been considerable recent work on how to efficiently store and compute with sparse polynomials @xcite . however , despite the memory advantage of sparse polynomials , the alternative dense representation is still widely used for an obvious reason : speed . it is now classical @xcite that two degree-@xmath0 dense polynomials can be multiplied in softly linear time : @xmath1 ring operations , and even better in many cases @xcite . by contrast , two size-@xmath2 sparse polynomials require @xmath3 operations , and this excludes the potentially significant cost of exponent arithmetic . much of the recent work on sparse arithmetic has focused on `` somewhat dense '' or structured cases , where the sparsity of the product is sub - quadratic @xcite . at the same time , sparse interpolation algorithms , which in the fastest case can learn an unknown @xmath2-sparse polynomial from @xmath4 evaluations , have gained renewed interest @xcite . most closely related to the current work , @xcite recently presented algorithms to discover the coefficients of a sparse polynomial product , provided a list of the exponents and some preprocessing . in the context of pattern matching problems , @xcite gave a las vegas algorithm to multiply sparse polynomials with nonnegative integer coefficients whose cost is @xmath5 . a remaining question is whether output - sensitive sparse multiplication is possible in time comparable to that of dense multiplication . this paper answers that question , with three provisos : first , our complexity is proportional to the `` structural sparsity '' of the output that accounts for exponent collisions but not coefficient cancellations ; second , our algorithms are randomized and may produce incorrect results with controllably low probability ; and third , we ignore logarithmic factors in the size of the input . to explain the first proviso , define for a polynomial @xmath6 its _ support _ @xmath7 to be the set of exponents of nonzero terms in @xmath6 . the _ sparsity _ of @xmath6 , written @xmath8 , is exactly @xmath9 . for two polyomials @xmath6 and @xmath10 , we have @xmath11 . but in many cases the set of _ possible exponents _ @xmath12 is much smaller than @xmath13 . this _ structural sparsity _ @xmath14 , is an upper bound on the actual sparsity @xmath15 of the product . strict inequality @xmath16 occurs only in the presence of _ coefficient cancellations_. part of our algorithm s cost depends only on the actual sparsity , and part depends on the potentially - larger structural sparsity . our algorithms have not yet been carefully implemented , and we do not claim that they would be faster than the excellent software of @xcite and others for a wide range of practical problems . however , this complexity improvement indicates that the barriers between sparse and dense arithmetic may be weaker than we once thought , and we hope our work will lead to practical improvements in the near future . our main algorithm is summarized in theorem [ thm : main ] . here and throughout , we rely on a version of `` soft - oh '' notation that also accounts for a bound @xmath17 on the probability of failure : @xmath18 , for any function @xmath19 , where @xmath20 means @xmath21 for some fixed @xmath22 ( * ? ? ? * see sec . 25.7 ) . [ thm : main ] given @xmath23 $ ] with degree bound @xmath24 and height bound @xmath25 , and @xmath26 , algorithm [ proc : sparsemulzz ] correctly computes the product @xmath27 with probability exceeding @xmath28 , using worst - case expected @xmath29 bit operations , where @xmath30 and @xmath31 are the actual and structural sparsity of the product , respectively . our algorithm relies on two subroutines , both of which are based on techniques from sparse interpolation and rely on number - theoretic results on the availability of primes . the first subroutine [ proc : sumset]@xmath32 computes the _ sumset _ of two sets of integers @xmath33 and @xmath34 , defined as @xmath35 this algorithm , which may be of independent interest , has softly - linear complexity in the size of the output @xmath36 . the second subroutine [ proc : knownsupp](@xmath37 ) requires a set containing @xmath38 in order to compute @xmath39 in time softly - linear in the input and output sizes . it is based on an algorithm in @xcite , but is more efficient for large exponents . the main steps of our multiplication algorithm are : 1 . use [ proc : sumset ] to compute @xmath40 . 2 . run [ proc : knownsupp ] with @xmath41 but with smaller coefficients , to discover the true @xmath38 . 3 . run [ proc : knownsupp ] again , with the smaller exponent set @xmath38 but with the full coefficients . steps 1 and 2 work with a size-@xmath2 exponent set but with small coefficients , and both contribute @xmath42 to the overall bit complexity . step 3 uses the size-@xmath43 true support but with the full coefficients , and requires @xmath44 bit operations , for a total of @xmath45 . section [ sec : prelim ] states our notational conventions and some standard results , and section [ sec : redexp ] contains the technical number theoretic results on which we base our randomizations . section [ sec : basecase ] revisits and adapts our sparse interpolation algorithm from issac 2014 that will be a subroutine for our sumset algorithm , presented in section [ sec : sumset ] . our new method to find the coefficients , once the support is known , is presented in section [ sec : knownsupp ] . this is then used in concert with our sumset algorithm in section [ sec : smul ] to describe fully the algorithm of theorem [ thm : main ] , and also to explain how this can be easily extended to output - sensitive sparse multiplication over @xmath46 $ ] , where @xmath47 is @xmath48 , @xmath49 , or @xmath50 .

we present randomized algorithms to compute the sumset ( minkowski sum ) of two integer sets , and to multiply two univariate integer polynomials given by sparse representations . our algorithm for sumset has cost softly linear in the combined size of the inputs and output . this is used as part of our sparse multiplication algorithm , whose cost is softly linear in the combined size of the inputs , output , and the sumset of the supports of the inputs . as a subroutine , we present a new method for computing the coefficients of a sparse polynomial , given a set containing its support . our techniques are based on sparse interpolation algorithms and results from analytic number theory .

we present randomized algorithms to compute the sumset ( minkowski sum ) of two integer sets , and to multiply two univariate integer polynomials given by sparse representations . our algorithm for sumset has cost softly linear in the combined size of the inputs and output . this is used as part of our sparse multiplication algorithm , whose cost is softly linear in the combined size of the inputs , output , and the sumset of the supports of the inputs . as a subroutine , we present a new method for computing the coefficients of a sparse polynomial , given a set containing its support . our multiplication algorithm extends to multivariate laurent polynomials over finite fields and rational numbers . our techniques are based on sparse interpolation algorithms and results from analytic number theory .

astro-ph0208289

i

in this series of articles , we report the analysis of the _ chandra _ data of n66 , the largest star formation region of the smc . in this first paper , we have focused on the most important objects of the field : the ngc346 cluster and hd5980 . + the cluster itself is relatively faint , with a total luminosity of @xmath0 erg s@xmath1 in the 0.3 - 10.0 kev energy range . most of this emission seems correlated with the location of the brightest stars of the core of the cluster , but the level of x - ray emission probably can not be explained solely by the emission from individual stars . + in this field lies another object of interest : hd5980 , a remarkable star that underwent a lbv - type eruption in 1994 . _ chandra _ is in fact the first x - ray telescope to detect hd5980 individually . in x - rays , the star appears very bright , comparable only to the brightest wr stars in the galaxy , but still fainter than @xmath47 carinae . the comparison of our results with future x - ray observations will enable us to better understand hd5980 : for example , phase - locked variations will be analysed in the perspective of the colliding wind behaviour of this binary , while other variations may be related to the recent lbv eruption . follow - up observations are thus needed to complete the study of this system . + a bright , extended x - ray emission is seen to surround hd5980 . it is most probably due to a snr whose progenitor is unknown . the spatial coincidence of this extended x - ray emission with the peculiar massive star suggest an association between these two objects . we also note the close resemblance of this x - ray emission to the carina nebula in which the lbv @xmath47 carinae lies . + we are grateful to dr martin a. guerrero roncel for useful suggestions on data analysis techniques . support for this work was provided by the national aeronautics and space administration through chandra award number go1 - 2013z issued by the chandra x - ray observatory center , which is operated by the smithsonian astrophysical observatory for and on behalf of nasa under contract nas8 - 39073 . y.n . acknowledges support from the prodex xmm - om and integral projects , contracts p4/05 and p5/36 ple dattraction interuniversitaire ( sstc - belgium ) and from pparc for an extended visit to the university of birmingham . irs and jmh also acknowledge support from pparc . afjm thanks nserc ( canada ) and fcar ( quebec ) for financial aid . this research has made use of the simbad databse , operated at cds , strasbourg , france and nasa s astrophysics data system abstract service . arnaud , k. 1996 , asp conf . ser . 101 , eds g. jacoby & j. barnes , p.17 behar , e. , rasmussen , a.p . , griffiths , r.g . , dennerl , k. , audard , m. , aschenbach , b. , & brinkman , a.c . 2001 , a&a , 365 , l242 berghfer , t.w . , schmitt , j.h.m.m . , danner , r. , & cassinelli , j.p . 1997 , a&a , 322 , 167 breysacher , j. & perrier , c. 1991 , iaus 143 , 229 cant , j. , raga , a.c . , & rodrguez , l.f . 2000 , apj , 536 , 896 chen , c .- h . r. , chu , y .- h . , gruendl , r.a . , & points , s.d . 2000 , aj , 119 , 1317 chu , y .- h . , & kennicutt , r.c . , jr 1988 , aj , 95 , 1111 danforth et al . , 2002 , in preparation de boer , k.s . , & savage , b.d . 1980 , apj , 238 , 86 getman , k.v . , feigelson , e.d . , townsley , l. , bally , j. , lada , c.j . , & reipurth b. 2002 , to be published in apj , 575 haberl , f. , filipovic , m. d. , pietsch , w. , & kahabka , p. 2000 , a&as , 142 , 41 ( hfp2000 ) haberl , f. , & sasaki , m. 2000 , a&a 359 , 573 henize , k.g . 1956 , apjs , 2 , 315 hoopes , c.g . , sembach , k.r . , howk , j.c . , & blair , w.p . 2001 , apj , 558 , l35 humphreys , r.m . & mcelroy , d.b . 1984 , apj , 284 , 565 inoue , h. , koyama , k. , & tanaka , y. 1983 , iaus 101 , 535 ( ikt ) ishibashi , k. , corcoran , m.f . , davidson , k. , swank , j.h . , petre , r. , drake , s.a . , damineli , a. , & white , s. 1999 , apj , 524 , 983 kaastra , j.s . 1992 , an x - ray spectral code for optically thin plasmas ( internal sron - leiden report , updated version 2.0 ) kahabka , p. , pietsch , w. , filipovic , m. d. , & haberl , f. 1999 , a&as , 136 , 81 koenigsberger , g. , georgiev , l. , barb , r. , tzvetanov , z. , walborn , n.r . , niemela , v.s . , morrell , n. , & schulte - ladbeck , r. 2000 , apj , 542 , 428 koenigsberger , g. , georgiev , l. , peimbert , m. , walborn , n.r . , barb , r. , niemela , v.s . , morrell , n. , tsvetanov , z. , & schulte - ladbeck , r. 2001 , aj , 121 , 267 massey , p. , parker , j.w . , & garmany , c.d . 1989 , aj , 98 , 1305 mathewson , d.s . , ford , v.l . , dopita , m.,a . , tuohy , i.r . , long , k.s . , & helfand , d.j . 1983 , apjs , 51 , 345 mathewson , d.s . , ford , v.l . , & visvanathan , n. 1986 , apj 301 , 664 moffat , a.f.j . , marchenko , s.v . , bartzakos , p. , niemela , v.s . , cerruti , m.a . , magalhaes , a.m. , balona , l. , st - louis , n. , seggewiss , w. , & lamontagne , r. 1998 , apj , 497 , 896 moffat , a.f.j . , et al . , 2002 , apj , ( in press ) naz et al . , in preparation ( paper ii ) ozernoy , l.m . , genzel , r. , & usov , v.v . 1997 , mnras , 288 , 237 pittard , j.m . , & corcoran , m.f . 2002 , a&a , 383 , 636 pollock , a.m.t . 2002 , interacting winds from massive stars , eds a.f.j . moffat & n. st louis , asp conf . series , 260 , p 363 puls , j. , kudritzki , r .- p . , herrero , a. , pauldrach , a.w.a . , haser , s.m . , lennon , d.j . , gabler , r. , voels , s.a . , vilchez , j.m . , wachter , s. , & feldmeier , a. 1996 , a&a , 305 , 171 raga , a.c . , velzquez , p.f . , cant , j. , masciadri , e. , & rodrguez , l.f . 2001 , apj , 559 , l33 sasaki , m. , haberl , f. , & pietsch , w. 2000 , a&as , 147 , 75 schmidtke , p.c . , cowley , a.p . , crane , j.d . , taylor , v.a . , mcgrath , t.k . , hutchings , j.b . , & crampton , d. 1999 , aj , 117 , 927 seward , f.d . & mitchell , m. 1981 , apj , 243 , 736 seward , f.d . , butt , y.m . , karovska , m. , prestwich , a. , schlegel , e.m . , & corcoran , m. 2001 , apj , 553 , 832 sterken , c. & breysacher , j. 1997 , a&a , 328 , 269 stevens i.r . , blondin j.m . , pollock , a.m.t . 1992 , apj , 386 , 265 townsley , l.k . , broos , p.s . , garmire , g.p . , & nousek , j.a . 2000 , apj , 534 , l139 usov , v.v . 1992 , apj , 389 , 635 walborn , n.r . 1978 , apj , 224 , l133 walborn , n.r . , howarth , i.d . , lennon , d.j . , massey , p. , oey , m.s . , moffat , a.f.j . , skalkowski , g. , morrell , n.i . , drissen , l. , & parker , j.w . 2002 , aj , 123 , 2754 wang , q. & wu , x. 1992 apjs , 78 , 391 weis , k. , duschl , w.j . , & bomans , d.j . 2001 , a&a , 367 , 566 wessolowski , u. 1996 , mpe report no . 263 , 75 ye , t. , turtle , a.j . , & kennicutt , r.c 1991 , mnras , 249 , 722 yokogawa , j. , imanishi , k. , tsujimoto , m. , nishiuchi , m. , koyama , k. , nagase , f. , & corbet , r.h.d . 2000 , apjs , 128 , 491 yusef - zadeh , f. , law , c. , wardle , w. , wang , q.d . , fruscione , a. , lang , c.c . , cotera a. 2002 , apj , 570 , 665

, we will focus on the characteristics of the main objects of the field . the ngc346 cluster itself shows only relatively faint x - ray emission ( with @xmath0 erg s@xmath1 ) , tightly correlated with the core of the cluster . in the field also lies hd5980 , a lbv star in a binary ( or possibly a triple system ) that is detected for the first time at x - ray energies .

we present results from a _ chandra _ observation of the ngc346 cluster . this cluster contains numerous massive stars and is responsible for the ionization of n66 , the most luminous hii region and the largest star formation region in the smc . in this first paper , we will focus on the characteristics of the main objects of the field . the ngc346 cluster itself shows only relatively faint x - ray emission ( with @xmath0 erg s@xmath1 ) , tightly correlated with the core of the cluster . in the field also lies hd5980 , a lbv star in a binary ( or possibly a triple system ) that is detected for the first time at x - ray energies . the star is x - ray bright , with an unabsorbed luminosity of @xmath2 erg s@xmath1 , but needs to be monitored further to investigate its x - ray variability over a complete 19d orbital cycle . the high x - ray luminosity may be associated either with colliding winds in the binary system or with the 1994 eruption . hd5980 is surrounded by a region of diffuse x - ray emission , which is a supernova remnant . while it may be only a chance alignment with hd5980 , such a spatial coincidence may indicate that the remnant is indeed related to this peculiar massive star .

1007.1123

c

in the heiles ( 1997 ) scenario , a typical cnm cloud consists of an inter - tsas medium and many discrete tsas features in the form of cylinders or disks , which are homogeneously and isotropically distributed within the cloud . an arbitrary line of sight samples many cylinders or disks ; however only cylinders seen end - on or disks seen edge - on have sufficient column densities to produce absorption features recognized as tsas . meanwhile , non - end - on cylinders or non - edge - on disks have very little column density and blend to form a smooth background which contributes very little to the measured hi absorption profile . the model assumed the following basic parameters for tsas : a cloud size perpendicular to the line of sight @xmath278 au , @xmath279 k , @xmath280 @xmath29 , and @xmath281 for the number of end - on cylinders or edge - on disks along every line of sight . two values were considered for @xmath282 , the ratio of the cnm to tsas column density : @xmath283 and 100 . the model predicts the elongation factor @xmath284 and the volume filling factor @xmath285 of tsas required to ameliorate the over - pressure problem , under the assumption that the asymmetric tsas features are uniformly and isotropically distributed throughout cnm clouds . if tsas is in the form of edge - on disks then @xmath286 and they fill about 3.3% of the cnm volume ; whereas if tsas is in the form of end - on cylinders then @xmath287 and they fill about 3.6% of the cnm volume . however , the volume filling factor of tsas is directly proportional to the number of end - on cylinders or edge - on disks @xmath288 along any line of sight . if we assume @xmath289 k for our tsas detections , a geometric factor @xmath290 is required to explain the observed tsas volume density and pressure within the context of the heiles model . this is in the range proposed by heiles ( 1997 ) . in addition , the tsas hi column density as well as the @xmath282 ratio are similar to values explored in the model . it is therefore reasonable to compare our estimated volume filling factor of tsas with the model predicted values . in the case of b1929 + 10 , as the pulsar moves through the ism our hi absorption spectra have essentially sampled a one - dimensional cut across the absorbing cnm cloud ( about 50 au long ) and detected at least two tsas features . this means that a one - dimensional covering fraction of tsas in this direction is at least 40% , if we assume a 10au plane - of - sky tsas size . we can now estimate the fraction of the line of sight occupied by tsas . we first estimate the line - of - sight size of the parent cnm cloud . as this cloud has @xmath291 @xmath29 ( from table [ t : table_wnm_cnm ] ) , and if we assume a cnm volume density of 100 @xmath5 , this results in a length of about @xmath292 au . assuming a cylindrical tsas with a 10au plane - of - sky size and a geometrical elongation @xmath293 , results in the volume filling factor of @xmath294% in the direction of b1929 + 10 . the volume filling factor in the case of other pulsars in our experiment is zero . we note that our sensitivity for b0823 + 26 and b1133 + 16 is equally good as for b1929 + 10 , and all three pulsars probe interstellar environments with a similar optical depth ( peak of @xmath295 , see figures 1 and 2 ) and a similar line - of - sight length . in a similarly sensitive experiment , @xcite had 18 observing epochs for one pulsar , about 150 trials , and _ no _ detections . the observationally inferred volume filling factor of tsas in the direction of our pulsars ( 0 or @xmath294% ) is lower than the model prediction ( @xmath296% ) . more importantly , we observe significant inhomogeneity in the galactic distribution of tsas : no detections toward four pulsars , and a high detection rate toward b1929 + 10 . for the heiles ( 1997 ) model to remain viable , our observations require inclusion of the possibility of different tsas properties ( specifically @xmath91 , @xmath284 and @xmath288 ) along different lines of sight , and/or additional local physical processes which can modify the tsas production rate . for example , a highly elongated tsas with @xmath91 a million times smaller than the size of its parent cnm cloud would theoretically result in a volume filling factor close to zero . while in principle this scenario could work , we are still left with the puzzle of what physical processes can produce such tiny clouds and at the same time greatly vary cloud properties across the ism . [ t : tsas_sig_features ] ccccccc @xmath88 & @xmath89 & @xmath297 & signif . & @xmath298 & @xmath299 & @xmath275 + ( yr ) & ( au ) & ( ) & ( @xmath18 ) & ( 10@xmath300 @xmath29 ) & ( 10@xmath301 @xmath5 ) & ( 10@xmath302 @xmath5 k ) + 0.16 & 6 & 0.046 & 2.8 & 1.4 & 16 & 27 + 0.33 & 12 & 0.083 & 3.3 & 2.6 & 14 & 24 + 0.75 & 28 & 0.040 & 2.5 & 1.2 & 3 & 5 + 1.24 & 46 & 0.089 & 3.5 & 2.8 & 4 & 7 + @xmath303 we have assumed @xmath304 k based on table [ t : table_wnm_cnm ] . + @xmath305 calculated assuming a spherical geometry . + [ t : tsas_upper ] cccccc psr & @xmath89 & @xmath297 & @xmath298 & @xmath299 & @xmath275 + & ( au ) & ( ) & ( 10@xmath306 @xmath29 ) & ( 10@xmath301 @xmath5 ) & ( 10@xmath302 @xmath5 k ) + b0823 + 26 & 5 - 50 & 0.05 & @xmath307 & @xmath308 & @xmath309 + b1133 + 16 & 20 - 170 & 0.06 & @xmath309 & @xmath310 & @xmath143 + b1737 + 13 & 20 - 180 & 0.35 & @xmath311 & @xmath308 & @xmath309 + b2016 + 28 & 1 - 10 & 0.45 & @xmath312 & @xmath313 & @xmath314 + @xmath303 we have assumed @xmath315 k. + @xmath305 calculated assuming a spherical geometry and the largest probed size . + several recent numerical simulations of the small - scale structure in the ism have addressed the tsas phenomenon . in particular , @xcite performed relatively high resolution numerical simulations of colliding wnm flows and the formation of cnm clouds . a collision of incoming wnm streams creates a thermally unstable region of higher density and pressure but lower temperature , which further fragments into cold structures . the thermally unstable gas has filamentary morphology and its fragmentation into cold clouds is promoted and controlled by turbulence . while typical cnm clouds are formed in these simulations within @xmath11 myr , transient shocked cnm regions , produced by supersonic collisions between cnm fragments , are also found , with properties similar to those of tsas : @xmath316 @xmath5 , @xmath317 k , @xmath318 k @xmath5 , and a slightly larger size of @xmath319 au . @xcite found that 10% of lines of sight cross dense cnm gas with @xmath320 @xmath5 , and only 0.1% of lines of sight cross gas denser than @xmath321 @xmath5 , suggesting that extremely dense tsas should rarely be detected . while this was a 2d simulation of a coherent region only @xmath322 pc large , basic observed properties of the cnm / wnm were surprisingly well captured . for example , the cnm column density peak , and the hi column density distribution function appear close to observed properties based on the heiles & troland ( 2003 ) survey . considering that the simulation has a resolution of 400 au ( cruder than the scales generally sampled in pulsar and interferometer experiments ) and probes regions only 20 pc across ( much smaller than our lines of sight ) , direct comparison with our observations is not straightforward . nevertheless , the predicted properties of the shocked cnm clouds , especially cloud abundance , are encouraging . considering that the cnm / tsas production in converging flows is controlled by the level of turbulence in colliding flows , local turbulent enhancements may be able to provide the necessary tuning and therefore explain the inhomogeneity in the spatial distribution of tsas observed in the direction of b1929 + 10 . in an attempt to compare various observations , we have investigated hi tsas detections and upper limits from all published and recent pulsar and interferometric experiments as a function of their spatial scale . the results are summarized in figures [ f : us_desh1 ] and [ f : us_desh2 ] . in figure [ f : us_desh1 ] we first show the maximum variation in hi optical depth ( @xmath15 ) as a function of peak optical depth along the line of sight ( @xmath323 ) . this plot separates all sources cleanly into two groups : `` low optical depth '' with @xmath324 ( b1929 + 10 , b0823 + 16 , b1133 + 16 , and b0301 + 19 ) , and `` high optical depth '' with @xmath325 ( 3 interferometric detections , pulsars b1737 + 13 b2016 + 28 from this study , highly sampled pulsar b0329 + 54 from minter et al . 2005 , and b0736 - 40 , b1451 - 68 , b1557 - 50 from johnston et al . 2003 ) . the only exception in this figure is the 2.6-@xmath18 detection by weisberg et al . ( 2008 ) in the case of b0301 + 19 which probes a low optical depth cnm but has @xmath326 . this plot suggests that regions with high optical depth ( and therefore high cnm column density ) have higher level of @xmath15 variations than regions with low cnm column density . in other words , this implies that the the level of @xmath53 fluctuations tracing tsas is intimately associated with the larger scale structure of the parental cnm . figure [ f : us_desh2 ] shows the detected level of optical depth variations , or upper limits , as a function of tsas spatial scale @xmath89 . no obvious correlation between the two quantities is noticeable . the kendall s tau correlation test for censored data @xcite gives a probability of 62% that the correlation is not present . the low and high @xmath323 groups of sources nicely separate in this plot around @xmath327 : the high-@xmath323 sources are above this line , while all low-@xmath323 sources except b0301 are below this line . we investigated whether a correlation between tsas scale @xmath89 and @xmath15 exists for the two groups separately . for both groups the kendall s tau correlation test for censored data gives a probability of @xmath328% that the correlation is not present . we therefore conclude that the detected level of optical depth variations , as well as upper limits , do not show evidence for a correlation between @xmath89 and @xmath15 . such a correlation , with @xmath329 , is expected in the deshpande ( 2000 ) power law model , and would represent the tail - end of the turbulent spectrum of the hi optical depth on larger scales ( 0.02 to 4 pc , deshpande et al . we overplot this predicted level of variations in figure [ f : us_desh2 ] as a sloping line . our compilation of recent interferometric and pulsar observations of tsas does not provide evidence for the power - law turbulent spectrum of @xmath15 on scales @xmath143 to 1000 au . while various sources probe separate lines of sight , we note that b0823 + 26 , b1133 + 16 and b1929 + 10 all probe the local ism ( within 400 pc ) , with similar peak optical depth , and with very similar sensitivity . this essentially provides an almost uniformly sampled region on this graph from @xmath330 to 200 au . similar arguments apply to the higher optical depth portion of this diagram . we are left with the conclusion that tsas is a sporadic phenomenon . it is interesting to note that the smallest spatial scale of tsas detections in both interferometric and b1929 + 10 studies is @xmath330 au . two pulsars ( b2016 + 28 and b0329 + 54 ) have probed scales @xmath331 au , however tsas was not detected . the spatial scales of @xmath330 au for tsas in the cnm are especially interesting , since in the case of hydrodynamic turbulence the cut - off scale of cnm turbulence corresponds to the viscous damping scale of @xmath332 au @xcite . however , in the case of magnetohydrodynamic ( mhd ) turbulence , the turbulent spectrum can cascade below the viscous cut - off scale down to the scale set by magnetic diffusion @xcite . in fact , magnetic and kinetic spectra can be greatly decoupled , with the magnetic spectrum being much shallower than the kolmogorov spectrum . our pulsar experiment shows only a few significant tsas detections , all in the direction of one pulsar b1929 + 10 . this result strongly suggests inhomogeneity in the galactic distribution of tsas . we have examined two proposed origins of tsas ( i ) discrete hi blobs elongated along the line of sight ; and ( ii ) fluctuations at the tail - end of the turbulent cnm spectrum ; but our data do not provide support for either of these models . the principal problem is that we do not find these features to be homogeneously distributed . meanwhile , recent numerical simulations do generate cnm clouds with a wide range of physical properties , including rare examples of very dense and over - pressured tsas - like clouds ; but the direct comparison between observations and simulated data is not straightforward since simulations probe much smaller ism regions on scales somewhat larger than these experiments . the most striking result from our examination of specific lines of sight is a possible correlation between the b1929 + 10 fluctuations and nai interstellar clouds inside the local cavity or at the lb wall . as about one - half of b1929 + 10 s line of sight is associated with the lb , and a significant fraction of this length appears to be traversing the lb wall , we suggest that the observed hi absorption fluctuations are most likely sampling small - scale structure in the lb . numerous observations have indicated that the lb wall is highly inhomogeneous . many interstellar cloudlets found inside the local cavity are thought to be caused by hydrodynamic instabilities fragmenting the lb wall . through various studies , it has been shown that these cloudlets have velocities of up to 25 relative to the sun @xcite . this translates to @xmath333 au yr@xmath0 . coupled with the transverse speed of b1929 + 10 of 37 au yr@xmath0 , this suggests that our observed tsas could result from the pulsar s line of sight crossing very local cloudlets . to investigate the origin of interstellar clouds inside the local cavity , we look to 2d hydrodynamical simulations of the wnm compression by supernova explosions and subsequent fragmentation into small clouds @xcite . they showed that within 0.3 myr a thermally collapsing layer is formed behind the ( supernova ) shock front where cooling dominates heating and temperature monotonically decreases . as the gas cools it becomes thermally unstable , with a temperature in the range of 300 - 6000 k. within @xmath11 myr this layer starts to fragment into many small ( @xmath334 pc ) cloudlets . finally , these cloudlets can even reach thermal equilibrium at a temperature of 20 k and density of 2000 @xmath5 . as the ism is frequently compressed by supernova explosions , fragmentation of the shock - compressed medium can provide a mechanism for the formation of many small cloudlets . in the @xcite simulation , the cloudlets become embedded in the hot high - pressure gas as the shocked layer fragments , leading to a situation similar to what is observed in the lb . the exact temperature inside the local cavity has been uncertain ( see @xcite for references ) , however it is clear that the cavity is occupied by a warm / hot ionized medium . the cold cloudlets will eventually evaporate in the surrounding warm / hot medium . this process has been studied by many authors . the mass - loss rate in the case of classic evaporation @xcite is slightly lower when cooling is included @xcite . the mass - loss rate of @xcite who considered both flux saturation effects and radiative cooling is about 100 times lower than the classic evaporation rate . we continue by assuming the lowest suggested mass - loss rate , which will have the gentlest effect on the cold clouds . the evaporation timescale depends greatly on the cloud size and the temperature of the surrounding medium . for a cloud size of 30 au , @xmath335 - @xmath336 yr , depending upon whether the cloud is surrounded by the hot ionized medium ( him ) or wnm . for a larger cloud with a size of @xmath337 au , @xmath338 ( him ) or 10@xmath339 ( wim ) yr . clearly larger clouds survive longer and can even coalesce to build larger structures , even if surrounded by a hot medium . in about 1 myr larger clouds could cross a large distance , @xmath332 pc , and may even escape outside of the lb into the ism through various chimneys and tunnels resulting from stellar winds and supernovae , and frequently observed in expanding shells . this scenario may be able to explain the existence of hi clouds on scales of thousands of au or more in the ism , as observed recently by @xcite . on the contrary , very small clouds will evaporate quickly and therefore may not be common in the ism . their short inferred lifetimes indicate that they would usually be found close to their formation sites .

while most of the observed pulsars show no significant change in their hi absorption spectra , we have identified at least two clear tsas - induced opacity variations in the direction of b1929 + 10 . an apparent correlation between tsas and interstellar clouds inside the warm local bubble ( lb ) indicates that tsas may be tracing the fragmentation of the lb wall via hydrodynamic instabilities .

we present results from multi - epoch neutral hydrogen ( hi ) absorption observations of six bright pulsars with the arecibo telescope . moving through the interstellar medium ( ism ) with transverse velocities of 10150 au yr@xmath0 , these pulsars have swept across 1200 au over the course of our experiment , allowing us to probe the existence and properties of the tiny scale atomic structure ( tsas ) in the cold neutral medium ( cnm ) . while most of the observed pulsars show no significant change in their hi absorption spectra , we have identified at least two clear tsas - induced opacity variations in the direction of b1929 + 10 . these observations require strong spatial inhomogeneities in either the tsas clouds physical properties themselves or else in the clouds galactic distribution . while tsas is occasionally detected on spatial scales down to 10 au , it is too rare to be characterized by a spectrum of turbulent cnm fluctuations on scales of @xmath1 au , as previously suggested by some work . in the direction of b1929 + 10 , an apparent correlation between tsas and interstellar clouds inside the warm local bubble ( lb ) indicates that tsas may be tracing the fragmentation of the lb wall via hydrodynamic instabilities . while similar fragmentation events occur frequently throughout the ism , the warm medium surrounding these cold cloudlets induces a natural selection effect wherein small tsas clouds evaporate quickly and are rare , while large clouds survive longer and become a general property of the ism .

1007.1123

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we have used the arecibo telescope to obtain multi - epoch hi absorption spectra in the direction of six bright pulsars , with the goal of searching for structure on au scales in the cnm . our target sources were observed previously by frail et al . ( 1994 ) , who found pervasive tiny - scale hi structure . we used an advanced spectrometer capable of more accurate measurements in the face of wildly fluctuating pulsar signals , and carefully analyzed noise statistics . to search for variability of hi absorption profiles , which signifies inhomogeneities on au scales in the cnm , we have searched for time - variability of the absorption line equivalent widths and of the absorption spectra themselves . while we had excellent sensitivity , significant variations in both ew and absorption spectra have been found only in the case of one pulsar : b1929 + 10 . these variations imply tsas on spatial scales @xmath340 au ( where @xmath267 is the distance to the tsas feature ) , with an inferred volume density of @xmath341 @xmath5 and thermal pressure of @xmath342 @xmath5 k. our study clearly shows the inhomogeneity in the galactic distribution of tsas : the detection rate toward four of our pulsars is zero , while the detection rate toward b1929 + 10 is high . such inhomogeneity is hard to explain with the model of discrete elongated disks or cylinders being a _ general _ property of cnm clouds ( heiles 1997 ) ; instead large spatial variations of tsas physical properties or abundances must be invoked . while the heiles ( 1997 ) model can help in bringing down the volume density and pressure of tsas , the puzzles regarding its distribution and origin still remain . our examination of all pulsar and interferometric tsas detections and upper limits does not show a correlation between the level of optical depth fluctuations and the tsas spatial scale , as would be expected if the turbulent spectrum on much larger scales is extrapolated to au - scales . the detections and non - detections probe an almost continuous range of spatial scales from @xmath343 to 1000 au . therefore , the large number of non - detections of tsas suggests that the cnm clouds on scales @xmath344 to @xmath336 au are not a pervasive property of the ism . the sporadic tsas detections on scales of tens of au may indicate occasional local bursts of turbulent energy dissipation , rather than end - points of the turbulent spectrum . another striking result from our study is a possible correlation between b1929 + 10 s tsas and interstellar clouds observed in nai absorption inside the local bubble . we find evidence that the tsas is likely to be within 106 pc of the sun , and is sampling the small - scale structure of the lb caused by hydrodynamic instabilities fragmenting the lb wall . we propose that the line of sight of b1929 + 10 is revealing this recently formed small - scale structure . similar bubbles and their walls are found throughout the milky way , but the lifetime of a tsas cloud created from them depends strongly on the its size and the temperature of the surrounding medium . larger fragments ( size @xmath345 au ) survive longer and can travel large ism distances , becoming a more general ism property . on the other hand , the smallest clouds ( size @xmath13 au ) evaporate quickly close to their formation site , and are therefore not very commonly observed in the ism . additional processes , such as stellar mass - loss and collisions of interstellar clouds / filaments , probably contribute to the cnm structure formation on somewhat larger ( sub - pc ) scales . we are grateful to caltech s center for advance computation and research for the use of their facilities for data storage and processing . we express our thanks to stuart anderson , rick jenet , and kathryn devine for help with observations and data processing . we acknowledge the use of the atnf pulsar catalog . we thank carl heiles , j .- macquart , miller goss , jay gallagher , and shu - ichiro inutsuka for stimulating discussions . we would also like to thank the anonymous referee , whose comments improved greatly the clarity of the paper . ss acknowledges support from nsf grants ast-0097417 and ast-9981308 , and the research corporation . she also thanks astron and the helena kluyver visiting program for their hospitality during the final stage of the manuscript preparation . jmw , zp , kt , and jtg were supported by nsf grants ast-0406832 and ast-0807556 . , c. l. , goss , w. m. , lazio , t. j. w. , & faison , m. d. 2007 , in astronomical society of the pacific conference series , vol . 365 , sins - small ionized and neutral structures in the diffuse interstellar medium , ed . m. haverkorn & w. m. goss , 12 , c. r. , reynolds , j. e. , & wilson , w. w. 2007 , in astronomical society of the pacific conference series , vol . 365 , sins - small ionized and neutral structures in the diffuse interstellar medium , ed . m. haverkorn & w. m. goss , 90 , s. , heiles , c. , & kanekar , n. 2007 , in astronomical society of the pacific conference series , vol . 365 , sins - small ionized and neutral structures in the diffuse interstellar medium , ed . m. haverkorn & w. m. goss , 22 , j. m. & stanimirovi , s. 2007 , in astronomical society of the pacific conference series , vol . 365 , sins - small ionized and neutral structures in the diffuse interstellar medium , ed . m. haverkorn & w. m. goss , 28

we present results from multi - epoch neutral hydrogen ( hi ) absorption observations of six bright pulsars with the arecibo telescope . moving through the interstellar medium ( ism ) with transverse velocities of 10150 au yr@xmath0 , these observations require strong spatial inhomogeneities in either the tsas clouds physical properties themselves or else in the clouds galactic distribution .

we present results from multi - epoch neutral hydrogen ( hi ) absorption observations of six bright pulsars with the arecibo telescope . moving through the interstellar medium ( ism ) with transverse velocities of 10150 au yr@xmath0 , these pulsars have swept across 1200 au over the course of our experiment , allowing us to probe the existence and properties of the tiny scale atomic structure ( tsas ) in the cold neutral medium ( cnm ) . while most of the observed pulsars show no significant change in their hi absorption spectra , we have identified at least two clear tsas - induced opacity variations in the direction of b1929 + 10 . these observations require strong spatial inhomogeneities in either the tsas clouds physical properties themselves or else in the clouds galactic distribution . while tsas is occasionally detected on spatial scales down to 10 au , it is too rare to be characterized by a spectrum of turbulent cnm fluctuations on scales of @xmath1 au , as previously suggested by some work . in the direction of b1929 + 10 , an apparent correlation between tsas and interstellar clouds inside the warm local bubble ( lb ) indicates that tsas may be tracing the fragmentation of the lb wall via hydrodynamic instabilities . while similar fragmentation events occur frequently throughout the ism , the warm medium surrounding these cold cloudlets induces a natural selection effect wherein small tsas clouds evaporate quickly and are rare , while large clouds survive longer and become a general property of the ism .

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quasars have been used as background sources to study the gaseous phases of a variety of objects that are located along our sight - lines to them . these objects include not only _ intervening _ absorbers such as intervening galaxies , the intergalactic medium ( igm ) , clouds in the halo of the milky way , and the host galaxies of the quasars themselves , but also _ intrinsic _ absorbers that are physically associated with the quasar central engines . one of the most promising candidates for the intrinsic absorbers are outflowing winds from the quasars that could be accelerated by radiation pressure from the accretion disk ( murray et al . 1995 ; arav et al . 1995 ; proga et al . 2000 ) or by magnetocentrifugal forces ( e.g. , everett 2005 ) . outflowing winds are important components of quasar central engines because they carry away angular momentum from the accretion disk and allow the remaining gas in the disk to accrete onto the central black hole . quasar outflows are also important for cosmology since they deliver energy , momentum , and metals to the interstellar and intergalactic media , thus significantly affecting star formation and galaxy assembly ( e.g. , granato et al . 2004 ; scannapieco & oh 2004 ; springel , di matteo & hernquist 2005 ) . intrinsic narrow absorption lines ( nals ; fwhm @xmath3 ) present a powerful way to determine physical parameters of the accretion disk winds . unlike the _ broad _ absorption lines ( bals ; fwhm @xmath4 ; weymann et al . 1991 ) that are also associated with quasars outflows , nals do not suffer from self - blending or from saturation , so that line parameters are more easily evaluated . bals are thought to be associated with radiatively - driven outflows from accretion disks ( e.g. , weymann et al . 1991 ; becker et al . 1997 ) , while it is difficult to separate intrinsic nals from intervening nals . mini - broad absorption lines ( mini - bals ) are an intermediate subclass between nals and bals , which are typically wider than those of nals , but narrower than bals . mini - bals have the advantages of both bals ( i.e. , high probability of being intrinsic lines ) and nals ( i.e. , line profiles can be resolved into individual components ) , which make them useful targets ( e.g. , churchill et al . 1999 ; hamann et al . 1997a ; narayanan et al . bals could probe the low - latitude , dense , fast portion of the wind , while the mini - bals and nals may probe the lower - density portion of the wind at high latitudes above the disk . thus , the study of mini - bals and nals complements the study of bals because the corresponding absorbers reside in different regions of the outflow and allow us to sample different sets of physical conditions . to isolate intrinsic nals , two tests are commonly used : ( i ) partial coverage , i.e. , trough dilution by un - occulted light ( e.g. , hamann et al . 1997b ; barlow & sargent 1997 ; ganguly et al . 1999 ) , and ( ii ) variability of the absorption profiles within a few years in the quasar rest frames ( e.g. , hamann et al . 1997a ; narayanan et al . 2004 ; wise et al . these effects occur for intrinsic absorbers that are very compact and very dense compared to intervening absorbers . the fraction of quasars that host intrinsic associated nals ( nals within 5,000 of the quasar emission redshifts ) has been estimated to be @xmath527% at @xmath6 , using the time variability technique ( narayanan et al . 2004 ; wise et al . 2004 ) , and @xmath723% at @xmath8 , based on partial coverage analysis ( misawa et al . these signatures are a sufficient , but not a necessary , condition to demonstrate the intrinsic nature of an absorber . it is very likely that some nals without time variability or partial coverage are also intrinsic . both of the above methods have been applied to bal and mini - bal systems . for example , partial coverage analysis has been carried out by petitjean & srianand ( 1999 ) , srianand & petitjean ( 2000 , ) yuan et al . ( 2002 ) , and ganguly et al . ( 2003 ) , while time - variability has been studied by foltz et al . ( 1987 ) , turnshek et al . ( 1988 ) , smith & penston ( 1988 ) , barlow et al . ( 1992 ) , barlow ( 1993 ) , vilkoviskij & irwin ( 2001 ) , ma ( 2002 ) , narayanan et al . ( 2004 ) , and lundgren et al . it is quite difficult ( or almost impossible ) to deblend kinematic components in those heavily blending absorption features using low / intermediate resolution spectra . however , some authors successfully deblended narrower absorption components from each other in such systems using high resolution spectra of @xmath9 ( e.g. , yuan et al . 2002 ; ganguly et al . systematic monitoring of individual mini - bals using high - resolution spectra taken on several epochs can potentially provide very important constraints on the properties of the absorbers . however , no such campaign has been attempted so far , to our knowledge . the optically bright quasar hs 1603 + 3820 ( @xmath10=2.542 , b=15.9 ) , first discovered in the hamburg / cfa bright quasar survey ( hagen et al . 1995 ; dobrzycki et al . 1996 ) , is known to have a large number ( 13 ) of doublets at @xmath11 ( dobrzycki , engels , & hagen 1999 ) . using high - resolution spectra ( @xmath12 ) taken with the subaru telescope , misawa et al . ( 2003 , 2005 ) classified all doublets into 8 systems , and found that only a mini - bal system at @xmath1 ( shift velocity , @xmath1310,600 ) shows both partial coverage and time variability in an interval of 0.36 years in the quasar rest frame . based on these results , misawa et al . ( 2005 ) placed constraints ( i ) on the electron density ( @xmath14 ) and the absorber s distance from the quasar ( @xmath15 kpc ) , if a change in the ionization state causes the variability , or ( ii ) on the time scale for the absorber to cross the continuum source and the distance from the continuum source , if gas motion across the background uv source causes the variability . in the latter case , the crossing velocity is constrained to be @xmath16 , and the distance from the continuum source , @xmath17 pc . this is larger than the size of the continuum source , @xmath18 pc , but smaller than that of the blr , @xmath19@xmath73 pc , estimated for this quasar . on the other hand , the other nals found towards the quasar show no sign of being intrinsic . further monitoring observations make it possible to ( i ) discriminate between changes in the ionization state and motion of the absorbers across the continuum source as the cause of the time variability seen in the mini - bal , and ( ii ) to confirm whether the other nals really show neither partial coverage nor variability . in this paper , we present the results of monitoring hs 1603 + 3820 over 4.2 years ( 1.2 years in the quasar rest frame ) based on eight spectra . six of these spectra were taken with the high dispersion spectrograph ( hds ; noguchi et al . 2002 ) on the subaru telescope , and two with the medium - resolution spectrograph ( mrs ; horner , engel , & ramsey , 1998 ) on the hobby - eberly telescope ( het ) . the first two spectra in this time series were presented and discussed by misawa et al ( 2003 , 2005 ) . with the new spectra we are able to sample the variations of the absorption lines more densely and probe the internal structure of the absorber . in 2 , we describe the observations and data reduction . the methods used for model fitting are outlined in 3 . the properties of the mini - bal and of the other nal systems are examined in 4 . the possible origins of the time variability seen in the mini - bal system are discussed in 5 , and a summary is given in 6 . we adopt @xmath20 as the systemic redshift of the quasar , which was estimated from its narrow emission lines ( misawa et al . time intervals between observations are given in the quasar rest frame throughout the paper , unless otherwise noted . we use a cosmology with @xmath21=75 mpc@xmath22 , @xmath23=0.3 , and @xmath24=0.7 .

we present six new and two previously published high - resolution spectra of the quasar hs 1603 + 3820 ( @xmath0 ) taken over an interval of 4.2 years ( 1.2 years in the quasar rest frame ) . the observations were made with the high - dispersion spectrograph on the subaru telescope and medium - resolution spectrograph on the hobby - eberly telescope . the purpose was to study the narrow absorption lines ( nals ) . only the mini - bal system at @xmath1 ( @xmath2 ) shows both partial coverage and time variability , although two nal systems possibly show evidence of partial coverage .

we present six new and two previously published high - resolution spectra of the quasar hs 1603 + 3820 ( @xmath0 ) taken over an interval of 4.2 years ( 1.2 years in the quasar rest frame ) . the observations were made with the high - dispersion spectrograph on the subaru telescope and medium - resolution spectrograph on the hobby - eberly telescope . the purpose was to study the narrow absorption lines ( nals ) . we use time variability as well as coverage fraction analysis to separate intrinsic absorption lines , which are physically related to the quasar , from intervening absorption lines . by fitting models to the line profiles , we derive the parameters of the respective absorbers as a function of time . only the mini - bal system at @xmath1 ( @xmath2 ) shows both partial coverage and time variability , although two nal systems possibly show evidence of partial coverage . we find that all the troughs of the mini - bal system vary in concert and its total equivalent width variations resemble those of the coverage fraction . however , no other correlations are seen between the variations of different model parameters . thus , the observed variations can not be reproduced by a simple change of ionization state nor by motion of a homogeneous parcel of gas across the cylinder of sight . we propose that the observed variations are a result of rapid continuum fluctuations , coupled with coverage fraction fluctuations caused by a clumpy screen of variable optical depth located between the continuum source and the mini - bal gas . an alternative explanation is that the observed partial coverage signature is the result of scattering of continuum photons around the absorber , thus the equivalent width of the mini - bal can vary as the intensity of the scattered continuum changes .

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we have been monitoring the absorption lines in the spectrum of the quasar hs 1603 + 3820 since 2002 , using the subaru and hobby - eberly telescopes . we have obtained six subaru+hds and two het+mrs spectra spanning an interval of approximately 1.2 years in the quasar rest frame and probing rest - frame time scales as short as 16 days . we have determined the physical parameters of the 9 absorption - line systems by fitting voigt models to the line profiles . our main results are as follows : 1 . we detect one mini - bal and eight nal systems in the quasar spectrum . the partial coverage signature and time variability of the mini - bal show it to be intrinsic to the quasar . two of the nal systems ( d and i ) may also be intrinsic , based upon our partial coverage analysis . we are able to fit models only to the bluest portion of the mini - bal profile where self - blending is not severe . all fit parameters ( i.e. , column density , doppler parameter , coverage fraction , and shift velocity ) as well as the total equivalent width of the system vary significantly with time , even on short time scales . however , the profile parameters do not appear to change in concert with each other , with one exception : the equivalent widths of all the troughs in this system vary together and approximately follow the variations of the coverage fraction determined from the model fits . we have examined a number of ways of explaining the above variations of the mini - bal and we have found two viable possibilities . the first possibility is that the observed partial coverage signature is the result of continuum photons scattering around the absorber and into our cylinder of sight . the observed changes in mini - bal equivalent widths are thus produced by variations in the scattered continuum that dilutes the absorption troughs . in the second possibility , the illumination of the uv absorber fluctuates on short time scales by a factor of up to 3 . we suggest that these fluctuations are caused by a screen of variable optical depth between the mini - bal gas and the continuum source . this screen might be identified with the shielding gas invoked or predicted in some outflow models . moreover , it could be analogous to the `` warm '' absorbers observed in the x - ray spectra of seyfert galaxies and some quasars . this picture can also explain the variations in the coverage fraction , which appear to be unrelated to the ionic column density changes . this work was supported by nasa grant nag5 - 10817 . we are grateful to the staff of the subaru telescope , which is operated by the national astronomical observatory of japan . we would also like to thank christopher churchill for providing us with the minfit software package . me acknowledges partial support from the theoretical astrophysics visitors fund at northwestern university and thanks the members of the theoretical astrophysics group for their warm hospitality . the hobby - eberly telescope ( het 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36,000 & 43.0 + 4 & 2005 may 10 & 0.89 & het+mrs & 45006200 & 1800 & 9,200 & 17.4 + 5 & 2005 jun 29 & 0.92 & subaru+hds & 35304855 , 49256280 & 3600 & 45,000 & 31.1 + 6 & 2005 aug 3,8 & 0.95 & het+mrs & 45006170 & 4000 & 9,200 & 28.5 + 7 & 2005 aug 19 & 0.96 & subaru+hds & 35204850 , 49206235 & 3600 & 36,000 & 43.6 + 8 & 2006 may 31jun 1 & 1.18 & subaru+hds & 43205630 , 57407050 & 9000 & 45,000 & 52.5 + clccccccccccccc 1 & 2002 mar 23 & 0.00 & 10648 & 14.55@xmath860.07 & 85@xmath863 & 0.32@xmath860.03 & 1.49 & & 10118 & 14.53@xmath860.04 & 233@xmath86 6 & 0.32@xmath860.03 & 1.88 + 2 & 2003 jul 7 & 0.36 & 10637 & 14.72@xmath860.07 & 98@xmath865 & 0.45@xmath860.04 & 2.79 & & 10273 & 14.64@xmath860.05 & 274@xmath8615 & 0.45@xmath860.04 & 3.32 + 3 & 2005 feb 26 & 0.83 & 10644 & 14.75@xmath860.03 & 84@xmath862 & 0.36@xmath860.01 & 2.15 & & 10309 & 14.53@xmath860.03 & 348@xmath8615 & 0.36@xmath860.01 & 2.22 + 4 & 2005 may 10 @xmath87 & 0.89 & 10643 & 14.70 & 81 & 0.33 & 1.83 & & 10259 & 14.67 & 692 & 0.33 & 2.86 + 5 & 2005 jun 29 & 0.92 & 10642 & 14.68@xmath860.05 & 80@xmath863 & 0.32@xmath860.02 & 1.72 & & 10235 & 14.74@xmath860.06 & 863@xmath8699 & 0.32@xmath860.02 & 3.20 + 6 & 2005 aug 38 @xmath88 & 0.95 & 10641 & 14.72 & 71 & 0.28 & 1.49 & & 10345 & 14.82 & 793 & 0.28 & 3.29 + 7 & 2005 aug 19 & 0.96 & 10641 & 14.74@xmath860.03 & 69@xmath862 & 0.27@xmath860.01 & 1.43 & & 10381 & 14.85@xmath860.02 & 770@xmath8631 & 0.27@xmath860.01 & 3.36 + 8 & 2006 may 31jun 1 & 1.18 & 10637 & 14.76@xmath860.03 & 71@xmath862 & 0.24@xmath860.01 & 1.32 & & 10291 & 14.90@xmath860.02 & 587@xmath8618 & 0.24@xmath860.01 & 3.27 + lcccccc + + 1 ............ & 5381.8 & 2.47618 & 5627 & 13.36 @xmath86 0.01 & 8.2 @xmath86 0.2 & 1.00 + 2 ............ & 5382.2 & 2.47642 & 5606 & 14.16 @xmath86 0.03 & 6.3 @xmath86 0.2 & 1.00 + 3 ............ & 5382.8 & 2.47685 & 5569 & 13.52 @xmath86 0.01 & 22.4 @xmath86 0.4 & 1.00 + 4 ............ & 5383.8 & 2.47749 & 5514 & 13.83 @xmath86 0.00 & 15.6 @xmath86 0.1 & 1.00 + 5 ............ & 5383.9 & 2.47752 & 5511 & 14.69 @xmath86 0.46 & 5.5 @xmath86 1.1 & 1.00@xmath89 + 6 ............ & 5384.3 & 2.47779 & 5488 & 12.87 @xmath86 0.29 & 4.1 @xmath86 2.1 & 0.90@xmath90 + 7 ............ & 5384.5 & 2.47793 & 5476 & 13.58 @xmath86 0.01 & 6.7 @xmath86 0.2 & 1.00 + 8 ............ & 5385.0 & 2.47826 & 5447 & 14.06 @xmath86 0.00 & 14.8 @xmath86 0.2 & 1.00 + 9 ............ & 5385.6 & 2.47862 & 5416 & 13.96 @xmath86 0.10 & 14.7 @xmath86 2.2 & 0.97@xmath89 + 10 ........... & 5386.2 & 2.47899 & 5384 & 14.13 @xmath86 0.00 & 27.1 @xmath86 0.2 & 1.00 + 11 ........... & 5386.2 & 2.47899 & 5384 & 13.62 @xmath86 0.21 & 5.6 @xmath86 1.2 & 0.76@xmath91 + 12 ........... & 5387.1 & 2.47959 & 5333 & 12.96 @xmath86 0.21 & 7.3 @xmath86 1.0 & 1.00@xmath92 + 13 ........... & 5387.4 & 2.47977 & 5317 & 13.74 @xmath86 0.01 & 7.8 @xmath86 0.1 & 1.00 + 14 ........... & 5388.2 & 2.48028 & 5273 & 13.56 @xmath86 0.18 & 28.1 @xmath86 2.2 & 0.45@xmath93 + 15 ........... & 5388.6 & 2.48055 & 5250 & 14.03 @xmath86 0.03 & 4.7 @xmath86 0.1 & 1.00 + + 1 ............ & 4308.0 & 2.47748 & 5514 & 13.26 @xmath86 0.01 & 7.7 @xmath86 0.3 & 1.00 + 2 ............ & 4308.4 & 2.47784 & 5483 & 12.73 @xmath86 0.06 & 9.4 @xmath86 1.5 & 1.00 + 3 ............ & 4308.9 & 2.47824 & 5449 & 13.13 @xmath86 0.06 & 19.7 @xmath86 2.7 & 1.00 + 4 ............ & 4309.6 & 2.47882 & 5399 & 13.22 @xmath86 0.05 & 28.2 @xmath86 4.0 & 1.00 + + 1 ............ & 4845.2 & 2.47635 & 5612 & 12.44 @xmath86 0.03 & 15.5 @xmath86 0.8 & 1.00 + 2 ............ & 4845.3 & 2.47642 & 5606 & 13.20 @xmath86 0.01 & 4.0 @xmath86 0.1 & 1.00 + 3 ............ & 4846.8 & 2.47751 & 5512 & 12.49 @xmath86 0.01 & 7.5 @xmath86 0.2 & 1.00 + 4 ............ & 4847.4 & 2.47793 & 5476 & 12.72 @xmath86 0.01 & 2.9 @xmath86 0.1 & 1.00 + 5 ............ & 4847.8 & 2.47824 & 5449 & 13.05 @xmath86 0.10 & 21.3 @xmath86 0.9 & 0.94@xmath94 + 6 ............ & 4848.3 & 2.47860 & 5418 & 13.12 @xmath86 0.00 & 9.3 @xmath86 0.1 & 1.00 + 7 ............ & 4848.9 & 2.47899 & 5384 & 13.05 @xmath86 0.07 & 11.9 @xmath86 0.3 & 0.69@xmath95 + 8 ............ & 4849.7 & 2.47960 & 5332 & 12.98 @xmath86 0.01 & 27.7 @xmath86 0.4 & 1.00 + 9 ............ & 4849.9 & 2.47976 & 5318 & 12.86 @xmath86 0.01 & 4.6 @xmath86 0.1 & 1.00 + 10 ........... & 4851.0 & 2.48054 & 5251 & 13.39 @xmath86 0.01 & 4.9 @xmath86 0.1 & 1.00 + + 1 ............ & 4194.8 & 2.47687 & 5567 & 15.14 @xmath86 0.30 & 20.1 @xmath86 1.4 & 1.00 + 2 ............ & 4195.8 & 2.47770 & 5496 & 13.97 @xmath86 0.01 & 84.7 @xmath86 1.6 & 1.00 + 3 ............ & 4196.9 & 2.47857 & 5420 & 14.31 @xmath86 2.23 & 6.9 @xmath86 4.5 & 1.00 + 4 ............ & 4197.4 & 2.47903 & 5381 & 12.57 @xmath86 0.04 & 8.4 @xmath86 0.8 & 1.00 + 5 ............ & 4198.0 & 2.47949 & 5341 & 13.71 @xmath86 1.57 & 4.6 @xmath86 2.7 & 1.00 + 6 ............ & 4198.3 & 2.47976 & 5318 & 14.43 @xmath86 0.57 & 3.1 @xmath86 0.7 & 1.00 + 7 ............ & 4198.3 & 2.47971 & 5322 & 13.06 @xmath86 0.03 & 32.7 @xmath86 1.4 & 1.00 + 8 ............ & 4199.2 & 2.48052 & 5252 & 13.99 @xmath86 0.38 & 5.6 @xmath86 0.7 & 1.00 + 9 ............ & 4200.1 & 2.48122 & 5192 & 13.10 @xmath86 2.41 & 2.2 @xmath86 3.2 & 1.00 + 10 ........... & 4200.3 & 2.48136 & 5180 & 12.51 @xmath86 0.04 & 4.8 @xmath86 0.7 & 1.00 + + 1 ............ & 4639.4 & 2.47642 & 5606 & 13.52 @xmath86 0.07 & 2.6 @xmath86 0.3 & 1.00 + 2 ............ & 4641.7 & 2.47811 & 5460 & 14.06 @xmath86 0.01 & 11.9 @xmath86 0.2 & 1.00 + 3 ............ & 4642.2 & 2.47852 & 5425 & 14.41 @xmath86 0.03 & 13.9 @xmath86 0.4 & 1.00 + 4 ............ & 4642.5 & 2.47871 & 5408 & 14.15 @xmath86 2.21 & 2.6 @xmath86 3.4 & 1.00 + 5 ............ & 4642.9 & 2.47904 & 5380 & 12.98 @xmath86 0.02 & 9.9 @xmath86 0.9 & 1.00 + 6 ............ & 4643.4 & 2.47944 & 5345 & 13.08 @xmath86 0.02 & 7.0 @xmath86 0.6 & 1.00 + 7 ............ & 4643.8 & 2.47970 & 5323 & 13.97 @xmath86 0.08 & 4.3 @xmath86 0.9 & 1.00 + 8 ............ & 4643.9 & 2.47981 & 5314 & 12.72 @xmath86 1.02 & 10.6 @xmath8613.0 & 1.00 + 9 ............ & 4644.7 & 2.48037 & 5265 & 12.26 @xmath86 0.70 & 1.1 @xmath86 5.1 & 1.00 + 10 ........... & 4644.9 & 2.48052 & 5252 & 14.92 @xmath86 0.80 & 3.6 @xmath86 0.9 & 1.00 + 11 ........... & 4645.8 & 2.48120 & 5194 & 15.33 @xmath86 1.70 & 2.7 @xmath86 1.2 & 1.00 + 12 ........... & 4646.0 & 2.48134 & 5182 & 13.89 @xmath86 0.08 & 3.7 @xmath86 0.6 & 1.00 + 13 ........... & 4646.3 & 2.48162 & 5158 & 12.72 @xmath86 0.03 & 5.0 @xmath86 0.8 & 1.00 + + 1 ............ & 5811.2 & 2.47814 & 5458 & 11.95 @xmath86 0.01 & 10.6 @xmath86 0.4 & 1.00 + 2 ............ & 5811.9 & 2.47856 & 5421 & 12.92 @xmath86 0.02 & 8.8 @xmath86 0.1 & 1.00 + 3 ............ & 5813.4 & 2.47944 & 5345 & 11.28 @xmath86 0.03 & 4.2 @xmath86 0.9 & 1.00 + 4 ............ & 5813.9 & 2.47972 & 5321 & 11.70 @xmath86 0.01 & 4.0 @xmath86 0.4 & 1.00 + 5 ............ & 5815.2 & 2.48053 & 5252 & 12.57 @xmath86 3.50 & 1.5 @xmath86 3.2 & 1.00 + 6 ............ & 5816.4 & 2.48121 & 5193 & 11.84 @xmath86 0.18 & 1.7 @xmath86 1.1 & 1.00 + 7 ............ & 5816.6 & 2.48135 & 5181 & 11.50 @xmath86 0.04 & 3.5 @xmath86 1.2 & 1.00 + + 1 ............ & 4381.3 & 2.47607 & 5636 & 12.08 @xmath86 0.02 & 4.1 @xmath86 0.6 & 1.00 + 2 ............ & 4381.7 & 2.47641 & 5607 & 13.26 @xmath86 1.78 & 1.8 @xmath86 1.5 & 1.00 + 3 ............ & 4383.6 & 2.47791 & 5477 & 12.55 @xmath86 2.19 & 1.5 @xmath86 3.3 & 1.00 + 4 ............ & 4383.9 & 2.47813 & 5458 & 13.11 @xmath86 0.01 & 9.0 @xmath86 0.4 & 1.00 + 5 ............ & 4384.3 & 2.47845 & 5431 & 15.74 @xmath86 0.39 & 1.9 @xmath86 0.1 & 1.00 + 6 ............ & 4384.6 & 2.47865 & 5414 & 13.48 @xmath86 0.37 & 5.8 @xmath86 1.9 & 1.00 + 7 ............ & 4384.8 & 2.47887 & 5395 & 12.07 @xmath86 0.04 & 3.2 @xmath86 1.5 & 1.00 + 8 ............ & 4385.1 & 2.47905 & 5379 & 11.97 @xmath86 0.03 & 3.7 @xmath86 0.9 & 1.00 + 9 ............ & 4385.6 & 2.47944 & 5345 & 12.22 @xmath86 0.02 & 5.9 @xmath86 0.5 & 1.00 + 10 ........... & 4385.9 & 2.47971 & 5322 & 13.03 @xmath86 0.07 & 4.1 @xmath86 0.3 & 1.00 + 11 ........... & 4386.9 & 2.48052 & 5252 & 14.13 @xmath86 0.28 & 3.1 @xmath86 0.3 & 1.00 + 12 ........... & 4387.8 & 2.48122 & 5192 & 13.63 @xmath86 1.30 & 3.2 @xmath86 2.0 & 1.00 + 13 ........... & 4388.0 & 2.48135 & 5181 & 12.93 @xmath86 4.77 & 2.0 @xmath86 6.3 & 1.00 + + 1 ............ & 5595.1 & 2.47857 & 5420 & 13.65 @xmath86 0.01 & 4.6 @xmath86 0.1 & 1.00 + + 1 ............ & 4529.7 & 2.47855 & 5422 & 14.58 @xmath86 0.03 & 6.9 @xmath86 0.2 & 1.00 + 2 ............ & 4533.2 & 2.48125 & 5190 & 13.41 @xmath86 0.02 & 10.7 @xmath86 0.8 & 1.00 + + 1 ............ & 5303.3 & 2.47369 & 5841 & 13.05 & 21.0 & 1.00 + 2 ............ & 5304.0 & 2.47416 & 5801 & 13.12 & 22.8 & 1.00 + 3 ............ & 5304.9 & 2.47476 & 5749 & 12.95 & 21.4 & 1.00 + 4 ............ & 5306.4 & 2.47570 & 5668 & 13.62 & 11.1 & 1.00 + 5 ............ & 5307.6 & 2.47647 & 5602 & 13.04 & 13.1 & 1.00 + 6 ............ & 5310.1 & 2.47815 & 5457 & 13.24 & 14.2 & 1.00 + 7 ............ & 5310.8 & 2.47857 & 5420 & 14.07 & 11.2 & 1.00 + 8 ............ & 5312.6 & 2.47976 & 5318 & 13.17 & 12.3 & 1.00 + 9 ............ & 5313.8 & 2.48055 & 5250 & 13.43 & 5.2 & 1.00 + 10 ........... & 5314.8 & 2.48124 & 5190 & 13.22 & 7.5 & 1.00 + 11 ........... & 5315.2 & 2.48147 & 5171 & 13.46 & 11.6 & 1.00 + + + + 1 ............ & 5475.9 & 2.53693 & 430 & 13.41 @xmath960.05 & 10.9 @xmath86 0.2 & 0.94@xmath95 + + + + 1 ............ & 5498.0 & 2.55125 & 782 & 13.18 @xmath86 0.22 & 3.0 @xmath86 0.7 & 0.30@xmath97 + 2 ............ & 5500.1 & 2.55261 & 897 & 13.05 @xmath86 0.14 & 4.5 @xmath86 0.6 & 0.81@xmath98 + 3 ............ & 5500.4 & 2.55280 & 913 & 13.54 @xmath86 0.15 & 8.2 @xmath86 3.3 & 0.23@xmath99 + 4 ............ & 5501.0 & 2.55314 & 942 & 14.26 @xmath86 0.02 & 11.7 @xmath86 0.5 & 0.99@xmath100 + 5 ............ & 5501.5 & 2.55351 & 973 & 16.66 @xmath86 0.06 & 5.6 @xmath86 0.1 & 0.99@xmath100 + + 1 ............ & 4952.2 & 2.55313 & 941 & 13.05 @xmath86 0.06 & 9.4 @xmath86 0.3 & 0.66@xmath101 + 2 ............ & 4952.7 & 2.55350 & 972 & 13.41 @xmath86 0.02 & 8.4 @xmath86 0.1 & 0.96@xmath89 + + + + 1 ............ & 4469.8 & 1.88708 & 60493 & 13.07 @xmath86 0.30 & 7.5 @xmath86 1.3 & 0.73@xmath102 + 2 ............ & 4470.1 & 1.88730 & 60471 & 13.61 @xmath86 0.08 & 14.2 @xmath86 2.3 & 0.93@xmath103 + 3 ............ & 4470.5 & 1.88753 & 60448 & 13.35 @xmath86 0.16 & 8.4 @xmath86 2.7 & 0.64@xmath104 + 4 ............ & 4470.7 & 1.88771 & 60430 & 13.06 @xmath86 0.33 & 7.7 @xmath86 3.1 & 0.78@xmath105 + 5 ............ & 4471.0 & 1.88788 & 60414 & 13.34 @xmath86 0.17 & 10.8 @xmath86 1.6 & 0.67@xmath106 + + + + 1 ............ & 4587.4 & 1.96305 & 52980 & 13.49 @xmath86 0.12 & 11.2 @xmath86 0.9 & 0.52@xmath107 + 2 ............ & 4587.7 & 1.96327 & 52959 & 13.86 @xmath86 0.02 & 5.9 @xmath86 0.2 & 1.00 + 3 ............ & 4588.0 & 1.96345 & 52941 & 13.78 @xmath86 0.01 & 7.5 @xmath86 0.3 & 1.00 + 4 ............ & 4588.6 & 1.96381 & 52906 & 13.04 @xmath86 0.44 & 5.1 @xmath86 0.9 & 0.37@xmath108 + 5 ............ & 4589.4 & 1.96436 & 52852 & 14.00 @xmath86 0.03 & 8.3 @xmath86 0.2 & 0.99@xmath89 + 6 ............ & 4589.8 & 1.96459 & 52829 & 13.26 @xmath86 0.17 & 9.4 @xmath86 1.2 & 0.71@xmath109 + 7 ............ & 4590.2 & 1.96486 & 52803 & 13.40 @xmath86 0.08 & 8.3 @xmath86 0.5 & 0.89@xmath110 + 8 ............ & 4590.5 & 1.96506 & 52783 & 12.85 @xmath86 0.02 & 5.9 @xmath86 0.4 & 1.00 + + + + 1 ............ & 4752.1 & 2.06947 & 42665 & 12.70 @xmath86 0.03 & 11.6 @xmath86 1.1 & 1.00 + 2 ............ & 4752.6 & 2.06974 & 42639 & 13.75 @xmath86 0.00 & 10.0 @xmath86 0.1 & 1.00 + 3 ............ & 4752.9 & 2.06997 & 42617 & 14.04 @xmath86 0.04 & 14.8 @xmath86 1.4 & 1.00@xmath100 + 4 ............ & 4753.2 & 2.07016 & 42599 & 13.47 @xmath86 0.01 & 12.0 @xmath86 0.2 & 1.00 + 5 ............ & 4753.7 & 2.07045 & 42571 & 13.01 @xmath86 0.02 & 9.1 @xmath86 0.6 & 1.00 + 6 ............ & 4754.0 & 2.07070 & 42547 & 12.56 @xmath86 0.05 & 11.8 @xmath86 1.8 & 1.00 + + 1 ............ & 4306.3 & 2.06984 & 42629 & 13.16 @xmath86 0.02 & 14.6 @xmath86 0.7 & 1.00 + 2 ............ & 4306.6 & 2.07010 & 42604 & 12.83 @xmath86 0.03 & 7.3 @xmath86 0.6 & 1.00 + + + + 1 ............ & 5055.2 & 2.26521 & 24357 & 13.05 @xmath86 0.22 & 5.9 @xmath86 0.5 & 0.75@xmath111 + 2 ............ & 5055.5 & 2.26542 & 24337 & 13.85 @xmath86 0.16 & 13.8 @xmath86 2.8 & 0.14@xmath112 + + 1 ............ & 3939.5 & 2.26520 & 24357 & 12.76 @xmath86 0.13 & 4.2 @xmath86 0.8 & 1.00 + 2 ............ & 3939.6 & 2.26534 & 24345 & 11.82 @xmath86 0.21 & 1.7 @xmath86 3.6 & 1.00 + + + + 1 ............ & 4914.9 & 2.17460 & 32722 & 12.83 @xmath86 0.01 & 9.9 @xmath86 0.5 & 1.00 + 2 ............ & 4915.2 & 2.17481 & 32703 & 12.97 @xmath86 0.22 & 8.7 @xmath86 1.4 & 0.90@xmath113 + 3 ............ & 4915.4 & 2.17494 & 32691 & 12.25 @xmath86 0.03 & 2.0 @xmath86 1.3 & 1.00 + 4 ............ & 4915.8 & 2.17520 & 32666 & 13.33 @xmath86 0.11 & 14.8 @xmath86 0.7 & 0.70@xmath114 + 5 ............ & 4916.2 & 2.17542 & 32646 & 13.17 @xmath86 0.46 & 0.8 @xmath86 0.6 & 0.37@xmath115 + 6 ............ & 4916.4 & 2.17558 & 32631 & 13.65 @xmath86 0.02 & 8.6 @xmath86 0.3 & 0.87@xmath100 + 7 ............ & 4916.7 & 2.17578 & 32612 & 12.76 @xmath86 0.03 & 27.4 @xmath86 2.4 & 1.00 + + 1 ............ & 4424.6 & 2.17462 & 32720 & 11.96 @xmath86 0.05 & 8.2 @xmath86 1.7 & 1.00 + 2 ............ & 4424.9 & 2.17480 & 32704 & 11.67 @xmath86 0.08 & 1.2 @xmath86 4.9 & 1.00 + 3 ............ & 4425.1 & 2.17495 & 32690 & 11.74 @xmath86 0.08 & 4.7 @xmath86 2.1 & 1.00 + 4 ............ & 4425.4 & 2.17519 & 32667 & 12.04 @xmath86 0.04 & 9.3 @xmath86 1.2 & 1.00 + 5 ............ & 4426.0 & 2.17557 & 32632 & 12.51 @xmath86 0.01 & 7.2 @xmath86 0.3 & 1.00 + + 1 ............ & 3830.9 & 2.17524 & 32663 & 12.35 @xmath86 0.03 & 7.7 @xmath86 0.8 & 1.00 + 2 ............ & 3831.4 & 2.17560 & 32629 & 12.61 @xmath86 0.03 & 6.8 @xmath86 0.5 & 1.00 + + 1 ............ & & + , , and are marked with downward arrows . the region blueward of the ly@xmath32 emission line is not shown because the spectrum normalization by continuum fitting is not reliable in the ly@xmath32 forest . the lower line is the 1@xmath46 error spectrum . the region of the mini - bal in system a ( 5288 5348 ) is shaded.,title="fig:",width=642 ] , , and are marked with downward arrows . the region blueward of the ly@xmath32 emission line is not shown because the spectrum normalization by continuum fitting is not reliable in the ly@xmath32 forest . the lower line is the 1@xmath46 error spectrum . the region of the mini - bal in system a ( 5288 5348 ) is shaded.,title="fig:",width=642 ] , , and are marked with downward arrows . the region blueward of the ly@xmath32 emission line is not shown because the spectrum normalization by continuum fitting is not reliable in the ly@xmath32 forest . the lower line is the 1@xmath46 error spectrum . the region of the mini - bal in system a ( 5288 5348 ) is shaded.,title="fig:",width=642 ] , for 8 observing epochs from march 23 , 2002 to may 31 , 2006 . filled stars with 1@xmath46 errors denote the coverage fractions of narrow ( left ) and broad ( right ) components . the stars are placed at the wavelengths of the blue members of the doublet ( i.e. , 1548 ) . open stars plotted in the het spectra are coverage fractions that are interpolated from the subaru spectra . in the top left panel , we also present models of the narrow and broad components as well as the @xmath441527 components in system b from the first observation.,width=453 ] error bars are coverage fractions determined by minfit . if a star is not displayed , the value of the coverage fraction is 1.0 . small dots with error bars denote the coverage fractions evaluated by the pixel - by - pixel method . the error values contain both poisson noise and error from continuum level uncertainty.,width=359 ] ) parameters over our monitoring period . from top to bottom , the frames show ( 1 ) rest frame equivalent width , ( 2 ) column densities , ( 3 ) doppler parameters , ( 4 ) coverage fractions , and ( 5 ) shift velocities . the solid line and triangles in the top panel refer to the equivalent width of the entire mini - bal profile ( see figures 1 and 2 ) , while the model parameters refer to the bluest troughs ( see figure 3 ) . the open and filled triangles in the top panel are measurements of the rest frame equivalent width , directly from the subaru and het data respectively . these include all and @xmath441527 components ( the components make only a small contribution ) . in all panels , the blue line and open stars refer to the narrow model component while the red line and open circles refer to the broad model component . the horizontal axis gives the observation time , both as the observed year ( top label ) and as the time in the quasar rest - frame , relative to the first observation ( bottom label ) . only the results from subaru spectra are shown , except for the equivalent width panel , because the low - resolution and low - s / n ratio of the het+mrs spectra prevented us from fitting models . the dotted lines in the 2nd , 3rd , and 4th panels show the best fit parameters for epoch 3 through epoch 8 , assuming a constant ( = 0.36 ) for the broad component.,width=283 ]

we propose that the observed variations are a result of rapid continuum fluctuations , coupled with coverage fraction fluctuations caused by a clumpy screen of variable optical depth located between the continuum source and the mini - bal gas . an alternative explanation is that the observed partial coverage signature is the result of scattering of continuum photons around the absorber , thus the equivalent width of the mini - bal can vary as the intensity of the scattered continuum changes .

we present six new and two previously published high - resolution spectra of the quasar hs 1603 + 3820 ( @xmath0 ) taken over an interval of 4.2 years ( 1.2 years in the quasar rest frame ) . the observations were made with the high - dispersion spectrograph on the subaru telescope and medium - resolution spectrograph on the hobby - eberly telescope . the purpose was to study the narrow absorption lines ( nals ) . we use time variability as well as coverage fraction analysis to separate intrinsic absorption lines , which are physically related to the quasar , from intervening absorption lines . by fitting models to the line profiles , we derive the parameters of the respective absorbers as a function of time . only the mini - bal system at @xmath1 ( @xmath2 ) shows both partial coverage and time variability , although two nal systems possibly show evidence of partial coverage . we find that all the troughs of the mini - bal system vary in concert and its total equivalent width variations resemble those of the coverage fraction . however , no other correlations are seen between the variations of different model parameters . thus , the observed variations can not be reproduced by a simple change of ionization state nor by motion of a homogeneous parcel of gas across the cylinder of sight . we propose that the observed variations are a result of rapid continuum fluctuations , coupled with coverage fraction fluctuations caused by a clumpy screen of variable optical depth located between the continuum source and the mini - bal gas . an alternative explanation is that the observed partial coverage signature is the result of scattering of continuum photons around the absorber , thus the equivalent width of the mini - bal can vary as the intensity of the scattered continuum changes .

1603.02284

i

star - formation rates ( sfrs ) are among the most fundamental measurements for constraining the physics of galaxy formation and evolution . the past decade has seen a multitude of studies that trace sfrs out to high redshift ( * ? ? ? * and references therein ) , and examined their correlation with other galaxy properties , such as stellar masses ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? the _ spitzer space telescope _ and _ herschel space observatory _ opened a new window into measuring bolometric sfrs by allowing us to directly correct the widely - used sfrs(uv ) for dust - obscured star formation ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . however , despite their common use , the uv+ir sfrs have several disadvantages : first , due to the limited spatial resolution and sensitivity of _ spitzer _ and _ herschel _ , most of the individual distant galaxies are not detectable in ir images , and second , the empirical templates used to convert the mid - ir ( restframe 8@xmath3 m ) fluxes to total ir luminosities result in systematic biases @xcite . hydrogen balmer emission lines are considered to be another gold standard for tracing robust sfrs in local galaxies ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * among many others ) . until recently , high - redshift studies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) only detected h@xmath2 with no ( or very limited ) h@xmath7 measurements , which are required for accurate dust corrections . however , with the new generation of multi - object near - ir ( nir ) spectrographs , both h@xmath2 and h@xmath7 are now detectable for normal star - forming galaxies at @xmath0 @xcite . while dust - corrected sfrs(h@xmath2 ) using balmer decrements ( hereafter , sfrs(h@xmath2,h@xmath7 ) ) are commonly used at low redshift , we still need to investigate how well balmer lines trace sfr at high redshifts , as galaxies were more star - forming at @xmath0 , the peak of the sfr density evolution @xcite . in particular , it has been argued that balmer lines may miss optically thick star - forming regions at these high redshifts ( e.g. , * ? ? ? * ) . in order to investigate this possible bias , one needs to compare the sfrs(h@xmath2,h@xmath7 ) with independently measured uv - to - far - ir ( uv - to - fir ) sfrs for star - forming galaxies at @xmath0 . fortunately , such dusty systems are among the luminous tail of the galaxy distribution within reach of _ herschel_. in this paper , we use the unique dataset of the mosfire deep evolution field ( mosdef ) survey @xcite in combination with _ herschel _ and _ spitzer _ data , to investigate how well sfrs(h@xmath2,h@xmath7 ) agree with uv - to - fir sfrs at @xmath0 . for the latter , we use the flexible stellar population synthesis ( fsps ) models @xcite , which utilize energy balance to fit the stellar and dust emission simultaneously @xcite . throughout this paper , we assumed a @xcite initial mass function ( imf ) , and h@xmath9 .

we also use our data to assess sfr indicators based on modeling the uv - to - mid - ir seds or by adding sfr(uv ) and sfr(ir ) , for which the latter is based on the mid - ir only or on the full ir sed .

we present the first direct comparison between balmer line and panchromatic sed - based sfrs for @xmath0 galaxies . for this comparison we used 17 star - forming galaxies selected from the mosfire deep evolution field ( mosdef ) survey , with @xmath1 detections for h@xmath2 and at least two ir bands ( _ spitzer_/mips 24@xmath3 m and _ herschel_/pacs 100 and 160@xmath3 m , and in some cases _ herschel_/spire 250 , 350 , and 500@xmath3 m ) . the galaxies have total ir ( @xmath4 m ) luminosities of @xmath5 and star - formation rates ( sfrs ) of @xmath6 . we fit the uv - to - far - ir seds with flexible stellar population synthesis ( fsps ) models which include both stellar and dust emission and compare the inferred sfrs with the sfr(h@xmath2,h@xmath7 ) values corrected for dust attenuation using balmer decrements . the two sfrs agree with a scatter of 0.17 dex . our results imply that the balmer decrement accurately predicts the obscuration of the nebular lines and can be used to robustly calculate sfrs for star - forming galaxies at @xmath0 with sfrs up to @xmath8 . we also use our data to assess sfr indicators based on modeling the uv - to - mid - ir seds or by adding sfr(uv ) and sfr(ir ) , for which the latter is based on the mid - ir only or on the full ir sed . all these sfrs show a poorer agreement with sfr(h@xmath2,h@xmath7 ) and in some cases large systematic biases are observed . finally , we show that the sfr and dust attenuation derived from the uv - to - near - ir sed alone are unbiased when assuming a delayed exponentially declining star - formation history .

astro-ph0411755

c

sn 1995n is one of the few supernovae detected in x - rays at an age of @xmath49 years . our _ xmm _ observation shows that the unabsorbed x - ray flux of sn 1995n dropped at a value of @xmath18 erg @xmath1 s@xmath2 , about an order of magnitude lower than that of the previous _ asca _ observation performed @xmath46 years before . the decline of the x - ray flux is signalling that sn 1995n probably started to evolve towards the remnant stage . interpreting the evolution of the x - ray light curve is not straigthforward . a complex scenario in which a two - phase ( clumpy and smooth ) csm contributes to the observed x - ray emission is consistent with the available data ( see z04 ) . the epic spectrum of sn 1995n shows statistically significant evidence for the presence of two distinct thermal ( mekal ) components at temperatures of 0.8 and 9.5 kev , respectively . in the standard model of ejecta / wind interaction @xcite , these represent the temperatures of the gas between the contact discontinuity and the reverse / forward shock . the temperature of the hotter phase is similar to the temperature of the single - component spectral fit of the _ asca _ data performed by @xcite . within the assumptions of the standard model , we can derive the exponent of the ejecta density distribution @xmath19 from the expression @xmath20 , where @xmath21 is the exponent of the cms density distribution @xcite . assuming a constant and homogeneous stellar wind ( @xmath22 ) , from the values of the temperatures @xmath23 and @xmath24 inferred from the x - ray spectrum , we obtain @xmath25 . benetti , s. , bouchet , p. , schwarz , h. , 1995 , iau circ . 6170 chevalier , r.a . , fransson , c. , 1994 , apj , 420 , 268 fox , d.w . , lewin , w.h.g . , fabian , a. , et al . , 2000 , mnras , 319 , 1154 fransson , c. , lundqvist , p. , chevalier , r.a . , 1996 , apj , 461 , 993 lewin , w.h.g . , zimmermann , h.u . , aschenbach , b. , 1996 , iau circ . 6506 pastorello , a. , aretxaga , i. , zampieri , l. , et al . 2004 , this proceedings van dyk , s.d . , sramek , r.a . , weiler , k.w . , et al . , 1996 , iau circ . 6386 zampieri , l. , mucciarelli , p. , pastorello , a. , et al . , 2004 , mnras submitted

we present the results of a new _ xmm - newton _ observation of the interacting supernova 1995n , performed on july 27 , 2003 . we find that the 0.2 - 10.0 kev flux has dropt at a level of @xmath0 erg @xmath1 s@xmath2 , about one order of magnitude lower than that of a previous _ asca _ observation performed on january 1998 . the x - ray spectral analysis shows statistically significant evidence for the presence of two distinct components , that can be modeled with emission from optically thin , thermal plasmas at different temperatures . from these temperatures we derive that the exponent of the ejecta density distribution is @xmath3 . sn 1995n , discovered on may 1995 several months after the explosion @xcite , is of special interest in the context of circumstellar medium ( csm ) interacting supernovae . the epoch of explosion is not known , but was estimated to be about 10 months before its optical discovery @xcite .

we present the results of a new _ xmm - newton _ observation of the interacting supernova 1995n , performed on july 27 , 2003 . we find that the 0.2 - 10.0 kev flux has dropt at a level of @xmath0 erg @xmath1 s@xmath2 , about one order of magnitude lower than that of a previous _ asca _ observation performed on january 1998 . the x - ray spectral analysis shows statistically significant evidence for the presence of two distinct components , that can be modeled with emission from optically thin , thermal plasmas at different temperatures . from these temperatures we derive that the exponent of the ejecta density distribution is @xmath3 . sn 1995n , discovered on may 1995 several months after the explosion @xcite , is of special interest in the context of circumstellar medium ( csm ) interacting supernovae . it is hosted in the ( ib(s)m pec ) galaxy mcg-02 - 38 - 017 , at a distance of @xmath4 24 mpc . the epoch of explosion is not known , but was estimated to be about 10 months before its optical discovery @xcite .

1301.5891

i

we are interested in numerical solutions of the fully nonlinear elliptic monge - ampre equation @xmath1 on a convex bounded domain @xmath2 of @xmath3 with boundary @xmath4 . the unknown @xmath5 is a real valued function and @xmath6 are given functions with @xmath7 in the non degenerate case and @xmath8 in the degenerate case . we will also assume that @xmath9 and @xmath10 in @xmath11 . starting with @xcite , interest has grown for finite element methods which are able to capture non smooth solutions of second order fully nonlinear equations . for smooth solutions , the problem was studied in the context of @xmath0 conforming approximations by b@xmath12hmer @xcite and in the context of lagrange elements by brenner and al @xcite . non smooth solutions can be handled in the context of the vanishing moment methodology @xcite which is a singular perturbation of . in this paper we give numerical evidence that @xmath0 conforming approximations of a natural variational formulation of converge for non smooth solutions of the two dimensional problem . this is achieved by discretizing new iterative methods we introduce . we establish the convergence of the iterative methods under the assumption that the discrete problem has a convex solution . we prove that such a solution exists when has a smooth convex solution . we do not assume that has a smooth solution for our iterative methods to converge . the existence of a convex solution to the discrete problem in the general case and the convergence of the discretization will be addressed in a subsequent paper . even with such an existence result , it is still a non trivial task to solve the discrete nonlinear systems in situations where has a non smooth solution . this paper addresses this issue . we refer to @xcite for a review of numerical methods for fully nonlinear equations of monge - ampre type . the main technical innovation of this paper is the proof that in the context of @xmath0 conforming approximations , discrete functions near a strictly convex solution are strictly convex . this explains why convexity did not need to be imposed explicitly in some previous studies . newton s method remains the most appropriate iterative method for solving the discrete nonlinear equations when has a smooth convex solution . we give a new proof of convergence of newton s method in the context of @xmath0 conforming approximations . the results of this paper extend easily to finite dimensional spaces of piecewise smooth @xmath0 functions provided that the approximation property and inverse estimates below hold . our results can be described in the general context of discretizations by @xmath0 elements of iterative methods for a general nonlinear elliptic equation @xmath13 . in the case of the monge - ampre equation , @xmath14 . we first describe the iterative methods at the continuous level . however , we will not address convergence at the continuous level . as an initial guess we take the solution of the poisson equation @xmath15 in @xmath16 on @xmath4 . we assume that @xmath17 differentiable and consider the sequence of problems @xmath18 where @xmath19 is a linear operator which can be taken as @xmath20 where @xmath21 is the identity operator or @xmath22 where @xmath23 is the laplace operator and @xmath24 is a parameter . pseudo transient continuation methods @xcite form a general class of methods for solving nonlinear singular equations . in the case of the monge - ampre equation , the method consists in solving the sequence of approximate problems @xmath25 here @xmath26 denotes the matrix of cofactors of the matrix @xmath27 . given @xmath24 , we consider the sequence of iterates @xmath28 this can be interpreted as an euler discretization of the pseudo time dependent equation @xmath29 or as a laplacian preconditioner of a simple pseudo time marching algorithm , @xcite @xmath30 see also a remark in @xcite . to the author s best knowledge , this is the first time the pseudo transient continuation method and the time marching method are used to indicate numerically convergence to viscosity solutions of finite element type methods for the monge - ampre equation . the methods we propose can be used in the context of different types of discretizations allowing us in particular to treat more easily non - rectangular domains . the methods can be accelerated with fast poisson solvers and multigrid methods . this latter property is even more striking for the time marching method as its implementation requires only having access to a multigrid poisson solver . although the theory of the monge - ampre equation has concentrated on convex solutions , one can equally focus on concave solutions . we found out that is better able to capture concave solutions . it is easy to implement , requiring only a poisson solver . for example one can capture weak solutions of the monge - ampere equation by simply discretizing with the standard lagrange finite elements . the time marching method can also be applied to fully nonlinear equations such as the pucci equation where @xmath17 is not differentiable . in summary the pseudo transient continuation methods are better for smooth solutions and singular solutions on a coarse mesh . otherwise the method of choice is the time marching method . we organize the paper as follows : in the second section we introduce some notation and prove the key result that discrete functions near a strictly convex solution are strictly convex . we introduce the natural variational formulation of and state an existence and uniqueness result for the discrete problem . the result can be inferred from the ones in @xcite . we give new proofs in section [ existence ] . as a corollary the discrete variational problem has a convex solution when has a smooth convex solution . we study the pseudo transient continuation methods in section [ continuation ] . a special case is newton s method for which we prove a quadratic convergence rate . the time marching methods are studied in section [ time ] . the last section is devoted to numerical results . we give a brief description of the spline element method which is used for the computations and offer heuristics about why our methods appear to preserve convexity .

we present two numerical methods for the fully nonlinear elliptic monge - ampre equation . the first is a pseudo transient continuation method and the second is a pure pseudo time marching method . the methods are proved to converge to a convex solution of a natural discrete variational formulation with @xmath0 conforming approximations . the assumption of existence of a convex solution to the discrete problem is proven for smooth solutions of the continuous problem and supported by numerical evidence for non smooth solutions .

we present two numerical methods for the fully nonlinear elliptic monge - ampre equation . the first is a pseudo transient continuation method and the second is a pure pseudo time marching method . the methods are proved to converge to a convex solution of a natural discrete variational formulation with @xmath0 conforming approximations . the assumption of existence of a convex solution to the discrete problem is proven for smooth solutions of the continuous problem and supported by numerical evidence for non smooth solutions .

astro-ph0302397

i

bl lacertae objects are an extreme type of active galactic nuclei ( agn ) , whose hallmark is their featureless " optical spectrum . by definition , any emission lines present must have rest @xmath0 ; e.g. , @xcite . bl lacs are a member of the blazar class ; and like other blazars , they are characterized by their rapid variability , polarized optical and radio emission and their flat - spectrum radio emission . see @xcite for an excellent summary of their properties . due to their luminous emission at these wavelengths , bl lacs have been primarily discovered via x - ray and radio surveys ; thus , traditionally they have been labeled as radio - selected and x - ray - selected ( rbls and xbls respectively ) . in recent years this terminology has given way to a more physically meaningful classification based upon the overall spectral energy distribution ( sed ) of the object . in low - energy - peaked " blazars ( lbls ) , the peak of the synchrotron radiation occurs at radio / ir wavelengths , whereas in high - energy - peaked " blazars ( hbls ) this peak occurs in the uv / x - ray . historically , optical surveys have not been efficient in discovering bl lacs @xcite . it is therefore not surprising that , until recently , known bl lacs have shown a bimodal distribution of logarithmic x - ray to radio flux ratios , log(@xmath1 ) from 1 kev to 5 ghz , with an approximate dividing line defined by log(@xmath1 ) @xmath2 @xcite . for the most part xbls are hbls and rbls are lbls , although exceptions do exist ( e.g. , mkn 501 is an hbl in the 1jy rbl sample ) . we choose to use the term hbl when referring to the bl lacs studied herein because all were chosen with a log(@xmath1 ) @xmath3 criterion . new surveys , e.g. , the rosat - green bank ( rgb ) survey @xcite and the dxrbs survey @xcite , have found bl lacs with intermediate log(@xmath1 ) values , indicating a continuum of seds in bl lacs and likely rendering the lbl / hbl terminology obsolete . the detailed properties of these new bl lac objects with intermediate log(@xmath1 ) values are not yet well - known . so , although lbls and hbls have different observed properties ( * ? ? ? * and references therein ) , it is not yet known whether lbls and hbls are distinct classes of agn or merely extremes of a continuum of properties for a single class of agn . we have therefore chosen to include three intermediate objects from the rgb sample in our sample of study . most bl lacs are believed to be low - power radio galaxies whose jet axes are oriented at small angles to the line of sight ; and as such their jets are relativistically beamed , e.g. , @xcite . it has been proposed that hbls and lbls are both beamed , low - luminosity fr - i radio galaxies , and that the observed differences between the two classes is a result of orientation . in this unification model , hereafter the orientation " model , hbls are believed to be viewed further from the jet axis than lbls @xcite . the comparable x - ray luminosities for hbls and lbls require that either the beam pattern or physical jet opening angle for the x - ray emission is larger than than for the radio emission , e.g. , @xcite . several observed properties are consistent with this hypothesis . compared to lbls , hbls are more numerous , their cores are less radio luminous , and they are less optically variable @xcite . hbls also emit less compact radio emission @xcite , contain larger fractions of starlight in the optical @xcite , and have smaller degrees of optical polarization , often with a preferred optical polarization angle , @xmath4 @xcite . however , several observed properties which should be independent of orientation , e.g. , observed evolution , optical emission - line strengths and extended radio powers , do not agree between hbls and lbls , indicating that orientation alone is insufficient to explain the observed distinctions between the two classes @xcite . in fact , many lbls appear to be beamed , high - luminosity fr - iis ; and at least one is a gravitationally lensed object , the smallest einstein ring " object 1jy 0218 + 357 @xcite . the picture seems to be more clear for hbls , whose properties are very consistent with being beamed fr - is @xcite . several observations support this picture , e.g. , extended radio luminosity and morphology @xcite , host galaxy luminosity and morphology @xcite , and comparative space densities and luminosity functions @xcite . alternatively , it has also been suggested that the difference between lbls and hbls lies not in orientation , but in the high - energy cutoff in their energy distributions , such that hbls and lbls represent a single family of objects with a smooth energy distribution followed by a sharp cutoff . for lbls this cutoff occurs in the near - ir / optical and for hbls it is at uv / x - ray or higher energies @xcite . in this model , hereafter the energy - cutoff " model , hbls have intrinsically lower radio luminosities than lbls , and strong selection effects explain why most known bl lacs are of the hbl variety . observational studies of bl lacs at radio wavelengths have proven to be an effective test of unification models for two reasons . first , the kpc - scale extended radio flux is likely unbeamed , and is therefore indicative of the actual agn power ; and second , the core and parsec - scale extended flux is highly beamed , and is therefore strongly dependent on the orientation and relativistic nature of the jet . if hbls are seen further off axis than lbls , radio images will reveal several distinct trends . first , relativistic doppler boosting and apparent proper motion are strongly sensitive to the orientation angle and bulk lorentz factor of the jet . thus , if seen close to their jet axis , lbls should be more core - dominated , show more instances of superluminal motion and have larger jet to counter - jet brightness ratios . and if hbls and lbls share the same parent population , both should have similar jet lorentz factors . second , geometrical projection effects will cause jets with intrinsically small bends to appear highly distorted when seen close to the line of sight . thus , the projected jet position angle ( pa ) in these highly inclined objects is very sensitive to the jet structure . it is known that lbls show a wide range of parsec- and kpc - scale jet misalignment angles ( @xmath5 @xmath6 ) , presumably from a knotty " or helical jet seen close to the line of sight @xcite . if hbls are seen further off - axis than lbls , geometrical projection effects will cause the parsec- and kpc - scale projected jet pas of hbls to be more aligned than lbls . if the energy - cutoff " model is correct and there is no orientation bias , lbls and hbls should show similar parsec- and kpc - scale radio structure , similar distributions of parsec- and kpc - scale jet misalignment , assuming they share the same parent population . but since lbls are generally more luminous than hbls @xcite , their parsec - scale structures may differ intrinsically from hbls . in this paper we present deep vla and first - epoch vlba observations of a sample of fifteen bl lacs which span the full range of log(@xmath1 ) seen in hbls ( 2 ) . these maps are used to compare the parsec and kpc - scale structure of these objects . in 3 we discuss the results of these observations , compare them to similar studies of lbls and discuss their implications for unification models . as these are only the first epoch of observations , proper motions of jet components are not yet available ; thus we consider only the alignment and structure of the parsec - scale jets . in 4 we present the conclusions .

the sample was chosen to span the range of logarithmic x - ray to radio flux ratios observed in hbls . as this is only the first epoch of observations , proper motions of jet components are not yet available ; thus we consider only the structure and alignment of the parsec- and kiloparsec - scale jets . like most low - energy - peaked bl lacs ( lbls ) , our hbl sample shows parsec - scale , core - jet morphologies and compact , complex kiloparsec - scale morphologies .

we present vla and first - epoch vlba observations that are part of a program to study the parsec - scale radio structure of a sample of fifteen high - energy - peaked bl lacs ( hbls ) . the sample was chosen to span the range of logarithmic x - ray to radio flux ratios observed in hbls . as this is only the first epoch of observations , proper motions of jet components are not yet available ; thus we consider only the structure and alignment of the parsec- and kiloparsec - scale jets . like most low - energy - peaked bl lacs ( lbls ) , our hbl sample shows parsec - scale , core - jet morphologies and compact , complex kiloparsec - scale morphologies . some objects also show evidence for bending of the jet 1020pc from the core , suggesting interaction of the jet with the surrounding medium . whereas lbls show a wide distribution of parsec- to kpc - scale jet misalignment angles , there is weak evidence that the jets in hbls are more well - aligned , suggesting that hbl jets are either intrinsically straighter or are seen further off - axis than lbl jets .

astro-ph0302397

c

we have completed vla and first - epoch vlba observations as part of a program to study the parsec - scale radio structure of a sample of fifteen hbls . all of the resolved objects are core dominated in the vla and vlba maps ; and they show a core - jet morphology on parsec scales , similar to lbls and core - dominated quasars . some sources show a well - collimated , parsec - scale jet with discrete components , whereas others show a diffuse jet with a wide opening angle . some objects also show evidence for the interaction of their parsec - scale jets with a dense gas environment . further modeling is warranted . while lbls show a wide distribution of parsec- and kpc - scale jet alignment angles , most of the hbls considered here have well - aligned jets , suggesting either that hbl jets are seen further off - axis than lbl jets , or that hbl jets are intrinsically straighter . complex bend geometries , such as those proposed by @xcite , are not necessary to explain the observed distributions of misalignment angles seen in our lbl or hbl samples . there is a hint in our data that extreme hbls ( log(@xmath1 ) @xmath52 ) have intrinsically straight jets that are viewed well off - axis in that all four extreme hbls in our sample have very small ( @xmath55% ) misalignment angles . observations of other extreme hbls are needed to test this preliminary result . while it is now clear that orientation alone can not be invoked to unify hbls and lbls @xcite , selection effects may nonetheless cause lbls to be seen closer to the jet axis than hbls . for example , lbls show optical emission lines which are several orders of magnitude more luminous than hbls . thus lbls may require larger doppler factors to sufficiently boost the jet continuum relative to the emission lines to remain within the bl lac spectral criterion ( rest @xmath0 ) . similarly , the bright radio flux limit as well as the flat radio spectrum criterion of the 1jy sample may also bias lbls towards more highly beamed objects , whereas the x - ray surveys used to draw our hbl sample do not have any radio - based selection criteria . thus , lbls may be systematically more beamed than hbls even though they may not necessarily share the same parent population . aurire , m. 1982 , 109 , 301 . abraham , r.g . , crawford , c.s . & mchardy , i.m . 1991 252 , 482 . appl , s. , sol , h. & vicente , l. 1996 310 , 419 . antonucci , r.r.j . & ulvestad , j.s . 1985 294 , 158 . bondi , m. , march , m.j.m . , dallacasa , d. & stanghellini , c. 2001 325 , 1109 . briggs , d. 1995 , phd dissertation , new mexico institute of mining and technology . brinkmann , w. , siebert , j. , kollgaard , r.i . & thomas , h .- c . 1996 313 , 356 . cassaro , p. , stanghellini , c. , dallacasa , d. , bondi , m. & zappal , r.a . 2002 381 , 378 . celotti , a. , maraschi , l. , ghisellini , g. , caccianiga , a. & maccacaro , t. 1993 416 , 118 . conway , j.e . & murphy , d.w . 1993 411 , 89 . conway , j.e . & wrobel , j.m . 1995 439 , 98 . cohen , m.h . 1988 , in bl lac objects , ed . l. maraschi , t. maccacaro & m .- h . ulrich ( heidelberg : springer - verlag ) , 13 . de young , d.s . 1991 371 , 69 . fanaroff , b.l . & riley , j.m . 1974 167 , 31 . fey , a.l . & charlot , p. 1997 fey , a.l . & charlot , p. 2000 fleming , t.a . , green , r.f . , jannuzi , b.t . , liebert , j. , smith , p.s . & fink , h. 1993 106 , 1729 . fomalont , e.b . , frey , s. , paragi , z. , gurvits , l.i . & scott , w.k . , taylor , a.r . , edwards , p.g . & hirabayshi , h. 2000 131 , 95 . fossati , g. , maraschi , l. , celotti , a. , comastri , a. & ghisellini , g. 1998 299 , 433 . gabuzda , d.c . , pushkarev , a.b . & cawthorne , t.v . 1999 307 , 725 . gabuzda , d.c . & cawthorne , t.v . 2000 319 , 1056 . gabuzda , d.c . , pushkarev , a.b . & cawthorne , t.v . 2000 319 , 1109 . ghisellini , g. , padovani , p. celotti , a. & maraschi , l. 1993 407 , 65 . giommi , p. & padovani , 268 , l51 . gmez , j.l . , guirado , j.c . , agudo , i. , marscher , a.p . , alberdi , a. , marcaide , j.m . & gabuzda , d.c . 2001 328 , 873 . hough , d.h . , vermeulen , r.c . , readhead , a.c.s . , cross , l.l . , barth , e.l . , yu , l.h . , beyer , p.j . & phifer , e.m . 2002 123 , 1258 . jannuzi , b.t . 1990 phd thesis , u. of arizona . jannuzi , b.t . , smith , p.s . & elston , r. 1993 85 , 265 . jannuzi , b.t . , elston , r. and smith , p. 1994 428 , 130 . kellermann , k.i . , vermeulen , r.c . , zensus , j.a . & cohen , m.h . 1998 115 , 1295 . kollgaard , r.i . , wardle , j.f.c . , roberts , d.h . & gabuzda , d.c . 1992 104 , 1687 . kollgaard , r.i . , gabuzda , d.c . and feigelson , e.d . 1996 460 , 164 . laurent - muehleisen , s.a . , kollgaard , r.i . , moellenbrock , g.a . & feigelson , e.d . 1993 106 , 875 . laurent - muehleisen , s.a . , kollgaard , r.i . , feigelson , e.d . , brinkmann , w. & siebert , j. 1999 525 , 127 . ma , c. , arias , e.f . , eubanks , t.m . , fey , a.l . , gontier , a .- m . , jacobs , c.s . , sovers , o.j . , archinal , b.a . & charlot , p. 1998 116 , 516 . morris , s.l . , stocke , j.t . , gioia , i.m . , schild , r.e . , wolter , a. & della ceca , r. 1991 380 , 49 . nilsson , k. , takalo , l.o . , pursimo , t. , sillanp , a. , heidt , j. , wagner , s.j . , laurent - muehleisen , s.a . & brinkmann , w. 343 , 81 . odea , c.p . , baum , s.a . , stanghellini , c. , dey , a. , van breugel , w. , deustua , s. & smith , e.p . 1992 104 , 1320 . orr , m.j.l . & browne , i.w.a . 1982 200 , 1067 . padovani , p. & urry , c.m . 1990 356 , 75 . padovani , p. & giommi , 444 , 567 . pearson , t.j . & readhead , a.c.s . 1988 328 , 114 . perlman , e.s . & stocke , j.t . 1993 406 , 430 . perlman , e.s . & stocke , j.t . 1994 108 , 56 . perlman , e.s . , stocke , j.t . , schachter , j.f . , elvis , m. , ellingson , e. , urry , c.m . , potter , m. , impey , c.d . & kolchinsky , p. 1996 104 , 251 . perlman , e.s . , padovani , p. , giommi , p. , sambruna , r. , jones , l.r . , tzioumis , a. & reynolds , j. 1998 aj 115 , 1253 . perlman , e.s . , schachter , j.f . & stocke , j.t . 1999 , in prep . rector , t.a . , stocke , j.t . , perlman , e.s . , morris , s.l . & gioia , i.a . 2000 120 , 1626 . rector , t.a . & stocke , j.t . 2001 122 , 565 . rector , t.a . & stocke , j.t . 2002 , in prep . ros , e. , marcaide , j.m . , guirado , j.c . & prez - torres , m.a . 2001 376 , 1105 . sambruna , r.m . maraschi , l. & urry , m. 1996 463 , 444 . scarpa , r. , urry , c.m . , falomo , r. , pesce , j.e . , webster , r. , odowd , m. & treves , a. 1999 521 , 134 . schwartz , d.a . , brissenden , r.j.v . , tuohy , i.r . , feigelson , e.d . , hertz , p.l . & remillard , r.a . 1989 baas 21 , 777 . shen , z .- q . , wan , t .- s . , moran , j.m . , jauncey , d.l . , reynolds , j.e . , tzioumis , a.k . , gough , r.g . , ferris , r.h . , sinclair , m.w . , jiang , d .- r . , hong , x .- y . , liang , s .- g . , costa , m.e . , tingay , s.j . , mcculloch , p.m. , lovell , j.e.j . , king , e.a . , nicolson , g.d . , murphy , d.w . , meier , d.l . , van ommen , t.d . & white , g.l . 1997 114 , 1999 . shen , z .- q . , wan , t .- s . , moran , j.m . , jauncey , d.l . , reynolds , j.e . , tzioumis , a.k . , gough , r.g . , ferris , r.h . , sinclair , m.w . , jiang , d .- r . , hong , x .- y . , liang , s .- g . , edwards , p.g . , costa , m.e . , tingay , s.j . , mcculloch , p.m. , lovell , j.e.j . , king , e.a . , nicolson , g.d . , murphy , d.w . , meier , d.l . , van ommen , t.d . , edwards , p.g . & white , g.l . 1998 1115 , 1357 . shepherd , m.c . 1997 , in asp conf . 125 , astronomical data analysis software and systems iv , eds . g. hunt & h.f . payne ( san francisco : asp ) , 77 . stickel , m. , padovani , p. , urry , c.m . , fried , j.w . & khr , h. 1991 374 , 431 . stocke , j.t . 1989 , in bl lac objects , ed . l. maraschi , t. maccacaro & m .- h . ulrich ( heidelberg : springer - verlag ) , 242 . stocke , j.t . , morris , s.l . , gioia , i.m . , maccacaro , t. , schild , r. , wolter , a. , fleming , t.a . & henry , j.p . 1991 76 , 813 . ulvestad , j.s . & antonucci , r.r.j . 1986 92 , 6 . urry , c.m . , padovani , p. & stickel , m. 1991 382 , 501 . urry , c.m . & padovani , p. 1995 107 , 803 . wang , z. , wiita , p.j . & hooda , j.s . 2000 534 , 201 . wardle , j.f.c . , moore , r.l . & angel , j.r.p . 1984 279 , 93 . wurtz , r. , stocke , j.t . & yee , h.k.c . 1996 103 , 109 . rllcl 1es 0033 + 595 & 00:35:52.644 & + 59:50:04.59 & -4.07 & 0.086 + 1es 0229 + 200 & 02:32:48.616 & + 20:17:17.45 & -4.23 & 0.139 + 1es 0414 + 009 & 04:16:52.494 & + 01:05:23.91 & -3.88 & 0.287 + 1es 0647 + 250 & 06:50:46.489 & + 25:02:59.63 & -4.09 & 0.203 : + rgb 0656 + 426 & 06:56:10.72 & + 42:37:02.7 & -5.49 & 0.059 + 1es 0806 + 524 & 08:09:49.188 & + 52:18:58.24 & -4.69 & 0.136 + 1es 1028 + 511 & 10:31:18.524 & + 50:53:35.79 & -3.96 & 0.359 : + 1es 1212 + 078 & 12:15:10.977 & + 07:32:04.67 & -5.14 & 0.135 + 1e 1415 + 259 & 14:17:56.680 & + 25:43:26.24 & -4.56 & 0.237 + rgb 1427 + 238 & 14:27:00.392 & + 23:48:00.04 & -5.60 & + 1es 1553 + 113 & 15:55:43.044 & + 11:11:24.37 & -4.99 & 0.360 + 1es 1741 + 196 & 17:43:57.838 & + 19:35:08.99 & -4.89 & 0.083 + rgb 1745 + 398 & 17:45:37.71 & + 39:51:31.8 & -5.66 & 0.267 + 1es 1959 + 650 & 19:59:59.852 & + 65:08:54.69 & -4.43 & 0.048 + 1es 2344 + 514 & 23:47:04.838 & + 51:42:17.88 & -4.87 & 0.044 + rrrrrrr 1es 0033 + 595 & 90.4 & @xmath56 & + 62 & 39.7 & @xmath57 & + 65 + 1es 0229 + 200 & 51.8 & @xmath58 & 180 & 22.7 & @xmath59 & + 170 + 1es 0414 + 009 & & & + 63 & 36.4 & @xmath60 & + 68 + 1es 0647 + 250 & & & & 46.0 & @xmath61 & + rgb 0656 + 426 & 252.8 & @xmath62 & @xmath63 & & & @xmath64 + 1es 0806 + 524 & 189.1 & @xmath65 & & 111.2 & @xmath66 & + 13 + 1es 1028 + 511 & 215.7 & @xmath67 & & 22.4 & @xmath68 & + 1es 1212 + 078 & 87.4 & @xmath69 & + 178 & 36.3 & @xmath70 & + 92 + 1e 1415 + 259 & & & & 8.7 & @xmath71 & + rgb 1427 + 238 & 331.7 & @xmath72 & @xmath28 & & & + 1es 1553 + 113 & 271.1 & @xmath73 & + 160 & 258.7 & @xmath74 & + 48 + 1es 1741 + 196 & & & + 91 & 83.5 & @xmath75 & + 86 + rgb 1745 + 398 & 372.5 & @xmath76 & + 105 & & & @xmath77 + 1es 1959 + 650 & 227.5 & @xmath78 & @xmath79 & 181.7 & @xmath80 & @xmath79 + 1es 2344 + 514 & 217.0 & @xmath81 & + 105 & 109 . & @xmath82 & + 145 +

we present vla and first - epoch vlba observations that are part of a program to study the parsec - scale radio structure of a sample of fifteen high - energy - peaked bl lacs ( hbls ) . some objects also show evidence for bending of the jet 1020pc from the core , suggesting interaction of the jet with the surrounding medium . whereas lbls show a wide distribution of parsec- to kpc - scale jet misalignment angles , there is weak evidence that the jets in hbls are more well - aligned , suggesting that hbl jets are either intrinsically straighter or are seen further off - axis than lbl jets .

we present vla and first - epoch vlba observations that are part of a program to study the parsec - scale radio structure of a sample of fifteen high - energy - peaked bl lacs ( hbls ) . the sample was chosen to span the range of logarithmic x - ray to radio flux ratios observed in hbls . as this is only the first epoch of observations , proper motions of jet components are not yet available ; thus we consider only the structure and alignment of the parsec- and kiloparsec - scale jets . like most low - energy - peaked bl lacs ( lbls ) , our hbl sample shows parsec - scale , core - jet morphologies and compact , complex kiloparsec - scale morphologies . some objects also show evidence for bending of the jet 1020pc from the core , suggesting interaction of the jet with the surrounding medium . whereas lbls show a wide distribution of parsec- to kpc - scale jet misalignment angles , there is weak evidence that the jets in hbls are more well - aligned , suggesting that hbl jets are either intrinsically straighter or are seen further off - axis than lbl jets .

1411.0970

i

strongly coupled matter - light systems , such as exciton - polariton microcavities , have recently witnessed an escalating interest thanks to the simultaneous versatility in manipulating and probing their intrinsic properties . resulting from the strong coupling of cavity photons and quantum well excitons , exciton - polaritons display unique properties deriving from both their constituents for recent reviews see refs . @xcite . in particular , the resonant excitation scheme , where polaritons are directly injected by an external laser near the energy of the lower polariton dispersion , allows to experimentally access a unique accurate tuning of the system parameters , such as the polariton density , current properties , as well as their phase , which is locked to the one of the external pump . much work has been already done both theoretically as well as experimentally for resonantly pumped single component polariton fluids in the pump - only configuration @xcite , i.e. , where only the pump state is occupied and no parametric scattering occurs . particular interest was dedicated in analysing the properties of the collective spectrum of excitations and relate them to the system superfluid behaviour @xcite . here , the spectrum could be classified either as gapped , or linear , or else diffusive - like , in terms of a single parameter , the renormalised pump detuning . interestingly , diffusive - like spectra in non - equilibrium fluids have been shown to be related to parametric scattering and amplification @xcite and to the occurrence of a negative drag force of the single component polariton fluid when scattering against a localised defect @xcite . in this article we consider the case of a spinor , i.e. , two - component , polariton fluid , by explicitly including the polarisation degrees of freedom . it has been observed that , for fixed pump detuning and degree of polarisation , the system undergoes a spin flip and a subsequent hysteresis curve when varying the pump power , promoting this system as an ideal environment where to realise an optical spin switch@xcite or a logical gate@xcite . interestingly , it has been recently demonstrated that spinor polariton systems have tunable cross - spin interaction properties @xcite . in previous recent work @xcite , the spectrum of elementary excitation for a resonantly excited pump - only polariton fluid including the spin degrees of freedom was analysed . in that work , by considering for simplicity only the limiting cases of a purely linearly polarised fluid and a purely circularly polarised one , the focus was on the superfluid properties of the system and the possiblity of reproducing a linear spectrum when the pump detuning compensates exactly the interaction - induced blueshift . here , we propose a pump - probe set - up tailored for analysing the properties of the collective excitation spectrum . we show that in the linear response approximation scheme , valid for a weak probe beam , the spectrum of excitations can be evaluated analytically even in the generic case of an elliptically polarised spinor polariton fluid . further , for fixed interaction strengths , the spectrum can be completely classified in terms of only two experimentally tunable parameters : the mean - field polarisation angle and a rescaled pump detuning . now the number of different class sets of spectra is much larger compared with the single fluid case . yet , depending how the two opposite circular polarisation degrees of freedom mix together in the spectra , we can single out three larger sets where the behaviour of the spectrum intrinsic degree of polarisation is qualitatively different . we name them as _ gapped _ , @xmath0-_diffusive _ , and @xmath1-_diffusive _ ; these regions in the two - parameter space are separated by conditions for which the spectrum can be _ linear_. while for gapped spectra , there is no mixing of opposite circular polarisation degrees of freedom , for both diffusive - like spectra , the mixing is responsible for flips of the intrinsic spin degree of polarisation along the branches . further , we evaluate the system response to the external probe and analyse the properties of the transmitted light and its relations to the collective excitation spectrum . in particular we determine the properties of the spin flip along the branches for diffusive - like spectra and how the spin rotation is larger , the closer the system is to a parametric instability . the paper is organised as follows : in sec . [ sec : model ] , we present the generalised gross - pitaevskii equation that describes the resonantly pumped spinor fluid and briefly discuss its mean - field solutions from existing literature . we introduce the proposed pump - probe scheme in sec . [ sec : linea ] and discuss the linear response approximation scheme . the spectrum of collective excitations is evaluated in sec . [ sec : spect ] , where we derive a `` phase diagram '' classifying all possible spectral categories . in sec . [ sec : eigen ] we derive the emission properties of the intrinsic degree of polarization for each spectrum branch . finally , in sec . [ sec : probe ] , we evaluate the spinor polariton fluid response to the additional probe beam and relate its properties to the spectrum intrinsic properties previously discussed . , are the sphere north and south poles , respectively . in contrast , all linear polarisation states ( parallel to the cavity mirror ) lie on the equator and for those one can choose two alternative basis , either @xmath2 or @xmath3 . a generic elliptically polarised state @xmath4 lies everywhere on the sphere , except at the poles and at the equator , and is defined by a polar angle @xmath5 ( characterising the degree of mixing between circular and linear polarisation ) and an azimuthal angle @xmath6 ( characterising the in - plane polarisation orientation with respect to an @xmath7-linearly - polarised state).,width=307 ]

we propose a pump - probe set - up to analyse the properties of the collective excitation spectrum of a spinor polariton fluid . by using a linear response approximation scheme , we carry on a complete classification of all excitation spectra , as well as their intrinsic degree of polarisation , in terms of two experimentally tunable parameters only , the mean - field polarisation angle and a rescaled pump detuning . we evaluate the system response to the external probe , and show that the transmitted light can undergo a spin rotation along the dispersion for spectra that we classify as diffusive - like . we show that in this case , the spin flip predicted along the dispersion is enhanced when the system is close to a parametrically amplified instability .

we propose a pump - probe set - up to analyse the properties of the collective excitation spectrum of a spinor polariton fluid . by using a linear response approximation scheme , we carry on a complete classification of all excitation spectra , as well as their intrinsic degree of polarisation , in terms of two experimentally tunable parameters only , the mean - field polarisation angle and a rescaled pump detuning . we evaluate the system response to the external probe , and show that the transmitted light can undergo a spin rotation along the dispersion for spectra that we classify as diffusive - like . we show that in this case , the spin flip predicted along the dispersion is enhanced when the system is close to a parametrically amplified instability .

cond-mat0502591

i

since the pioneering papers by watts and strogatz on small - world networks @xcite and barabsi and albert on scale - free networks @xcite , complex networks have received considerable attention as an interdisciplinary subject @xcite . complex networks describe many systems in nature and society , such as internet @xcite , world wide web @xcite , metabolic networks @xcite , protein networks in the cell @xcite , co - author networks @xcite and sexual networks @xcite , most of which share three apparent features : power - law degree distribution , small average path length ( apl ) and high clustering coefficient . in recent years , many evolving models @xcite have been proposed to describe real - life networks . the original ba model @xcite captures the two main mechanisms responsible for the power - law degree distribution of degrees , namely growth and preferential attachment . dorogovtsev , mendes , and samukhin @xcite gave an exact solution for a class of growing network models thanks to the use of a `` master - equation '' . krapivsky , redner , and leyvraz @xcite examined the effect of a nonlinear preferential attachment on network dynamics and topology . amaral et al . @xcite studied models that incorporate aging and cost and capacity constraints in order to explain the deviations from the power - law behavior in several real - life networks . dorogovtsev and mendes @xcite also addressed the evolution of networks with aging of sites . bianconi and barabsi @xcite offered a model addressing the competitive aspect in many real networks such as world wide web . additionally , in real systems a series of microscopic events shape the network evolution , including the addition or rewiring of new edges or the removal of vertices or edges . albert and barabsi @xcite discussed a model that incorporates new edges between existing vertices and the rewiring of edges . dorogovtsev and mendes @xcite considered a class of undirected models in which new edges are added between old vertices and existing edges can be removed . although it is now established that preferential attachment can explain the power - law characteristic of networks , there is a wide range of microscopic alternative mechanisms that could affect the evolution of growing networks and still lead to the observed scale - free topologies . kleinberg et al . @xcite and kumar et al . @xcite proposed copying mechanisms motivated by the desire to explain the power - law degree distribution of the world wide web . chung et al . @xcite introduced also a duplication model for biological networks . krapivsky and render @xcite presented edge redirection mechanisms which are mathematically equivalent to the model of kumar et al @xcite . inspired by citation networks vzquez proposed in @xcite the walking mechanism . actually scale - free networks can be created by various methods . comellas , fertin and raspaud @xcite introduced a category of graphs via a recursive construction . specific recursive and general scale - free constructions are given also in @xcite and scale - free trees ( without clustering ) in @xcite . zhou et al . construct in @xcite an integer network using a pure mathematical method . in relation to the problem of apollonian packing , a two - dimensional example of which is shown in fig . 1 , andrade et al . introduced apollonian networks @xcite which were also proposed by doye and massen in @xcite . it should be pointed out that high - dimensional apollonian networks were already introduced in @xcite , but in this work the emphasis is placed on two - dimensional apollonian networks and to provide a model to help understanding the energy landscape networks . zhang et al . in @xcite offer a simple general algorithm producing high - dimensional apollonian networks and derive in detail analytical expressions for their order , size , degree distribution , clustering coefficient and diameter . inspired also by the apollonian packing , zhou et al . @xcite proposed a simple rule that generates random two - dimensional apollonian networks with very large clustering coefficient and very small apl . in this paper , motivated by high - dimensional apollonian packings , we present a simple iterative algorithm for high - dimensional random apollonian networks ( hdran ) which extends the idea introduced in @xcite for dimension two to any dimension . the algorithm can concretize the problems of abstract high - dimensional random apollonian packings . using the algorithm we determine relevant characteristics of hdran : scale - free degree distribution and large clustering coefficient which depend on the dimension of the apollonian packing . based on the algorithm , we estimate also that the average path length of the networks increases logarithmically with the number of vertices . therefore , these networks ( hdran ) have a small - world scale - free topology .

we propose a simple algorithm which produces a new category of networks , high dimensional random apollonian networks , with small - world and scale - free characteristics . we estimate also analytically that the average path length of the networks increases at most logarithmically with the number of vertices .

we propose a simple algorithm which produces a new category of networks , high dimensional random apollonian networks , with small - world and scale - free characteristics . we derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension of the network . the values obtained for these parameters are in good agreement with simulation results and comparable to those coming from real networks . we estimate also analytically that the average path length of the networks increases at most logarithmically with the number of vertices . complex networks , scale - free networks , small - world networks , disordered systems , networks 89.75.da,89.75.fb,89.75.hc

1512.06276

i

a promising platform to quantum simulate such novel phenomena of condensed matter physics as topological insulators @xcite and superconductors @xcite is the spin - orbit coupled cold atomic systems @xcite which have drawn great attention in recent years . raman dressed coupling between atomic pseudo - spin and its linear momentum was first realized by lin and co - workers @xcite in a two - component ( spin-1/2 ) @xmath0rb condensate , and were soon generalized to spin-1/2 degenerate fermi gases of @xmath1k @xcite and @xmath2li @xcite . in this scheme , photon recoil associated with the raman transition facilitated by two counter - propagating laser beams changes the center - of - mass momentum of the atom when it jumps from one spin state to the other . very recently , the same spin - orbit coupling ( soc ) scheme was achieved in a spin-1 condensate @xcite . in general , the physics becomes richer in larger spin systems @xcite simply because more spin states are involved and more control knobs can be utilized . when the two laser beams that induce the raman transition are made to co - propagating , but possess different orbital angular momenta ( e.g. , in the form of laguerre - gaussian , or lg , beams ) @xcite , the raman transition will be accompanied by a transfer of the orbital angular momentum ( oam ) , instead of the linear momentum , to the atom this situation has been achieved in experiment where this transfer of oam from photon to the atom was exploited to create spin textures in a spinor condensate @xcite . several recent theoretical proposals also explored this effect to realize spin - orbit - angular - momentum ( soam ) coupling in spin-1/2 condensate @xcite , where interesting quantum states such as the half skyrmion , the meron pair and the annular striped phase , are predicted to exist . in this paper , we provide our study of the soam coupling in a weakly interacting spin-1 condensate . we show that the interplay between the soam coupling and the quadratic zeeman shift produces a rich phase diagram , and a coherent oscillation between two different many - body quantum phases can be induced by quenching the quadratic zeeman term . our paper is organized as follows . in sec . ii , we present the model and discuss the single - particle properties , particularly the single - particle energy spectrum , of the system . in sec . iii , we focus on the properties of a spin-1 condensate . both the ground state properties and the quench dynamics will be presented . in sec . iv , we provide a brief summary .

we propose a simple model with spin and orbit angular momentum coupling in a spin-1 bose - einstein condensate , where three internal atomic states are raman coupled by a pair of co - propagating laguerre - gaussian beams . we show that the weak interatomic interaction in the condensate produces a rich phase diagram , and that a many - body rabi oscillation between two quantum phases can be induced by a sudden quench of the quadratic zeeman shift .

we propose a simple model with spin and orbit angular momentum coupling in a spin-1 bose - einstein condensate , where three internal atomic states are raman coupled by a pair of co - propagating laguerre - gaussian beams . the resulting raman transition imposes a transfer of orbital angular momentum between photons and the condensate in a spin - dependent way . focusing on a regime where the single - particle ground state is nearly three - fold degenerate , we show that the weak interatomic interaction in the condensate produces a rich phase diagram , and that a many - body rabi oscillation between two quantum phases can be induced by a sudden quench of the quadratic zeeman shift . we carried out our calculations using both a variational method and a full numerical method , and found excellent agreement .

dg-ga9703007

i

the goal of this paper is to understand representation varieties of artin and shephard groups and thereby obtain information on serre s problem of determining which finitely - presented groups are fundamental groups of smooth complex ( not necessarily compact ) algebraic varieties . the first examples of finitely - presented groups which are not fundamental groups of smooth complex algebraic varieties were given by j. morgan @xcite , @xcite . we find a new class of such examples which consists of certain artin and shephard groups . since all artin and shephard groups have quadratically presented malcev algebras , morgan s test does not suffice to distinguish artin groups from fundamental groups of smooth complex algebraic varieties or even from fundamental groups of compact khler manifolds , see [ completion ] . our main results are the following theorems ( artin and shephard groups are defined in [ groups ] below ) : [ moremorgan ] there are infinitely many distinct artin groups that are not isomorphic to fundamental groups of smooth complex algebraic varieties . [ morereps ] for any affine variety @xmath0 defined over @xmath1 there are shephard and artin groups @xmath2 such that a zariski open subset @xmath3 of @xmath0 is biregular isomorphic to zariski open subsets of the character varieties @xmath4 . the subset @xmath3 contains all real points of @xmath0 . the surprising thing about theorem [ moremorgan ] is that artin groups look very similar to the fundamental groups of smooth complex quasi - projective varieties . for example the free group on @xmath5 letters is the fundamental group of @xmath6 with @xmath5 points removed and it is the artin group associated with the graph with @xmath5 vertices and no edges . on the other extreme , take a finite complete graph where each edge has the label @xmath7 . the corresponding artin group is free abelian , hence it is the fundamental group of the quasi - projective variety @xmath8 . yet another example is the braid group which is the artin group associated with the permutation group @xmath9 . theorem [ moremorgan ] is a consequence of theorems [ moremnev ] , [ t3 ] , [ t4 ] , [ t6 ] , [ t7 ] and corollary [ c5 ] below . the main body of this paper is concerned with a study of the following diagram : @xmath10 the arrow @xmath11 is tautological , the arrow @xmath12 is pull - back . the arrows @xmath13 and @xmath14 are defined below . in [ abstract arrangements ] , [ projective arrangements ] we define _ abstract arrangements _ ( essentially bipartite graphs ) and their projective realizations . the space @xmath15 of projective realizations of a given abstract arrangement has a canonical structure of a projective variety ( i.e. projective scheme , see the preceeding footnote ) over @xmath1 . in fact we refine the notion of projective arrangement to obtain the affine variety @xmath16 of _ finite based realizations_. the variety @xmath16 injects as an open subvariety into the _ moduli space _ @xmath17 of the arrangement @xmath18 . our version of mnev s theorem @xcite is then [ moremnev ] for any affine algebraic variety @xmath0 defined over @xmath1 there is a marked based abstract arrangement @xmath18 such that the varieties @xmath16 , @xmath0 are isomorphic . it appears that mnev s theorem @xcite implies only that there is a stable homeomorphism between the sets of real points of @xmath16 and @xmath0 . in addition mnev gives only an outline of the proof . for our application to serre s problem it is critical to prove an isomorphism on the scheme level . the key idea in proving theorem [ moremnev ] is to construct a cross - section @xmath13 to @xmath11 ( over the category of affine varieties ) by showing that one can do `` algebra via geometry '' , that is one can describe elementary algebraic operations over any commutative ring using projective arrangements ( see [ algebraic operations ] ) . this idea actually goes back to the work of von staudt @xcite ( the `` fundamental theorem of the projective geometry '' ) . the abstract arrangement @xmath18 corresponding to @xmath0 under @xmath13 depends upon a choice of affine embedding @xmath19 ( i.e. defining equations ) for @xmath0 and upon a choice of particular formulae describing these equations . moreover we obtain isomorphism @xmath20 of affine schemes over @xmath1 . we will abuse notation and use @xmath13 to denote this isomorphism as well . thus the symbol @xmath13 has two meanings : @xmath21 is the arrangement determined by the above data , but if @xmath22 then @xmath23 is a point in @xmath16 . the meaning to be assigned to @xmath24 will be clear from its argument . we make analogous abuses of notation with mappings @xmath11 and @xmath14 below . the arrow _ alg _ encodes the points and lines of an _ anisotropic projective realization _ ( see [ s14 ] for the definition ) @xmath25 of the abstract arrangement @xmath18 into a representation @xmath26 of the shephard group @xmath27 associated to the abstract arrangement @xmath18 . a choice of a nondegenerate bilinear form on @xmath28 determines anisotropic points and lines in @xmath29 ( we choose the bilinear form so that all real points of @xmath29 are anisotropic ) . each anisotropic point in @xmath29 determines the cartan involution in @xmath30 around this point or the rotation of order @xmath31 having this point as neutral fixed point ( i.e. a fixed point where the differential of the rotation has determinant 1 ) . there are two such rotations of order @xmath31 , we choose one of them . similarly every anisotropic line @xmath32 uniquely determines the reflection in @xmath30 which keeps @xmath32 pointwise fixed . finally one can encode the incidence relation between points and lines in @xmath29 using algebra : two involutions generate the subgroup @xmath33 in @xmath34 iff the neutral fixed point of one belongs to the fixed line of the other , rotations of orders @xmath7 and @xmath31 anticommute iff the neutral fixed point of the rotation of order @xmath31 belongs to the fixed line of the involution , etc . we get a morphism @xmath35 in the following theorem we shall identify @xmath36 with its projection to the character variety @xmath37 [ t3 ] the mapping @xmath38 is a biregular isomorphism onto a zariski open ( and closed ) subvariety @xmath39 . the mapping @xmath14 has the following important property : let @xmath0 be an affine variety defined over @xmath1 and @xmath40 be a rational point . then we can choose an arrangement @xmath18 so that @xmath41 corresponds to a realization @xmath42 under the mapping @xmath43 such that the image of the representation @xmath44 is a finite subgroup of @xmath34 with trivial centralizer . there is an artin group @xmath45 and a canonical epimorphism @xmath46 associated with the shephard group @xmath27 . it remains to examine the morphism @xmath47 given by pull - back of homomorphisms . [ t4 ] suppose that @xmath18 is an admissible based arrangement . then the morphism @xmath12 is an isomorphism onto a union of zariski connected components . [ c5 ] the variety @xmath48 inherits all the singularities of the representation variety @xmath49 corresponding to points of @xmath50 , whence ( since all real points of @xmath51 are anisotropic ) to all singularities of @xmath51 at real points . combining corollary [ c5 ] with theorem [ moremnev ] we obtain [ t6 ] let @xmath0 be an affine algebraic variety defined over @xmath1 and @xmath40 be a rational point . then there exists an admissible based arrangement @xmath18 and a representation @xmath52 with finite image such that the ( analytical ) germ @xmath53)$ ] is isomorphic to @xmath54 . thus the singularities of representation varieties of artin groups at representations with finite image are at least as bad as germs of affine varieties defined over @xmath1 at rational points . on the other hand , if @xmath55 is a ( connected ) smooth complex algebraic variety and @xmath2 is an algebraic lie group , the singularities of @xmath56 at representations with finite image are severely limited by theorem [ t7 ] below . we will need the following let @xmath57 be a real or complex analytic space , @xmath58 and @xmath2 a lie group acting on @xmath57 . we say that there is a local _ cross - section _ through @xmath59 to the @xmath2-orbits if there is a @xmath2-invariant open @xmath3 of @xmath59 and a closed analytic subspace @xmath60 such that the natural map @xmath61 is an isomorphicm of analytic spaces . [ t7 ] suppose @xmath55 is a smooth connected complex algebraic variety , @xmath2 is an algebraic lie group and @xmath62 is a representation with finite image . then the germ @xmath63 is analytically isomorphic to a quasi - homogeneous cone with generators of weights @xmath64 and @xmath7 and relations of weights @xmath65 and @xmath66 . in the case there is a local cross - section through @xmath67 to @xmath68-orbits , then the same conclusion is valid for the quotient germ @xmath69)\quad .\ ] ] we present two proofs of this result : in [ hain s theorem ] we deduce it from a theorem of r. hain @xcite and , since hain s paper is still in preparation , in [ direct ] we also deduce theorem [ t7 ] from results of j. morgan @xcite on sullivan s minimal models of smooth complex algebraic varieties . note that in the case when @xmath55 is a _ compact _ smooth complex algebraic variety ( or more generally a compact khler manifold ) then a more general theorem holds : [ gms ] ( w. goldman , j. millson @xcite , c. simpson @xcite ) . suppose that @xmath55 is a compact khler manifold @xmath2 is an algebraic lie group and @xmath62 is a representation such that the zariski closure of @xmath70 is a reductive subgroup of @xmath2 . then the germ @xmath63 is analytically isomorphic to a ( quasi)-homogeneous cone with generators of weight @xmath64 and relations of weight @xmath7 ( i.e. a homogeneous quadratic cone ) . in the case there is a local cross - section through @xmath67 to @xmath68-orbits , then the same conclusion is valid for the quotient germ @xmath69)\quad .\ ] ] our proof of theorem [ t7 ] is in a sense analogous to the proof of theorem [ gms ] in @xcite , @xcite : we construct a differential graded lie algebra @xmath71 which is weakly equivalent to the algebra of bundle - valued differential forms @xmath72 on @xmath55 so that @xmath71 _ controls _ a germ which is manifestly a quasi - homogeneous cone with the required weights . in figure [ fig9 ] we describe the graph of an artin group @xmath45 which admits a representation with finite image @xmath73 such that the germ @xmath74)$ ] is isomorphic to the germ at @xmath75 defined by @xmath76 . thus theorem [ t7 ] implies that the group @xmath45 is not the fundamental group of a smooth complex algebraic variety . our convention for coxeter graphs is different from the standard convention for dynkin diagrams . namely , if two vertices are not connected by an edge * it does not mean that corresponding generators commute*. if on our diagram an edge has no label , we assume that the edge has the label @xmath7 . on the diagram for a * shephard group * if a vertex has no label this means that the corresponding generator has * infinite order*. there is a local cross - section to the @xmath77-orbit through the representation @xmath78 ( that appears is theorem [ t6 ] ) , hence we apply theorem [ t7 ] and conclude that @xmath45 is not the fundamental group of a smooth complex algebraic variety . to see that there are infinitely many distinct examples we may proceed as follows . take the varieties @xmath79 , @xmath80 are prime numbers . clearly @xmath81 is not analytically isomorphic to @xmath82 for @xmath83 . thus for all @xmath84 the varieties @xmath81 are not analytically isomorphic to quasi - homogeneous varieties described in the theorem [ t7 ] . hence the artin groups @xmath85 corresponding to @xmath81 are not fundamental groups of smooth complex quasi - projective varieties . note that among the groups @xmath85 we have infinitely many ones which are not mutually isomorphic . the reason is that for any finitely - generated group @xmath86 the character variety @xmath87 has only finite number of isolated singular points whose germs are isomorphic to one of @xmath81 . this proves theorem [ moremorgan ] . in [ triv ] we use the results of [ completion ] to show that for every artin group @xmath86 and lie group @xmath2 the germ @xmath88 is quadratic where @xmath67 is the trivial representation . the first author is grateful to a. vershik for a lecture on mnv s result in 1989 . the authors are grateful to e. bierstone , j. carlson , r. hain , j. kollar , p. millman , c. simpson and d. toledo for helpful conversations .

we prove that for any affine variety @xmath0 defined over @xmath1 there exist shephard and artin groups @xmath2 such that a zariski open subset @xmath3 of @xmath0 is biregular isomorphic to a zariski open subset of the character variety @xmath4 . the subset @xmath3 contains all real points of @xmath0 . as an application we construct new examples of finitely - presented groups which are not fundamental groups of smooth complex algebraic varieties .

we prove that for any affine variety @xmath0 defined over @xmath1 there exist shephard and artin groups @xmath2 such that a zariski open subset @xmath3 of @xmath0 is biregular isomorphic to a zariski open subset of the character variety @xmath4 . the subset @xmath3 contains all real points of @xmath0 . as an application we construct new examples of finitely - presented groups which are not fundamental groups of smooth complex algebraic varieties .

0804.0892

i

the formation of galaxies and their systems ( ` haloes ' ) is known to be more intricate than its simplified rendering in the context of spherical collapse models . the process is characterised by gradual growth of the system mass and evolution of its morphological properties through multiple merging events , evidence for which comes from observations and hydrodynamical simulations . in clusters , mergers affect also the evolution of intracluster ( ic ) gas density and temperature and their spatial profiles . on the theoretical side , studies of halo mergers and related issues began with the works of bond et al . ( 1991 ) and lacey & cole ( 1993 ) , who developed the theory of _ excursion sets _ in the context of structure formation . this approach was originally devised by bond et al . in order to address the `` cloud - in - cloud '' problem , who showed that the press & schechter ( 1974 ) mass function , including the `` fudge factor '' of 2 , could be derived under certain assumptions . they also used their formalism to derive expressions for merger probabilities . lacey & cole ( hereafter lc ) used the excursion set formalism ( esf ) to extract such related quantities as halo merger rates , halo survival times , and halo formation times . the nfw concentration parameter ( navarro , frenk , & white 1995 ) , which characterises dark matter ( dm ) distribution in a halo is known from n - body simulations to be correlated with its formation time ( e.g. jing 2000 ; bullock et al . 2001 ; zhao et al . 2003 ) due to the fact that haloes which form earlier are likely to have more condensed cores , reflecting the higher background density of the universe . we use this inferred correlation , and the probability distribution function ( pdf ) of halo formation times , to construct pdfs of halo concentrations . this provides a convenient framework for a comparison of theoretically predicted values of the concentration parameter to observational results . our calculations of the formation time and concentration parameter pdfs are carried out in a standard @xmath0cdm cosmology , adopting the set of cosmological parameters,(@xmath3 , extracted from the 3-year wmap+wl data ( spergel et al . these parameters are selected for the sake of consistency with results obtained in other works , including calculations of the pdf of einstein radii . specifically , we show that the observed high einstein radius in the lensing cluster a1689 , whose value is roughly in the range @xmath4 ( e.g. , broadhurst & barkanna 2008 ) , is very improbable in the standard @xmath0cdm cosmology , but much more probable in a cosmological model characterised by an early component of dark energy , provided that its virial radius is larger ( within a plausible range of variance ) than what is predicted in the simple spherical collapse scenario . this paper is arranged as follows : in 2 we briefly detail the derivation of the pdfs of halo formation time and concentration parameter ; results are provided in 3 . the case of the lensing cluster a1689 is explored in 4 , followed by a discussion , 5 .

we do so by using the probability distribution function of halo formation times , calculated by means of the excursion set formalism , and a formation redshift - concentration scaling derived from results of n - body simulations . our results suggest that the observed high concentrations of several clusters are quite unlikely in the standard @xmath0cdm cosmological model , but that due to various inherent uncertainties , the statistical range of the predicted distribution may be significantly wider than commonly acknowledged . in addition , the probability distribution function of the einstein radius of a1689 is evaluated , confirming that the observed value of @xmath1 is very improbable in the currently favoured cosmological model .

we provide a quantitative assessment of the probability distribution function of the concentration parameter of galaxy clusters . we do so by using the probability distribution function of halo formation times , calculated by means of the excursion set formalism , and a formation redshift - concentration scaling derived from results of n - body simulations . our results suggest that the observed high concentrations of several clusters are quite unlikely in the standard @xmath0cdm cosmological model , but that due to various inherent uncertainties , the statistical range of the predicted distribution may be significantly wider than commonly acknowledged . in addition , the probability distribution function of the einstein radius of a1689 is evaluated , confirming that the observed value of @xmath1 is very improbable in the currently favoured cosmological model . if , however , a variance of @xmath2 in the theoretically predicted value of the virial radius is assumed , then the discrepancy is much weaker . the measurement of similarly large einstein radii in several other clusters would pose a difficulty to the standard model . if so , earlier formation of the large scale structure would be required , in accord with predictions of some quintessence models . we have indeed verified that in a viable early dark energy model large einstein radii are predicted in as many as a few tens of high - mass clusters . [ firstpage ] cosmology : large - scale structure of universe gravitational lensing galaxies : clusters : general

0804.0892

i

recently , broadhurst & barkanna ( 2007 , hereafter bb ) have reported the results of a comparative study of einstein radii calculated for a large sample of simulated clusters of masses @xmath58 , and those observed in the three massive clusters a1689 , c10024 - 17 , and a1703 . while the simulations yield einstein radii in the range @xmath59 , the measured values for these clusters are @xmath60 , and @xmath61 , respectively , a result which is seen by bb to constitute a challenge to the standard @xmath0cdm model . since we know all relevant properties of a1689 , namely its virial mass , virial radius , concentration parameter ( assuming an nfw dm profile ) , redshift , and the lensed source redshift , it is possible to construct a pdf of einstein radii for an a1689-like cluster . the equation governing the relation between the concentration parameter and the einstein radius is , assuming an nfw profile ( bb ) , @xmath62 where @xmath63 , @xmath64 , @xmath65 , and @xmath66 are the virial radius , critical density at redshift @xmath67 , overdensity at virialisation , and critical surface density , respectively . all these quantities are specified by bb , with the exception of the virial radius , for which we adopt the theoretical value found from the relation @xmath68 , resulting in @xmath69 , for @xmath70 . also , @xmath71 , where @xmath72 is the einstein radius , and @xmath73 the solution of eq . ( [ eq : gx ] ) provides the einstein radius as a function of @xmath56 , from which it is trivial to derive the angular einstein radius , @xmath74 , the ratio between the ( physical ) einstein radius and the angular diameter distance to the lens , the measured redshift of a1689 , @xmath75 . it remains to determine the pdf of the angular einstein radius . this can be accomplished using once more the transformation law of probability distribution functions : @xmath76 from which we obtain @xmath77 the first derivative is calculated analytically using eq . ( [ eq : cv2 ] ) , whereas a numerical calculation based on the @xmath78 relation in eq . ( [ eq : gx ] ) is used in order to infer the second derivative . results for the pdf and cdf of the angular einstein radius for an a1689-like cluster are presented in fig . ( [ fig : er ] ) . the results generated within the framework of the standard @xmath0cdm are represented by the black continuous curve ; the shaded areas represent the @xmath79 uncertainties in the cosmological parameters @xmath80 , @xmath81 , and @xmath82 . as is clear from the figure , large einstein radii ( @xmath83 ) have extremely low probabilities in the standard @xmath0cdm universe . in fact , the cumulative probability for an a1689-like cluster to induce an angular einstein radius larger than @xmath84 amounts to @xmath85 in this model ; the corresponding probability for the @xmath86 level increases to @xmath87 . non - standard cosmological models characterised by earlier evolution of the large scale structure may resolve the apparent discrepancy between measured and predicted values of @xmath72 , by virtue of earlier halo formation times , reflected in higher central halo concentrations and , therefore , higher probabilities for large einstein radii . for example , models based on positively skewed primordial density fluctuations lead to earlier growth of the large scale structure . early dark energy ( hereafter ede ) models provide another alternative for inducing earlier formation times by virtue of the modified cosmic dynamics implied by a non - negligible de component in the early universe . to explore this possibility , we have repeated our calculations for a specific ede model , with an early quintessence density parameter @xmath88 and equation of state coefficient @xmath89 at @xmath12 . these parameters are consistent with recent wmap results ( doran & robbers , 2006 ) . the other cosmological parameters were not modified , with the exception of @xmath90 , a value obtained by normalizing the cumulative halo mass function to the same number of halos generated in the standard @xmath0cdm model . complete details concerning the calculation of the relevant large scale quantities within the framework of ede models can be found in , e.g. , bartelmann , doran , & wetterich ( 2006 ) and sadeh , rephaeli & silk ( 2007 ) . the latter work was motivated by the possible need to have a higher level of cmb anisotropy induced by the sunyaev - zeldovich effect than is predicted in the standard @xmath0cdm model . results of the pdf and cdf of the einstein radius for a1698 are shown by the continuous orange curve of fig . ( [ fig : er ] ) . note that for the ede model the theoretically inferred virial radius reduces slightly to @xmath91 . the probability for an a1689-like cluster to produce an einstein radius larger than @xmath84 in this model is @xmath92 , i.e. , approximately two orders of magnitude higher than the corresponding probability in the @xmath0cdm model . the @xmath86 uncertainty ( which is not shown in the plot ) in the cosmological parameters would lead to even higher probabilities than those indicated by the orange curve of the ede model . however , these probabilities are still very low .

if , however , a variance of @xmath2 in the theoretically predicted value of the virial radius is assumed , then the discrepancy is much weaker . the measurement of similarly large einstein radii in several other clusters would pose a difficulty to the standard model . if so , earlier formation of the large scale structure would be required , in accord with predictions of some quintessence models . we have indeed verified that in a viable early dark energy model large einstein radii are predicted in as many as a few tens of high - mass clusters . [ firstpage ] cosmology : large - scale structure of universe gravitational lensing galaxies : clusters : general

we provide a quantitative assessment of the probability distribution function of the concentration parameter of galaxy clusters . we do so by using the probability distribution function of halo formation times , calculated by means of the excursion set formalism , and a formation redshift - concentration scaling derived from results of n - body simulations . our results suggest that the observed high concentrations of several clusters are quite unlikely in the standard @xmath0cdm cosmological model , but that due to various inherent uncertainties , the statistical range of the predicted distribution may be significantly wider than commonly acknowledged . in addition , the probability distribution function of the einstein radius of a1689 is evaluated , confirming that the observed value of @xmath1 is very improbable in the currently favoured cosmological model . if , however , a variance of @xmath2 in the theoretically predicted value of the virial radius is assumed , then the discrepancy is much weaker . the measurement of similarly large einstein radii in several other clusters would pose a difficulty to the standard model . if so , earlier formation of the large scale structure would be required , in accord with predictions of some quintessence models . we have indeed verified that in a viable early dark energy model large einstein radii are predicted in as many as a few tens of high - mass clusters . [ firstpage ] cosmology : large - scale structure of universe gravitational lensing galaxies : clusters : general

1312.2897

i

water is a key element for life , but nevertheless its properties arising from its unique structure are not fully understood yet . a large amount of published works explored the several phases of water and many efforts have been spent by the scientific community in order to match experimental findings with theoretical predictions . from the chemical and biological points of view , a deep understanding of the properties of acqueous systems and therefore of liquid water is fundamental . over the past years , the structural and dynamical properties of liquid water have been investigated relying on the state - of - the - art molecular dynamics techniques such as empirical force field methods @xcite and _ ab initio _ molecular dynamics ( aimd ) . the latter methodology has been extensively employed for the study of liquid water @xcite as well as acqueous solution of biological interest @xcite ; within , this technique , the atomic force fields required as input by any molecular dynamics simulation are constructed from _ ab initio _ potential energy surfaces ( pess ) and therefore directly derived from first principles electronic structure calculations . working out an accurate pes for liquid water has been a longstanding challenge in the scientific community ; this is due mainly to the absence of an _ ab initio _ method able to develop a reliable pes that describes breaking and formation of hydrogen bonds ; other issues are related to difficulties in simulating weak interaction and polarization effects in the network of polar molecules . the simulation of liquid systems requires model clusters with a large amount of molecules and therefore a good scalability is fundamental in order to carry out simulations in a reasonable computational time ; therefore the technique which has been mostly employed over the past years is density functional theory ( dft ) which combines scalability and flexibility features . nevertheless , molecular dynamics simulations which start from dft - based pes fail in reproducing basic properties of liquid water such as the melting point temperature @xcite and the oxygen - oxygen radial distribution function @xmath4 @xcite . another major problem which has not been elucidated yet by aimd is the description of proton transfer ( pt ) in liquid water , phenomenon which goes under the name of grotthuss mechanism @xcite . this process is extremely important in a wide range of biological systems and it influences many dynamical processes in material science , biochemistry and bioenergetics ; for example , pt is one of the main mechanism for charge transport through the cell membranes @xcite ; it plays an important role in several enzymathic reactions and photosynthesis @xcite and moreover proton has the role of mediator and promoter of many acid - base reactions in solution @xcite . although over the past years many experimental and theoretical works have been devoted to the study of grotthuss reaction , an accurate quantitative explanation of the underlined mechanism is not fully reached yet . theoretical investigations still fail in pt basic properties predictions , such as the activation barrier . experimental measures of this quantity have been carried out @xcite and followed by many attempts of its numerical estimation @xcite , without a satisfactory accordance . nevertheless , over the past years aimd simulations have given many insights on the physics of grotthuss mechanism @xcite . it has been found that proton transport is abnormally high and it is not driven by any ordinary diffusion process . the picture which is instead commonly accepted describes the translocation of excess positive charge along the hydrogen - bonded network as structural diffusion of the defects . has very recently shed new lights on proton transfer and has highlighted the complex nature of the process which involves both structural and dynamical changings of the hydrogen - bonded network . one of the main issues which sets back from a complete understanding of pt in water , is related to the very sensitive thermal behavior of pt . the required pes precision of the order of few tenths of kcal / mol has been reached only recently by the state - of - the - art computational methods beyond dft , such as coupled cluster ( cc ) , multi - reference configuration interaction ( mrci ) and the full configuration interaction quantum monte carlo ( fciqmc ) methods ; on the other hand , they are characterized by a much poorer scalability with respect to dft and therefore they do not allow simulation of sufficiently large molecular clusters . over the past years , two main structural models has been proposed to explain proton hydration : m. eigen @xcite considered as core of pt the complex @xmath5 in which an hydronium @xmath6 is strongly bounded to three water molecules ; g. zundel @xcite proposed a different reaction which involves the simpler @xmath0 complex ( the `` zundel ion '' or `` protonated water dimer '' ) as core of the transfer of proton between two h@xmath7omolecules . it has been demonstrated @xcite that these two models occur only as limiting or ideal structures for a more complex phenomenon which involves a large portion of the hydrogen - bonded network . nevertheless they constitute a perfect testing ground for the most advanced simulation techniques . in particular , the protonated water dimer @xmath0 is the smallest system in which an excess proton is shared between water molecules ; due to its simplicity , many studies have been carried out to elucidate its properties . over the past years , several accurate theoretical works have appeared on the zundel ion to study its structure and energetics@xcite ; the fast development of spectroscopical instruments allowed to probe experimentally vibrational properties of ionic species and therefore many studies on this side have been published @xcite on @xmath0.also molecular dynamics simulations which include quantum effects via feynman path integrals have been performed ( see ref . as a relevant example ) and recently an accurate pes has been produced @xcite with state - of - the - art coupled cluster technique including single , double and perturbative triple excitations ( ccsd(t ) ) . in the present paper , we report on an extensive study of the protonated water dimer using a quantum monte carlo ( qmc ) approach based on a highly correlated variational wave function for energy and geometry calculations . this approach has a very good scalability with the number of particles with respect to other post - dft methods . we demonstrate that it also insures the precision of a few tenths of kcal / mol required for an accurate study of the system . these appealing targets are achieved by our jastrow correlated antisymmetrized geminal power wave function ( jagp ) , developed on an efficient contracted single particle basis set . while the jagp provides the necessary ingredients to treat both dynamical and static correlations , the contracted basis set , based on atomic hybrid orbitals , reduces dramatically the computational cost to optimize the jagp wave function . thanks to these promising features , we hope that it will pave the way to a complete understanding of the underlined physics of pt and other properties of liquid water . the paper is organized as follows . in sec [ comp_methods ] we introduce the computational techniques used in this work . in particular , in subsec . [ qmc_wf ] we describe the variational ansatz and basis set which are the optimal compromise between accuracy and computational cost for water clusters . in sec . [ qmc_water_sec ] we present our results on the single h@xmath7o molecule , the subject of a vast amount of literature . it represents thus the most suitable system for a first benchmark of our approach . for the single h@xmath7o , we study the basis set and wave function convergence and show that we have an accuracy comparable to the latest qmc studies . [ water_dimer ] is devoted to the main results of our paper on the protonated water dimer . we performed structural calculations which aim at finding the ground state geometry of @xmath0 at the jagp level of theory . in order to work out a zero - temperature potential energy landscape , we chose the distance between the two oxygens as a natural reaction coordinate . along this path , we investigated how the symmetric `` zundel '' configuration - namely the one with the proton evenly shared between the two oxygens - evolves to a symmetry - broken geometry , where the excess proton is more bounded to one of the two molecules . we believe that this crossover is critical to understand the physics of pt in larger water clusters . here we show how our approach describes this relevant region of the @xmath0 pes . the evaluation of proton transfer static barriers at fixed @xmath8 distances shows that our qmc approach has a global accuracy close to the state - of - the - art ccsd(t ) calculations performed by huang et al . @xcite , with a discrepancy of 0.2 kcal / mol obtained by diffusion monte carlo ( dmc ) on the variational monte carlo ( vmc ) geometries . in conclusion ( sec . [ conclusions ] ) , we show that the favorable scalability of our method allows one to simulate larger protonated water clusters in a reasonable computational cost without loosing the accuracy reached in the smaller zundel ion . for the sake of test , we performed a structural optimization on a more realistic pt model , i.e. the cluster of 6 water molecules and one excess proton , to study the behavior of the computational cost with the system size in practice .

we report an extensive theoretical study of the protonated water dimer @xmath0 ( zundel ion ) by means of the highly correlated variational monte carlo and lattice regularized monte carlo approaches . our jastrow correlated agp wave function ensures an accurate treatment of electron correlations . exploiting the advantages of contracting the primitive basis set over atomic hybrid orbitals , we are able to limit dramatically the number of variational parameters with a systematic control on the numerical precision , a crucial ingredient in order to simulate larger systems . we investigate the energetics and geometrical properties of the @xmath0 as a function of the oxygen - oxygen distance , taken as reaction coordinate . in both cases , the qmc approach used here represents a promising candidate to provide the first high - level _ ab - initio _ description of pt in water .

we report an extensive theoretical study of the protonated water dimer @xmath0 ( zundel ion ) by means of the highly correlated variational monte carlo and lattice regularized monte carlo approaches . this system represents the simplest model for proton transfer ( pt ) and a correct description of its properties is essential in order to understand the pt mechanism in more complex acqueous systems . our jastrow correlated agp wave function ensures an accurate treatment of electron correlations . exploiting the advantages of contracting the primitive basis set over atomic hybrid orbitals , we are able to limit dramatically the number of variational parameters with a systematic control on the numerical precision , a crucial ingredient in order to simulate larger systems . we investigate the energetics and geometrical properties of the @xmath0 as a function of the oxygen - oxygen distance , taken as reaction coordinate . in both cases , our qmc results are found in excellent agreement with state - of - the - art coupled cluster ccsd(t ) techniques . calculations on proton transfer static barriers and dissociation energies display the same agreement . a comparison with density functional theory results in the pbe approximation points out the crucial role of electron correlations for a correct description of the pt in the dimer . finally , the ability of our method to resolve very tiny energy differences ( @xmath1 kcal / mol ) at which the proton hopping takes place and the corresponding structural variations optimized directly in the vmc framework is also proven . our approach combines these features with a @xmath2-@xmath3 scaling with number of particles . this value is favorable with respect to other highly correlated _ ab initio _ approaches and it allows the simulation of more realistic pt models ; a test calculation on a larger protonated water cluster is hence carried out . the qmc approach used here represents a promising candidate to provide the first high - level _ ab - initio _ description of pt in water .

1312.2897

m

in this section we present how we performed dft - based calculations on the zundel ion . they are carried out to obtain optimized starting geometries and wave functions for further quantum monte carlo calculations . the dft geometry has been obtained by a car - parrinello dynamics performed in a plane waves basis set with the quantum espresso@xcite suite of codes . the technical details of this calculation are reported in subsec . [ car_parri_dft ] . once the ground - state dft geometry is found , the kohn - sham ( ks ) orbitals , used as starting input of our qmc wave function , are determined by the dft code of the turborvb package @xcite which works in a localized gaussian basis set , as described in subsec . [ gaussian_dft ] . with the aim at finding the optimal dft geometry for further qmc structural relaxation ( see sec . [ qmc_methods ] ) , we use the perdew - burke - ernzerhof @xcite ( pbe ) version of the generalized gradient approximation for the exchange - correlation functional . it has been proven to be quite reliable in describing properties of liquid water@xcite . core electrons are taken into account using a norm conserving trouiller - martins pseudopotential@xcite . the kohn - sham orbitals are expanded over plane waves up to a cutoff of @xmath9 h for the wave function and @xmath10 h for the charge density in a periodic box of 30 bohr radii ( @xmath11 ) per side . the zero - temperature geometry relaxation is performed with damped dynamics within the car - parrinello ( cp ) approach @xcite . this method allows a very small force convergence threshold of @xmath12 h@xmath13 on each atomic component at the end of the relaxation . the potential energy surface of the dimer is very flat @xcite and it develops on energy differences of less than 1 kcal / mol . therefore such an accuracy on atomic forces is essential for the minimization to provide a reliable dft description of the system . we perform gaussian dft calculations with both pseudopotentials and full electron - ion potentials . the single - particle kohn - sham ( ks ) orbitals @xmath14 are used later on as optimized starting guess for the qmc wave function , as discussed in sec . [ qmc_wave_function_ansatz ] . the one - body dft wave function is expanded over a primitive basis of _ gaussian type orbitals _ ( gto s ) centered on the atom @xmath15 , defined up to a normalization constant as : @xmath16 with @xmath17 $ ] and @xmath18 $ ] , where @xmath19 are angular momentum quantum numbers , @xmath20 identifies the number of gaussians for each angular momentum shell , @xmath21 are the spherical harmonics , and @xmath22 and @xmath23 are the electron and ion positions , respectively . our dft basis set is _ even tempered _ , namely for each angular momentum @xmath24 the exponents of the gaussians are expressed as a power series : @xmath25 for @xmath26 . this allows a reduction of the number of parameters , as for each shell @xmath24 the full @xmath27 series is fixed just by three values : @xmath28 , @xmath29 , and @xmath20 . denoting the set of gto quantum numbers as @xmath30 , the dft orbitals @xmath31 expanded over the primitive basis set read : @xmath32 where @xmath33 identifies the number of atoms of the system , @xmath34 is the size of the gto set of the atom @xmath15 . thus the global dft wave function can be expressed as the determinant of the matrix @xmath35 : @xmath36 with @xmath37 the spatial and spin coordinates of the @xmath38 electrons in the system , and @xmath39 are the spin orbitals . the ab - initio hamiltonian of a quantum system is characterized by the divergence of the coulomb potential at the electron - electron and electron - ion coalescence points . when the potential energy becomes infinite , the wave function of the system must have a cusp to cure the corresponding singularity of the hamiltonian@xcite . these singularities represent a serious issue when an approximated wave function ansatz is employed to solve the schrdinger equation of a quantum system . within a dft framework , the divergence created by electron - electron coalescence is intrinsically solved by the mean - field description of the system , which maps the interacting hamiltonian onto a one with independent electrons . nevertheless , the electron - ion coalescence still represents a problem . one way to cure the latter divergence is to employ a smooth pseudopotential . the pseudo - interaction is chosen such that it eliminates the need of electron - ion cusps in the wave function , by leading to a faster basis set convergence . in this work we employ an alternative way to solve this issue . we introduce an additional factor to the dft wave function ansatz which automatically satisfies the electron - ion cusp conditions and cancels out the corresponding divergences of the hamiltonian . we rewrite eq . [ global_dft_wf ] as : @xmath40 where the function @xmath41 is called one - body jastrow factor , borrowed from the qmc notation . it is defined by means of a simple function @xmath42 which contains only one variational parameter @xmath43 : @xmath44 the one - body jastrow factor @xmath41 then reads : @xmath45 where @xmath46 are the atomic coordinates corresponding to the atomic number @xmath47 . in the function @xmath48 , the multiplicative factor @xmath49 is set by the electron - ion cusp conditions , while the scaling length @xmath50 deals with the large distance behavior set by the random phase approximation@xcite . [ corrected_dft_wf ] has the typical functional form of the jastrow - single determinant ( jsd ) variational ansatz for quantum monte carlo calculations . indeed the one - body jastrow of eq . [ jas_dft ] has been introduced in ref . to provide a solution of the electron - ion cusp conditions within a qmc framework . differently from qmc , our @xmath51 presents only the one - body jastrow factor since in dft the many - body electron - electron interaction is solved within a mean - field description . by letting the wave function to fulfill the electron - ion cusp conditions , we are able to perform calculations considering the bare interaction for both oxygen and hydrogen atoms ( full potential calculations ) . furthermore , at variance with conventional dft calculations based on gaussian localized orbitals , in our approach all the overlap matrix elements involved are computed as numerical integrals over a uniform mesh . such integrals , due to the presence of the jastrow factor , converge very rapidly with the number of points in the mesh and thus can be evaluated with a reasonable computational effort.@xcite with the aim at reducing the computational cost , calculations are carried out also by replacing the 1s core electrons of oxygen with the pseudopotential approximation , while the hydrogen atoms are treated always with the full coulomb potential . the oxygen pseudopotential that we used in both dft and qmc calculations is the burkatzki - filippi - dolg ( bfd ) pseudopotential , introduced in ref . . it is built by means of an energy - consistent approach in order to reproduce the valence all - electron excitation energies for a number of different atomic configurations computed at a scalar relativistic hartree - fock ( hf ) level . gaussian dft calculations are performed with a local density approximation ( lda ) for the exchange - correlation functional . the optimal basis sets which approach the dft complete basis set limit are @xmath52 and @xmath53 for the pseudopotential and full potential cases , respectively . expanding the wave function over these basis sets , the variational parameters ( @xmath28 , @xmath29 , @xmath20 for each angular momentum @xmath24 and the one - body jastrow parameter @xmath43 ) are optimized at the dft level of theory , by minimizing the total lda - dft energy . quantum monte carlo ( qmc ) refers to several numerical techniques for electronic structure calculations of quantum systems . the interest of the scientific community for these methods has remarkably grown over the last three decades since they were successfully applied to highly correlated electronic systems , and from small- to medium - size quantum chemistry systems . the qmc techniques used in this work are wave function - based , hence they aim at finding the many - body wave function in a representation as close as possible to the true ground state of the system . the analytic form of the wave function has to be square - integrable and computable in a finite amount of time , but it does not present any further restrictions . this property allows us to introduce correlations in a compact and efficient way . another appealing feature of qmc methods is the scaling with the number of particles . indipendently of the technique , qmc provides an intrinsic scaling of @xmath54-@xmath3 , with @xmath38 the number of electrons , whereas state - of - the - art coupled cluster single and double ( ccsd ) is @xmath55 and coupled cluster single , double and triple ( ccsd(t ) ) methods are @xmath56 . therefore qmc approaches allow the treatment of larger molecular clusters with respect to other highly - correlated methods . major efforts have been done to reduce the multiplicative scaling prefactor of qmc techniques , i.e. the cost of a single - point calculation . the research has followed two main paths . from one side more compact trial wave functions have been developed . one of the most promising functions is the jastrow - antisymmetrized geminal power ( jagp ) used in this work . a description of the wave function ansatz is given in subec . [ qmc_wave_function_ansatz ] . a second way to decrease the scaling prefactor relies on improving the quantum monte carlo estimators . qmc total energy calculations are in general much more efficient than those of other observables , due to the _ zero - variance _ property of the energy estimator . generally speaking , estimators of other important observables , as the charge density , do not possess this property . some other bare estimators , as the one for the atomic forces , could have infinite variance . thus they affect the overall computational efficiency of the qmc calculation . in particular , over the recent years a major improvement has been achieved in the development of an efficient estimator for nuclear forces@xcite . in the present work , we use a version of this estimator based on the space - warp coordinate transformation@xcite and implemented with an exact infinitesimal differentiation method@xcite . this allows a single sample calculation of the ionic forces with a computational effort of the order of @xmath2 ; this scaling is comparable to the one for total energy . moreover , the infinite variance of the space - warped force estimator in the proximity of the nodal surface of the wave function is solved as explained in refs . . the latter reference provides also a nice review on the latest progress in the qmc nuclear forces evaluation . therefore , by means of this state - of - the - art scheme force estimator we are able to perform efficient structural optimizations at the qmc level of theory also for not - so - light atoms as oxygen . the typical quantum monte carlo wave function is made of a symmetric bosonic factor ( _ jastrow factor _ applied to an antisymmetric fermionic part ( _ determinantal part _ ) : @xmath57 where the set @xmath58 represents spatial and spin coordinates of the electrons , as in eq . [ global_dft_wf ] . the jastrow factor is a function of the electron - electron separation . it has been proven to be a crucial ingredient in order to well reproduce correlations of the true many - body wave function ; it contributes mainly in the description of dynamical correlation effects arising from charge fluctuations . furthermore , it has been shown @xcite that the jastrow factor is particularly suitable in the treatment of van der waals intermolecular forces . they play an important role also in the physics of the protonated water dimer , therefore an efficient parametrization of the jastrow is essential . we split this factor in one - body , two - body and three / four - body terms ( @xmath59 ) . the one - body factor accounts for electron - ion interactions and it has been already introduced in eqs . [ jas_u],[jas_dft ] . the two - body term deals with the electron - electron interactions . in complete analogy with the one - body jastrow , it is parametrized by a simple function of the electron - electron separation : @xmath60 then it reads : @xmath61 @xmath41 and @xmath62 satisfy the kato cusp conditions@xcite , therefore correcting the divergence of the coulomb potential energy at electron - ion and electron - electron coalescence points , respectively . the function @xmath48 rapidly decays to a constant value as the electron - ion and electron - electron distances increase ; thus the large distance behavior of correlations is described by the three / four - body jastrow term @xmath63 . it deals with electron - electron - ion ( if @xmath64 ) and electron - ion - electron - ion ( in the case @xmath65 ) correlations effects and it represents an essential part of our wave function ; therefore we parametrize it in a richer way than the other jastrow terms : @xmath66 where @xmath67 represents the number of gto s of the primitive jastrow basis for each atom . the jastrow uncontracted orbitals @xmath68 have the same form as the primitive gto basis set @xmath69 for the determinantal part in eq . [ gaussians ] . the jastrow primitive gto basis used in this work is @xmath703s2p1d[h]2s1p$ ] . the choice of the fermionic part of the wave function is more delicate . in the case of spin unpolarized systems ( @xmath71 ) of @xmath38 electrons , we can express it in a general way as an antisymmetrized product of the _ geminals _ or pairing functions @xmath72 of the system : @xmath73 \nonumber \\ & = & { \rm pf}(\phi(\mathbf{x}_i,\mathbf{x}_j ) ) . \label{global_wf } \end{aligned}\ ] ] the geminals are antisymmetric functions of two electron coordinates expressed as a product of a spatial symmetric part and a spin singlet : @xmath74 the simplest , but compuationally most expensive expansion of the geminal is over the _ uncontracted atomic orbitals _ , and it reads : @xmath75 where the orbitals @xmath76 have the form reported in eq . [ gaussians ] with @xmath77 . @xmath78 represents the number of primitive gto s per atom . the introduction of the many - body jastrow factor @xmath79 in the total qmc wave function ( eq . [ total_qmc_wf ] ) allows a reduction of the primitive basis set size without loss of accuracy . this reduction has several advantages in the qmc framework . at first it obviosly decreases the computational effort for the wave function calculation . furthermore it also guarantees a more robust energy minimization . indeed , given the fact that qmc energy derivatives are noisy , using a more compact primitive basis set reduces its redundancy and helps in finding more quickly the global minimum since the number of the effective directions in the hilbert space is smaller . the size - reduced primitive basis employed for the determinantal part is @xmath80 and @xmath81 for pseudopotential and all - electron calculations , respectively . the number of variational parameters expanded over gto s atomic orbitals is @xmath82 , where @xmath83 is the total number of gto s in the whole system . in this work we use two distinct functional forms for @xmath84 . they are distinguished by the number of non zero eigenvalues - i.e. the rank - of the matrix @xmath85 in eq . [ atomic_expansion ] . the first one is commonly referred as single determinant ( sd ) and it is recovered when the @xmath85 matrix has the lowest possible rank compatible with the number of electrons in the system , namely when its rank is equal to @xmath86 . it can be shown that it is equivalent to the slater determinant ansatz for hf calculations . in this case the general expansion ( [ atomic_expansion ] ) , after diagonalization of the matrix @xmath85 , is written as : @xmath87 where @xmath88 are _ molecular orbitals _ ( mo ) . in this work we obtain them starting from the optimized kohn - sham orbitals of gaussian dft calculations discussed in sec . [ gaussian_dft ] . the number of variational parameters in this case is @xmath89 where @xmath83 is the number of linear coefficients for each mo , equal to the total number of gto s . close to the cbs limit @xmath90 , and so in the sd there is a significant reduction of the number of parameters with respect to the fully uncontracted agp expansion in eq . [ global_wf ] . multiplying the sd by the jastrow factor one obtains the jsd wave function , which is optimized simultaneously in both the j and sd parts . the sd represents a particular limit of the function in eq . [ global_wf ] . letting the rank of @xmath85 be greater than @xmath86 , one introduces multiconfigurational states and goes beyond the single determinant representation . in this more general case the determinantal wave function is called antisymmetrized geminal power ( agp ) . the agp is the particle - conserving version of the bardeen - cooper - schrieffer ( bcs ) wave function and it accounts for static correlations in the system , namely deriving from nearly - degenerate electronic energy levels . together with the jastrow factor it forms the jastrow - antisymmetrized geminal power ( jagp ) wave function which represents a practical implementation of the resonance valence bond idea introduced by linus pauling for chemical systems @xcite . the jagp wave function has been proven to be particulary accurate in describing a wide range of strongly correlated systems @xcite , and it is the second variational form we tested in our work after the jsd . in order to benefit from the agp ansatz without paying the cost of dealing with a too large number of variational parameters , which will make the calculation unfeasible for big systems , we develop the agp expansion on a contracted basis set . we used atomic hybrid orbitals , also employed in ref . , as contractions of the primitive gto s . one of the features of the agp ansatz ( without jastrow ) is that the geminal is also the one - body density matrix of the system . with the aim at finding the most effective local ( atomic ) basis set to describe the whole system , we project the full one - body density matrix on its local atomic constituents , by retaining in the expansion of eq . [ atomic_expansion ] only the @xmath91 s with @xmath64 , and setting to zero the other terms . by diagonalizing the projected one - body density matrix , we obtain a set of local natural orbitals for each atomic fragment . the atomic orbitals obtained in this way are hybrid ( i.e. linear combination of primitive gaussians not restricted to a given angular momentum shell ) , as they describe the hybridization arising from the atomic embedding , which breaks the spherical symmetry around the nucleus . we call them _ atomic hybrid orbitals_. thanks to this feature , for each atom we keep not only the information on the local electronic structure due to the nuclear charge , but also the information of the nuclear embedding in the compound , namely the impact of the environment on its electronic structure . the initial agp useful to fix the hybrid basis can be determined by dft calculations ( in that case the rank of the agp is n/2 as it comes directly from an sd wave function ) , or by a previously optimized jagp wave funtion ( in the latter case the jastrow factor is disregarded and only the determinantal part is taken in the one - body density matrix determination ) . once the hybrid basis set is chosen , and the agp expanded upon it , the geminal reads : @xmath92 where @xmath93 are the contracted atomic hybrid orbitals , and @xmath94 as before . @xmath95 is the number of atomic hybrid orbitals required for an accurate description of each atom . after their first determination by dft or by previous jagp calculations , they are further optimized in the qmc energy minimization . the number of variational parameters of the wave function is @xmath96 , where @xmath97 is the total nuber of hybrid gaussians in the whole system . since @xmath98 , the hybrid orbitals represent the optimal basis set , which reduces at most the total number of parameters in the correlated agp framework . in order to find the best value of @xmath95 for oxygen and hydrogen , we carried out a detailed analysis of the variational energy versus the hybrid basis size for the single water molecule , reported in sec . [ qmc_water_sec ] . all qmc calculations of this work have been carried out with the turborvb program@xcite . all the variational parameters of the jsd and jagp wave functions have been optimized by means of the stochastic reconfiguration method with hessian accelerator , also called `` linear method''@xcite . the forces on the parameters and ionic positions have always finite variance thanks to a reweighting scheme for finite systems introduced in ref . to cure the variance explosion around the nodes of the wave function . a systematic way of improving the quality of the vmc ansatz is to perform lattice regularized diffusion monte carlo ( lrdmc ) calculations@xcite , a projective technique which filters out the high - energy components yielding a more accurate evaluation of the correlation energy . in the case of non - local pseudopotentials , as the one for the oxygen , lrdmc goes beyond the locality approximation , by providing always a variational upper bound of the true ground state energy . in the present paper , we report on both vmc and lrdmc calculations of the protonated water dimer . the bfd energy - consistent pseudopotential described in sec . [ gaussian_dft ] has been employed to replace the oxygen - core 1s electrons . statistical error bars are kept smaller than @xmath99 kcal / mol in all qmc final calculation .

our qmc results are found in excellent agreement with state - of - the - art coupled cluster ccsd(t ) techniques . a comparison with density functional theory results in the pbe approximation points out the crucial role of electron correlations for a correct description of the pt in the dimer .

we report an extensive theoretical study of the protonated water dimer @xmath0 ( zundel ion ) by means of the highly correlated variational monte carlo and lattice regularized monte carlo approaches . this system represents the simplest model for proton transfer ( pt ) and a correct description of its properties is essential in order to understand the pt mechanism in more complex acqueous systems . our jastrow correlated agp wave function ensures an accurate treatment of electron correlations . exploiting the advantages of contracting the primitive basis set over atomic hybrid orbitals , we are able to limit dramatically the number of variational parameters with a systematic control on the numerical precision , a crucial ingredient in order to simulate larger systems . we investigate the energetics and geometrical properties of the @xmath0 as a function of the oxygen - oxygen distance , taken as reaction coordinate . in both cases , our qmc results are found in excellent agreement with state - of - the - art coupled cluster ccsd(t ) techniques . calculations on proton transfer static barriers and dissociation energies display the same agreement . a comparison with density functional theory results in the pbe approximation points out the crucial role of electron correlations for a correct description of the pt in the dimer . finally , the ability of our method to resolve very tiny energy differences ( @xmath1 kcal / mol ) at which the proton hopping takes place and the corresponding structural variations optimized directly in the vmc framework is also proven . our approach combines these features with a @xmath2-@xmath3 scaling with number of particles . this value is favorable with respect to other highly correlated _ ab initio _ approaches and it allows the simulation of more realistic pt models ; a test calculation on a larger protonated water cluster is hence carried out . the qmc approach used here represents a promising candidate to provide the first high - level _ ab - initio _ description of pt in water .

1312.2897

r

we report the results of our qmc study of protonated water dimer . this section is organized as follows . the first part ( sec . [ qmc_water_sec ] ) is devoted to benchmark computations on water molecule which aim at proving the quality of our qmc ansatz . the second part ( sec . [ water_dimer ] ) presents the qmc study on the protonated water dimer . different level of theory are compared with qmc calculations for both geometry and energetics outcomes in order to assess the accuracy of our approach in the study of proton transfer systems . the single water molcule has been the subject of many numerical studies based on several quantum chemistry methods . it is essential to have a good description of its structural and electronic properties in order to tackle the study of larger water clusters , as the intramolecular degrees of freedom will significantly affect the intermolecular environment due to the large water dipole moment and the strong directionality of the h bond . here we report our pseudopotential and all - electron calculations on the water molecule with different wave function types and basis sets , with the aim at choosing the best compromise bewteen accuracy and efficiency in order to transfer the most convenient ansatz to the zundel complex and eventually to larger water clusters . & & & & & & + jsd ( uncontracted orbitals ) & -17.24821(7 ) & 0.2655(6 ) & 0.0 & 682 & 18 & 895^_a_^ + jagp ( hybrid orbitals : 4o 1h ) & -17.25013(8 ) & 0.2635(12 ) & -1.91(11 ) & 21 & 158 & 374 + jagp ( hybrid orbitals : 4o 5h ) & -17.25183(6 ) & 0.2510(6 ) & -3.62(10 ) & 105 & 238 & 538 + jagp ( hybrid orbitals : 8o 2h ) & -17.25267(7 ) & 0.2426(18 ) & -4.46(10 ) & 78 & 298 & 571 + jagp ( hybrid orbitals : 8o 5h ) & -17.25302(6 ) & 0.2412(34 ) & -4.89(10 ) & 171 & 358 & 724 + jagp ( uncontracted orbitals ) & -17.25389(6 ) & 0.2296(5 ) & -5.68(10 ) & 682 & 18 & 895 + & & & & & & + jsd ( uncontracted orbitals ) & -76.40025(8 ) & 1.412(3 ) & 0.0 & 1383 & 19 & 1819 + jagp ( hybrid orbitals : 9o 2h ) & -76.40504(9 ) & 1.399(6 ) & -4.79(12 ) & 91 & 361 & 870 + jagp ( uncontracted orbitals ) & -76.40660(7 ) & 1.374(3 ) & -6.35(11 ) & 1383 & 19 & 1819 + pseudo jsd & 0.9542(4 ) & 104.730 + pseudo jagp & 0.9549(4 ) & 104.549 + all - electron jsd & 0.9539(4 ) & 105.187 + all - electron jagp & 0.9557(4 ) & 105.101 + experiment@xcite & 0.95721(30 ) & 104.522(50 ) + @xmath101 ( h ) & -17.26280(6 ) & -76.42475(15 ) + @xmath102 ( h ) & -17.26528(6 ) & -76.42690(14 ) + @xmath103 ( mh ) & -2.48(9 ) & -2.15(21 ) + as reported in sec . [ comp_methods ] , the bfd pseudopotential@xcite has been used for oxygen , while the two hydrogens have been treated all - electron . the primitive gaussian basis set is o(5s,5p,2d ) and h(4s,2p ) for the determinant , while for the jastrow factor it is o(3s,2p,1d ) and h(2s,1p ) . note that the latter basis set has been recently claimed to be one of the most accurate in an extensive qmc study of single molecule water properties@xcite , which used the same jastrow ansatz as ours . the inhomogeneous three- and four - body jastrow term ( eq . [ 3body ] ) has been developed directly on the uncontracted primitive basis set , whose flexibility guarantees a very good description of dynamical correlations . on the other hand , for the antisymmetric part we tested two main wave function forms , the single slater determinant ( obtained by using a geminal with rank @xmath86 ) , and the agp function . the difference in energy between the jsd and the jagp wave functions , reported in tab . [ table_pseudo_water_energy ] , shows the size of static correlations in the system , which amounts to 5 - 6 mh . this leads also to better geometrical properties , as seen in tab . [ table_geometry_h2o ] . the jagp geometry is closer to the experiment than the jsd one , in both the oh distance and the hoh angle . the structural effects of static correlations in the water molecule have been already pointed out in ref . , where they were attributed mainly to a change in the local description of the oxygen atom . in order to analyze in deeper detail the role of the agp correlations in the water molecule , we studied the natural orbital occupations coming from the diagonalization of the geminal . one of the appealing features of the agp theory is that the geminal wave function is directly related to the one - body density matrix of the system ( without jastrow factor ) . its diagonalization yields the molecular natural orbitals as eigenvectors and their weights are related to the modulus of the agp eigenvalues which are plotted in fig . [ agp_eigenvalues ] . the figure shows that indeed the orbitals above the homo ( highest occupied molecular orbital in the single slater determinant representation ) have a sizable weight , with a distribution which falls abruptly to zero only after the 40-th orbital ( gray area in the plot ) . this reflects the multi determinant character of the water molecule , taken into account by the agp ansatz . we thus believe that , although the entanglement of quantum levels at the origin of static correlations can come from the oxygen atom , its impact in water has a genuine molecular character . last but not least , the multi determinant agp representation leads to a better description of the nodal surface of the true ground state , with a gain of about 2.5 mh in the fixed node lrdmc energy with respect to the one obtained by using the jsd as trial wave function , as reported in tab . [ table_lrdmc_water_energy ] . we turn now the attention on how to reduce the agp basis set in an effective way . so far , both the jsd and jagp wave functions have been developed on the uncontracted primitive basis in order to exploit at most its flexibility . thus , the total number of variational parameters is 895 ( see the last column of tab . [ table_pseudo_water_energy ] ) , quite large for a single molecule , particularly if one would like to tackle the study of larger water clusters by means of qmc techniques . the most important limitation of this approach is that the number of variational parameters corresponding to the matrix elements @xmath104 increases clearly as the square of the atomic basis size ; therefore this should be reduced at minimum in order to make this approach feasible for a large number of molecules . to this porpouse , as explained in sec . [ qmc_wave_function_ansatz ] , we define a new smaller basis set by contracting the o(5s,5p,2d)/h(4s,2p ) gaussian primitive basis via atomic natural hybrid orbitals . each atom in the system is described by its own set of hybrid orbitals . we study how the size of the contracted hybrid basis set affects the quality of the geminal expansion . we compare it with its rigorous lowest energy limit provided by the uncontracted jagp reference previously computed . the results are reported in tab . [ table_pseudo_water_energy ] . the smallest basis set which includes the 1s for h and the 2s and 2p orbitals for o , thus taking into account the 2s2p near degeneracy at the atomic o level , is the 4o 1h hybrid set ( in self - explaining notations ) . it gives the poorest energy and variance among the hybrid basis sets considered , though being lower than the jsd ansatz . the best energy is obtained with the largest hybrid basis tried here , namely the 8o 5h set . it recovers a large fraction of static correlations and its energy is less than 1mh above the uncontracted jagp one . however , the price to pay is that the parameter reduction is weak , the total number of parameters being close to the one of the full jagp expansion ( see last column of tab . [ table_pseudo_water_energy ] ) . indeed , while the number of @xmath104 is still significantly lower than the one for the uncontracted basis set , nevertheless the parameters in the contracted orbitals grow too much . the best compromise between efficiency , i.e. total number of variational parameters , and accuracy , i.e. variational energy , is provided by the 8o 2h basis , as it yields a significant gain in energy with a small / moderate number of parameters . this advantage will be remarkable for large number of atoms , as the number of variational parameters corresponding to this atomic natural hybrid orbitals grows only _ linearly _ with the number of atoms ; on the other hand the number of parameters corresponding to @xmath104 , grows instead quadratically , but it remains still affordable since it is dramatically reduced by this approach ( see tab . [ table_allel_water_energy ] ) . finally , we study how the agp spectrum changes with the contracted hybrid basis sets . [ agp_eigenvalues ] shows that , after a complete wave function optimization , the natural orbital eigenvalues magnitude of the hybrid agp covers the @xmath105 range of the fully uncontracted agp expansion , except for the shortest 4o 1h basis , which clearly spans a too small hilbert space . moreover , we checked that the jagp expanded on the optimal 8o 2h basis gives the same fixed node lrdmc energy as the full jagp , signalling that the nodal surface is properly described even by the hybrid 8o 2h contraction . therefore we are going to use it in the study of the protonated water dimer presented after in the paper . as reported in the method section , the gain in efficiency of the hybrid basis set is expected to be larger and larger as the system size increases , as the quadratic growth of the @xmath104 with the number of atoms depends strongly on the atomic basis size . to study the accuracy of the pseudopotential approximation , we carried out also all - electron calculations of the water molecule . with respect to the pseudopotential calculations , the primitive and contracted basis sets for o have been extended in order to account for the additional 1s electrons . the primitive basis set is then o(6s6p2d ) and o(3s3p1d ) for the determinant and jastrow term respectively , while the optimal contracted hybrid basis set is 9o 2h . in tab . [ table_allel_water_energy ] we report the variational energies for different wave functions . the energy gain provided by the all - electron jagp wave function is very close to the one in pseudopotential calculations . the substantial agreement between the two calculations is apparent also in fig . [ agp_eigenvalues ] , where the eigenvalues of the higher energy molecular natural orbitals in the agp behave similarly . the lrdmc energy difference between the jagp and jsd trial wave functions coincides within the error bars with the one with pseudopotentials . the nodal contribution to the fixed - node energy is the same . the jagp lrdmc energy is one of the best ever published in literature , in statistical agreement with the one computed by luchow and fink@xcite ( -76.429(1 ) ) h ) , who used 300 determinants in the trial wave function , and with the one by zen et al.@xcite ( -76.42660 h ) , who used the same ansatz as ours in the trial . the jagp lrdmc projected energy is only 11 mh higher than the extrapolated exact result of 76.438 h@xcite . for @xmath106 and @xmath107 for @xmath108 . in the agp representation , by diagonalizing the geminal we obtain the corresponding molecular orbitals ( eigenvecotors ) and their occupations @xmath109 ( eigenvalues ) . in the agp , also the orbitals above the homo are occupied , with a weight which jumps across the homo to lumo transition ( in going from the green to white region ) . the gray area shows when the mo occupation tail falls rapidly to zero in the full agp ( expanded on a primitive basis set ) , signaling that the mo s above that threashold start to be irrelevant to describe the static correlations in the system . ] the all - electron calculations confirm the importance of including static correlations to have a better description of the geometry , as shown in tab . [ table_geometry_h2o ] . however the hoh angle turns out to be less accurate than the one obtained with pseudopotentials if compared to the experiment , most probably because it is a quantity very sensitive to the basis set convergence , which is harder to reach in all - electron calculations . another drawback of all - electron calculations is of course the larger variance for an equivalent wave function ansatz , due to the 1s electron fluctuations , as one can easily evince from the comparison between tab . [ table_pseudo_water_energy ] and tab . [ table_allel_water_energy ] . due to the larger primitive basis set required in all - electron calculations , the parameter reduction allowed by the hybrid basis contraction ( 9o 2h ) has a great impact on the efficiency . the total number of parameters is reduced by almost a factor of 4 in the determinantal part of the single molecule , without any significant loss of accuracy in the jagp total energy ( see tab . [ table_allel_water_energy ] ) . the use of the bfd pseudopotential for oxygen , and the jagp ansatz together with the hybrid basis set , tested in the water molecule , is transferred to the protonated water dimer . the protonated water dimer represents the simplest model for proton transfer in acqueous systems . in our work we focus on the energetics of @xmath0 related to proton transfer by choosing suitable reaction coordinate ( rc ) . selecting a rc allows to reduce the complexity of the full - dimensional pes . it projects it onto a single - dimensional subset which retains the most important physical features of the full hypersurface . since it is not unique , a correct choice of rc is essential in order to filter out the physical features which suitably describe the considered phenomenon . we propose a mechanism of proton transfer within the dimer which leads to a natural definition of our rc . as modeled by our system , the proton transfer reaction takes place in three different steps . at first the excess proton is bounded to one water molecule forming an @xmath110 complex . by thermal fluctuations the oxygen - oxygen separation can get closer to the optimal distance of the zundel complex ( around @xmath111 ) ; at this stage the system assumes a `` zundel configuration '' with the proton equally shared between the two oxygens . a further stretch of @xmath8 disfavors the zundel configuration and a new @xmath112 complex is produced . the overall effect of this process is a transfer of a proton along the hydrogen bond between two oxygen atoms . this mechanism suggests to choose the oxygen - oxygen separation as rc for the dimer potential energy curve . we present in the following the geometry and energetics of the protonated water dimer . results on the global minimum geometry are reported at first . the potential energy curve is the result of a stretching of the oxygen - oxygen distance ; the behavior of the excess proton is thus investigated along the same path . a particular attention is devoted to the behavior of the @xmath110 complex in the broken - symmetry region of the energy landscape . proton transfer static barriers at different @xmath8 distances are calculated in order to further estimate the accuracy of our approach . all qmc calculations are performed with the jagp wave function ansatz developed on an atomic hybrid basis set , as discussed in the previous sec . [ qmc_water_sec ] . the minimum energy structure of @xmath0 has been debated in the scientific community , as there are two candidates with competing energies : a @xmath113-symmetric structure , commonly addressed as zundel configuration , with the proton evenly shared between the two oxygens , and a @xmath114-symmetric one with the proton slightly localized on one @xmath100 molecule ( see fig . [ geometries ] ) . several _ ab - initio _ investigations @xcite have shown that a better treatment of electron correlations turns out in a change of the ground state ( gs ) geometry from the @xmath114-sym to the @xmath113-sym configuration . accurate highly - correlated studies @xcite has eventually confirmed that the global minimum is @xmath113 symmetric . at a qmc level of theory , the @xmath0 gs shows a @xmath113 zundel configuration with centrosymmetric excess proton ( left part of figure [ geometries ] ) , in agreement with the previous studies . the main geometrical parameters of the global minimum are presented in tab . [ table_geometry_c2 ] , both for the pseudopotential and all - electron calculations . dft - pbe & 2.4111 & 1.2074 & 1.2074 & 173.661 & 0.9697 & 0.9691 + dft - b3lyp@xcite & & & 1.2172 & 173.6 & 0.9706 & 0.9701 + qmc - with pseudo & 2.3847(5 ) & 1.1930(5 ) & 1.1942(8 ) & 174.71(7 ) & 0.9605(8 ) & 0.9650(8 ) + qmc - all - electron & 2.3905(4 ) & 1.1944(6 ) & 1.1989(5 ) & 174.43(9 ) & 0.9630(7 ) & 0.9628(6 ) + ccsd(t)@xcite & 2.3864 & 1.1950 & 1.1950 & 173.730 & 0.9686 & 0.9682 + dft - b3lyp@xcite & & & 1.2507 & 175.4 & 0.9746 & 0.9741 + qmc - with pseudo & 2.3996(6 ) & 1.1154(8 ) & 1.2852(4 ) & 176.5(1 ) & 0.9641(7 ) & 0.9625(4 ) + qmc - all - electron & 2.3913(3 ) & 1.1285(5 ) & 1.2648(4 ) & 175.29(6 ) & 0.9635(4 ) & 0.9616(5 ) + ccsd(t)@xcite & 2.3989 & 1.1233 & 1.2720 & 175.646 & 0.9641 & 0.9645 + if compared with ccsd(t ) , the qmc ground state geometries show an agreement of up to @xmath115 in the atomic separations , and up to @xmath116 in the angles . as the angle is close to @xmath117 , in this case its determination is more delicate and could be affected by a larger statistical bias . therefore we notice a slight discrepancy on this quantity between qmc and coupled cluster outcomes . nevertheless , these differences do not affect the overall description of the gs and the energetics of the system . in the present work , also the @xmath114-symmetric structure has been taken into account ( left - hand side of fig . [ geometries ] ) . tab . [ table_geometry_cs ] , which reports the vmc optimized @xmath114 geometries , confirms the trend seen in tab . [ table_geometry_c2 ] for the gs , although the discrepances in the bond lengths are slightly larger between different methods , the ccsd(t ) values being in between the all - electron and pseudopotential vmc results . the energy difference between the @xmath114 configuration and the @xmath113-symmetric global minimum turns out to be @xmath118 kcal / mol at vmc level and @xmath119 kcal / mol with lrdmc . this is in satisfactory agreement with previous results carried out with mller - plesset pertubation theory@xcite ( @xmath120 kcal / mol ) and ccsd(t)@xcite ( @xmath121 kcal / mol ) techniques . the quality of pseudopotential is hence verified also for the zundel complex . in view of this , its pes along the chosen rc will be worked out mainly with this approximation due to its substantially lower computational demand . comparison between different computational methods . structural relaxation is performed at each level of theory . each curve has its minimum as reference point . ] from the global minimum @xmath113-sym configuration we stretch the oxygen - oxygen distance in order to study the potential energy curve and to elucidate the proton transfer properties in the dimer . the structural relaxation at the vmc level for fixed @xmath8 separation requires a careful procedure due to the flatness of the pes . starting from a pbe - dft optimized geometry ( see sec . [ car_parri_dft ] for technical details ) and a jagp variational wave function fully optimized in the electronic part , the atomic coordinates are relaxed with the steepest descent method , considering them as additional variational parameters of the qmc wavefunction . for the sake of comparison , we minimize a parametrized full - dimensional pes fitted from ccsd(t ) calculations@xcite to find the best coupled cluster estimates of energy and geometry . by means of the _ downhill simplex _ minimization technique , we find the configuration of lowest ccsd(t ) energy at the same constrained @xmath8 distance as the corresponding qmc and dft calculations . in fig . [ landscape1 ] we plot the energy landscape along the rc for pbe - dft , ccsd(t ) , vmc and lrdmc , the latter computed at the vmc geometry . for vmc technique , we report also full potential calculations for some @xmath8 separations . we notice a substantial agreement among all techniques in the region at the left of the global minimum of the curve , except for a rigid shift by 0.02 between the pbe - dft results and the others . the pbe @xmath8 minimum is indeed located at 2.41 , while the minimum of the other methods turns out to be at @xmath122 2.39 . hence this part of the energy curve is only slightly influenced by a better treatment of correlations . on the other hand , the region at the right of the minimum , at intermediate @xmath8 distances ( @xmath123 ) , displays a different behavior . the pbe - dft overestimates the slope of the curve with respect to the most accurate techniques . lrdmc , which yields the best qmc correlation energy , shows a remarkably good agreement with the state - of - the - art ccsd(t ) results . in particular all ccsd(t ) outcomes are in the range of @xmath124 kcal / mol , three times the statistical error of the lrdmc calculations , as shown in fig . [ blowup_landscape ] . the curves reported in fig . [ landscape1 ] are obtained with the minimum energy geometry at each level of theory ( except for the lrdmc , whose geometry is set at the vmc level ) . in order to obtain a more reliable comparison and avoid the bias coming from the use of different geometries , we carried out the same calculations employing the vmc - optimized structures for every technique . the result is reported in fig . [ landscape2 ] . the trend displayed in fig . [ landscape1 ] for method - optimized geometries is remarkably enhanced when the same configuration of the dimer is considered . away from the minimum , the pbe - dft energies show a larger overestimation of the slope . distance ( ) . all the calculations are performed with vmc - optimized geometry . the zero energy reference point corresponds to the minimum of each curve . ] the slope of the dimer potential energy curve is related to the behavior of the excess proton in the system . in fig . [ oh_distances ] this property is elucidated . we report in the same plot the separations between the excess proton and each of the two oxygens : @xmath125 and @xmath126 . the structure of the dimer is relaxed at different level of theories with the same procedure carried out for the potential energy curve in fig . [ landscape2 ] . the plot clearly shows the appeareance of two distinct regimes of the dimer . one is characterized by a symmetric zundel configuration with the proton evenly bonded to the two oxygens ; from the point of view of proton transfer physics , it is basically equivalent to the gs configuration . stretching the @xmath8 distance results in the formation of a @xmath110 complex with the proton localized on one water molecule . these configurations belong to the _ asymmetric regime _ of the dimer . within this regime , the initial @xmath113 point symmetry of the gs geometry is broken due to proton localization . notice that the @xmath114-sym local minimum presented in sec . [ global_minimum ] displays a localized proton at a distance of @xmath127 , smaller than the symmetry - breaking distance shown in fig . [ oh_distances ] . however , we verified that if one stretches the @xmath8 distance starting from this local minimum , the energies obtained are higher than the values plotted in fig . [ landscape1 ] and fig . [ landscape2 ] . the distances obtained by the qmc relaxation of the atomic coordinates are in excellent agreement with the ccs(t ) calculations ; in particular the root mean square distance between the two data sets over the whole @xmath8 range is of @xmath128for both @xmath125 and @xmath129 . electron correlation plays a key role in determining the stability of the symmetric configuration of the dimer . the overestimation of the potential energy curve slope by pbe - dft in fig . [ landscape1 ] corresponds to an overestimation of the symmetry - breaking @xmath8 separation by @xmath130 with respect to higher - level post - dft _ ab - initio _ methods , and to a very poor description od the geometry in the symmetry - broken region close to the symmetry - breaking point , where the discrepancy in the @xmath131 distances is the largest ( going up to 0.15 ) . the zero - temperature potential energy curves reported in fig . [ landscape1 ] and fig . [ landscape2 ] seem to conflict with the proton transfer mechanism discussed in the introduction of sec . [ water_dimer ] , since the configuration with centrosymmetric proton is energetically favored and therefore it represents a stable state rather than a transition state between two asymmetric configurations with localized proton . this contraddiction is only apparent . indeed , ref . has shown that the introduction of thermal and polarization effects due to the physical environment , favors the asymmetric regime of the complex . indeed , at finite temperature the _ free energy _ landscape displays a global minimum shifted towards the asymmetric regime and the zundel - like structure does not represent anymore the energetically favored configuration . moreover , a recent experimental result shows that the average @xmath8 distance in liquid water is of @xmath132 @xcite which clearly corresponds to a symmetry - broken configuration of the dimer ( see fig . [ oh_distances ] ) . anyway , in order to jump from a water molecule to one of its neighbors , the proton must pass through a zundel configuration . describing correctly the energetics and geometry of the protonated water dimer in the symmetry - breaking transition region is therefore of paramount importance to hope having an accurate description of the pt in more realistic models . indeed , as already mentioned , fig . [ oh_distances ] highlights that at @xmath133 k a better treatment of electronic correlations turns out in a stability of the asymmetric regime over a considerably wider range of @xmath8 distances with respect to dft results . hence we expect that , at finite temperature and including the sorrounding physical environment , the value of the free energy activation barrier for proton transfer would be significantly higher than the pbe - dft prediction . in this section we focus the attention on some relevant properties of the broken - symmetry region where the excess proton is localized on a water molecule . at the qmc level of theory , the formation of a @xmath110 complex occurs at an oxygen - oxygen distance of @xmath134 in perfect accordance with ccsd(t ) results , as seen in fig . [ oh_distances ] . a quantity which has been extensively studied over the past years@xcite is the _ static proton transfer barrier _ , i.e. the barrier that the @xmath135 has to overcome in order to jump from one h@xmath7omolecule to the other at a fixed @xmath8 distance in the symmetry - broken regime . this quantity does not provide a realistic comparison with the experimental activation barrier for pt , as the @xmath8 distance will shorten during the proton hopping . nevertheless , it is relevant in order to provide a further check of the accuracy of our qmc approach . fixing the @xmath8 distance , the barriers are obtained as difference between the asymmetric configuration with localized proton and a structure with the excess proton in a centrosymmetric position . calculations are performed in three representative @xmath8 separations ; the results are shown in tab . [ static_barrier ] where they are compared with existent data in literature . the first @xmath8 distance is @xmath136 , very close to the symmetry - breaking point of the dimer as displayed by highly correlated approaches ; on the contrary , at a dft level the configuration with centrosymmetric proton is still energetically favored , as shown by fig.[oh_distances ] . it has been noticed@xcite that the pes in this region is particulary flat . furthermore the potential energy curve of the dimer develops on very tiny energy differences around the symmetry - breaking point . these issues make the calculations in this region of the pes extremely delicate since the stochastic noise can considerably affect the quality of the qmc predictions . indeed , tab . [ static_barrier ] shows that qmc and ccsd(t ) display a vanishing energy barrier of the order of @xmath99 kcal / mol as the hydrogen is displaced along the oxygen - oxygen axis . the height of this barrier is slightly above the attained statistical error in our typical qmc run . however , despite the very sensitive behavior of the dimer pes around the symmetry - breaking point , the accuracy of our force minimization algorithm allows to account for the tiny energy differences involved ; thus it ensures the necessary precision to describe the pt physics in the dimer . as we discuss in the next section , a similar accuracy can be achieved in larger molecular clusters with a reasonable amount of computational time . therefore our qmc framework guarantees a reliable description of the pt physics also for more realistic models . .static proton transfer barriers ( kcal / mol ) at fixed @xmath8 separations . comparison between different level of theory . [ cols="^,^,^,^",options="header " , ] the other results are obtained at larger oxygens separations , further from the symmetry - breaking point . they confirm the general behavior already seen along the @xmath8 rc . lrdmc and cc results are in a good agreement up to @xmath137 kcal / mol , whereas the vmc slightly overestimates the barrier . as well known from previous works , dft substantially underestimates the barrier with respect to post - dft methods which provide a better treatment of correlations . finally , let us analyze the extreme limit of the asymmetric zundel configuration , namely when @xmath138 , with the formation of one h@xmath7o and one hydronium . the dissociation energy @xmath139 of @xmath0 is computed by setting the distance between the two oxygens to @xmath140 . with the ccsd(t ) pes , we checked that this is already in the large distance plateau . we get a @xmath139 of @xmath141 kcal / mol by vmc , and @xmath142 kcal / mol by lrdmc , to be compared with the ccsd(t ) value of @xmath143 kcal / mol from ref . , while the pbe - dft gives @xmath144 kcal / mol . the agreement between the lrdmc and ccsd(t ) is impressive , while it is already good for the vmc estimate.this is mainly due to the size consistency of the jagp ansatz , obtained once the jastrow is close to the complete basis set limit . the vmc and ccsd(t ) dissociation energies are plotted in fig . [ blowup_landscape ] with respect to lrdmc values . & & + 1 & 0.05 & 0.15 + 2 & 0.24 & 2.13 + 6 & 6.49 & 164.35 + qmc methods present a favorable scalability with the number of particles with respect to other highly correlated approaches such as cc . with the aim at proving this feature also for our approach , we performed a benchmark calculation on a more realistic pt model composed of 6 water molecules and one excess proton , which will be the subject of a further study . in table [ comp_time ] we report a comparison of the computational time required to carry out typical vmc and lrdmc runs for different sizes of the protonated water cluster at fixed optimized variational parameters and geometry . the calculations have been carried out on the hpc curie thin nodes ( 2.7 ghz 8 core intel sandy bridge processors ) , and performed with a target statistical error of @xmath145 kcal / mol in the total energy . by performing a simple fit on the data in table [ comp_time ] , we notice that the simple vmc displays a @xmath54 scaling with the number of particles ; the more accurate lrdmc , carried out at a lattice space of @xmath146 , shows instead an almost perfect @xmath3 scaling . however , the lrdmc calculations are still feasible in a reasonable computational time for the 6 h@xmath7o cluster , while the vmc is still cheap at that cluster size .

this system represents the simplest model for proton transfer ( pt ) and a correct description of its properties is essential in order to understand the pt mechanism in more complex acqueous systems . finally , the ability of our method to resolve very tiny energy differences ( @xmath1 kcal / mol ) at which the proton hopping takes place and the corresponding structural variations optimized directly in the vmc framework is also proven .

we report an extensive theoretical study of the protonated water dimer @xmath0 ( zundel ion ) by means of the highly correlated variational monte carlo and lattice regularized monte carlo approaches . this system represents the simplest model for proton transfer ( pt ) and a correct description of its properties is essential in order to understand the pt mechanism in more complex acqueous systems . our jastrow correlated agp wave function ensures an accurate treatment of electron correlations . exploiting the advantages of contracting the primitive basis set over atomic hybrid orbitals , we are able to limit dramatically the number of variational parameters with a systematic control on the numerical precision , a crucial ingredient in order to simulate larger systems . we investigate the energetics and geometrical properties of the @xmath0 as a function of the oxygen - oxygen distance , taken as reaction coordinate . in both cases , our qmc results are found in excellent agreement with state - of - the - art coupled cluster ccsd(t ) techniques . calculations on proton transfer static barriers and dissociation energies display the same agreement . a comparison with density functional theory results in the pbe approximation points out the crucial role of electron correlations for a correct description of the pt in the dimer . finally , the ability of our method to resolve very tiny energy differences ( @xmath1 kcal / mol ) at which the proton hopping takes place and the corresponding structural variations optimized directly in the vmc framework is also proven . our approach combines these features with a @xmath2-@xmath3 scaling with number of particles . this value is favorable with respect to other highly correlated _ ab initio _ approaches and it allows the simulation of more realistic pt models ; a test calculation on a larger protonated water cluster is hence carried out . the qmc approach used here represents a promising candidate to provide the first high - level _ ab - initio _ description of pt in water .

1312.2897

c

in this paper we presented an extensive study of the protonated water dimer by means of the vmc and lrdmc techniques . the jagp ansatz employed in this work implements an accurate treatment of both static and dynamical correlations among electrons . the expansion of the determinantal part over atomic hybrid orbitals ensures a drastic reduction of the number of variational parameters thus making the wave function optimization procedure efficient and robust even for large systems . the comparison with previous published qmc calculations on the single water molecule showed the quality of our wave function ansatz . total energy calculations are performed with the less expensive variational monte carlo approach along with the more precise projective diffusion monte carlo . the powerful minimization algorithm implemented in our qmc software , allows an efficient estimation of the forces acting on each atomic component with a reasonable computational cost . hence both energetics and geometry calculations are perfomed within the qmc framework . a simple mechanism of proton transfer in the dimer has been presented and exploited to choose a suitable reaction coordinate for the potential energy curve . the energy landscape as a function of the oxygen - oxygen distance is computed and compared with density functional theory in the pbe approximation and with ccsd(t ) results ; lrdmc is in excellent agreement with ccsd(t ) calculations ( within @xmath137 kcal / mol ) , whereas minor differences ( up to about @xmath147 kcal / mol ) are shown by vmc . ref . has recently reported a similar accuracy for small water clusters by diffusion monte carlo calculations . geometrical properties of the excess proton are also investigated by vmc structural relaxations , which provide geometries remarkably close to the ones obtained by a ccsd(t ) fitted pes . we show the presence of two distinct regimes of the dimer depending on the oxygen - oxygen distance : one with a centrosymmetric excess proton and the other with the proton localized on one of the water molecules . the stability of these configurations crucially depends on the level of theory employed to describe the electronic structure of the system . a better treatment of electron correlation results in the stability of the asymmetric proton geometry over a wider range of @xmath8 distances . these results , together with the proton transfer static barrier and the dissociation energy @xmath139 , show that our qmc approach has a global accuracy comparable with the state - of - the art coupled cluster in both geometry and energetics of the dimer , with the advantage of having a better scaling with the number of particles . the accuracy shown by our qmc calculations combines with a favorable scalability with the number of particles with the respect to other highly correlated techniques , as demonstrated with a test simulation on a larger protonated water cluster . these features make this approach a very promising candidate for the study of proton transfer in complex acqueous systems . in particular , we have shown that the vmc method is cheap , provides very accurate geometries and a global accuracy of less than 1 kcal / mol in the most important region for the pt physics . we hope that our work will inspire further studies on this direction , and pave the way for accurate highly - correlated simulations of more realistic proton transfer models which will eventually shed new insights onto the pt mechanism in water . we thank joel m. bownman and xinchuan huang who provided us the coupled cluster potential energy surface of @xmath0 . one of us ( michele casula ) acknowledges computational resources in the form of the genci grant number x2013096493 . 99 w. l. jorgensen , j. chandrasekhar , j. d. madura , r. w. impey , m. l. klein , j. chem . phys . * 79 * , 926 ( 1983 ) . m. sprik , j. phys . chem . * 95*,2283 ( 1991 ) . m. w. mahoney , w. l. jorgensen , j. chem . phys . * 112 * , 8910 ( 2000 ) . p. l. silvestrelli , m. parrinello , j. chem . phys * 111 * , 3572 ( 1999 ) . j. c. grossman , e. schwegler , e. w. draeger , f. gygi , g. galli , j. chem . * 120 * , 300 ( 2004 ) . j. vandevondele , f. m. and m. krack , j. hutter , m. sprik , m. parrinello , j. chem . phys . * 122 * , 014515 ( 2005 ) . r. jonchiere , a. p. seitsonen , g. ferlat , a. m. saitta , r. vuilleumier , j. chem . phys . * 135 * , 154503 ( 2011 ) . r. z. khaliullin , t. d. khne , arxiv/1303.2067 ( 2013 ) . p. carloni , u. rothlisberger , m. parrinello , acc . 35 * , 455 ( 2002 ) . r. a. friesner , b. d. dunietza , acc . chem . res . * 34 * , 351 ( 2001 ) . s. yoo , x. c. zeng , s. s. xantheas , j. chem . phys . * 130 * , 221102 ( 2009 ) . h. s. lee , m. e. tuckerman , j. chem . phys . * 126 * , 164501 ( 2007 ) . c. j. d. von grotthuss , ann . lviii * , p. 54 n. agmon , chem . . lett . * 244 * , 456 ( 1995 ) . d. marx , chemphyschem , * 7 * , 1848 ( 2006 ) . t. e. decoursey , physiol rev . * 83 * , 475 ( 2003 ) . e. freiera , s. wolfb , k. gerwerta , proc . * 108*,11435 ( 2011 ) . j. deisenhofer , o. epp , i. sinning , h. michel , j. mol . biol . * 246 * , 429 ( 1995 ) . d. lancaster , h. michel , b. honig , m. gunner , biophys . j. * 70 * , 2469 ( 1996 ) . m. eigen , angew . int . ed . * 3 * , 1 ( 1964 ) . o. f. mohammed , d. pines , j. dreyer , e. pines , e. t. j. nibbering , science * 310 * , 83 ( 2005 ) . o. f. mohammed , d. pines , e. pines , e. t. j. nibbering , chem . phys . * 341 * , 240 ( 2007 ) . z. luz , s. meiboom , j. am . soc . * 86 * , 4768 ( 1964 ) . noam agmon , _ hydrogen bonds , water rotation and proton mobility . _ , j. chim . 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calculations on proton transfer static barriers and dissociation energies display the same agreement . our approach combines these features with a @xmath2-@xmath3 scaling with number of particles . this value is favorable with respect to other highly correlated _ ab initio _ approaches and it allows the simulation of more realistic pt models ; a test calculation on a larger protonated water cluster is hence carried out .

we report an extensive theoretical study of the protonated water dimer @xmath0 ( zundel ion ) by means of the highly correlated variational monte carlo and lattice regularized monte carlo approaches . this system represents the simplest model for proton transfer ( pt ) and a correct description of its properties is essential in order to understand the pt mechanism in more complex acqueous systems . our jastrow correlated agp wave function ensures an accurate treatment of electron correlations . exploiting the advantages of contracting the primitive basis set over atomic hybrid orbitals , we are able to limit dramatically the number of variational parameters with a systematic control on the numerical precision , a crucial ingredient in order to simulate larger systems . we investigate the energetics and geometrical properties of the @xmath0 as a function of the oxygen - oxygen distance , taken as reaction coordinate . in both cases , our qmc results are found in excellent agreement with state - of - the - art coupled cluster ccsd(t ) techniques . calculations on proton transfer static barriers and dissociation energies display the same agreement . a comparison with density functional theory results in the pbe approximation points out the crucial role of electron correlations for a correct description of the pt in the dimer . finally , the ability of our method to resolve very tiny energy differences ( @xmath1 kcal / mol ) at which the proton hopping takes place and the corresponding structural variations optimized directly in the vmc framework is also proven . our approach combines these features with a @xmath2-@xmath3 scaling with number of particles . this value is favorable with respect to other highly correlated _ ab initio _ approaches and it allows the simulation of more realistic pt models ; a test calculation on a larger protonated water cluster is hence carried out . the qmc approach used here represents a promising candidate to provide the first high - level _ ab - initio _ description of pt in water .

cond-mat0509295

c

as has been recently proposed @xcite , ru1222 materials consist of two phases , the minority one that orders around 180 k and the majority one that orders around 100 k ( depending on the eu / ce ratio ) . exact nature of both orderings is still unclear . although ferromagnetic - like features have been observed , detailed investigation of butterfly hysteresis in ru1222 reveals a more complex magnetism characterizing this material . temperature dependence of the inverted part ( fig . [ hystemp ] ) shows that it emerges at the main peak t@xmath7 where the majority phase orders , progressively freezing out as the temperature is lowered . we have investigated samples with x from 0.5 to 1.0 and they all show the same behavior , suggesting similar magnetic ordering to take place in all compositions . the h@xmath14 peak , which marks the coercive field , gradually increases as the temperature is decreased and reaches the value of 100 oe for 4.2 k. it can be compared with the values of 250 oe obtained in @xcite for much larger maximum fields ( 50 koe ) . from the figs . [ hystemp ] and [ maxdc ] it is obvious that h@xmath14 is not affected by the presence of the inverted peak , suggesting two separate contributions to the ac susceptibility . presently , we are unable to provide a full interpretation of the exponential dependence shown in the inset of the fig . [ maxdc ] . we note however that it indicates the presence of some fundamental interaction which is susceptible to small magnetic fields . also , a remarkable fact is that no feature can be seen in the magnetization measurements ( either vsm or squid ) that would correspond to the inverted part of the butterfly hysteresis . we suggest that the inverted behavior might reflect the interaction of the two magnetic phases , namely the ferromagnetic clusters and the background matrix , ordering at t@xmath6 and at t@xmath7 , respectively . as suggested by cardoso et al . @xcite the phenomenology of spin glasses could be relevant for ru1222 as well . indeed , we have observed the frequency dependence of the main peak at t@xmath7(not shown ) . the magnitude of the shift follows the spin - glass - like behavior @xcite but the magnitude of the ac susceptibility signal is orders of magnitude larger than for the usual spin - glass material . we speculate that the ferromagnetic clusters , randomly distributed and oriented in matrix , could impose a frustration on the surrounding matrix , giving rise to the spin - glass behavior and the observed frequency dependence .

two separate contributions to these hysteresis have been identified and studied . another contribution , represented by the so called inverted maximum , is related to the unusual inverted loops , unique feature of ru1222 butterfly hysteresis . the different nature of the two identified magnetic contributions is proved by the different temperature dependences involved . by lowering the temperature the inverted peak gradually disappears while the coercive field slowly raises . if the maximum dc field for the hysteresis is increased , the size of the inverted part of the butterfly hysteresis monotonously grows while the position of the peak saturates . in reaching saturation exponential field dependence has been demonstrated to take place . at t = 78 k the saturation field is 42 oe .

we report detailed studies of the ac susceptibility butterfly hysteresis on the ru1222 ruthenocuprate compounds . two separate contributions to these hysteresis have been identified and studied . one contribution is ferromagnetic - like and is characterized by the coercive field maximum . another contribution , represented by the so called inverted maximum , is related to the unusual inverted loops , unique feature of ru1222 butterfly hysteresis . the different nature of the two identified magnetic contributions is proved by the different temperature dependences involved . by lowering the temperature the inverted peak gradually disappears while the coercive field slowly raises . if the maximum dc field for the hysteresis is increased , the size of the inverted part of the butterfly hysteresis monotonously grows while the position of the peak saturates . in reaching saturation exponential field dependence has been demonstrated to take place . at t = 78 k the saturation field is 42 oe .

0909.1607

i

1a 1744@xmath0361 is a neutron star low mass x - ray binary ( lmxb ) discovered by the _ ariel v _ satellite @xcite . this source is a transient lmxb , and several outbursts have been observed with a number of missions , most notably the _ rossi x - ray timing explorer _ ( _ rxte _ ) . in 2001 @xcite discovered a burst from the direction of 1a 1744@xmath0361 , however , it could not be unambiguously identified as a thermonuclear burst . the first thermonuclear ( type i ) burst from 1a 1744@xmath0361 was discovered by @xcite using _ rxte_. this type i x - ray burst exhibited a 530-hz burst oscillation which provided a measurement of the neutron star s spin frequency . the burst also provided an upper limit of @xmath10 kpc , under the assumption that its maximum luminosity could not exceed the eddington luminosity for a 1.4-@xmath11 neutron star @xcite . this source also shows regular incidents of intensity `` dips '' in its x - ray emission . according to @xcite , such dips are produced by obscuring material associated with a structured accretion disk . dips would only be visible for inclination angles 60@xmath12@xmath1380@xmath12 @xcite . in principle dips could occur every orbital cycle , however , because of variations in the obscuring material in the disk , the presence of dips often varies from cycle to cycle and from source to source . the dips observed in 1a 1744@xmath0361 , as is the case for other dipping lmxbs , exhibit complex structure ( see * ? ? ? * fig . 4 ) . by measuring the spacing between two closely spaced dip episodes observed by _ rxte _ , @xcite estimated the orbital period of 1a 1744@xmath0361 to be @xmath1497 minutes , however these dip episodes were separated by a data gap , thus not precluding shorter orbital periods . narrow absorption features have been seen in the persistent emission of many `` dipping '' lmxbs . for example , xb 1916@xmath0053 @xcite , x 1624@xmath0490 @xcite , 4u 1323@xmath062 @xcite . by far , the most prominent features are the ( he - like ) and ( h - like ) lines . the ubiquity of narrow features in dipping lmxbs suggests that they are a property of all lmxbs , but are seen predominately in dipping lmxbs because their particular geometry is optimal for viewing them @xcite . these features allow one to probe the structure , dynamics , and evolution of the material surrounding the neutron star . thus , the spectral properties of 1a 1744@xmath0361 are of great interest . using _ rxte _ data , @xcite found that the persistent spectrum of this source is well modeled by a comptonized blackbody model @xcite , and they also found evidence of a broad ( @xmath140.6 kev ) iron emission feature at @xmath146 kev and an iron absorption edge at @xmath148 kev . _ rxte _ is not sensitive to narrow spectral features given its coarse spectral resolution and large fov , thus , during the july 2008 outburst of this source we triggered _ chandra x - ray observatory _ ( _ cxo _ ) target - of - opportunity observations for this purpose . in [ sec : analysis ] we present our analysis of the _ cxo_( [ sec : hetg ] ) and _ rxte _ ( [ sec : xte ] ) data from 1a 1744@xmath0361 . in [ sec : spec ] we present high resolution spectra of the source in which we find a absorption feature . in [ sec : c - c diagram ] we present an updated color - color diagram , and in [ sec : dips ] we describe how we used the new observations of dips to constrain the orbital period of the source . in [ sec : discussion ] we discuss our results .

we find that its persistent emission is well modeled by a blackbody ( @xmath1 kev ) plus power - law ( @xmath2 ) with an absorption edge at 7.6 kev . in the residuals of the combined spectrum rossi x - ray timing explorer _

we report on _ chandra x - ray observatory _ ( _ cxo _ ) high - energy transmission grating ( hetg ) spectra of the dipping low mass x - ray binary ( lmxb ) 1a 1744@xmath0361 during its july 2008 outburst . we find that its persistent emission is well modeled by a blackbody ( @xmath1 kev ) plus power - law ( @xmath2 ) with an absorption edge at 7.6 kev . in the residuals of the combined spectrum we find a significant absorption line at 6.961@xmath30.002 kev , consistent with the ( hydrogen - like fe ) 2 - 1 transition . we place an upper limit on the velocity of a redshifted flow of @xmath4 km s@xmath5 . we find an equivalent width for the line of @xmath6 ev , from which we determine a column density of @xmath7 @xmath8 via a curve - of - growth analysis . using xstar simulations , we place a lower limit on the ionization parameter of @xmath9 erg cm s@xmath5 . the properties of this line are consistent with those observed in other dipping lmxbs . using _ rossi x - ray timing explorer _ ( _ rxte _ ) data accumulated during this latest outburst we present an updated color - color diagram which clearly shows that 1a 1744@xmath0361 is an `` atoll '' source . finally , using additional dips found in the _ rxte _ and _ cxo_data we provide an updated orbital period estimate of 52@xmath35 minutes .

0909.1607

c

we present _ cxo _ hetg observations of 1a 1744@xmath0361 during its latest outburst , in which we have discovered a significant absorption feature at 6.961@xmath30.002 kev in its persistent emission . we identify this feature as a line , analogous to those seen in other dipping lmxbs . the width of the line was found to be @xmath128 ev , which corresponds to a dynamic temperature of @xmath79 kev . we place an upper limit on the velocity of a redshifted flow of @xmath4 km s@xmath5 . the line had an equivalent width of @xmath85 ev , for which we find a column density of @xmath129 @xmath8 via a cog analysis . we place an upper limit on the ionization parameter of @xmath130 erg cm s@xmath5 . all these values are consistent with the features seen in other dipping lmxbs . using additional _ rxte _ data we generated an updated color - color diagram for the source , which confirms the suggestion of @xcite that this source is an `` atoll '' source . we report two bursts in addition to the one reported by @xcite . performing a `` dip '' timing analysis , and under the assumption that dips only occur at a particular range of orbital phases , we find that @xmath13152@xmath35 minutes is the most likely orbital period , nearly half the frequency found by @xcite . 1a 1744@xmath0361 has demonstrated many of the properties of a canonical dipper , however , because it not as well sampled as the others , many of its parameters remain unconstrained . further observations with _ rxte _ and _ cxo _ during its next outburst are definitely warranted . we thank c. b. markwardt for useful discussions and for providing support for his numerical integration algorithm . this work has been supported by nasa via an adp grant and a _ chandra _ guest observer grant , as well as by the national science foundation ( us nsf grant ast 0708424 ) . this research has made use of data obtained through the high energy astrophysics science archive research center online service , provided by the nasa / goddard space flight center . , c. r. , davis , j. e. , dewey , d. , flanagan , k. a. , galton , e. b. , huenemoerder , d. p. , ishibashi , k. , markert , t. h. , marshall , h. l. , mcguirk , m. , schattenburg , m. l. , schulz , n. s. , smith , h. i. , & wise , m. 2005 , , 117 , 1144

we report on _ chandra x - ray observatory _ ( _ cxo _ ) high - energy transmission grating ( hetg ) spectra of the dipping low mass x - ray binary ( lmxb ) 1a 1744@xmath0361 during its july 2008 outburst . we find a significant absorption line at 6.961@xmath30.002 kev , consistent with the ( hydrogen - like fe ) 2 - 1 transition . we find an equivalent width for the line of @xmath6 ev , from which we determine a column density of @xmath7 @xmath8 via a curve - of - growth analysis . ( _ rxte _ ) data accumulated during this latest outburst we present an updated color - color diagram which clearly shows that 1a 1744@xmath0361 is an `` atoll '' source . finally , using additional dips found in the _ rxte _ and _ cxo_data we provide an updated orbital period estimate of 52@xmath35 minutes .

we report on _ chandra x - ray observatory _ ( _ cxo _ ) high - energy transmission grating ( hetg ) spectra of the dipping low mass x - ray binary ( lmxb ) 1a 1744@xmath0361 during its july 2008 outburst . we find that its persistent emission is well modeled by a blackbody ( @xmath1 kev ) plus power - law ( @xmath2 ) with an absorption edge at 7.6 kev . in the residuals of the combined spectrum we find a significant absorption line at 6.961@xmath30.002 kev , consistent with the ( hydrogen - like fe ) 2 - 1 transition . we place an upper limit on the velocity of a redshifted flow of @xmath4 km s@xmath5 . we find an equivalent width for the line of @xmath6 ev , from which we determine a column density of @xmath7 @xmath8 via a curve - of - growth analysis . using xstar simulations , we place a lower limit on the ionization parameter of @xmath9 erg cm s@xmath5 . the properties of this line are consistent with those observed in other dipping lmxbs . using _ rossi x - ray timing explorer _ ( _ rxte _ ) data accumulated during this latest outburst we present an updated color - color diagram which clearly shows that 1a 1744@xmath0361 is an `` atoll '' source . finally , using additional dips found in the _ rxte _ and _ cxo_data we provide an updated orbital period estimate of 52@xmath35 minutes .

1204.0506

i

the use of lasers in atomic physics often demands long term stability of the central frequency of the light emission . for metrological applications the stabilization technique @xcite should be very carefully chosen and applied , frequently controlling the laser linewidth and avoiding to introduce any artificial shift in the laser emission frequency . moreover , locking to the center of an atomic or molecular transition usually requires modulation techniques and lock - in detection . on the other hand , for many scientific and technical applications one only needs to avoid frequency drifts and , sometimes , the desired laser frequency does not lay at the maximum of an atomic lineshape , but rather at a displaced frequency , as for instance , when operating an optical cooler @xcite . for such applications a few simple and reliable techniques were developed @xcite and allow on e to deal with lasers in various long run experiments . the main idea behind many of these techniques is to generate a dispersive lineshape that will produce an error signal . in particular , for the dichroic atomic vapor laser lock ( davll ) @xcite and its variants @xcite , the stabilization frequency may easily be chosen around the center of the doppler - broadened line . however , a relatively uniform external magnetic field is needed to generate the zeeman split of the probed hyperfine transition and a double detection with well balanced photodetectors is also necessary . + in this work we report on a simple method to generate a dispersive signal in a very direct way , and therefore of easy implementation . our technique explores the dispersive signal obtained when a gaussian - profile light beam is sent through an atomic vapor cell and is detected after spatial filtering by an aperture ( fig . [ setup ] ) . we call this method angells , an acronym for atomic non - linearly generated laser locking signal . +

we report on a simple and robust technique to generate a dispersive signal which serves as an error signal to electronically stabilize a monomode cw laser emitting around an atomic resonance . we explore nonlinear effects in the laser beam propagation through a resonant vapor by way of spatial filtering . the performance of this technique is validated by locking semiconductor lasers to the cesium and rubidium @xmath0 line and observing long - term reduction of the emission frequency drifts , making the laser well adapted for many atomic physics applications .

we report on a simple and robust technique to generate a dispersive signal which serves as an error signal to electronically stabilize a monomode cw laser emitting around an atomic resonance . we explore nonlinear effects in the laser beam propagation through a resonant vapor by way of spatial filtering . the performance of this technique is validated by locking semiconductor lasers to the cesium and rubidium @xmath0 line and observing long - term reduction of the emission frequency drifts , making the laser well adapted for many atomic physics applications .

1504.03067

r

figure [ fig : profave ] shows the averaged h@xmath2 , h@xmath3 , and h@xmath0 profiles . in these profiles , the vertical scale of the h@xmath2 line profile is half that of the other line profiles , because the flux is much stronger in the h@xmath2 . the h@xmath2 line is very strong ( @xmath17 ) and significantly asymmetric . the profile exhibits a double peak at @xmath18 and @xmath19 , with the latter being brighter than the former , and a hump at @xmath20 on the blue wing . on the other hand , the averaged h@xmath3 line profile ( @xmath21 ) is rather symmetric , with a slightly stronger blue peak . the h@xmath0 line , which is on a broad absorption component , also exhibits a double - peaked profile with stronger blue peak . balmer lines exhibited complicated line profile variabilities during the monitoring period . figure [ fig : prof_ind ] displays all observed profiles of the h@xmath2 , h@xmath3 , and h@xmath0 lines , while fig . [ fig : prof_diff ] presents the time sequence of the residual spectra of these lines from the average . the variation in the equivalent width , ew , the full width at half maximum , fwhm , and the centroid velocity , @xmath22 , of the h@xmath2 line profile are shown in fig . [ fig : prof_param_ha ] . note that fwhm and @xmath22 are measured by fitting the whole profile with a single gaussian and the line wings with a voigt profile , respectively . in the long term ( @xmath23 days , from @xmath24 ) , the h@xmath2 line changed from a red - enhanced profile to a rather symmetric profile , while the stronger peak of the h@xmath3 and h@xmath0 lines changed from the red side to the blue side . in the residual spectra of these lines , s - shaped variability is visible ; the bright part at @xmath25 migrates from the blue side to the red side at @xmath26 , and returns to the blue side at @xmath27 . simultaneously , the faint part at @xmath28 migrates in the opposite direction . at the same time , the maximum and minimum , respectively at @xmath29 and @xmath30 in the residual spectra , migrate in a similar fashion . the period of these variations is estimated at @xmath31 days using fourier analysis , which is about twice the @xmath32-day variation period reported by @xcite . we will discuss this in more detail in the next section . on the other hand , in the short term ( @xmath33 days ) , a bright hump appears at @xmath29 in balmer line profiles at @xmath34 . this hump disappears by @xmath35 ( see the third , forth , and fifth profiles from the bottom in figs . [ fig : prof_ind ] and [ fig : prof_diff ] ) . when the hump appears , ew(h@xmath2 ) increases by @xmath36 and fwhm(h@xmath2 ) decreases by @xmath37 . these long- and short - term variabilities respectively seem to occur in phase in different lines , although time lags between lines can not be ruled out because of the low cadence of the observations . recently , @xcite reported the orbital modulation of the profile parameters of the h@xmath2 line . their data cover the phase intervals of 00.6 and 0.81 , using the orbital period of 321 days @xcite . if we take the same orbital period , our data spans the orbital phase 0.41 , which overlaps with @xcite in the phase range 0.40.6 and 0.81 and provides for the first time the modulation data in the phase interval of 0.60.8 . in fig . [ fig : prof_param_ha ] , ew(h@xmath2 ) seems to increase ( phase 0.40.5 ) and then decrease back to the previous value in about 30 days ( phase 0.50.6 ) , as reported by @xcite . afterwards , it seems to fluctuate for about 60 days ( phase 0.60.8 ) , which could be associated with the variabilities mentioned above . @xmath22(h@xmath2 ) , whose variation is thought to reflect the orbital motion of the be star , shows a similar pattern to @xcite except just after the apastron and just before the periastron . this difference in @xmath22 is possibly caused by the profile variabilities . fwhm(h@xmath2 ) , on the other hand , shows a different variation pattern from @xcite . it stays constant except around apastron ( phase 0.450.55 for the period of 321 days ) in this work , whereas in @xcite it showed a sinusoidal pattern . although many lines are contaminated by neighboring lines , there are six less - contaminated lines ( @xmath385018 , 5316 , 5363 , 5535 , 6433 , and 6456 ) that enable us to analyze the line profile variabilities . in our analysis , we have used these six lines . the averaged @xmath395363 line profile in fig . [ fig : profave ] is shown as a representative profile . in contrast to the balmer lines , the emission lines show symmetric double - peaked profiles , as predicted for a rotating , axi - symmetric disk . figures [ fig : prof_ind ] and [ fig : prof_diff ] also display the time sequence of the observed and residual @xmath395363 profiles , respectively . as seen in these figures , lines exhibited no variation . @xcite analyzed the spectra of several be stars and confirmed that emission lines arise from a disk region of radius of @xmath40 . they also found empirical relationships between the projected rotational velocity of the central star ( @xmath41 ) and the profile parameters . applying their relationships , we have derived @xmath41 to be @xmath42 . finally , we estimate the radii of emitting regions of balmer lines . for the h@xmath2 line , we use the mean peak separation of the last six profiles ( @xmath43 ) , because the averaged profile in fig . [ fig : profave ] , in which all our observed epochs were used , has too complicated features to determine the peak velocities . for the h@xmath3 and h@xmath0 lines , we use the averaged profiles . as a result , we have the peak separations of the h@xmath2 , h@xmath3 , and h@xmath0 lines to be @xmath44 , @xmath45 and @xmath46 , respectively . adopting @xmath41 derived above , we obtain the radii of the emitting region of these lines as @xmath47 @xmath5 ( h@xmath2 ) , 11 @xmath5 ( h@xmath3 ) , and 7 @xmath5 ( h@xmath0 ) , where @xmath48 is the radius of the be star . throughout our monitoring period ( from apastron to periastron ) , optical brightness of stayed constant in the range of 9.059.32 ( @xmath14 ) mag , 8.538.71 ( @xmath49 ) mag , and 8.588.67 ( @xmath50 ) mag , within the typical 1-@xmath51 error of 0.05 mag . the average values are @xmath52 mag , @xmath53 mag and @xmath54 mag .

the h@xmath2 , h@xmath3 , and h@xmath0 line profiles are found to exhibit remarkable short - term variability for @xmath41 month after the apastron ( phase 0.60.7 ) , whereas they show little variation near the periastron . these emission lines show `` s - shaped '' variations with timescale of @xmath4150 days , which is about twice that reported previously . in contrast to the balmer lines , no profile variability is seen in any emission line . we estimate the radii of emitting regions of the h@xmath2 , h@xmath3 , h@xmath0 , and emission lines to be @xmath430 , 11 , 7 , and 2 stellar radii ( @xmath5 ) , respectively .

we report on monitoring observations of the tev @xmath0-ray binary , which were carried out to constrain the interaction between the be circumstellar disk and the compact object of unknown nature , and provide for the first time high - dispersion ( r@xmath1 ) optical spectra in the second half of the orbital cycle , from apastron through periastron . the h@xmath2 , h@xmath3 , and h@xmath0 line profiles are found to exhibit remarkable short - term variability for @xmath41 month after the apastron ( phase 0.60.7 ) , whereas they show little variation near the periastron . these emission lines show `` s - shaped '' variations with timescale of @xmath4150 days , which is about twice that reported previously . in contrast to the balmer lines , no profile variability is seen in any emission line . we estimate the radii of emitting regions of the h@xmath2 , h@xmath3 , h@xmath0 , and emission lines to be @xmath430 , 11 , 7 , and 2 stellar radii ( @xmath5 ) , respectively . the amplitudes of the line profile variations in different lines indicate that the interaction with the compact object affects the be disk down to , at least , the radius of 7 @xmath5 after the apastron . this fact , together with little profile variability near the periastron , rules out the tidal force as the major cause of disk variability . although this leaves the pulsar wind as the most likely candidate mechanism for disk variations , understanding the details of the interaction , particularly the mechanism for causing a large - scale disk disturbance after the apastron , remains an open question .

1504.03067

c

although the monitoring was performed mostly after apastron , the line profiles exhibited remarkable variabilities . wide wavelength coverage revealed that the variations are seen not only in the h@xmath2 line but also in the h@xmath3 and h@xmath0 lines . no variation in lines indicates the inner part of the be disk was kept undisturbed during the observing period . this fact is in agreement with little variability in the optical brightness , which is thought to originate from the disk region within 23 @xmath5 @xcite . the slight , but significant , variation in the h@xmath0 line profile implies that the interaction with the compact object affects the be disk down to , at least , a radius of 7 @xmath5 . the dynamical residual spectra of the balmer lines showed an s - shaped variation ( fig . [ fig : prof_diff ] ) , as @xcite reported . high - dispersion residual spectra clearly show that there are two pairs of peaks at @xmath55 and @xmath56 . the lower velocity peaks are the same as those of @xcite ( see their fig . the period of the variation is @xmath4150 days , which is about twice the @xmath4 60-day variation period @xcite . the s - shaped variation seen in many be stars is thought to be caused by global disk oscillations . they are mostly low - frequency @xmath57 oscillations , where @xmath58 is the azimuthal wave number @xcite , but in eccentric binaries , it is also possible that @xmath59 oscillations are excited by the corresponding fourier components of the tidal potential ( e.g. , * ? ? ? if the period of observed variation is @xmath4 150 days , about half the orbital period , it might be due to an @xmath60 oscillation mode in the be disk , which could be excited by the @xmath60 fourier component of the tidal potential of the compact object . the difference of the periods between this work and @xcite might be caused by the difference of the length and frequency of the observations . because we observed for about half an orbital cycle ( @xmath61 days ) , variabilities of this timescale can be detected . with low cadence of observation , typically once every 1020 days , however , profile variabilities of shorter timescales are invisible . on the contrary , the short monitoring epoch of @xcite ( 35 days ) would have hidden the variability with longer timescales ( @xmath62 days ) . moreover , observations of this work and @xcite have an interval of @xmath41800 days . therefore , there are possibilities that the oscillation mode has changed or that both oscillation modes exist . in addition to the s - shaped variation , a remarkable variability was seen in the balmer lines after apastron ( @xmath8=0.600.65 ) . the short lifetime of this variability ( @xmath63 days ) indicates that it is temporarily caused by an external force such as the tidal force and the ram pressure of the pulsar wind , because internal waves / oscillations have much longer lifetimes ( @xmath64 days ; * ? ? ? * and references therein ) . it is surprising , however , that such a remarkable variability appeared after apastron , when the interaction is expected to be weak because of the large distance between the be disk and the compact object . in order to understand this phenomenon , it is essential to constrain the starting phase and repeatability of the variability . comparison of the ew(h@xmath2 ) between this work and @xcite implies the presence of a regular orbital modulation , but different absolute values due to different spectral resolutions make it difficult to quantitatively analyze it . given the orbital period close to one year , it is necessary to monitor over two or three more successive cycles , within the timescale of be disk variability ( @xmath65 days ) , in order to cover the full orbital phase with the same spectral resolution . because the compact object is located far away from the be star around apastron ( @xmath66 ) , the gas in the be disk at the radius of 7 @xmath5 can not be significantly affected by the tidal force of the compact object , whose strength is less than @xmath67 of the gravity of the be central star at this radius . this leaves the interaction with the pulsar wind as the most likely mechanism for the balmer line variability . at the periastron passage , on the other hand , the compact object is thought to pass through the be disk at @xmath68 . nonetheless , the h@xmath3 line , emitted from the disk region of the similar radius , showed no remarkable variation at @xmath690.06 ( see the top profile in the upper right panel of fig . [ fig : prof_ind ] ) . this fact suggests that either the tidal interaction is very weak in this system or the orbital period is longer than 315 days , so that the compact object had not passed the disk yet at the time of observation . the former possibility could be realized if the be disk rotates in the retrograde direction or is tilted by a large angle with respect to the orbital plane , where the disk gas and the compact object interact on a very short timescale . future observations at significantly later phases will distinguish between these two possibilities . as described in sects . [ sec : short ] and [ sec : imp ] , our observations leave the pulsar wind model as the sole candidate for . if the compact object is a pulsar , little line profile variation around periastron ( the top two profiles in each panel of fig . [ fig : prof_diff ] ) suggests that the pulsar wind is too weak to significantly affect the be disk during these phases . @xcite proposed a flip - flop scenario for another gamma - ray binary , , where the pulsar is in a rotationally powered regime in the apastron , while it is in a propeller regime in the periastron ( see also * ? ? ? * ) . in a flip - flop system , if the gas pressure of the be disk overcomes the pulsar - wind ram pressure , the pulsar wind is quenched . because the be disk of is estimated to be about three times larger than the binary separation at periastron , the compact object crosses a dense region of the disk near the periastron . in such a situation , the strong gas pressure is likely to quench the pulsar wind and hence suppress high - energy emissions . in the framework of the pulsar wind model , there are a few mechanisms that might explain the short - term episodic variability discussed above . the be disk is likely as large as the binary orbit because of no tidal truncation in highly eccentric , large orbit @xcite . because the disk density rapidly decreases with radius ( e.g. , * ? ? ? * ) , the wind from the pulsar close to the outer part of the disk effectively changes its structure , giving rise to remarkable variability in emission lines arising from the disk outer part . if the be disk is misaligned with the orbital plane and a node happens to be in the direction corresponding to the phase of the variation ( @xmath70 ) , the pulsar - wind effect on the be disk will be the strongest in this phase interval . after @xmath71 the pulsar comes close to the denser disk region , which is not easily affected by the pulsar wind . this might be a cause of the short - term episodic variation after aspastron . it is not clear , however , how the pulsar wind can affect the inner disk at the radius of 7 @xmath5 . alternatively , the short - term post - apastron variations might be explained as the emission from the gas captured by the pulsar , if the pulsar wind is not strong enough to expel the surrounding gas . this picture seems to fit well with the flip - flop model . at any rate , observational investigation in the first half of the orbital cycle is needed in order to further test the pulsar - wind scenario . the next periastron passage of will take place in 2015 december , according to the ephemeris of @xcite ( 2016 january if the ephemeris is taken from @xcite ) . observations covering this period will provide more clues to the complex interaction and the nature of the compact object in this puzzling @xmath0-ray binary . this paper is based on the observations taken at the okayama astrophysical observatory . we are grateful for dr . eiji kambe to kindly observe . this work was supported by research fellowships for the promotion of science for young scientists ( ym , kt ) . ato acknowledges support by the jsps grant - in - aid for scientific research ( 24540235 ) and a research grant from hokkai - gakuen educational foundation . acc acknowledges support from cnpq ( grant 307076/2012 - 1 ) . aharonian , f. a. et al . 2007 , , 469 , l1 aliu , e. , archambault , s. , aune , t. et al . 2014 , , 780 , 168 aragona , c. , mcswain , m. v. & de becker , m. 2010 , , 724 , 306 arias , m. l. , zorec , j. , cidale , l. , ringuelet , a. e. , morrell , n. i. & ballereau , d. 2006 , , 460 , 821 artymowicz , p. , & lubow , s. h. 1994 , , 421 , 651 bongiorno , s. d. , falcone , a. d. , stroh , m. , holder , j. , skilton , j. l. , hinton , j. a. , gehrels , n. & grube , j. 2011 , , 737 , 11 carciofi , a. c. & bjorkman , j. e. 2006 , , 639 , 1081 casares , j. , rib , m. , ribas , i. , paredes , j. m. , vilardell , f. & negueruela , i. 2012 , , 421 , 1103 dubus , g. , 2013 , , 21 , 64 kambe , e. , yoshida , m. , izumiura , h. at al . 2013 , 65 , 15 kawabata , k. s. , nagae , o. , chiyonobu , s. , et al . 2008 , proc . spie , 7014 , 70144l levinson , a. & blandford , r. 1996 , , 456 , l29 manset , n. & donati , j .- f . 2003 , proc . spie , 4843 , 425 maraschi , l. & treves , a. 1981 , , 194 , 1 okazaki , a. t. 1991 , , 43 , 75 okazaki , a. t. & negueruela , i. 2001 , , 377 , 161 papaloizou , j. c. , savonije , g. j. & henrichs , h. f. 1992 , , 265 , l45 papitto , a. , torres , d. f. & rea , n. 2012 , , 756 , 188 rivinius , th . , carciofi , a. c. , & martayan , c. 2013 , , 21 , 69 sakimoto , k. , akitaya , h. , yamashita , t. et al . 2012 , proc . spie , 8446 , 844673 torres , d. f. , rea , n. , esposito , p. , li , j. , chen , y. , zhang , s. 2012 , , 744 , 106 lccc + & date & jd & phase + oao / hides + & 2013.10.31 & 2456597.278 & 0.555 + & 2013.11.08 & 2456605.275 & 0.580 + & 2013.11.11 & 2456608.274 & 0.589 + & 2013.11.19 & 2456616.199 & 0.615 + & 2013.12.01 & 2456628.219 & 0.653 + & 2013.12.19 & 2456646.201 & 0.710 + & 2013.12.29 & 2456656.007 & 0.741 + & 2014.01.02 & 2456660.047 & 0.754 + & 2014.01.15 & 2456673.095 & 0.795 + & 2014.01.23 & 2456681.094 & 0.821 + & 2014.02.08 & 2456696.968 & 0.871 + & 2014.03.11 & 2456728.008 & 0.969 + cfht / espadons + & 2014.02.05 & 2456693.843 & 0.861 + & 2014.04.10 & 2456757.772 & 0.064 + + & filter & jd & nights + kanata / howpol + & @xmath14 & 24565512456795 & 73 + & @xmath15 & 24565512456795 & 71 + & @xmath16 & 24567222456795 & 10 + kanata / honir + & @xmath14 , @xmath15 , @xmath16 & 24567432456769 & 8 +

we report on monitoring observations of the tev @xmath0-ray binary , which were carried out to constrain the interaction between the be circumstellar disk and the compact object of unknown nature , and provide for the first time high - dispersion ( r@xmath1 ) optical spectra in the second half of the orbital cycle , from apastron through periastron . the amplitudes of the line profile variations in different lines indicate that the interaction with the compact object affects the be disk down to , at least , the radius of 7 @xmath5 after the apastron . this fact , together with little profile variability near the periastron , rules out the tidal force as the major cause of disk variability . although this leaves the pulsar wind as the most likely candidate mechanism for disk variations , understanding the details of the interaction , particularly the mechanism for causing a large - scale disk disturbance after the apastron , remains an open question .

we report on monitoring observations of the tev @xmath0-ray binary , which were carried out to constrain the interaction between the be circumstellar disk and the compact object of unknown nature , and provide for the first time high - dispersion ( r@xmath1 ) optical spectra in the second half of the orbital cycle , from apastron through periastron . the h@xmath2 , h@xmath3 , and h@xmath0 line profiles are found to exhibit remarkable short - term variability for @xmath41 month after the apastron ( phase 0.60.7 ) , whereas they show little variation near the periastron . these emission lines show `` s - shaped '' variations with timescale of @xmath4150 days , which is about twice that reported previously . in contrast to the balmer lines , no profile variability is seen in any emission line . we estimate the radii of emitting regions of the h@xmath2 , h@xmath3 , h@xmath0 , and emission lines to be @xmath430 , 11 , 7 , and 2 stellar radii ( @xmath5 ) , respectively . the amplitudes of the line profile variations in different lines indicate that the interaction with the compact object affects the be disk down to , at least , the radius of 7 @xmath5 after the apastron . this fact , together with little profile variability near the periastron , rules out the tidal force as the major cause of disk variability . although this leaves the pulsar wind as the most likely candidate mechanism for disk variations , understanding the details of the interaction , particularly the mechanism for causing a large - scale disk disturbance after the apastron , remains an open question .

0806.4001

i

more than ten years after the first measurements by the cdf collaboration of the _ direct _ production of @xmath1 and @xmath3 at @xmath4 tev @xcite we are still facing disagreements between theoretical predictions from the various available models and experimental studies of the cross section and the polarisation from the tevatron and rhic ( for reviews see @xcite ) . cdf @xcite recently confirmed their previous polarisation measurement @xcite showing an unpolarised or slightly longitudinally polarised prompt @xmath1 yield . this has reinforced the doubts cast on the dominance of the colour octet mechanism ( com ) coming from the application of nrqcd @xcite . at the same time , many new results became available , _ e.g. _ the long - awaited nlo qcd corrections to the csm @xcite showing significant enhancement of the cross section , an up - to - date proof @xcite of nrqcd factorisation ; an improved treatment of nrqcd factorisation in fragmentation regions where three heavy quarks have similar momenta @xcite and last but not least a recent evaluation of the dominant @xmath5 ( nnlo ) @xcite correction to @xmath6 production , the latter solving the longstanding conflict between the experimental measurements from the tevatron at _ mid and large _ @xmath2 @xcite and the prediction from the csm @xcite . considering that none of the existing theoretical approaches could reproduce all available experimental data , we undertook in @xcite a systematic study of the cut contributions due to off - shell and non - static quarks . in particular , we questioned the assumption of the csm that takes the heavy quarks forming the quarkonium ( @xmath7 ) as being on - shell @xcite . if they are not , the usual @xmath0-channel cut contributes to the imaginary part of the amplitude and need to be considered on the same footing as the csm cut . current conservation for such off - shell configuration responsible for the @xmath0-channel cut imposes the introduction of an additional four - point function , or contact current @xcite , accounting for the interactions between the @xmath8 pair emitting the external gluon . in fact , this mechanism arises because of the possibility that the outgoing gluon is emitted by the particle interacting in the dressed @xmath9 vertex ( see figure [ fig : illus_gi_break ] ( a ) ) , as depicted in figure [ fig : illus_gi_break ] ( b ) . the pair of on - shell quarks that makes the final @xmath1-gluon state is now in a colour - octet state which thus recovers the necessity for such configurations as a natural consequence of restoring gauge invariance . although current conservation imposes the introduction of such a 4-point vertex , it does not enable to relate it univocally to the 3-point one . yet , there exist certain minimal requirements @xcite which such a 4-point function should satisfy . the 4-point function proposed in @xcite provided a conserved current but was not entirely satisfactory since it contained poles ( by construction similar to the basic direct and crossed contributions ) , and such poles for the contact current are unphysical and therefore should be avoided @xcite . another caveat to avoid was formerly identified by drell and lee @xcite . indeed , the minimal substitution prescription @xmath10 ( @xmath11 : charge , @xmath12 : vector potential ) in an effective lagrangian corresponding to the dressed hadronic vertex is deficient in that it violates the high - energy scaling behaviour , because in avoiding poles for the 4-point function , it partially replaces the true momentum dependence of the vertices by constants . such an issue can be easily avoided in the approach which we shall follow and which was applied to pion photoproduction processes @xcite . as we shall show in the following , it is hence possible to build a 4-point vertex encompassing two limiting behaviours , when the final - state gluon is soft or hard @xcite . in turn , we shall show that this enables to reproduce experimental data from the tevatron up to mid @xmath2 by adjusting the unconstrained parameters of the 4-point vertex and hence to get a remarkable agreement with data from rhic down to low @xmath2 .

we show that it is likely significantly larger than the usual cut contribution of the colour - singlet model ( csm ) , which is known to underestimate the experimental measurements . here the @xmath0-channel cut develops for configurations with off - shell quarks in the bound state . a correct treatment of its contribution requires the introduction of a four - point function , partially constrained by gauge invariance and limiting behaviours at small and large momenta . address = institut fr theoretische physik , universitt heidelberg , + philosophenweg 19 , 69120 heidelberg , germany address = center for nuclear studies , department of physics , the george washington university , washington , dc 20052 , usa + e - mail : lansberg@tphys.uni-heidelberg.de,helmut@gwu.edu

we report on our recent evaluation of the @xmath0-channel cut contribution to @xmath1 hadro - production . we show that it is likely significantly larger than the usual cut contribution of the colour - singlet model ( csm ) , which is known to underestimate the experimental measurements . here the @xmath0-channel cut develops for configurations with off - shell quarks in the bound state . a correct treatment of its contribution requires the introduction of a four - point function , partially constrained by gauge invariance and limiting behaviours at small and large momenta . when the unconstrained degrees of freedom are fixed to reproduce the tevatron data , we show that rhic data are remarkably well reproduced down to very low transverse momenta @xmath2 without need of resummation of initial - state gluon effects . this unique feature might be typical of @xmath0-channel cut contribution . address = institut fr theoretische physik , universitt heidelberg , + philosophenweg 19 , 69120 heidelberg , germany address = center for nuclear studies , department of physics , the george washington university , washington , dc 20052 , usa + e - mail : lansberg@tphys.uni-heidelberg.de,helmut@gwu.edu

0806.4001

c

in @xcite , we showed that there exist two singularities contributing to the imaginary part of the amplitude for @xmath90 . the first can be identified to the csm contribution when the static limit is taken ( no relative momentum between quarks ) . the second can be referred to as an @xmath0-channel cut and was never considered before @xcite . to deal with such configurations , we have to introduce a four - point function @xmath91 , complementing the information given by the three - point function ( or bethe - salpeter amplitude ) @xmath92 . such a four - point function is a priori constrained by a low - energy limit ( when the emitted gluon is soft ) and a scaling limit ( when the emitted gluon is hard ) . given those two physical constraints , we constructed a four - point functions exhibiting a dependence only on two parameters , which we fixed to reproduce the tevatron measurements up to mid @xmath2 . we then used the latter to compute the cross section for the rhic kinematics , for which we obtained a striking agreement with phenix data . this agreement can be employed @xcite to investigate on the kinematical effects attributable to the final - state - gluon emission in studies of shadowing effects on @xmath1 production in @xmath93 , @xmath94 and @xmath95 collisions , in the spirit of the study @xcite . our prediction for the polarisation for the prompt @xmath1 yield at mid @xmath2 at the tevatron is mostly longitudinal . in the com , colour - octet matrix elements account for transitions between a coloured heavy - quark pair into a quarkonium by soft unseen gluon emissions in the final state . in the present approach , the 4-point function accounts for gluon exchanges between the heavy quarks emitting the final - state gluon . as for the matrix elements of nrqcd , which are unknown and then fit , we fixed the unconstrained parameters of this function in order to reproduce the experimental data at @xmath4 tev from the cdf collaboration at the tevatron for @xmath96 gev . contrary to usual results obtained with lo calculations , our approach agrees with data down to very low values of the transverse momentum without need of resummation of initial - state gluon effects . this feature could be attributed to the threshold associated with the cut in the @xmath0-channel and should be analysed in more details in the future . before drawing further conclusions , several points have to be addressed : firstly , the size of the real part of the amplitude has to be evaluated . when fixing the parameter of our four - point function to describe the tevatron data we have implicitly assumed that such a real part was small ; this has to verified . secondly , the four - point function we proposed here has to be applied to other regimes of production : a similar enhancement by inclusion of the @xmath0-channel cut is expected in all production processes where the @xmath1 is associated with a gluon , _ e.g. _ , photon - photon collision at lep as well as in photo- and lepto - production at hera . on the other hand , other observables insensitive to the com or the @xmath0-channel cut and thus to the ambiguity attached to the description of the four - point function should be studied in the future , especially at the lhc . to conclude , let us mention two promising new observables , @xmath1 production in association with a @xmath97 pair @xcite and the hadronic activity around the @xmath1 @xcite .

we report on our recent evaluation of the @xmath0-channel cut contribution to @xmath1 hadro - production . when the unconstrained degrees of freedom are fixed to reproduce the tevatron data , we show that rhic data are remarkably well reproduced down to very low transverse momenta @xmath2 without need of resummation of initial - state gluon effects

we report on our recent evaluation of the @xmath0-channel cut contribution to @xmath1 hadro - production . we show that it is likely significantly larger than the usual cut contribution of the colour - singlet model ( csm ) , which is known to underestimate the experimental measurements . here the @xmath0-channel cut develops for configurations with off - shell quarks in the bound state . a correct treatment of its contribution requires the introduction of a four - point function , partially constrained by gauge invariance and limiting behaviours at small and large momenta . when the unconstrained degrees of freedom are fixed to reproduce the tevatron data , we show that rhic data are remarkably well reproduced down to very low transverse momenta @xmath2 without need of resummation of initial - state gluon effects . this unique feature might be typical of @xmath0-channel cut contribution . address = institut fr theoretische physik , universitt heidelberg , + philosophenweg 19 , 69120 heidelberg , germany address = center for nuclear studies , department of physics , the george washington university , washington , dc 20052 , usa + e - mail : lansberg@tphys.uni-heidelberg.de,helmut@gwu.edu

1507.01410

i

field - effect - transistors ( fets ) have emerged as promising devices for sensitive and fast room temperature detection of terahertz ( thz ) radiation @xcite . they are considered as a good candidate for real - time thz imaging and spectroscopic analysis @xcite as well as future thz wireless communications @xcite . devices employing plasmonic effects in fets have already been applied for room temperature detection of radiation with frequencies from tens of ghz up to several thz and enable the combination of individual detectors in a matrix . they are characterized by high responsivity ( up to a few kv / w ) , low noise equivalent power ( down to 10 pw/@xmath1 ) , fast response time ( tens of picoseconds ) and large dynamic range ( linear power response up to 10 kw/@xmath2 ) , see e.g. ref.@xcite . the operation principle of fet thz detectors used so far is based on the nonlinear properties of the two - dimensional ( 2d ) plasma in the transistor channel . the standard dyakonov - shur model @xcite assumes that radiation is coupled to the transistor by an effective antenna , which generates an @xmath3 voltage predominantly on one side of the transistor . both resonant @xcite and non - resonant @xcite regimes of thz detection have been studied . while research aimed to development of thz fet detectors is focused on single gate structures recently several groups have shown that higher sensitivities are expected for structures with periodic symmetric and asymmetric metal stripes or gates @xcite . in particular , dual - grating - gate fet are considered as a good candidate for sensitive thz detection . the first data obtained on dual - gated - structures demonstrated a substantial enhancement of the photoelectric response and an ability to control detector parameters by variation of individual gate bias voltage @xcite . at the same time , thz electric field applied to fets with asymmetric periodic dual gate structure is expected to give rise to electronic ratchet effects @xcite ( for review see @xcite ) and plasmonic ratchet effects @xcite . besides improving the figure of merits of fet detectors , ratchet effects may also result in new functionalities . in particularly , they may induce photocurrents driven solely by the radiation helicity . here , we report on the observation of a radiation helicity sensitive photocurrent excited by thz radiation in dual - grating - gate inalas / ingaas / inalas / inp high electron mobility transistors ( hemt ) . we show that artificial non - centrosymmetric microperiodic structures with a two - dimensional electron system excited by thz radiation exhibit a @xmath0 photocurrent caused by the lateral asymmetry of the applied static potential and terahertz electric field . we demonstrate that depending on gate voltages applied to the individual gratings of the dual - grating - gate the response can be proportional to either the stokes parameters @xcite defining the radiation helicity or those for linear polarization . as an important result , for a wide range of gate voltages we observed a photocurrent @xmath4 being proportional to the radiation helicity @xmath5 , where @xmath6 and @xmath7 are intensities of right- and left - handed circularly polarized light . for the circular photocurrent @xmath4 measured between source and drain contacts changes its sign with the inversion of the radiation helicity . this observation is of particular importance for a basic understanding of plasmon - photogalvanic and quantum ratchet effects . it also has a large potential for the development of an all - electric detector of the radiation s polarization state , which was so far realized applying less sensitive photogalvanic effects only @xcite . the observed phenomena is discussed in the framework of electronic ratchet @xcite and plasmonic ratchet effects excited in a 2d electron system with a spatially periodic _ dc _ in - plane potential @xcite .

we report on the observation of a radiation helicity sensitive photocurrent excited by terahertz ( thz ) radiation in dual - grating - gate ( dgg ) inalas / ingaas / inalas / inp high electron mobility transistors ( hemt ) . for a circular polarization the current measured between source and drain contacts changes its sign with the inversion of the radiation helicity . for elliptically polarized radiation the total current is described by superposition of the stokes parameters with different weights . moreover , by variation of gate voltages applied to individual gratings the photocurrent can be defined either by the stokes parameter defining the radiation helicity or those for linear polarization . we show that artificial non - centrosymmetric microperiodic structures with a two - dimensional electron system excited by thz radiation exhibit a @xmath0 photocurrent caused by the combined action of a spatially periodic in - plane potential and spatially modulated light . the results provide a proof of principle for the application of dgg hemt for all - electric detection of the radiation s polarization state .

we report on the observation of a radiation helicity sensitive photocurrent excited by terahertz ( thz ) radiation in dual - grating - gate ( dgg ) inalas / ingaas / inalas / inp high electron mobility transistors ( hemt ) . for a circular polarization the current measured between source and drain contacts changes its sign with the inversion of the radiation helicity . for elliptically polarized radiation the total current is described by superposition of the stokes parameters with different weights . moreover , by variation of gate voltages applied to individual gratings the photocurrent can be defined either by the stokes parameter defining the radiation helicity or those for linear polarization . we show that artificial non - centrosymmetric microperiodic structures with a two - dimensional electron system excited by thz radiation exhibit a @xmath0 photocurrent caused by the combined action of a spatially periodic in - plane potential and spatially modulated light . the results provide a proof of principle for the application of dgg hemt for all - electric detection of the radiation s polarization state .

1509.04892

r

the main panel of figure[fig1 ] shows the rietveld refined xrd patterns for @xmath0 . the inset shows schematic digram of crystal structure . evidently , there are two positions for sn atoms ; those that are at the corners of unit cell ( sn1 ) and the rest that form the polyhedra enclosing the co atom at the center ( sn2 ) . thus co and sn2 atoms form corner sharing @xmath22 trigonal prisms . reitveld refinement of xrd data of @xmath0 . inset shows schematic crystal structure of @xmath0 . ] figure[fig2 ] compares the xrd patterns for @xmath16 ( where x = 0 , 0.65 and 1.3).the peaks are indexed with @xmath9-type structure of space group pm-3n . the lattice parameter of @xmath16 are estimated to be a = 9.636 @xmath23 , 9.637 @xmath23 and 9.639 @xmath23 for x = 0 , 0.65 and 1.3 respectively . two impurity phases , @xmath24 and @xmath25 , have also been identified which are marked by @xmath26 and @xmath27 respectively . the edax measurements provide the percentage of the constituent elements in the compound . combined xrd of @xmath0 , @xmath28 , and @xmath6 samples . inset ( i ) shows edax data for @xmath6 and inset ( ii ) depicts sem image of @xmath6 . ] for 5% indium substituted compound , the atomic percentage for la , co , sn and in are 14.09% , 20.74% and 62.0% and 3.16% respectively , while for 10% indium substituted sample the percentages are 15.1% , 20.21% , 58.32% and 6.37% respectively ( inset ( i ) ) . sem image of @xmath6 is shown in inset ( ii ) of figure[fig2 ] . it shows grains with varying sizes and the features are unlike layered structures observed in cuprate and chalcogenide superconductors . in figure[fig3 ] we discuss the electronic density of states analysis of @xmath0 . using vasp 5.3 codes we have studied the electronic band structure of @xmath0 and its possible tunability towards achieving higher @xmath29 phases by chemical substitution . for the calculation of band structure and density of state of the parent compound , we employed paw ( projected augmented waves ) and plane wave basis set of 360 ev cut off . the dft calculations were performed using gga - pbe ( generalized gradient approximation - perdewburke ernzerhof ) approximations . typically @xmath30 mesh points were used with k - point grid of @xmath31 to achieve optimal convergence . ( a ) band structure of @xmath0 . ( b ) calculated density of states , and ( c ) phonon dispersion curve of @xmath0 . ] figure[fig3](a ) shows results of band structure calculation in high symmetry directions of @xmath32 . from the large dispersion of bands near fermi level it is evident that that the parent compound is metallic in nature . the density of state at fermi level ( figure[fig3](b ) ) reveals that there is strong hybridization of co 3d orbital and sn 5p orbital that contributes to observed superconductivity . at the fermi level the value of dos is around 15 states / ev [ in formula unit ] , which reconfirm metallicity in the parent compound . presumably , superconductivity arises due to orbital hybridization of sn2 and co atoms . the outer sn1 atoms at the corners of the unit cell , do not contribute to superconductivity . in effect , the tuning of superconducting properties of this skutterudite would depend on effective modification of the density of states at fermi level by appropriate substitution at the sn2 site . further , as seen in figure[fig3](c ) , only positive frequencies are seen in phonon dispersion curve indicating absence of structural instability . this is in contrast to what was reported from specific heat measurements by liu et al.@xcite . in the skutterudite family , structural instabilities were also reported in @xmath15 and @xmath12 where negative frequencies in phonon dispersion curves were observed . this was associated with cdw transitions around 147 k and 35 k respectively @xcite . but we find no evidence for such instabilities either in the parent or in substituted @xmath0 . + electrical resistivity is plotted as a function of temperature for ( a ) @xmath0 , ( b ) @xmath28 and ( c ) @xmath6 . insets ( i ) and ( ii ) in each panel show superconducting transition and fermi liquid fitting respectively . ] figure[fig4 ] shows the temperature dependence of resistivity from 1.7 k to 300 k for @xmath16(x = 0 , 0.65 and 1.3 ) . the insets show magnified superconducting transition and fermi liquid fitting . as seen in inset of figure[fig4](a ) , the parent @xmath0 shows @xmath33 = 2.5 k and @xmath34 = 1.77 k. this value is in accordance with earlier reports @xcite . most notably , there is significant enhancement in superconducting transition to @xmath33 = 4.7 k and @xmath34= 3.2 k for 5% indium doped @xmath35 compound . on careful analysis we find the deviation from normal state resistivity actually begins from 5.3 k ( inset ( i ) figure [ fig4](b ) ) . this is suggestive of inhomogeneous distribution of grains . more striking is the low temperature resistivity data of @xmath6 ( inset ( i ) figure[fig4](c ) ) where an extremely sharp transition of @xmath33 = 5.1 k is seen with transition width @xmath36 t @xmath37 0.1k . this is more than two times than that for the parent compound . the residual resistivity ratio ( rrr ) for @xmath16 is found to be 2.18 , 1.37 and 2.15 for x = 0 , 0.65 and 1.3 respectively . but we note that unit of resistivity is in @xmath38 @xmath39 for the parent compound in contrast to @xmath40 @xmath39 for the doped specimen . the resistivity variation with temperature indicates the metallic nature of the parent as well as doped compounds in the normal state . in contrast , iso - structural compounds with ge at the sn place , i.e. @xmath41 , @xmath42 , @xmath43 etc show semiconducting behaviour in normal state @xcite . the reason for different normal state conduction mechanism is attributed to the atomic displacement parameter ( adp ) and compounds with smaller adp are found to exhibit metallic ground state while those with large adp have semiconducting ground state @xcite . moreover , no evidence for the presence of cdw is observed either in the parent or in the indium doped samples which has been observed in other stannides such as @xmath15 and @xmath12 @xcite . in @xmath15 the cdw emerges because of structural transition from simple cubic to a body centered cubic superstructure with doubling of the cell parameter below 147 k. this is confirmed by optical spectroscopy , hall , specific heat and nmr measurements @xcite . a first - order phase transition has been observed in single - crystal of @xmath0 with a marked peak at t @xmath37152 k by specific heat and nmr measurements@xcite . the observed transition has been related to a structural change from a simple cubic to a body - centred - cubic super - structure with crystallographic cell doubling . but we do not observe this behaviour in our polycrystalline samples . further , we did not find any anomaly in the specific heat measurements ( not included here ) around the reported cdw transition temperature range . the normal state resistivity curves ( figure[fig4 ] ) have also been fitted to the formula @xmath44 . the values of residual resistivity @xmath45 for @xmath46 are 0.644 @xmath38 @xmath39 , 31.30 @xmath47 @xmath39 16.45 @xmath47 @xmath39 ; and values for a are 5.482 @xmath48 @xmath49 , 4.542 @xmath50 @xmath49 and 7.632 @xmath51 @xmath52 for x = 0 , 0.65 and 1.3 respectively . it is interesting to note that the residual resistivity decreased for higher indium percentage . further , magnitude of parameter a , which provides a scale for the degree of electronic correlation , increased reflecting an enhanced electronic correlation for higher indium percentage . overall , the normal state resistivity data of @xmath0 can be categorized as weak fermi liquid behaviour@xcite . resistivity variation with respect to temperature of ( a ) @xmath28 and ( b ) @xmath6 in the presence of applied magnetic field . for @xmath28 the applied field values are 0 t , 0.1 t , 0.15 t , 0.2 t , 0.25 t , 0.3 t , 0.35 t , 0.4 t , 0.45 t , 0.5 t , and 0.65 t. similarly , for @xmath6 , the corresponding field values are 0 t. 0.05 t , 0.1 t,0.15 t , 0.2 t , 0.25 t , 0.3 t , 0.35 t , 0.4 t , 0.45 t , 0.55 t and 0.7 t. inset ( i ) shows @xmath53 and @xmath54 variation as a function of temperature for @xmath6 . inset ( ii ) shows extrapolated @xmath53 - @xmath55 phase diagram according to ginzburg - landau model . ] figure[fig5 ] shows the resistivity variation with temperature at different applied external magnetic field for @xmath46 with ( a ) x= 0.65 and ( b ) 1.3 . in both cases , the superconducting transition broadens with the application of magnetic fields along with decrease in @xmath14 . the inhomogeneous nature of x= 0.65 sample is evident in in - field study as well . for x= 1.3 , the @xmath14(h ) values for onset and offset superconducting transition as a function of magnetic field and temperature were ascertained . the corresponding upper critical @xmath2(t ) and irreversibility @xmath54(t ) fields are plotted in the inset of the figure[fig5](a ) . using generalized ginzburg - landau model for upper critical field @xmath2(t ) = @xmath2(0)[(1- @xmath56)/ ( 1 + @xmath56 ) ] with t = t/@xmath14 , the h(t ) phase diagram is sketched in inset of figure[fig5](b ) . the extrapolated @xmath53 ( 0 ) is 0.68 tesla . using this value , the ginzburg landau coherence length @xmath57= @xmath58 , with flux quantum @xmath59 , is estimated to be @xmath60 nm , 21.6 nm for 5% , 10% indium doped specimen respectively . in type - ii superconductors the pair breaking occurs mainly in two ways , either by orbital effect or by spin paramagnetic effect . further , in clean limit the orbital upper critical field is given by @xmath61 ( 0 ) = -0.72@xmath14 [ dh / dt]@xmath62 . this is found to be 0.615 t for 10% indium substituted sample . on the other hand , using the formula , @xmath63 = 1.82 @xmath14 in the weak coupling pauli paramagnetic limit,@xmath64 is found to be 9.1 t. it is seen that , @xmath65 and this indicates that upper critical field in @xmath46 is pauli limited . the main panel shows zfc - fc data at 20 g external field for ( a ) @xmath0 , ( b ) @xmath28 , and ( c ) @xmath6 . the insets show m - h loop at 1.7 k for the corresponding samples . ] the magnetization measurements were performed under zero field cooled ( zfc ) & field cooled ( fc ) protocols . figure[fig6 ] shows the magnetization measurement in zfc and fc condition in applied field of 20 gauss . the superconducting transition temperature for @xmath46 is marked at 2.2 k , 5.1 k and 4.6 k for x = 0 , 0.65 and 1.3 respectively . from the zfc - fc data of the parent material and the doped compound , we get that the irreversible region to be more in case of indium substituted ones . the increasing irreversibility region indicates that the vortex pinning has been enhanced with indium substitution . the m - h loop taken at 1.7 k is shown in insets of figure 6 . in indium substituted compounds , the m - h loop shows the characteristic features of the type - ii superconductors . the lower critical field ( @xmath1 ) which is marked by a deviation from linearity in the diamagnetic state is 0.0028 t in 10% indium doped @xmath0 . using the values of @xmath2 and @xmath1 , penetration depth ( @xmath4 ) and ginzburg landau parameter ( @xmath5 ) are calculated by @xmath66 and @xmath67 . the values of @xmath4 = 33.2 nm and @xmath68 are obtained for @xmath6 . variation of resistivity of @xmath6 upto room temperature at various external pressure . superconducting transition of @xmath6 at pressure between 0.35 gpa and 2 gpa is shown in inset(i ) . variation of @xmath69 and @xmath70 at pressure upto 2 gpa is plotted in inset(ii ) ] like magnetic field , applied pressure also tunes various parameter of superconductivity like density of states at fermi level and electron - phonon coupling etc . in conventional superconductors @xmath14 decreases with pressure@xcite , but in cuprates @xmath14 first increases till optimum pressure and then decreases on further increase in pressure@xcite . figure[fig7 ] shows the impact of pressure on the @xmath14 of 10% indium substituted sample . the main panel of figure[fig7 ] shows the variation of resistivity till 300 k at different pressure ranging between 0.35 gpa and 2 gpa . variation in superconducting transition at different pressure is shown in inset(i ) of figure[fig7 ] which clearly shows that @xmath33 as well as @xmath71 are decreasing monotonously . at p= 0.35 gpa , @xmath72 decreases from 5.1 k to 4.3 k and with increasing pressure till 2 gpa it decreases to 3.85 k. similarly the @xmath70 also decreases with pressure from 5 k to 4.13 k for 0.35 gpa and further to 3.67 for 2gpa . the values of corresponding pressure coefficients @xmath73 and @xmath74 are -0.311 , -0.267 k / gpa respectively . this result is in contrast with the earlier report on pressure effects in parent compound @xmath75 @xcite where @xmath14 increased with application of external pressure . this indicates with indium doping and consequent positive chemical pressure optimal @xmath76 increase has been achieved . although not reported here , higher indium substitution led to inhomogeneous samples with no clear evidence for increase in transition temperature . we note that @xmath0 is assigned as a bcs superconductor and in weak coupling theory , @xmath10 @xmath7 @xmath77 @xmath78 @xmath79 , where @xmath77 is the debye temperature,@xmath80 is electron phonon coupling strength , and density of state is @xmath81 goes as @xmath82 where @xmath83 is effective mass and n is carrier density . in figure[fig7 ] along with decrease in @xmath33 , we find increase in metallicity with increase in external pressure . this implies we can not assign the decrease in @xmath10 with pressure merely to change in carrier concentration . further a low carrier concentration @xmath84 @xmath85 per cc is estimated from room temperature hall measurements . therefore some aspects of unconventional superconductivity involving effective mass @xmath83 is indicated in indium substituted optimal @xmath0 compositions . ( a ) arrhenius plot of @xmath28 . variation of vortex activation energy as a function magnetic field is plotted in the inset ( b ) arrhenius plot of @xmath6 . insets show magnetic field dependence of vortex activation energy . ] the broadening in the resistivity curve on application of the applied external magnetic field is due to the vortex motion in the mixed state and dissipation of energy because of the vortex motion . vortex activation energy variation with applied magnetic fields provides the scale for a material towards potential applications . this arrhenius plot provides the flux flow activation energy dependence on the applied magnetic field through the relation @xmath86 . the activation energy @xmath87 is determined by taking the slope of the linear part of arrhenius plot while @xmath88 is the field independent pre - exponential factor . the activation energy exhibits different power - law dependences on a magnetic field , i.e. @xmath89 . the values of @xmath87 , are deduced from the limited temperature intervals below @xmath90 , in which the data of the arrhenius plot of @xmath91 yield straight lines . the arrhenius plots are shown in the figure[fig8 ] and activation energy is plotted in the inset . the straight line behaviour over 3 decades of the resistivity data validates the thermally activated flux flow ( taff ) process as described by the arrhenius law . for 5% in doped sample ( figure[fig8](a ) ) , the activation energy dependence on the magnetic field is @xmath87 ( b ) @xmath92 for b @xmath93 0.25 t and @xmath87 ( b)@xmath94 @xmath95 for b @xmath96 0.25 t. here , the activation energy is @xmath97 k in low magnetic field ( 0.01 t ) and @xmath98 k in high field region ( 0.65 t ) . for 10% in doping ( shown in figure[fig8](b ) ) , the values of activation energy are 684.6 k ( 0.05 t ) and 9.4 k ( 0.35 t ) . the exponent n in the power law equation @xmath99 are 0.44 for b @xmath100 0.25 t and 1.97 for b @xmath96 0.25 t. +

the band structure and density of states calculations also indicate such a possibility . hydrostatic external pressure leads to decrease in transition temperature and the calculated pressure coefficient is @xmath7 -0.311 k / gpa . flux pinning and vortex activation energies also improved with indium addition . only positive frequencies are observed in phonon dispersion curve that relate to the absence of charge density wave or structural instability in the normal state .

we report on two fold increase in superconducting transition temperature of @xmath0 by substituting indium at the tin site . the transition temperature of this skutterudite is observed to increase from 2.5 k to 5.1 k for 10% indium substituted sample . the band structure and density of states calculations also indicate such a possibility . the compounds exhibit type - ii superconductivity and the values of lower critical field ( @xmath1 ) , upper critical field ( @xmath2 ) , ginzburg - landau coherence length ( @xmath3 ) , penetration depth ( @xmath4 ) and gl parameter ( @xmath5 ) are estimated to be 0.0028 t , 0.68 t , 21.6 nm , 33.2 nm and 1.53 respectively for @xmath6 . hydrostatic external pressure leads to decrease in transition temperature and the calculated pressure coefficient is @xmath7 -0.311 k / gpa . flux pinning and vortex activation energies also improved with indium addition . only positive frequencies are observed in phonon dispersion curve that relate to the absence of charge density wave or structural instability in the normal state .

1509.04892

c

in summary , the superconducting transition temperature increased more than twice compared to @xmath0 ( from 2.5 k to 5.1 k ) after substituting indium in place of tin . the substituted indium effectively tunes the lattice instabilities of the caged skutterudite leading to a higher @xmath14 phase . theoretical calculation of band structure and density of states indicate that the co 3d and sn 5p orbitals contribute to the higher density of states about the fermi level . it is understood that added indium would be preferentially substituting sn2 atoms leading to enhancement in @xmath14 . calculated phonon dispersion curves rule out the presence of lattice instability . the parent and doped stannides are found to exhibit weak electronic correlation that increased with increasing indium substitution . the value of lower critical field , upper critical field , ginzburg - landau coherence length , penetration depth and gl parameter are found to be 0.0028 t , 0.68 t , 21.6 nm , 33.2 nm and 1.53 respectively for the 10% indium substituted @xmath0 sample . the superconducting transition temperature of @xmath6 decreased on application of external pressure in contradiction to what is reported for @xmath0 .

the compounds exhibit type - ii superconductivity and the values of lower critical field ( @xmath1 ) , upper critical field ( @xmath2 ) , ginzburg - landau coherence length ( @xmath3 ) , penetration depth ( @xmath4 ) and gl parameter ( @xmath5 ) are estimated to be 0.0028 t , 0.68 t , 21.6 nm , 33.2 nm and 1.53 respectively for @xmath6 .

we report on two fold increase in superconducting transition temperature of @xmath0 by substituting indium at the tin site . the transition temperature of this skutterudite is observed to increase from 2.5 k to 5.1 k for 10% indium substituted sample . the band structure and density of states calculations also indicate such a possibility . the compounds exhibit type - ii superconductivity and the values of lower critical field ( @xmath1 ) , upper critical field ( @xmath2 ) , ginzburg - landau coherence length ( @xmath3 ) , penetration depth ( @xmath4 ) and gl parameter ( @xmath5 ) are estimated to be 0.0028 t , 0.68 t , 21.6 nm , 33.2 nm and 1.53 respectively for @xmath6 . hydrostatic external pressure leads to decrease in transition temperature and the calculated pressure coefficient is @xmath7 -0.311 k / gpa . flux pinning and vortex activation energies also improved with indium addition . only positive frequencies are observed in phonon dispersion curve that relate to the absence of charge density wave or structural instability in the normal state .

astro-ph0407154

c

the most important result of the present work is the detection of complex molecules in the hot corino of iras4a , the second class 0 in which those molecules have been searched for , after iras16293 ( cazaux et al . 2003 ) . this result demonstrates that as soon as a warm region is created in the center of the envelope of low mass protostars , complex molecules are readily formed and/or injected on timescales lower than the estimated class 0 source ages ( @xmath30 yr in iras16293 and @xmath31 yr in iras4a ; e.g. maret et al . 2002 ) , and , most importantly , shorter than the transit time in the hot corinos . the latter is @xmath32 yr and @xmath33 yr in iras16293 and iras4a respectively , based on the hot corino sizes quoted in maret et al . ( 2004 ) and assuming free - falling gas . we compare the measured composition of the hot corino of iras4a to iras16293 ( cazaux et al . 2003 ) and the massive hot core of omc-1 ( sutton et al . 1995 ) in table [ t+n ] . note that the latter abundances are derived from single dish measurements with a @xmath34 beam , which encompasses several hot cores ( wright et al . 1996 ) . unfortunately , not all the molecules considered here have interferometric measurements available , so that we can only use these @xmath34 beam - averaged estimates of the abundances . the first remark is that the absolute abundances of the observed molecules are one order of magnitude smaller in iras4a than in iras16293 , but their relative abundances with respect to h@xmath4co are quite similar , with the exception of methanol , which is underabundant with respect to h@xmath4co by about a factor 10 in iras4a ( fig . [ xratio ] ) . there are two reasons to consider abundances with respect to formaldehyde . the first one is observational : while the iras16293 hot core has now been imaged with the plateau de bure interferometer ( bottinelli et al . in preparation ) and its size confirmed to be @xmath29 , the iras4a core size is only indirectly estimated from dust continuum single dish ( @xmath35 ) observations to be @xmath36 and no interferometric observations are available yet with such a high resolution . so the iras4a core size might be wrong by up to a factor three ( maret et al . 2004 ) and the abundances by up to a factor ten , i.e. the absolute abundances of iras4a could be comparable to those of iras16293 . using abundance ratios allow us to remove this size uncertainty . the second reason is theoretical : `` standard '' hot core models predict that molecules like methyl formate or methyl cyanide are second generation molecules formed in the warm gas from the evaporated grain mantle constituents ( formaldehyde , ammonia and methanol : e.g. charnley et al . 1992 ; caselli et al . 1993 ; rodgers & charnley 2003 ) . it is therefore interesting to compare the abundances of the complex molecules to those of one of these supposed parent molecules . formaldehyde was chosen because we only have an upper limit on the methanol abundance ( maret et al . in preparation ) and no measurements of the ammonia abundance are available . a possible interpretation for the similarity in the complex molecules relative abundances , with respect to h@xmath4co and not with respect to ch@xmath0oh , is that the former is the mother molecule of the observed o - bearing species , e.g. likely the case of hcooch@xmath0 ( charnley et al . 1992 ) , and that the chemical evolution timescale is shorter than the age of the youngest source . charnley et al . ( 1992 ) also predict that methanol is the mother molecule of ch@xmath0och@xmath0 , but we can not say whether the available data confirm this hypothesis since we only have an upper limit on the abundance of this molecule in iras4a and a large error in iras16293 . similarly , the n - bearing molecules ch@xmath0cn and c@xmath4h@xmath6cn could both be daughters of the same mother molecule , probably ammonia . this would imply that the two sources have a similar ammonia mantle abundance . alternatively , ( some of ? ) the reported molecules are possible mantle constituents themselves . this may be the case for formic acid , as predicted by tielens & hagen ( 1982 ) , and suggested by the observational study by liu et al . moreover , the analysis of iso absorption spectra towards the massive hot core w33a ( e.g. schutte et al . 1997 ) is consistent with the presence of solid formic acid and would also support the idea of this species being a mantle constituent . however , these considerations do not take into account the evolutionary state of the objects and the fundamental question is : does the abundance of any of these complex molecules have anything to do with the age and/or evolutionary stage of the protostar , or is it dominated by the initial mantle composition ? evidently , two sources are not enough to answer this question , and observations of more low mass sources are required . regarding the comparison with the massive hot core(s ) in orion , fig . [ xratio ] would suggest that , with respect to formaldehyde , there is a deficiency of methanol and of n - bearing complex molecules in the low mass hot corinos . it is possible that these differences are mostly due to a different grain mantle composition , i.e. to a different pre - collapse density . however , recall that the abundance ratios of ch@xmath0cn and ch@xmath0oh in figure [ xratio ] refer to the @xmath34 beam - averaged values around the omc-1 hot core , which in fact includes several smaller cores ( wright et al . 1996 ) . therefore , in order to make precise comparisons , higher resolution observations of the omc-1 hot core are needed . it is also worth noting that if we consider for example the measurements by wright et al . 1996 in the compact ridge component ( a region about @xmath37 away from the hot core central position , which is also a site of mantle evaporation and of active gas phase chemistry ; e.g. charnley et al . 1992 ) , the ch@xmath0cn and ch@xmath0oh abundance ratios with respect to h@xmath4co are ( surprisingly ) close to those found for the hot corinos of iras16293 and iras4a . hence , interferometric observations of a larger number of massive hot cores are necessary to provide a significant comparison of the hot corinos with their high mass counterparts . in summary , although the present observations do not allow us to answer the questions why and how complex molecules are formed , they do show that hot corinos , in the wide definition of chemically enriched regions , are a common property of solar - type protostars in the early stages . the evidence is that the types of complex molecules that are formed are determined primarily by the composition of the grain mantles . at this stage , it is not clear whether the evolutionary stage of the protostar plays any role at all , other than governing the presence and size of the mantle evaporation region .

this is the second low mass protostar where such complex molecules have been searched for and reported , the other source being iras162932422 . it is therefore likely that compact ( few tens of aus ) regions of dense and warm gas , where the chemistry is dominated by the evaporation of grain mantles , and where complex molecules are found , are common in low mass class 0 sources . given that the chemical formation timescale is much shorter than the gas hot core crossing time , it is not clear whether the reported complex molecules are formed on the grain surfaces ( first generation molecules ) or in the warm gas by reactions involving the evaporated mantle constituents ( second generation molecules ) . we do not find evidence for large differences in the molecular abundances , normalized to the formaldehyde abundance , between the two solar type protostars , suggesting perhaps a common origin .

we report the detection of complex molecules ( hcooch@xmath0 , hcooh and ch@xmath0cn ) , signposts of a `` hot core '' like region , toward the low mass , class 0 source ngc1333-iras4a . this is the second low mass protostar where such complex molecules have been searched for and reported , the other source being iras162932422 . it is therefore likely that compact ( few tens of aus ) regions of dense and warm gas , where the chemistry is dominated by the evaporation of grain mantles , and where complex molecules are found , are common in low mass class 0 sources . given that the chemical formation timescale is much shorter than the gas hot core crossing time , it is not clear whether the reported complex molecules are formed on the grain surfaces ( first generation molecules ) or in the warm gas by reactions involving the evaporated mantle constituents ( second generation molecules ) . we do not find evidence for large differences in the molecular abundances , normalized to the formaldehyde abundance , between the two solar type protostars , suggesting perhaps a common origin .

1506.01231

i

there is a growing consensus that the fundamental mechanism of human intelligence is simply pattern recognition , the retrieval of information based on content association , albeit repeated in ever increasing hierarchical structures @xcite . correspondingly , pattern recognition in machine intelligence @xcite has made enormous progress in the last decade or so and such systems are now to be found in applications ranging from medical diagnosis to facial and voice recognition in security and digital personal assistants , the latest addition to the the family being self - driving cars . on the other side , the last two decades have seen the birth of , and an explosion of research in a new information - theoretic field : quantum information theory and quantum computation @xcite . this chapter deals with quantum pattern recognition , with particular emphasis on models that are both accessible to detailed analytical treatment and efficiently implementable within the framework of the quantum circuit model . pattern recognizers , which go also under the name of _ associative memories _ ( or more precisely autoassociative memories ) , are fundamentally different than von neumann or turing machines @xcite , which have grown into the ubiquitous computers that permeate our information society . computation is not sequential but , rather , based on collective phenomena due to interactions among a large number of , typically redundant , elementary components . information is not address - oriented , i.e. stored in look - up tables ( random access memories , rams ) but , rather , distributed in often very complex ways over the connections and interactions parameters . in traditional computers information is identified by a label and stored in a database indexed by these labels . retrieval requires the exact knowledge of the relevant label , without which information is simply not accessible . this is definitely not how our own brain works . when trying to recognize a person from a blurred photo it is totally useless to know that it is the 16878th person you met in your life . rather , the recognition process is based on our strong power of association with stored memories that resemble the given picture . association is what we use every time we solve a crossword puzzle and is distinctive of the human brain . the best known examples of pattern recognizers are neural networks @xcite and hidden markov models @xcite , the hopfield model @xcite ( and its generalization to a bidirectional associative memory @xcite ) being the paradigm , since it can be studied analytically in detail by the techniques of statistical mechanics @xcite . the great advantage of these architectures is that they eliminate the extreme rigidity of ram memories , which require a precise knowledge of the memory address and , thus , do not permit the retrieval of incomplete or corrupted inputs . in associative memories , on the contrary , recall of information is possible also on the basis of partial knowledge of its content , without knowing a precise storage location , which typically does not even exist . this is why they are also called content - addressable memories " . unfortunately , classical associative memories suffer from a severe capacity shortage . when storing multiple patterns , these interfere with each other , a phenomenon that goes under the name of crosstalk . above a critical number of patterns , crosstalk becomes so strong that a phase transition to a completely disordered spin glass phase @xcite takes place . in this phase there is no relation whatsoever between the information encoded in the memory and the original patterns . for the hopfield model , the critical threshold on the number @xmath0 of patterns that can be stored in a network of @xmath1 binary neurons is @xmath2 @xcite . while various possible improvements can be envisaged , the maximum number of patterns remains linear in the number of neurons , @xmath3 . the power of quantum computation @xcite is mostly associated with the speed - up in computing time it can provide with respect to its classical counterpart , the paramount examples being shor s factoring algorithm @xcite and grover s database search algorithm @xcite . the efficiency advantage over classical computation is due essentially to the quantum superposition principle and entanglement , which allow for massively parallel information processing . the bulk of the research effort in quantum computation has focused on the quantization " of the classical sequential computer architecture , which has led to the quantum circuit model @xcite , in which information processing is realized by the sequential application of a universal set of elementary one- and two - qubit gates to typically highly entangled quantum states of many qubits . the computation is said to be efficient if the desired unitary evolution of the quantum state can be realized by the application of a polynomial number ( in terms of the number of involved qubits ) of these elementary quantum gates . however , the question immediately arises if quantum mechanics can be applied successfully also to the collective information processing paradigm typical of machine intelligence algorithms and , specifically , if there are advantages in doing so . while this research has trailed the development of the quantum circuit model , it is presently experiencing a flurry of increased interest , so much so that last year nasa and google have teamed up to found the quantum artificial intelligence laboratory , entirely dedicated to develop and advance machine intelligence quantum algorithms . while speed has been the main focus of quantum computation , it can be shown that quantum mechanics also offers a way out from the impossibility of reconciling the association power of content - addressable memories with the requirement of large storage capacity . indeed , one of us pointed out already in 2001 @xcite that storage capacity of associative memories can also be greatly enhanced by the quantum superposition principle . the key idea is to exploit the fundamental probabilistic nature of quantum mechanics . if one is willing to abandon the classical paradigm of one - off retrieval and sacrifice some speed by repeating the information retrieval step several times , then it is possible to store any desired polynomial number ( in terms of the number of qubits ) of patterns in a quantum associative memory and still tune the associative retrieval to a prescribed accuracy , a large advantage with respect to the classical linear limitation described above . quantum entanglement permits to completely eliminate crosstalk and spurious memories in a tuneable probabilistic content association procedure with polynomial complexity for a polynomial number of stored patterns . such probabilistic quantum associative memories can thus be implemented efficiently . similar ideas in this direction were developed simultaneously in @xcite . in this chapter we will review our own work on fundamental aspects of quantum associative memories and quantum pattern recognition . we will begin by a short survey of the main features of classical fully coupled neural networks like the hopfield model and its generalizations , with a special emphasis on the capacity limitation and its origin . we will then describe the quantization of the hopfield model @xcite : the idea is to replace the classical irreversible dynamics that attracts input patterns to the closest minima of an energy function , representing the encoded memories , with a reversible unitary quantum evolution that amplifies an input quantum state to an output quantum state representing one of the stored memories at a given computational time @xmath4 . in the classical model there is a complex phase diagram in terms of the two noise parameters , the temperature @xmath5 and the disorder @xmath6 with @xmath1 the number of bits and @xmath0 the number of stored patterns . it is , specifically the disorder due to an excessive loading factor @xmath6 that prevents the storage of more than a critical number of patterns by causing the transition to a spin glass phase @xcite , even at zero temperature . correspondingly , in the quantum version there are quantum phase transitions due to both disorder and quantum fluctuations , the latter being encoded in the effective coupling @xmath7 , with @xmath8 being the energy parameter of the model and @xmath4 being the computational time ( throughout the review we will use units in which @xmath9 and @xmath10 ) . these are first examples of quantum collective phenomena typical of quantum machine intelligence . it turns out that , barring periodicity effects due to the unitary time evolution , the phase diagram for the quantum hopfield model is not so different from its classical counterpart . specifically , for small loading factors the quantum network has indeed associative power , a very interesting feature by itself , but the maximum loading factor is still limited to @xmath11 , above which there is a totally disordered spin glass phase , with no association power for any computational time . the transition to this quantum spin glass phase takes place when one tries to store a number of memories that is not anymore linearly independent . we then turn our attention to probabilistic quantum associative memories @xcite . the basic idea underlying their architecture is essentially the same as above , with one crucial difference : they exploit , besides a unitary evolution , a second crucial aspect of quantum mechanics , namely wave function collapse upon measurement @xcite . a generic ( pure ) quantum state is a superposition of basis states with complex coefficients . a measurement projects ( collapses ) the state probabilistically onto one of the basis states , the probability distribution being governed by the squared absolute values of the superposition coefficients . probabilistic quantum associative memories involve , besides the memory register itself a certain number @xmath12 of control qubits . the unitary evolution of the input state is again determined by a hamiltonian that depends only on the stored patterns . contrary to quantized hopfield memories , however , this unitary evolution mixes the memory register and the control qubits . after having applied the unitary evolution to the initial input state , the control qubits are measured . only if one obtains a certain specific result , one proceeds to measure the memory register . this procedure is called probabilistic postselection of the measurement result and guarantees that the memory register is in a superposition of the stored patterns such that the measurement probabilities are peaked on those patterns that minimize the hamming distance to the input . a measurement of the memory register will thus associate input and stored patterns according to this probability distribution . of course , if we limit ourselves to a maximum number @xmath5 of repetitions , there is a non - vanishing probability that the memory retrieval will fail entirely , since the correct control qubit state will never be measured . one can say that information retrieval in these quantum memories consists of two steps : recognition ( the correct state of the control qubits has been obtained ) and identification ( the memory register is measured to give an output ) . both steps are probabilistic and both the recognition efficiency and the identification accuracy depend on the distribution of the stored patterns : recognition efficiency is best when the number of stored patterns is large and the input is similar to a substantial cluster of them , while identification accuracy is best for isolated patterns which are very different from all other ones , both very intuitive features . both recognition efficiency and identification accuracy can be tuned to prescribed levels by varying the repetition threshold @xmath5 and the number @xmath12 of control qubits . the accuracy of the input - output association depends only on the choice of the number @xmath12 of control qubits . indeed , we will show that @xmath13 plays the role of an effective temperature @xcite . the lower @xmath4 , the sharper is the corresponding effective boltzmann distribution on the states closest in hamming distance to the input and the better becomes the identification . by averaging over the distribution of stored patterns with hamming distance to the input above a threshold @xmath14 one can eliminate the dependence on the stored pattern distribution and derive the effective statistical mechanics of quantum associative memories by introducing the usual thermodynamic potentials as a function of @xmath14 and the effective temperature @xmath13 . in particular , the free energy @xmath15 describes the average behaviour of the recall mechanism and provides concrete criteria to tune the accuracy of the quantum associative memory . by increasing @xmath12 ( lowering @xmath4 ) , the associative memory undergoes a phase transition from a disordered phase with no correlation between input and output to an ordered phase with perfect input - output association encoded in the minimal hamming distance @xmath14 . this extends to quantum information theory the relation with ising spin systems known in error - correcting codes @xcite and in public key cryptography @xcite . the recognition efficiency can be tuned mainly by varying the repetition threshold @xmath5 : the higher @xmath5 , the larger the number of input qubits that can be corrupted without affecting recognition . the crucial point is that the recognition probability is bounded from below by @xmath16 . for any number of patterns , thus , a repetition threshold @xmath5 polynomial in @xmath1 guarantees recognition with probability @xmath17 . due to the factor @xmath18 in the numerator , whose origin is exclusively quantum mechanical , the number of repetitions required for efficient recognition would actually be polynomial even for a number of patterns exponential in @xmath1 . the overall complexity of probabilistic associative quantum memories is thus bounded by the complexity @xmath19 of the unitary evolution operator . any polynomial number of patterns @xmath20 can be encoded and retrieved efficiently in polynomial computing time . the absence of spurious memories leads to a substantial storage gain with respect to classical associative memories , the price to pay being the probabilistic nature of information recall .

we review our models of quantum associative memories that represent the quantization " of fully coupled neural networks like the hopfield model . the idea is to replace the classical irreversible attractor dynamics driven by an ising model with pattern - dependent weights by the reversible rotation of an input quantum state onto an output quantum state consisting of a linear superposition with probability amplitudes peaked on the stored pattern closest to the input in hamming distance , resulting in a high probability of measuring a memory pattern very similar to the input . probabilistic quantum memories , that make use of postselection of the measurement result of control qubits , overcome the famed linear storage limitation of their classical counterparts because they permit to completely _ eliminate crosstalk and spurious memories_. the number of control qubits plays the role of an inverse fictitious temperature , the accuracy of pattern retrieval can be tuned by lowering the fictitious temperature under a critical value for quantum content association while the complexity of the retrieval algorithm remains polynomial for any number of patterns polynomial in the number of qubits . these models solve thus the capacity shortage problem of classical associative memories , providing a _ polynomial improvement _ in capacity .

we review our models of quantum associative memories that represent the quantization " of fully coupled neural networks like the hopfield model . the idea is to replace the classical irreversible attractor dynamics driven by an ising model with pattern - dependent weights by the reversible rotation of an input quantum state onto an output quantum state consisting of a linear superposition with probability amplitudes peaked on the stored pattern closest to the input in hamming distance , resulting in a high probability of measuring a memory pattern very similar to the input . the unitary operator implementing this transformation can be formulated as a sequence of one - qubit and two - qubit elementary quantum gates and is thus the exponential of an ordered quantum ising model with sequential operations and with pattern - dependent interactions , exactly as in the classical case . probabilistic quantum memories , that make use of postselection of the measurement result of control qubits , overcome the famed linear storage limitation of their classical counterparts because they permit to completely _ eliminate crosstalk and spurious memories_. the number of control qubits plays the role of an inverse fictitious temperature , the accuracy of pattern retrieval can be tuned by lowering the fictitious temperature under a critical value for quantum content association while the complexity of the retrieval algorithm remains polynomial for any number of patterns polynomial in the number of qubits . these models solve thus the capacity shortage problem of classical associative memories , providing a _ polynomial improvement _ in capacity . the price to pay is the probabilistic nature of information retrieval .

0810.4255

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fragmentation functions ( ffs ) constitute one of the most important free inputs required for a comprehensive description of most collider processes to which perturbative qcd is applicable , being a necessary ingredient in any sufficiently complete calculation of processes involving detected hadrons in the final state . they quantify the hadronization of quarks and gluons which must eventually occur in every process in which hadrons are produced . while parton distribution functions ( pdfs ) , another of the important free inputs , are relevant for collisions involving at least one hadron , most importantly at present for @xmath4 collisions at the lhc , ffs are relevant in principle for all collisions , even those without any initial state hadrons such as electron - positron collisions at the future ilc . furthermore , while knowledge and application of pdfs is limited to the types of hadrons that can be practically used in the initial state , being almost exclusively nucleons , ffs can be constrained by , and/or used for the predictions of , measurements of the inclusive productions of neutral and charged hadron species ranging from the almost massless to the very heavy . such a large range of processes provides a large range of information on hadronization , and hence provides an important contribution to our understanding of non perturbative physics in general , and allows for a particularly incontrovertible phenomenological determination of the applicability and limitations of the various approximations used in the context of qcd factorization . such data are also sufficiently accurate to allow for competitive extractions of @xmath1 , the strong coupling constant of qcd evolved for convenience to the @xmath5-pole mass @xmath6 and the remaining of the most important free inputs , which improves the accuracy of perturbative qcd calculations in general and imposes constraints on new physics . we note here that while other inputs such as higher twist , multi - hadron ffs , fracture functions , and so on become important in certain kinematic limits , ffs are always necessary for a complete description of inclusive hadron production . in this article , we review the progress in understanding the hadronization of partons , embodied in ffs , and their application to inclusive hadron production . the concept of fragmentation was first introduced by feynman and field in 1977 @xcite to explain the limited transverse momenta and energy fraction scaling of hadrons in jets produced in @xmath0 collisions , as well as the presence of a few high transverse momentum ( @xmath7 ) gev hadrons in hadron - hadron collisions . in the latter case , the collision of a pointlike constituent particle of one hadron with that of another produces a pair of particles whose directions of motion are opposite to one another but at any angle to the parent particles , including large angles . these elementary particles must eventually hadronize to produce the high @xmath8 hadrons . intuitively , any inclusive single hadron production processes may be predicted by first calculating the equivalent partonic process ( i.e. replacing the produced hadron by a parton and the inclusive sum over hadron final states by partonic ones ) , then allowing the produced parton to hadronize . this _ parton model _ is made more precise by the factorization theorem . our discussion will be limited to inclusive single unpolarized hadron production , being better understood than its polarized counterpart . final state partons will on average hadronize to hadrons of all species that are not kinematically forbidden by the particular reaction , but , of all the charged hadrons , partons will mostly hadronize to the 3 lightest ones , being , and , so their ffs are the most phenomenologically well constrained . ( for a concise summary of the properties of some known mesons and baryons , see ref . the species of neutral meson and neutral baryon most likely to be produced in the hadronization process are @xmath9 , and @xmath10 respectively , but their ffs are accurately approximated by the ffs for and due to su(2 ) ( nuclear ) isospin symmetry between the @xmath11 and @xmath12 quark flavours . the next lightest species of meson and baryon is and respectively , whose ffs have therefore also been greatly studied . ( @xmath13 is not usually observed in experiment because it takes a long time to decay into charged particles . ) together with @xmath14 , @xmath15 , @xmath16 , @xmath17 , @xmath18 , @xmath19 , @xmath20 , @xmath21 and @xmath22 mesons , whose ffs are unfortunately either unknown or rather poorly known at present , the particles mentioned in this paragraph complete the list of known hadrons which have a mass less than or equal to the mass and which are the most copiously produced in hadron production , and thus measurements of their production lead to a rather comprehensive picture of the hadronic final state . in this review we shall focus on the productions of these particles only , with the exceptions of the productions of those mesons just listed . much of the techniques for global fitting of pdfs can be carried over to global fitting of ffs , for example the treatment of systematic errors on the experimental data and the propagation of experimental errors to the ffs , as well as the techniques used for the minimization of chi - squared . on the theoretical side , much of the formalism of both the _ fixed order _ ( fo ) calculations and its improvement via e.g. large @xmath23 resummation and incorporation of heavy quarks and their masses , is also very similar . to date , the subject of fragmentation has been important in various areas of phenomenology @xcite , and we give an incomplete list of examples : phenomenological constraints on the nucleon pdfs for polarized quarks and antiquarks separately , which are important for the determination of the source of nucleon spin , can be obtained from measurements of semi - inclusive dis with polarized initial state particles for the inclusive production of single unpolarized light charged hadrons using knowledge of the ffs for these particles @xcite . valence quark pdfs can be similarly extracted , but from data for which the initial state particles are unpolarized @xcite . in both cases , the differences between ffs for positively and negatively charged particles , are required , which are relatively poorly constrained by data from e.g. @xmath4 reactions , and not by accurate @xmath0 reaction data . polarized @xmath3 reaction data from e.g. rhic can also impose constraints on the nucleon pdf for the polarized gluon @xcite , and measurements of photoproduction in polarized @xmath2 reaction at e.g. the proposed erhic @xcite or lhec @xcite colliders can impose constraints on the photon pdf for polarized partons @xcite . ffs provide a consistency check on transverse momentum dependent ffs , which replace ffs when the transverse momentum of the produced hadron is measured in addition to the longitudinal , since formally the ffs are reproduced by integrating them over the transverse momentum . the suppression of @xmath9 production in heavy ion collisions ( au au ) relative to @xmath4 collisions @xcite measured by the phenix collaboration at rhic , and to be further investigated by the alice , atlas and cms collaborations at the lhc , provides information on the much anticipated scenario of a quark - gluon plasma ( qgp ) that filled the universe the first ten millionths of a second after the big bang and created the primordial matter . such studies may therefore contribute to our understanding of both cosmology and the physics of non perturbative qcd . photons produced by partonic fragmentation @xcite contribute significantly to the photonic background of various direct photon signals in dis , such as that of higgs boson production from hadrons . fragmentation of a quark to a lepton pair @xcite or , equivalently , to a virtual photon @xcite , is perturbatively calculable if the invariant mass is much greater than @xmath24 , in contrast to ffs for hadrons and the photon , so measurement of the polarization of the virtual photon that decays to the lepton pair of the drell - yan cross section can be used to test models of the formation of @xmath25 particles , whose production from fragmentation is otherwise similar to that of the virtual photon . in ref . @xcite it has been proposed to identify exotic hadrons such as tetraquarks by identifying properties of ffs which are typical for quarks whose flavour is favoured , i.e. that are of the same flavour as any of the produced hadron s valence quarks . some studies of the fragmentation of squarks and gluinos into hadrons have been performed in ref . @xcite and much more recently into supersymmetric hadrons in ref . @xcite , which may be relevant at the lhc . the supersymmetric extension of the dglap evolution of ffs for light charged hadrons has been studied in ref . @xcite in the context of ultra high energy cosmic rays . ffs for light charged hadrons are required for the calculation of hadronic signatures of black hole production at the lhc @xcite . the rest of this review is structured as follows . the basic results of the qcd factorization theorem , which forms the starting point of all calculations of inclusive hadron production , are given in section [ resoffacttheorem ] , in particular the separation from the overall cross section of the process dependent parts , which can be calculated using the fo approach to perturbation theory . ( the derivation of these results is outlined in appendix [ outlinederivfacttheo ] . ) then in section [ epemxs ] we discuss the extraction of ffs from accurate @xmath0 data and from various well motivated non perturbative assumptions . the ability of calculations using these fitted ffs to reproduce measurements is studied in section [ predfromffs ] . then we turn to more recent progress : improvements to the standard fo approach that have not been incorporated into nearly all global fits are given in section [ impstand ] , namely hadron mass effects and large @xmath23 resummation . the treatment of experimental errors and their propagation to fitted quantities , which has been rather comprehensively implemented in pdf fits but to a somewhat lesser degree in ff , is discussed in section [ treaterrs ] . the 3 most recent global fits , in which the implementation of these improvements can be found , are discussed and compared in section [ currglobalfits ] . finally , in section [ sglres ] we examine the improvement of the standard fo approach at small @xmath23 by resummation of _ soft gluon logarithms _ , which has so far been successfully tested at lo , and we consider what is needed for a full treatment of soft gluon logarithms to nlo . in section [ outlook ] we predict the future experimental and theoretical progress of ff extraction , and give a summary of the current progress in section [ summary ] . the lo splitting functions are given in appendix [ losplitfunc ] for reference , the relevant mellin space formulae in appendix [ mellinspace ] , and a summary of all data that can be reasonably reliably calculated and which can be used to provide constraints on ffs in appendix [ sumofexp ] . some of these issues have also been discussed very recently in ref . @xcite , with an aim towards the modification of fragmentation in qcd media .

we review the description of inclusive single unpolarized light hadron production using fragmentation functions in the framework of the factorization theorem . we summarize the factorization of quantities into perturbatively calculable quantities and these universal fragmentation functions , and then discuss some improvements beyond the standard fixed order approach . these global fits also impose competitive constraints on @xmath1 .

we review the description of inclusive single unpolarized light hadron production using fragmentation functions in the framework of the factorization theorem . we summarize the factorization of quantities into perturbatively calculable quantities and these universal fragmentation functions , and then discuss some improvements beyond the standard fixed order approach . we discuss the extraction of fragmentation functions for light charged ( , and ) and neutral ( and ) hadrons using these theoretical tools through global fits to experimental data from reactions at various colliders , in particular from accurate @xmath0 reactions at lep , and the subsequent successful predictions of other experimental data , such as data gathered at hera , the tevatron and rhic from these fitted fragmentation functions as allowed by factorization universality . these global fits also impose competitive constraints on @xmath1 . emphasis is placed on the need for accurate data from @xmath2 and @xmath3 reactions in which the hadron species is identified in order to constrain the separate fragmentation functions of each quark flavour and hadron species .

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a quantum computer comprising many two - level systems qubits , exhibits coherent superpositions and entanglement . quantum computing , which is based on these features , enables some computational problems to be solved faster than would ever be possible with a classical computer @xcite , and exponentially speeds up solutions to other problems over the best known classical algorithms @xcite , is currently attracting enormous interests . among the promising candidates for quantum computing , solid - state implementations such as spin qubits in quantum dots @xcite and bulk silicon @xcite , and charge qubits in bulk silicon @xcite and in superconducting josephson junctions @xcite , are especially attractive because of stability and expected scalability of solid - state systems ; of these competing technologies , semiconductor double quantum dots ( dqds ) are particularly important because of the combination spin and charge manipulations to take advantage of long memory times associated with spin states and at the same time to enable efficient readout and coherent manipulation of charge states . our goal is to develop a realizable architecture for semiconductor quantum computation . the qubit is manifested as a nanowire ( nw ) quantum dot pair such that each having an electron and thus the singlet and one of the triplets of two - electron states correspond to the logical state @xmath0 and the orthogonal state @xmath1 . the resonator - assisted interaction between dqds and a microwave transmission line resonator ( tlr ) is used to implement a universal set of quantum gates and readout of the qubits . from two points , we show the advantages of our scheme compared to the previous proposals on semiconductor quantum computation . firstly , for the previous proposals which make use of single or double quantum dots defined by a two - dimensional electron gas ( 2deg ) @xcite , it would be difficult to implement a double - dot in a planar resonator with lateral dots , shaped in a 2deg by surface gates . the reason being is that it would be difficult to prevent absorption of microwaves in the 2deg unless one can make the electric field non - zero only in the double - dot region , which is not realistic experimentally yet . our strategy is to use the two - electron states of dqds inside nws instead of 2deg , which is more realistic for implementing quantum computing experimentally . secondly , there are previous proposals making use of nw dqds @xcite , in which the spin - orbit interaction is used to couple the spins and resonator . however the weak coupling between the dqd spins and resonator mode is a challenge in experiments . our strategy to enhance the interaction is to make use of the coupling between the electric dipole of charge states of dqds and resonator , which is much stronger compared to that in @xcite . however the decoherence of charge states is another obstacle . in this work , combining the advantages of spin and charge states and avoiding the weak points of both , we propose a different mechanism , namely via resonator - assisted interaction which leads to a strong coupling between the resonator photons and effective electric dipole of the state @xmath0 and an ancillary state of dqds , while the state @xmath1 is driven by a classical field , and then eventually implements quantum control on the singlet and one of the triplet spin states . thus we encode the quantum information in spin states and the quantum control is implemented via the charge dipole transition which is driven by a tlr . and @xmath2 singlets , the three @xmath2 triplets and qubit states @xmath3 and @xmath4 with the energy gap @xmath5 ( the exchange energy @xmath6 ) . schematic of the double - well potential with an energy offset @xmath7 provided by the external electric field . ( b ) the relevant three - level structure of dqds . the dipole transition @xmath8 is coupled to the fundamental mode of the resonator with the coupling coefficient @xmath9 and detuning @xmath10 , while the transition @xmath11 is driven by a classical field with the rabi frequency @xmath12 and detuning @xmath13.,width=321 ] a solid - state realization cavity qed is proposed in sec . ii and then we discuss the case where the resonator and qubit are tuned on- and off - resonance which can be used to implement a universal set of gates including single- and two - qubit gates in sec . iii a - c . the initialization of qubit states can be implemented by an adiabatic passage shown in sec . iii d. the readout of qubits can be realized via microwave irradiation of the tlr by probing the transmitted or reflected photons shown in sec . iii e. in sec . iii f , the main decoherence processes are dissipation of the tlr , charge - based relaxation and dephasing of the nw dqds occurring during gate operations and transportation of qubits , and spin dephasing limited by hyperfine interactions with nuclei . by numerical analysis we show all gate operations and measurements can be implemented within the coherent life time of qubits . thus we address all divincenzo criteria @xcite and show all play important roles in the dynamics of the two - electron system but none represents a fundamental limit for quantum computing . we make a summary in sec . iv .

we show a method for implementing universal quantum computing using of a singlet and triplets of nanowire double quantum dots coupled to a one - dimensional transmission line resonator . this method is attractive for both quantum computing and quantum control with inhibition of spontaneous emission , enhanced spin qubit lifetime , strong coupling and quantum nondemolition measurements of spin qubits .

we show a method for implementing universal quantum computing using of a singlet and triplets of nanowire double quantum dots coupled to a one - dimensional transmission line resonator . this method is attractive for both quantum computing and quantum control with inhibition of spontaneous emission , enhanced spin qubit lifetime , strong coupling and quantum nondemolition measurements of spin qubits . we analyze the performance and stability of all required operations and emphasize that all techniques are feasible with current experimental technology .

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we have shown that irradiation of a voltage - biased superconducting quantum point contact at frequencies @xmath169 can remove the suppression of subgap dc transport through andreev levels . quantum interference among resonant scattering events can be used for microwave spectroscopy of the andreev levels . the same interference effect can also be applied for detecting weak electromagnetic signals up to the gap frequency . due to the resonant character of the phenomenon , the current response is proportional to the ratio between the amplitude of the applied field and the applied voltage , @xmath170 . at the same time , for common sis detectors a non - resonant current response is proportional to the ratio between the amplitude and the frequency of the applied radiation @xcite ) , @xmath171 , i.e. it depends entirely on the parameters of the external signal and can not be improved . finally , we note that the classic double - slit interference experiment , where two spatially separated trajectories combine to form an interference pattern , clearly demonstrates the wave - like nature of electron propagation . for a 0-dimensional system , with no spatial structure , we have shown that a completely analogous interference phenomenon may occur between two distinct trajectories in the _ temporal _ evolution of a quantum system . * acknowledgment . * support from the swedish kva , ssf , materials consortia 9 & 11 , nfr and from the national science foundation under grant no . phy94 - 07194 is gratefully acknowledged . nil and mj are grateful for the hospitality of the institute for theoretical physics , uc santa barbara , where part of this work was done . the role of photoinduced interference effects in a normal junction was discussed by l. y. gorelik , a. grincwajg , v. kleiner , r. i. shekhter , and m. jonson , phys . lett . * 73 * , 2260 ( 1994 ) ; l. y. gorelik , f. maa , r. i. shekhter , and m. jonson , phys . rev . lett . * 78 * , 3169 ( 1997 ) . this result is obvious for a pure sns contact ( @xmath64 ) since the two andreev states involved in the transition at the band edge have momenta @xmath172 and @xmath63 pointing in opposite directions . see also @xcite .

we show that irradiation of a voltage - biased superconducting quantum point contact at frequencies of the order of the gap energy can remove the suppression of subgap dc transport through andreev levels . we also discuss how the same interference effect can be applied for detecting weak electromagnetic signals up to the gap frequency , and how it is affected by dephasing and relaxation .

we show that irradiation of a voltage - biased superconducting quantum point contact at frequencies of the order of the gap energy can remove the suppression of subgap dc transport through andreev levels . quantum interference among resonant scattering events involving photon absorption is furthermore shown to make microwave spectroscopy of the andreev levels feasible . we also discuss how the same interference effect can be applied for detecting weak electromagnetic signals up to the gap frequency , and how it is affected by dephasing and relaxation .

1402.3806

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here we have shown that the null em torus knot solutions correspond to a class of elementary states characterized the poloidal and toroidal winding numbers of the associated field configuration . using the relationship between fields of different spin in the twistor formalism , we constructed the analogous gravitational radiation configuration that possesses tendex and vortex lines based on a torus knot structure . since the topology is manifest in the tendex and vortex lines , the gravito - electromagnetic tidal tensor decomposition is a straightforward method for characterizing these field configurations . the elementary states were known as early as the 1970 s @xcite , however the explicit forms of their associated spinor and tensor representations on @xmath8 were never published . the modern rediscovery of these solutions has raised interest in obtaining a more complete physical understanding of the topological properties of these fields . the parameterization of the twistor functions corresponding to the elementary states in terms of the poloidal and toroidal winding indicates that the torus knot structure is indeed inherent in the elementary states . for both electromagnetism and gravity , the topology appears in the configuration of the lines of force .

the twistor functions corresponding to the elementary states admit a parameterization in terms of the poloidal and toroidal winding numbers of the torus knots , allowing one to choose the degree of linking or knotting of the associated field configuration . using the gravito - electromagnetic formalism , we show that the torus knot structure is exhibited in the tendex and vortex lines for the analogous linearized gravitational solutions .

we show that the torus knot topology is inherent in electromagnetic and gravitational radiation by constructing spin-@xmath0 fields based on this topology from the elementary states of twistor theory . the twistor functions corresponding to the elementary states admit a parameterization in terms of the poloidal and toroidal winding numbers of the torus knots , allowing one to choose the degree of linking or knotting of the associated field configuration . using the gravito - electromagnetic formalism , we show that the torus knot structure is exhibited in the tendex and vortex lines for the analogous linearized gravitational solutions . we describe the topology of the gravitational fields and its physical interpretation in terms of the tidal and frame drag forces of the gravitational field .

cond-mat0006175

i

expreimental studies of coherent backscattering ( cbs ) of light from disordered media have been completed by many groups during the last decade.@xmath1 cbs measurements are of great interest because they have allowed to test the physics of weak localization , which was first uncovered in electronic transport,@xcite when applied to light waves and also to determine the light mean - free - path , @xmath2 in random media . in cbs measurements the normalized reflected light intensity ( also called the albedo , @xmath3 ) is monitored versus the deviation angle , @xmath4 from the backscattering direction of the incident laser beam . in the multiple scattering regime interference effects are averaged out except in a small angular range around @xmath5 , where constructive interference originating from reciprocal light paths enhance the diffusive reflection from the sample . as a result a coherent scattering intensity cone is formed in the albedo , @xmath6 for small @xmath7 . from the full width , @xmath8 of the cbs cone at quarter maximum , @xmath2 is obtained using the relation @xmath9 , where @xmath10 is the impinging laser wavelengh . the first cbs measurements were performed on suspensions of polystyrene spheres.@xcite since the suspension particles were very small in diameter , their brownian motion provided a natural ensemble averaging . for solid materials , however cbs usually shows a noisy but repeatable mesoscopic pattern.@xcite under these conditions the cbs cone around @xmath5 can be obtained by applying an elaborate ensemble - averaging technique in order to suppress the dominant mesoscopic fluctuations . the averaging techniques employed to get the cone include spot variation,@xcite tilt angle variation,@xcite and sample spin - rotation.@xcite all the above experimental studies@xmath1 were performed on completely disordered , isotropic and homogeneous media . photonic crystals have recently attracted a lot of attention@xcite because of potential optical device applications . these applications pertain to photonic crystals with _ complete _ band gaps _ i.e. _ with no propagating solutions of the maxwell equations within a certain frequency range . however , most of the available three dimensional photonic crystals nowadays have _ incomplete _ gaps in their photonic band structure , with light propagation forbidden only along certain directions . along these directions and for frequencies within the gap the light intensity decays with a certain decrement @xmath11-that is the bragg attenuation length . in the ideal case ( when disorder is negligibly small ) the length @xmath11 can be extracted from spectroscopic reflectivity measurements . since @xmath11 is directly related to the gap width , then its value can be deduced from the angular ( or spectral ) width of the bragg peak in reflectivity . however , in the more realistic situation disorder is present in the sample and this broadens the bragg band . we also note that even if @xmath12 broadening can be substantial due to the sensitivity of the bragg diffraction to the properties of the surface boundary . under these conditions a separate determination of @xmath11 and @xmath2 is a challenge . in general , despite the conceptual elegance of the cbs technique , the main quantitative information it has provided@xmath13 so far is @xmath2 value in _ macroscopically homogeneous _ and isotropic disordered media . we note that @xmath2 value in such media can be also determined from more conventional measurements of the transmission versus thickness@xcite that do not rely on the interference of clockwise and anticlockwise scattering paths . in the present work we show that for optically _ periodic _ structures _ with disorder _ the cbs measurements provide a unique opportunity to separate the two effects , namely bragg attenuation and light diffusion lengths . this reveals the tremendous potential of the cbs technique as compared to the more conventional optical spectroscopies .

we studied coherent backscattering ( cbs ) of light from opal photonic crystals in air at different incident inclination angles , wavelengths and along various @xmath0 $ ] directions inside the opals . using the modified theory we extract from our cbs data the light mean free path and bragg attenuation length at different @xmath0 $ ] . our study shows that cbs measurements are a unique experimental technique to explore photonic crystals with disorder , when other spectroscopical methods become ambiguous due to disorder - induced broadening .

we studied coherent backscattering ( cbs ) of light from opal photonic crystals in air at different incident inclination angles , wavelengths and along various @xmath0 $ ] directions inside the opals . similar to previously obtained cbs cones from various random media , we found that when bragg condition with the incident light beam is not met then the cbs cones from opals show a triangular line shape in excellent agreement with light diffusion theory . at bragg condition , however , we observed a dramatic broadening of the opal cbs cones that depends on the incident angle and @xmath0 $ ] direction . this broadening is explained as due to the light intensity decay in course of propagation along the bragg direction _ before the first _ and _ after the last _ scattering events . we modified the cbs theory to incorporate the attenuation that results from the photonic band structure of the medium . using the modified theory we extract from our cbs data the light mean free path and bragg attenuation length at different @xmath0 $ ] . our study shows that cbs measurements are a unique experimental technique to explore photonic crystals with disorder , when other spectroscopical methods become ambiguous due to disorder - induced broadening .

cond-mat0006175

c

in conclusion , we have demonstrated that cbs is a powerful technique for investigating photonic crystals with incomplete photonic band gaps . these measurements show that the remarkable universality of cbs characteristics for diverse disordered materials is not valid for photonic crystals at near bragg conditions . using the major effects on light transport near bragg conditions and their influence on cbs cones , we deduce the values of several fundamental parameters of an opal photonic crystal . remarkably , despite the existence of substantial scattering due to disorder , nevertheless we showed in this work that the bragg attenuation length and , thus the photonic band gap width of an `` ideal '' crystal along @xmath30 $ ] , as well as light mean - free - path can be readily extracted from the cbs measurements , even if they are comparable in magnitude ( unlike the situation in ref . ) . the reason why for @xmath167 disorder is unable to completely mask the contribution of bragg scattering to the cbs inside the photonic crystal , is that at bragg conditions the cbs involves @xmath168 light propagation _ before the first _ and _ after the last _ scattering events , when the existing disorder is _ not yet relevant_. this makes the cbs measurements a much more sensitive tool for characterizing the inherent band gap features for disordered photonic crystals as compared to the more conventional measurements of optical reflectivity . the only other study of cbs from photonic crystals that we know of was recently reported in ref . . the cbs measurements in that work were performed on photonic crystals based on polystyrene spheres and also on crystals composed of air spheres in a @xmath169 matrix . in contrast to the present study that has been performed on a _ single _ opal sample where the stop - band was `` swept '' by changing the angle of incindence , @xmath39 ; in ref . , on the contrary the incident angle was kept close to normal . under this condition , in order to explore the cbs within the stop - band frequency range in the polystyrene opals , the authors measured cbs on a _ set _ of samples with different sphere diameters using three different wavelenghts for the incident light beam . also the band edge frequencies were determined from _ reflectivity _ measurements , rather than by cbs as in our work . even under these assumptions , the authors failed to measure cbs cones _ inside _ the stop - band.@xcite for air - sphere @xmath169 crystal , however , the authors@xcite used a setup allowing continuous tuning of @xmath10 . they observed that between the red and blue edges of the stop - band , @xmath8 _ decreases _ by a factor of @xmath170 . this observation , which actually contradicts our own study , was explained on the basis of a previous theoretical work.@xcite it was claimed that for light frequencies above the lower band - edge the electromagnetic wave , in course of the diffusion process , can occasionally `` hit '' the boundary interface at the bragg angle @xmath63 ; thus rather than exiting the sample , it experiences instead the bragg diffraction to the interior . as a result of such events the diffusive trajectories become longer ( on average ) leading to the narrowing of the cbs cone . in light of the cbs model that was outlined in section iii , the above explanation corresponds to the modification of the propagator @xmath86 in eq . ( [ albedo ] ) . in contrast , our analysis suggests that @xmath88 is not appreciably affected by the bragg conditions , whereas the prime effect of the photonic band structure is the modification of the surviving probability densities @xmath83 and @xmath171 in eq . ( [ albedo ] ) . the apparent contradiction between our results and those of ref . can be probably accounted for by the difference in the `` strenghts''of the bragg diffraction process , or @xmath11 in synthetic @xmath14 opals and air - sphere crystals in @xmath169 . we note , however that the relative width of the bragg reflectivity peaks in both samples is comparable @xmath172 . , ed . by c. m. soukoulis ( plenum , new york , 1993 ) ; j. d. joannopoulos , r. d. meade , and j. n. winn , _ photonic crystals : molding the flow of light _ ( princeton university press , princeton , new jersey , 1995 ) .

similar to previously obtained cbs cones from various random media , we found that when bragg condition with the incident light beam is not met then the cbs cones from opals show a triangular line shape in excellent agreement with light diffusion theory . at bragg condition , however , we observed a dramatic broadening of the opal cbs cones that depends on the incident angle and @xmath0 $ ] direction . this broadening is explained as due to the light intensity decay in course of propagation along the bragg direction _ before the first _ and _ after the last _ scattering events . we modified the cbs theory to incorporate the attenuation that results from the photonic band structure of the medium .

we studied coherent backscattering ( cbs ) of light from opal photonic crystals in air at different incident inclination angles , wavelengths and along various @xmath0 $ ] directions inside the opals . similar to previously obtained cbs cones from various random media , we found that when bragg condition with the incident light beam is not met then the cbs cones from opals show a triangular line shape in excellent agreement with light diffusion theory . at bragg condition , however , we observed a dramatic broadening of the opal cbs cones that depends on the incident angle and @xmath0 $ ] direction . this broadening is explained as due to the light intensity decay in course of propagation along the bragg direction _ before the first _ and _ after the last _ scattering events . we modified the cbs theory to incorporate the attenuation that results from the photonic band structure of the medium . using the modified theory we extract from our cbs data the light mean free path and bragg attenuation length at different @xmath0 $ ] . our study shows that cbs measurements are a unique experimental technique to explore photonic crystals with disorder , when other spectroscopical methods become ambiguous due to disorder - induced broadening .

1305.3736

i

a diffusive electron - electron interaction correction ( eec ) to the conductivity was predicted theoretically @xcite about 30 years ago . in 2d system it is proportional to @xmath5 ( @xmath6 is the momentum relaxation time ) and grows in amplitude as temperature decreases . a way to experimentally single - out eec among other numerous effects is based on its property not to affect hall component of magnetoconductivity tensor @xmath7 in perpendicular magnetic field @xcite . eec therefore gives birth to temperature - dependent and parabolic with field contribution to the diagonal magnetoresistance @xmath8 and correction to the hall coefficient @xmath9 , both being proportional to @xmath5 . the predicted features were observed in numerous experiments , mainly with n - type gaas - based 2d systems @xcite . however , the quantitative level of agreement between theory and experiment was achived only in the 2000s by minkov group @xcite from simultaneous analysis of both hall and diagonal components of resistivity tensor . the suggested method was later approbated by others @xcite . we note , that zeeman splitting effects were negligible in most of the studied systems . zeeman splitting was predicted to decrease the eec value @xcite , the physical interpretation of this effect introduced later in ref . @xcite consists in decreasing the effective number of triplet channels with field . for the diffusive regime @xmath10 , the eec is predicted to be quadratic - in - field in the low field limit , and proportional to logarithm of field in the high field limit . experimentally , however , the effect of zeeman splitting on eec in the diffusive regime was only briefly considered in refs . @xcite . for the most ubiquitous 2d system known , 2deg in si - mosfet , which fits well all theory requirements , no convincing measurements of the eec have been done so far . at the same time this system demonstrates positive magnetoresistance in parallel field , the behavior expected for eec . in the 1980-s there were attempts to reveal eec in si from temperature and magnetic field dependences @xcite of resistivity ; these attempts were based on not yet developed theoretical concepts and did not lead to a self - consistent picture of magnetotransport . interest to zeeman splitting effects was resumed in 1997 with observation of a huge rise in resistivity of 2deg in clean si - mosfets in parallel magnetic field @xcite , close to metal - to - insulator transition . the interest further increased with interpretation of this magnetoresistance as a signature of magnetic quantum phase transition @xcite . in the 2000s several attempts to treat the parallel field magnetoresistance ( mr ) in terms of renormalization - group approach were taken both theoretically @xcite and experimentally @xcite . this approach is in fact self - consistent generalization of the eec for arbitrary interaction strength and conduction . independently , another theoretical approach was developed in refs . @xcite , and successfully applied @xcite , which accounts for resistivity increase with field simply by renormalization of the density of states and single impurity scattering time . the latter effect is essentially different from logarithmic eec which emerges from multiple electron - impurity scattering . the experimental situation , however , is more complicated : studies @xcite showed a strong effect of disorder on the parallel field magnetoresistance , that was discussed in terms of the band tail effects in refs . moreover , detailed studies of the mr on different material systems @xcite did demonstrate quantitative disagreement between the fitted - to - eec theory temperature- and magnetic field dependences of the conductivity . to summarize the present state of the field , there seems to be a common agreement on the zeeman nature of parallel field mr in 2d carrier systems . however , two conceptually different underlining mechanisms of mr were put forward : ( i ) eec ( multiple - scattering effect ) and ( ii ) screening change in magnetic field ( single - scattering effect ) . which of them is responsible for the experimentally observed strong mr in parallel field ? the answer is especially crucial in the vicinity of the metal - to - insulator transition , where the mr is dramatically strong . unfortunately , both theories become inapplicable in this regime of small conductances @xmath11 . to address this issue , we have chosen to approach the problem from the large conductance regime , where both theories have solid ground , though the mr is low . in our paper we contest possible origin of the parallel field magnetoresistance of weakly interacting 2d electron gas . in order to study eec , we take detailed measurements of the magnetoresistance tensor in tilted field , and analyze the data using the procedure developed in refs . we stress that our approach does not rely on any particular microscopic theory , rather , it is _ ab - initio _ phenomenological and uses only general property of the eec in the diffusive regime to affect @xmath12 solely . for the experiments we have chosen the simplest model system , the 2d electron gas in si in diffusive regime @xmath13 , @xmath14 . to vary the strength of the zeeman splitting , and thus , the eec magnitude , we tilted magnetic field with respect to the 2d plane . this procedure allowed us to extract eec on top of other magnetoresistivity effects and to establish two principally different regions : ( i ) high - field region , where eec depends on total field and quantitatively agrees with the theoretically predicted @xmath15 asymptotics , and ( ii ) low - field region , where eec unexpectedly depends on perpendicular field component , grows with field and does not match existing theories . our observations suggest a new insight on the origin of the parallel field mr : ( i ) the high - field small and @xmath16independent eec @xmath17 , revealed in the current study , can not be responsible for large and @xmath18-dependent parallel field mr , and ( ii ) application of even low @xmath19 perpendicular field component strongly suppresses mr . the latter fact proves not purely spin nature of the parallel field mr and points at the incompleteness of the existing theory of mr . the paper is organized as follows : after a brief description of experimental details in section ii , we give theoretical background in section iii , and describe the results in section iv , first on the eec , then on the experimental proof of the zeeman origin of the magnetic field effect on eec , and further we compare the known eec with the parallel field magnetoresistance to show that the eec is not the main origin of the parallel field magnetoresistance . in section v we discuss the obtained result and suggest possible directions of further development .

we study diffusive electron - electron interaction correction to conductivity by analyzing simultaneously @xmath0 and @xmath1 for disordered 2d electron systems in si in tilted magnetic field . tilting the field the correction behaves as @xmath4 , as expected theoretically ( lee , ramakrishnan , phys .

we study diffusive electron - electron interaction correction to conductivity by analyzing simultaneously @xmath0 and @xmath1 for disordered 2d electron systems in si in tilted magnetic field . tilting the field is shown to be a straightforward tool to disentangle spin and orbital effects . in particular , by changing the tilt angle we prove experimentally that in the field range @xmath2 the correction depends on modulus of magnetic field rather than on its direction , which is expected for a system with isotropic @xmath3-factor . in the high - field limit the correction behaves as @xmath4 , as expected theoretically ( lee , ramakrishnan , phys . rev . b*26 * , 4009 ( 1982 ) ) . our data prove that the diffusive electron - electron interaction correction to conductivity is not solely responsible for the huge and temperature dependent magnetoresistance in parallel field , typically observed in si - mosfets .

0808.1280

c

in this paper we have studied gravitational instabilities in disks , with special attention to the most massive clumps that form because they are expected to be the progenitors of globular - type clusters . the maximum unstable mass is set by rotation and depends only on the surface density and orbital frequency of the disk , unlike other mass scales such as the jeans mass that depend on the complex gas physics . this mass scale is due to a purely local instability and not dependent on large - scale ordered motion . the maximum unstable mass is therefore a well - defined quantity even if the interstellar medium is not well described by a simple equation of state . the maximum clump mass can be expressed in terms of the total gas mass and the gas fraction in a galaxy , and this formulation makes it clear that environments with a high gas fraction are the most promising places to form massive clusters . using data from the literature , we predict that massive globular - like clusters can form in nuclear starburst disks and protogalactic disks but not in typical spiral galaxies , in agreement with observations . the scenario proposed here relates massive clusters to the largest scale in galaxies not stabilized by rotation , which is the only scale intermediate between stars and galaxies that has a clear physical basis . there is no well - defined ` jeans mass ' on these intermediate scales , and the next smaller scale that has any clear physical basis is the thermal jeans scale in molecular clouds , which is related to the masses of individual stars . the next larger physical scale is that of the galaxy itself , so we predict three physically well - motivated scales corresponding to stars , massive stellar clusters , and galaxies . another application of studies of the stability of nuclear gas disks , not discussed here , is to their likely role in feeding supermassive central black holes in galaxies ( escala 2007 ) . this requires the outward transfer of angular momentum , and if gravity is the most important force involved , the same mass concentrations that form massive clusters may also play an important role in the outward transfer of angular momentum and the growth of a central black hole . we plan to investigate this problem further in ongoing work . ashman , k.m . , zepf , s.e . 1992 , , 394 , 50 ashman , k.m . , zepf , s.e . 1998 , globular cluster systems . cambridge university press , cambridge ashman , k.m . , zepf , s.e . 2001 , aj , 122 , 1888 balbus , s. a. 1988 , apj , 324 , 60 ballesteros - paredes , j. , et al . 2007 . protostars and planets v , university of arizona press , tucson . binney , j. , tremaine , s. 1987 , galactic dynamics . princeton university press , princeton c^ ot , s. , et al . 2000 , aj , 120 , 3027 downes , d. , solomon , p. m. 1998 , , 507 , 615 drissen , l. , et al . 1999 , , 117 , 1249 elmegreen , b. g. 1994 , apj , 433 , 39 elmegreen , b. g. 2002 , apj , 577 , 206 escala , a. 2007 , apj , 671 , 1264 fall , s. m. , & rees , m. j. 1985 , apj , 298 , 18 figer , d. f. 2008 arxiv : astro - ph/08014178 giraud , e. 1998 , aj , 116 , 1125 harris , w. , pudritz , r. 1994 , , 429 , 177 helfer , t.t . , 2003 , apjs , 145 , 259 kent , s.m . 1987 , aj , 93 , 816 kim , w .- t . , ostriker , e.c . 2001 , apj , 559 , 70 krabbe , a. , et al . 1995 , apj , 447l , 95 lada , c.j . , lada , l.a . 2003 , , 41 , 57 larson , r.b . 1981 , mnras , 194 , 809 larson , r.b . 1985 , mnras , 214 , 379 larson , r.b . 1988 . proceedings of the 126th iau symposium , kluwer academic publishers . larson , r.b . formation of the galactic halo ... inside and out , asp conference series , vol . 92 , 1996 . peng , e.w . , jordan , a. , cote , p. 2008 , arxiv : astro - ph/08030330 schweizer , f. 1998 . galaxies : interactions and induced star formation , ed . r. c. kennicutt et al . , springer : berlin . toomre , a. 1964 , apj , 139 , 1217 van den bosch , f.c . 2001 , mnras , 326 , 1205

we study gravitational instabilities in disks , with special attention to the most massive clumps that form because they are expected to be the progenitors of globular - type clusters . the maximum unstable mass is set by rotation and depends only on the surface density and orbital frequency of the disk . we propose that the formation of massive clusters is related to this largest scale in galaxies not stabilized by rotation . using data from the literature , we predict that globular - like clusters can form in nuclear starburst disks and protogalactic disks but not in typical spiral galaxies , in agreement with observations .

we study gravitational instabilities in disks , with special attention to the most massive clumps that form because they are expected to be the progenitors of globular - type clusters . the maximum unstable mass is set by rotation and depends only on the surface density and orbital frequency of the disk . we propose that the formation of massive clusters is related to this largest scale in galaxies not stabilized by rotation . using data from the literature , we predict that globular - like clusters can form in nuclear starburst disks and protogalactic disks but not in typical spiral galaxies , in agreement with observations .

0711.1040

c

we studied the average density of resonances ( dor ) for a semi - infinite disordered chain , coupled to the outside world by a ( semi - infinite ) perfect lead . the main result of this work is the expression ( 18 ) for the average dor , supplemented by the three integral equations , ( 22 - 24 ) , for the three functions , @xmath205 and @xmath89 . this set of equations provide the general framework for calculating the average dor , for an arbitrary disorder and coupling strength . we applied these general equations to the case of weak coupling and derived an asymptotically exact expression for the average dor , in the limit of small resonance width ( eq.(39 ) ) . this expression is universal , in the sense that it holds for any degree of disorder and everywhere in the ( unperturbed ) energy band . it is worthwhile to emphasize the essential difference between the average dor , as defined in this paper , and the probability distribution of the resonance widths , often used in the literature ( e.g.@xcite ) . for a finite size chain , of @xmath62 sites , the two quantities differ only by a factor @xmath62 . however , when @xmath62 approaches @xmath206 , the probability distribution shrinks towards a delta - function , while the average dor approaches a perfectly well defined limit . since we have taken a semi - infinite chain from the start , it was essential for us to work with the average dor , rather than with the probability distribution of the resonant widths . this enabled us to obtain the @xmath166-behavior in the @xmath207 limit , in contrast to the statement of @xcite that in that limit the @xmath166-behavior has no region of applicability . the authors acknowledge useful conversations with e. gurevich and o. kenneth . one of the authors ( b.s . ) acknowledges the hospitality of epfl where most of this work was done . the work was supported in part by the israel science foundation ( isf ) .

we study the average density of resonances ( dor ) for a semi - infinite disordered chain , coupled to the outside world by a ( semi - infinite ) perfect lead . a set of equations is derived , which provides the general framework for calculating the average dor , for an arbitrary disorder and coupling strength . these general equations are applied to the case of weak coupling and an asymptotically exact expression for the averaged dor is derived , in the limit of small resonance width . this expression is universal , in the sense that it holds for any degree of disorder and everywhere in the ( unperturbed ) energy band .

we study the average density of resonances ( dor ) for a semi - infinite disordered chain , coupled to the outside world by a ( semi - infinite ) perfect lead . a set of equations is derived , which provides the general framework for calculating the average dor , for an arbitrary disorder and coupling strength . these general equations are applied to the case of weak coupling and an asymptotically exact expression for the averaged dor is derived , in the limit of small resonance width . this expression is universal , in the sense that it holds for any degree of disorder and everywhere in the ( unperturbed ) energy band . 21 cm 16 cm -0.15 cm

hep-th0306064

i

quantum field theories with canonical noncommutativity of particle coordinates became a subject of intensive investigation over the past years @xcite . characterized by the relation @xmath2=i\theta^{\mu\nu } , \label{1}\ ] ] where @xmath3 is an antisymmetric constant tensor , these theories were shown to emerge as a natural approximation of string theory in its low - energy limit @xcite , in d - brane physics and matrix theory @xcite , and in the context of semiclassical gravity @xcite . they have also proved to be applicable to condensed matter physics for the description of the quantum hall effect @xcite and superconductivity @xcite . among many interesting phenomena discovered in the study of noncommutative quantum field theories , we quote lorentz violation @xcite , nonlocality @xcite , and ir - uv mixing @xcite . the latter was shown to have deep consequences , such as the modification of the conventional wilsonian picture of renormalization group flows in the very - low - momentum domain @xcite and a change in the phase structure of a number of models @xcite . from the experimental point of view , several attempts to establish an empirical basis for noncommutativity are also under consideration ( see , e.g. , @xcite ) . investigations were carried out to understand the role of noncommutativity in the process of spontaneous symmetry breaking ( ssb ) , most of them focused on the @xmath4model @xcite . currently , there are few investigations in ( 2 + 1)-dimensional @xmath0 theory @xcite . reference @xcite is the only one on ssb , where an@xmath5 model is analyzed with emphasis on the issue of ir - uv mixing and renormalizability aspects . the aim of the present work is to verify how noncommutativity may affect the behavior of the @xmath0 model as long as the conditions for ssb are considered . we shall work with a cutoff field theory . our motivation for this comes mainly from three reasons . until now , it has been unknown if the noncommutative @xmath0 model is renormalizable . the renormalizability of noncommutative field theories is still under discussion ( see , e.g.,@xcite and references therein ) . the second motivation is that , recently , numerical simulations @xcite are corroborating results provided by noncommutative field theories based on a wilsonian approach @xcite , where a cutoff momentum is introduced . therefore , the cutoff models can provide interesting information on the vacuum structure of field theories . a third reason comes from the fact that , after all , quantum field theory is presently in the era of effective field theories @xcite . the most successful theories , which are renormalizable , are nowadays understood as low - energy approximations of a more fundamental theory ( perhaps not yet a field theory ) and thus have their validity expected to be limited up to an energy scale . additional motivation , from the phenomenological point of view , to consider the noncommutative models as cutoff theories may be found in @xcite . we shall restrict our considerations to the case of small @xmath1 and assume translational symmetry as a property of the vacuum state . this assumption was recently reassessed in the framework of noncommutative field theory ( see , e.g. , @xcite ) . the argument behind these papers is that , as a consequence of noncommutativity , the vacuum state of the models is no longer realized for a constant @xmath6 when this is the case , the effective potential is not a useful tool to analyze ssb . however , as pointed out in @xcite , the particular case where @xmath1 is small , ssb is expected to occur from a uniform - ordered to a disordered domain . actually , this prediction seems to be connected to the adoption of an explicit cutoff for the theory , as we shall discuss later . it is interesting to quote that the existence of a uniform - ordered domain was verified in a nonperturbative calculation @xcite involving the three - dimensional @xmath4 model . once a system is found in such a state , the minimum of the effective action is realized for a constant @xmath7 and translational symmetry is a property of the vacuum state . the noncommutative effects relevant in the regime under consideration come from the crossing of internal lines in the feynman diagrams . since the finiteness of some of these diagrams is attributed to an effective cutoff @xcite @xmath8 , introduced by noncommutativity , for @xmath1 sufficiently small these diagrams may become dominant and drastically modify the behavior of the field theories . indeed , this is exactly what will be shown to occur in this work . this paper is organized as follows . section ii presents the noncommutative version of the @xmath0 model and path integral method employed for the perturbative calculation of the effective potential . in sec . iii , the effective potential is evaluated up to two - loop order . section iv is devoted to an analysis of the properties of the effective potential and the conditions for ssb . finally , in sec . v , we end up with a general discussion and outlook .

we study the conditions for spontaneous symmetry breaking of the ( 2 + 1)-dimensional noncommutative @xmath0 model in the small-@xmath1 limit . in this regime , considering the model as a cutoff theory , it is reasonable to assume translational invariance as a property of the vacuum state and study the conditions for spontaneous symmetry breaking by an effective potential analysis .

we study the conditions for spontaneous symmetry breaking of the ( 2 + 1)-dimensional noncommutative @xmath0 model in the small-@xmath1 limit . in this regime , considering the model as a cutoff theory , it is reasonable to assume translational invariance as a property of the vacuum state and study the conditions for spontaneous symmetry breaking by an effective potential analysis . an investigation of up to the two loop level reveals that noncommutative effects can modify drastically the shape of the effective potential . under reasonable conditions , the nonplanar sector of the theory can become dominant and induce symmetry breaking for values of the mass and coupling constants not reached by the commutative counterpart .

hep-th0306064

c

in this work , we have carried out the study of aspects of ssb for the noncommutative @xmath0 model . our main goal was the investigation of the relevance of noncommutativity effects when @xmath1 is small . an analysis carried out at two - loop order in perturbation theory revealed that the noncommutative corrections to the effective potential are dominated by the nonplanar contributions . these are very different from the corresponding planar counterparts , which , except for weight factors , are functionally similar to the ordinary commutative ones . the bad behavior of the nonplanar diagrams in the @xmath72 limit can be interpreted as a consequence of the removal of the effective cutoff @xmath144 naturally introduced by noncommutative geometry . this is exactly what makes the study of the nonplanar contributions in the small-@xmath1 limit especially interesting , since they can drastically modify the shape of the effective potential . indeed , this was the general conclusion of our qualitative analysis in all cases covered . as the main result of our investigation , we found that , at the two - loop level , noncommutativity effects can induce a ssb for positive values of the mass parameter and the coupling constants . the conditions for this to occur were determined in a quantitative analysis , which provided an analytical expression for the square of the mass parameter , @xmath107 , where the ssb takes place . for the values fixed for the coupling constants @xmath80 and @xmath145 the mass channel for which the noncommutativity - induced ssb occurs , @xmath146 , was shown to comprise a reasonable range of values and to become large as long as @xmath1 gets smaller . other choices for @xmath80 , @xmath78 may yet expand the possibilities for the mass channel . for the fixed values for @xmath80 and @xmath78 , we showed that , for acceptable @xmath147 and reasonable values of @xmath148 translational symmetry can be assumed as a property of the vacuum state . if one considers @xmath127 as a parameter to vary , the corresponding @xmath149 is a decreasing function . in the continuum limit ( in the case it makes sense ) , @xmath150 and the translational invariant phase ceases to exist . the same occurs if one considers , e.g. , the expression for @xmath121 presented for the @xmath4 model in @xcite : @xmath151 , where @xmath152 is the coupling constant . the existence of a translational invariant phase seems to be a common feature of the cutoff models , where , for @xmath1 sufficiently small , @xmath153 admits its global minimum at @xmath120 . in a previous work @xcite it was argued that , for the noncommutative scalar field theories to be renormalizable , it would be necessary to relax the hypothesis of translational invariance . perhaps translational invariance for small @xmath1 is therefore a property only of the cutoff models . beyond the natural interest that is motivating the investigation of noncommutativity from the theoretical point of view , knowledge of how it can modify the shape of the effective potential for scalar theories could be of great relevance , for example , in cosmology . the analysis of effective potentials plays a fundamental role in the study of inflationary universe models @xcite . since the @xmath154 s , if nonvanishing , should be very small , the results obtained in this work may be useful as clues for a possible application of noncommutativity as a mechanism for generating a symmetry breaking in the inflationary scenario . an example of how noncommutative field theory may be applied to inflationary cosmology may be found in @xcite .

an investigation of up to the two loop level reveals that noncommutative effects can modify drastically the shape of the effective potential . under reasonable conditions , the nonplanar sector of the theory can become dominant and induce symmetry breaking for values of the mass and coupling constants not reached by the commutative counterpart .

we study the conditions for spontaneous symmetry breaking of the ( 2 + 1)-dimensional noncommutative @xmath0 model in the small-@xmath1 limit . in this regime , considering the model as a cutoff theory , it is reasonable to assume translational invariance as a property of the vacuum state and study the conditions for spontaneous symmetry breaking by an effective potential analysis . an investigation of up to the two loop level reveals that noncommutative effects can modify drastically the shape of the effective potential . under reasonable conditions , the nonplanar sector of the theory can become dominant and induce symmetry breaking for values of the mass and coupling constants not reached by the commutative counterpart .

1304.7565

i

quantum degenerate ultracold atoms with spin - degree of freedom exhibit both magnetic order and superfluidity , offering a rich system in which to explore quantum coherence , long - range order , magnetism and symmetry breaking . many aspects of spinor atoms in a trap have been investigated with spin @xmath3 atoms , such as @xmath0na and @xmath1rb @xcite . spin-2 @xcite and spin-3 @xcite spinor gases have been studied to a lesser extent . spinor condensates are described by a vector order parameter @xcite . the distinctive feature is its spin - dependent interaction which organizes spins giving rise to ferromagnetic and antiferromagnetic ( polar ) order . it can also coherently convert a spin @xmath4 and a @xmath5 atom to two @xmath6 atoms and vice versa @xcite , while conserving magnetization and energy . in parallel to ultracold spinor physics , optical lattices have become a powerful tool to create strongly correlated many - body states of bosons and fermions @xcite . lattice systems offer flexibility as the lattice parameters and particle interactions can be controlled easily , thereby facilitating progress towards the creation of quantum emulators @xcite . since the seminal observation of the superfluid to mott insulator transition with spinless bosons @xcite , steady progress is being made towards the understanding of spinor atoms in an optical lattice @xcite . issues of temperature and entropy @xcite are among the challenges that need to be overcome to create a many - body correlated state of spin-1 atoms . theoretical studies of lattice - trapped spinor condensates have mainly explored the phase diagram and the nature of the superfluid - mott insulator transition @xcite . due to the tunability of cold atom and optical lattice parameters , it is also possible to study non - equilibrium dynamics . dynamics of many - body quantum systems is still an emerging field , and only a number of issues have so far been investigated @xcite . an early experiment @xcite studied the dynamics of spinless bosons in a suddenly - raised optical lattice , observing the collapse and revival of the matter wave field in the momentum distribution . in a more - recent experiment @xcite , tens of oscillations in the momentum distribution or visibility were observed , and the predicted @xcite signature of effective higher - body interactions confirmed . as for spin-1 atoms , dynamical studies have mainly focused on large atom continuum or trapped systems in the mean field regime exploring spin - mixing dynamics @xcite , quantum quench dynamics @xcite , and various instabilities @xcite . the goal of this paper is to study the dynamics of spin-1 bosonic atoms in a three - dimensional ( 3d ) optical lattice and probe its many - body state and system properties . starting with a ferromagnetic ( @xmath1rb ) or antiferromagnetic ( @xmath0na ) superfluid ground state in a shallow lattice , suddenly raising the lattice depth creates a non - equilibrium state , which can be followed in various scenarios with and without a magnetic field and with and without effective three - body interactions . the evolution shows collapse and revival of matter - wave coherence measured by visibility oscillations , in a more complex pattern than for spinless bosons @xcite . it also shows oscillations in spin populations due to the combined effect of the spin - mixing collisions of the @xmath6 and @xmath7 components and differential level shifts proportional to the square of the magnetic field strength , the quadratic zeeman shift . linear zeeman shifts do not affect the behavior of spinor condensates . both spin - mixing and visibility oscillations reveal details about the system such as the composition of the initial many - body state , and thereby its superfluid and magnetic properties . by analyzing the frequency spectrum of the visibility , we show that the ratio @xmath8 of spin - dependent and spin - independent atom - atom interactions can be deduced . combined with spectra of spin - mixing dynamics at various magnetic field strengths , this gives us a method to measure the interaction couplings for spin-1 atoms . finally , we find that the presence of quadratic zeeman shift enhances spin mixing oscillations for ferromagnets and shows collapse and partial revivals in the transverse magnetization . the hamiltonian that quantitatively describes the physics of the final deep lattice comprises of two - body as well as effective multi - body interactions , which arise due to virtual excitations to higher bands . we derive the induced three - body interaction parameters for spin-1 atoms in a deep harmonic well , approximating the minimum of a single lattice site as such , and find the existence of _ spin - dependent _ three - body interactions . we show how to detect the signature of the three - body interactions and argue that they are directly exhibited in the _ in situ _ density as opposed to the time of flight visibility measurements as is the case for spinless bosons @xcite . the article is organized as follows . in sec . [ sec : model ] we setup the spin-1 bose - hubbard model , sketch the mean - field theory to determine the initial ground state , describe the exact hamiltonian after the quench , and discuss observables and computational aspects . we present our main results in sec . [ sec : polar ] , [ sec : ferro ] , and [ sec : three ] . section [ sec : polar ] explores the non - equilibrium dynamics of antiferromagnetic spin-1 atoms , with and without a magnetic field . section [ sec : ferro ] describes the dynamics for a ferromagnetic spinor . section [ sec : three ] shows the effects of effective three - body interactions in the dynamics . we summarize our results in sec . [ sec : conclusion ] . a derivation of the effective three - body interaction is given in the appendix .

the time evolution of the non - equilibrium state , thus created , shows collective collapse - and - revival oscillations of matter - wave coherence as well as oscillations in the spin populations . we show that the complex pattern of these two types of oscillations reveals details about the superfluid and magnetic properties of the initial many - body ground state . furthermore , we show that the strengths of the spin - dependent and spin - independent atom - atom interactions can be deduced from the observations . the hamiltonian that describes the physics of the final deep lattice not only contains two - body interactions but also effective multi - body interactions , which arise due to virtual excitations to higher bands .

we study the dynamics of spin-1 atoms in a periodic optical - lattice potential and an external magnetic field in a quantum quench scenario where we start from a superfluid ground state in a shallow lattice potential and suddenly raise the lattice depth . the time evolution of the non - equilibrium state , thus created , shows collective collapse - and - revival oscillations of matter - wave coherence as well as oscillations in the spin populations . we show that the complex pattern of these two types of oscillations reveals details about the superfluid and magnetic properties of the initial many - body ground state . furthermore , we show that the strengths of the spin - dependent and spin - independent atom - atom interactions can be deduced from the observations . the hamiltonian that describes the physics of the final deep lattice not only contains two - body interactions but also effective multi - body interactions , which arise due to virtual excitations to higher bands . we derive these effective spin - dependent three - body interaction parameters for spin-1 atoms and describe how spin - mixing is affected . spinor atoms are unique in the sense that multi - body interactions are directly evident in the _ in - situ _ number densities in addition to the momentum distributions . we treat both antiferromagnetic ( e.g. @xmath0na atoms ) and ferromagnetic ( e.g. @xmath1rb and @xmath2k ) condensates .

1304.7565

c

in this paper we performed a theoretical study of the dynamics of spin-1 bosons in an optical lattice in a quench scenario where we start from a ground state in a shallow lattice and suddenly raise the lattice depth . we have shown that the ensuing spin - mixing and visibility oscillations can be used as a probe of the initial superfluid ground state . the spectral analysis of time evolution reveals the fock state composition of the initial state and thereby its superfluid and magnetic properties . analysis of visibility oscillations , i.e. quantum phase revival spectroscopy , further yields a method to determine the spin - dependent and spin - independent interaction ratio @xmath8 , which is an important quantity for spinor gases . we treat both antiferromagnetic ( e.g. @xmath0na atoms ) and ferromagnetic ( e.g. @xmath1rb ) condensates . for ferromagnetic interactions the spin - mixing oscillation amplitudes are small . when external magnetic field can not be ignored , the inclusion of a quadratic zeeman field is necessary , and we have quantified such dynamics . we have shown that the presence of a magnetic field increases the spin - mixing amplitude for a ferromagnetic condensate . the hamiltonian that more accurately describes the physics of the final deep lattice comprises of two - body as well as effective multi - body interactions , which arise due to virtual excitations to higher bands . we derive the induced three - body interaction parameters for spin-1 atoms in a deep harmonic well and show its effect on the spin - mixing dynamics . we demonstrate that a frequency analysis of the oscillations can detect the signature and strength of the spin - dependent three - body interactions . we stress our finding that the three - body interactions for spinor atoms can be observed directly in the _ in - situ _ number densities in addition to the time of flight visibility as observed for spinless bosons @xcite . although there have been many theoretical studies for spin-1 bosons in an optical lattice , a many - body correlated ground state has not yet been achieved experimentally . there are many unexplored questions in that regard . here , we have combined the study of dynamics with optical lattice spinors to show how non - equilibrium dynamics can be used as a probe for revealing ground state properties and spinor interactions . there are other dynamic scenarios that can give different perspectives on spinor lattice physics , such as a quench from mott insulator to superfluid , evolution in a tunnel coupled lattice , to name a few . interplay of superfluidity , magnetism and strong correlations makes this a rich system where study of quantum dynamics may lead to a better understanding of collective phenomena .

we study the dynamics of spin-1 atoms in a periodic optical - lattice potential and an external magnetic field in a quantum quench scenario where we start from a superfluid ground state in a shallow lattice potential and suddenly raise the lattice depth . we derive these effective spin - dependent three - body interaction parameters for spin-1 atoms and describe how spin - mixing is affected . spinor atoms are unique in the sense that multi - body interactions are directly evident in the _ in - situ _ number densities in addition to the momentum distributions . we treat both antiferromagnetic ( e.g. @xmath0na atoms ) and ferromagnetic ( e.g. @xmath1rb and @xmath2k ) condensates .

we study the dynamics of spin-1 atoms in a periodic optical - lattice potential and an external magnetic field in a quantum quench scenario where we start from a superfluid ground state in a shallow lattice potential and suddenly raise the lattice depth . the time evolution of the non - equilibrium state , thus created , shows collective collapse - and - revival oscillations of matter - wave coherence as well as oscillations in the spin populations . we show that the complex pattern of these two types of oscillations reveals details about the superfluid and magnetic properties of the initial many - body ground state . furthermore , we show that the strengths of the spin - dependent and spin - independent atom - atom interactions can be deduced from the observations . the hamiltonian that describes the physics of the final deep lattice not only contains two - body interactions but also effective multi - body interactions , which arise due to virtual excitations to higher bands . we derive these effective spin - dependent three - body interaction parameters for spin-1 atoms and describe how spin - mixing is affected . spinor atoms are unique in the sense that multi - body interactions are directly evident in the _ in - situ _ number densities in addition to the momentum distributions . we treat both antiferromagnetic ( e.g. @xmath0na atoms ) and ferromagnetic ( e.g. @xmath1rb and @xmath2k ) condensates .

1007.5446

i

experimental investigations of the rheology of concentrated suspensions often involve a vane - in - cup geometry ( see @xcite for a review ) . the vane tool offers two main advantages over other geometries . first , it allows the study of the properties of structured materials with minimal disturbance of the material structure during the insertion of the tool [ @xcite ] . it is thus widely used to study the properties of gels and thixotropic materials [ @xcite ] and for in situ study of materials as e.g. in the context of soil mechanics [ @xcite ] . second , it is supposed to avoid wall slip [ @xcite ] , which is a critical feature in concentrated suspensions [ @xcite ] ; the reason for this belief is that the material sheared in the gap of the geometry is sheared by the ( same ) material that is trapped between the blades . consequently , it is widely used to study the behavior of pasty materials containing large particles , such as fresh concrete [ @xcite ] and foodstuff [ @xcite ] . the constitutive law of materials can be obtained from a rheological study with the vane - in - cup geometry provided one knows the coefficients called `` geometry factors '' that allow the conversion of the raw macroscopic data ( torque , rotational angle or velocity ) into local data ( shear stress , shear strain or shear rate ) . however , in contrast with other classical geometries , even the _ a priori _ simple linear problem ( for hookean or newtonian materials ) is complex to solve with a vane tool . this linear problem was studied theoretically by @xcite and @xcite in the general case of a @xmath2-bladed vane tool embedded in an infinite linear medium . the analytical expression found for the torque vs. rotational velocity is in rather good agreement with macroscopic experimental data [ @xcite ] . note however two possible shortcomings of this theoretical approach for its use in practice : the blades are infinitely thin and there is no external cylinder . there is no such approach in the case of nonlinear media ( _ i.e. _ complex fluids ) . a practical method used to study the flow properties of non - linear materials , known as the couette analogy [ @xcite ] , consists in calibrating the geometry factors with hookean or newtonian materials . one defines the equivalent inner radius @xmath3 of the vane - in - cup geometry as the radius of the inner cylinder of a couette geometry that would have the same geometry factors for a linear material . for any material , all macroscopic data are then analyzed as if the material was sheared in a couette geometry of inner cylinder radius @xmath3 . the nonlinearity ( that affects the flow field ) is sometimes accounted for as it is in a standard couette geometry [ @xcite ] . this approach may finally provide constitutive law measurements within a good approximation [ @xcite ] . however , simulations and observations show that @xmath3 is not a universal parameter of the vane tool independent of the properties of the studied material . while the streamlines go into the virtual cylinder delimited by the blades in the case of newtonian media [ @xcite ] , yielding an equivalent radius lower than the vane radius [ @xcite ] , it was found from simulations [ @xcite ] that the streamlines are nearly cylindrical everywhere for shear - thinning fluids if their index @xmath4 is of order 0.5 or less , and thus that @xmath5 in these cases . moreover , for yield stress fluids , simulations and photographs of the shearing zone around a four - bladed vane rotating in bingham fluids [ @xcite ] , simulations of herschel - bulkley and casson fluids flows in a four - bladed vane - in - cup geometry [ @xcite ] , and simulations of bingham fluids flows in a six - bladed vane - in - cup geometry [ @xcite ] , all show that at yield ( _ i.e. _ at low shear rates ) , the material contained in the virtual cylinder delimited by the blades rotates as a rigid body , and that it flows uniformly in a thin cylindrical layer near the blades . this is now widely accepted [ @xcite ] and used to perform a couette analogy with @xmath5 ; the yield stress @xmath6 is then simply extracted from torque @xmath7 measurements at low velocity thanks to @xmath8 , where @xmath9 is the vane tool height ( neglecting end effects ) [ @xcite ] . the flow field in a vane - in - cup geometry and its consequences on the geometry factors have thus led to many studies . however , only theoretical calculations , macroscopic measurements and simulation data exist in the literature : there are no experimental local measurements of the flow properties of newtonian and non - newtonian materials induced by a vane tool except the qualitative visualization of streamlines made by @xcite for newtonian media , and the photographs of @xcite for yield stress fluids . moreover , while the main advantage of the vane tool is the postulated absence of wall slip , as far as we know , this widely accepted hypothesis has been neither investigated in depth nor criticized . in order to provide such local data , we have performed velocity measurements during the flows of a newtonian medium and of a yield stress fluid in both a coaxial cylinder geometry and a vane - in - cup geometry . we have also performed particle concentration measurements in a concentrated suspension of noncolloidal particles in a yield stress fluid , which is a good model system for complex pastes such as fresh concrete [ @xcite ] . our main results are that : 1 . in the newtonian fluid , the @xmath0-averaged strain rate component @xmath1 decreases as the inverse squared radius in the gap , as in a couette geometry , which allows direct determination ( without end - effect corrections ) of the value of @xmath3 : it is here found to be lower than @xmath10 , but slightly higher than for a vane in an infinite medium ; the flow enters deeply the region between the blades , leading to a significant extensional flow ; 2 . in the yield stress fluid , in contrast with results from the literature , the layer of material that is sheared near the blades at low velocity does not have a cylindrical shape ; 3 . in the suspension of noncolloidal particles in a yield stress fluid , the noncolloidal particles are quickly expelled from a thin zone near the blades , leading to the development of a thin slip layer made of the pure interstitial yield stress fluid , in sharp contradiction with the common belief that the vane tool prevents slippage . in sec . [ section_display ] , we present the materials employed and the experimental setup . we present the experimental results in sec . [ section_results ] : velocity profiles obtained with a newtonian oil and with a yield stress fluid are presented in sec . [ section_results][section_oil ] and sec . [ section_results][section_emulsion ] , while sec . [ section_results][section_suspension ] is devoted to the case of suspensions , with a focus on the slip layer created by a shear - induced migration phenomenon specific to the vane tool . throughout this paper , we use cylindrical coordinates @xmath11 . all flows are supposed to be @xmath12 invariants ( _ i.e. _ there are no flow instabilities ) . we define the @xmath0-average @xmath13 of a function @xmath14 as @xmath15 .

this allows direct comparison ( without end - effect corrections ) of the resistances to shear in vane and couette geometries . here , the mean shear stress in the vane - in - cup geometry is slightly lower than in a couette cell of same dimensions , and a little higher than when the vane is embedded in an infinite medium . we also observe that the flow enters deeply the region between the blades , leading to significant extensional flow . in the yield stress fluid , in contrast with the usually accepted picture based on simulation results from the literature , we find that the layer of material that is sheared near the blades at low velocity is not cylindrical . there is thus a significant extensional component of shear that should be taken into account in the analysis . finally and surprisingly , in the suspension

we study the local flow properties of various materials in a vane - in - cup geometry . we use mri techniques to measure velocities and particle concentrations in flowing newtonian fluid , yield stress fluid , and in a concentrated suspension of noncolloidal particles in a yield stress fluid . in the newtonian fluid , we observe that the @xmath0-averaged strain rate component @xmath1 decreases as the inverse squared radius in the gap , in agreement with a couette analogy . this allows direct comparison ( without end - effect corrections ) of the resistances to shear in vane and couette geometries . here , the mean shear stress in the vane - in - cup geometry is slightly lower than in a couette cell of same dimensions , and a little higher than when the vane is embedded in an infinite medium . we also observe that the flow enters deeply the region between the blades , leading to significant extensional flow . in the yield stress fluid , in contrast with the usually accepted picture based on simulation results from the literature , we find that the layer of material that is sheared near the blades at low velocity is not cylindrical . there is thus a significant extensional component of shear that should be taken into account in the analysis . finally and surprisingly , in the suspension , we observe that a thin non - cylindrical slip layer made of the pure interstitial yield stress fluid appears quickly at the interface between the sheared material and the material that moves as a rigid body between the blades . this feature can be attributed to the non - symmetric trajectories of the noncolloidal particles around the edges of the blades . this new important observation is in sharp contradiction with the common belief that the vane tool prevents slippage , and may preclude the use of the vane tool for studying the flows of pasty materials with large particles .

1007.5446

r

in this section , we study successively the flow properties of the newtonian oil , the yield stress fluid , and the suspension . in this section , we study the flows observed with a newtonian fluid . we first present a basic theoretical analysis of the flows in a vane - in - cup geometry as compared to flows in a standard couette geometry , which provides the basis for a couette analogy . the @xmath42-averaged azimuthal profiles @xmath59 are then shown , and are compared to predictions of the couette analogy . the full velocity field @xmath60 , @xmath46 is finally presented and analyzed . the stress balance equation projected along the azimuthal axis is : ( 1/r)_r(r^2)+_()-_p=0 [ equation_balance]where @xmath61 is the deviatoric stress tensor and @xmath62 the pressure . the strain rate tensor component @xmath1 is given by : ( r,)=((1/r)_(v_r)+r_r ( v_/r))[equation_strain_rate ] we recall that the constitutive law of a newtonian fluid of viscosity @xmath63 is : = 2[equation_newtonian ] . in all the following analysis , we assume a no - slip boundary condition at the walls of the inner tool and of the cup . in a standard coaxial cylinders couette geometry , due to cylindrical symmetry , eq . [ equation_balance ] becomes @xmath64 which means that the whole shear stress distribution @xmath65 in the gap is known whatever the constitutive law of the material is . if a torque @xmath66 is exerted on the inner cylinder driven at a rotational velocity @xmath41 , @xmath65 is given by : ( r)=-[equation_tau_couette]for a newtonian fluid of viscosity @xmath63 , it follows that the strain rate component @xmath67 is given by : ( r)=-as eq . [ equation_strain_rate ] becomes @xmath68 with cylindrical symmetry , due to the boundary conditions @xmath69 and @xmath70 , from @xmath71 , one gets alternatively @xmath72 $ ] . this yields the following azimuthal velocity profile : v_(r)=[equation_velocity_couette]finally , the viscosity @xmath63 of a newtonian fluid is obtained from the measured torque / rotational velocity relationship @xmath66 through = [ equation_visco_couette ] these equations will be used for the comparison with the flows observed in a vane - in - cup geometry , in particular to determine the radius @xmath3 of the equivalent couette geometry . in a vane - in - cup geometry , there is _ a priori _ no cylindrical symmetry and all quantities _ a priori _ depend on @xmath0 . however , averaging eq . [ equation_balance ] over @xmath42 yields @xmath73 . this means that what is true in a couette geometry , @xmath74 , is still true on average with a vane - in - cup geometry : @xmath75 independently of the material s constitutive law . note that this derivation is true only between @xmath10 and @xmath76 ; this is not true for the material between the blades as the unknown @xmath61 distribution in the blades contributes to the @xmath0-average . the link between this stress distribution and the torque @xmath66 exerted on the vane tool may then seem difficult to build . however , it can be equivalently computed on the outer cylinder as @xmath77 . this means that eq . [ equation_tau_couette ] is still valid for the @xmath42-averaged shear stress in the vane - in - cup geometry , for @xmath78 : _ r(r)=-[equation_tau_vane ] from the @xmath0-averaged eq . [ equation_newtonian ] , this means that the @xmath0-averaged strain rate distribution in a newtonian fluid , for @xmath78 , is : |d_r(r)=-from the @xmath42-averaged eq . [ equation_strain_rate ] @xmath79 , this means that the @xmath0-averaged azimuthal velocity profile of a newtonian fluid of viscosity @xmath63 in a vane - in - cup geometry for @xmath78 , with a boundary condition @xmath80 is given by : ( r)=[equation_velocity_vane ] finally , the only difference with a standard couette flow , as regards these @xmath42-averaged quantities , is that we do not know the value of @xmath81 ; we only know that @xmath82 , for @xmath83 integer , where @xmath2 is the number of blades . this means that @xmath84 and @xmath59 follow the same scaling with @xmath37 and @xmath41 as in the standard couette geometry , but with a different prefactor . nevertheless , these equations provide a new insight in the couette analogy . the usual way of performing the couette analogy consists in defining the radius of the equivalent couette geometry @xmath3 as the radius that allows measuring the viscosity @xmath63 of a newtonian fluid with the standard couette formula . from eq . [ equation_visco_couette ] , @xmath63 should then be correctly obtained from the torque / rotational velocity relationship @xmath66 measured in a vane - in - cup geometry with : = [ equation_visco_vane]from eqs . [ equation_visco_couette ] and [ equation_visco_vane ] , it means in particular that the torque @xmath85 exerted by the vane tool is decreased by a factor = [ equation_torque_rieq]as compared to the torque @xmath86 exerted by the inner cylinder of a couette geometry of same radius @xmath10 at a same rotational velocity . here , from eqs . [ equation_velocity_vane ] and [ equation_velocity_couette ] , we see that from the local flow perspective , there is a couette analogy in the sense that the @xmath0-averaged azimuthal velocity ( and shear ) profiles will be exactly the same as in a couette geometry . this defines a radius @xmath3 of the equivalent couette geometry , such that @xmath59 and @xmath84 for @xmath78 are given by : ( r)=[equation_velocity_vane_eq ] + @xmath3 are equivalent : combining eqs . [ equation_velocity_vane ] and [ equation_visco_vane ] yields eq . [ equation_velocity_vane_eq ] . this point of view provides an additional meaning to the couette analogy , namely the similarity of the average flows , and offers a new experimental mean to determine @xmath3 , which is more accurate than calibration . in rheological measurements , the @xmath66 relationship has to be corrected for end effects [ @xcite ] and the couette analogy has to be calibrated on a reference material of known viscosity . here , the @xmath59 or @xmath87 measurements provide the value of @xmath3 directly without any correction , as only shear in the gap is involved in the analysis , and independent of the viscosity of the material . this will be illustrated in the following . the only theoretical prediction of the stress field associated with a vane tool is that of @xcite for an infinite @xmath2-bladed vane embedded in an infinite linear medium . in this case , it is shown that the torque @xmath88 exerted on the vane is well approximated by = 1-[equation_prediction_atkinson ] where @xmath89 is the torque exerted on a cylinder of same radius @xmath10 as the vane in an infinite medium ( _ i.e. _ with @xmath90 ) . [ equation_prediction_atkinson ] is in agreement with experimental results [ @xcite ] . @xcite argue that , as the stress distribution varies as @xmath91 in a couette geometry , @xmath92 should be of the order of 1% or less in order to nullify the influence of the outer boundary ; this is clearly the case in their experiments and in field experiments where the vane is embedded e.g. in a soil ; this is clearly not the case in our experiments and in most rheological experiments that make use of a vane - in - cup geometry . however , when the cup to vane radius ratio @xmath93 is not large , no generic theoretical expression exists in the literature . nevertheless , bounds of the value of the torque @xmath94 can be derived using classical results of linear elasticity [ @xcite ] . our starting points are the variational approaches to the solution of the stokes equations describing the flow of an incompressible linear material induced by the rotation of an inner tool ( of any shape ) at a rotational velocity @xmath41 within a cup . in this framework , it can be shown that [ @xcite ] : @xmath95 where @xmath96 denotes the inner tool - fluid interface and @xmath97 the domain occupied by the fluid . in the first inequality , @xmath98 is any stress tensor complying with the stress balance equations , @xmath99 is the azimuthal component of the surface forces applied by the tool on the fluid and @xmath100 is the deviatoric stress tensor associated to @xmath98 . in the second inequality , @xmath101 is the strain rate tensor associated with any velocity field @xmath102 complying with the incompressibility constraint and the boundary conditions prescribed on the tool - fluid and cup - fluid interfaces . [ eq : bounds ] leads in particular to the expected inequalities : @xmath103 the lower bound is obtained by using the velocity field defined by @xmath104 for @xmath105 and @xmath106 for @xmath107 , where @xmath108 is the solution for the @xmath2-bladed vane of radius @xmath10 in a cup of radius @xmath76 . @xmath102 complies with the boundary conditions for the @xmath2-bladed vane of radius @xmath10 in an infinite domain problem . then , putting this test velocity field within the second inequality ( [ eq : bounds ] ) with @xmath109 and using @xmath110 yields the lower bound of the inequality ( [ eq : expectedbounds ] ) for the quantity @xmath111 . in eq . [ eq : clapeyron ] , @xmath112 denotes the strain rate tensor associated with @xmath113 while @xmath114 is the domain occupied by the fluid . the upper bound is obtained using the test velocity field defined by @xmath115 with @xmath116 defined by eq . [ equation_velocity_couette ] for @xmath117 and by @xmath118 for @xmath119 . it is easily checked that @xmath102 complies with the velocity boundary conditions for any vane - in - cup geometry with vane radius @xmath10 and cup radius @xmath76 . putting this test velocity field into the second inequality ( [ eq : bounds ] ) then yields the upper bound of inequality ( [ eq : expectedbounds ] ) . finally , combining inequalities ( [ eq : expectedbounds ] ) , eq . [ equation_prediction_atkinson ] and eq . [ equation_visco_couette ] yields @xmath120 of course , it is possible to improve the lower bound by determining admissible test stress fields for the problem under consideration and the inequalities ( [ eq : bounds ] ) . for example , let us consider the stress field defined between the two blades positioned at @xmath121 by @xmath122 with @xmath123 for @xmath119 and by @xmath124 for @xmath117 . this stress field complies with the balance equations within the fluid domain . let us recall that a stress field does not need to be continuous to comply with the balance equations ( of course , this stress field is not the solution of the problem ) . putting this stress field into the first inequality ( [ eq : bounds ] ) and using a numerical optimization tool to choose the optimal value of the parameter @xmath125 yields a new lower bound for the @xmath2-bladed vane in cup problem , which depends on @xmath2 and @xmath126 . in some cases , this test stress field improves the lower bound of inequality ( [ eq:17dego ] ) : e.g. , for the geometry we use in this study ( @xmath127 ) , the new lower bound is @xmath128 while the lower bound given by inequality ( [ eq:17dego ] ) is @xmath129 . nevertheless , such an improvement is not obtained for all parameter sets ( @xmath2,@xmath126 ) . it is thus necessary to compute the two lower bounds for each value of ( @xmath2,@xmath126 ) in order to obtain the more accurate lower estimate of the torque . although application of variational approaches to the derivation of estimates of the applied torque of a vane - in - cup problem is not classical , it is believed that such a strategy is able to provide useful results when no theoretical prediction of the solution is available for particular geometries . lower bounds of @xmath130 computed using the approach presented above are displayed in tab . [ tab_torque_reduction ] and are compared below to our results and to data in the literature . we first study the @xmath0-averaged azimuthal velocity profiles @xmath59 observed during the flows of a newtonian oil ( fig . [ figure_mean_velocity_vane ] ) . as shown above , these profiles can be used to check the validity of the couette analogy and to determine the couette equivalent radius @xmath3 . the azimuthal dependence of the velocity profiles between two adjacent blades of the vane tool will then be considered . of a newtonian oil in a couette geometry ( @xmath31 cm ) , at various rotational velocities @xmath41 ranging from 2 to 20 rpm ; the solid line is the theoretical profile for a newtonian fluid . b ) dimensionless @xmath0-averaged velocity profile @xmath131 of a newtonian oil in a six - bladed vane - in - cup geometry ( @xmath28 cm ) for @xmath41 ranging from 1 to 9 rpm ; the vertical dashed line shows the radius of the vane ; the dotted line is the theoretical profile for a rigid body rotation ( for @xmath132 ) ; the solid lines are the theoretical profiles for a newtonian fluid in couette geometries of radii , from right to left : ( i ) @xmath28 cm , ( ii ) @xmath133 cm , and ( iii ) @xmath134 cm corresponding to the @xcite theory in an infinite medium.,title="fig:",width=298 ] of a newtonian oil in a couette geometry ( @xmath31 cm ) , at various rotational velocities @xmath41 ranging from 2 to 20 rpm ; the solid line is the theoretical profile for a newtonian fluid . b ) dimensionless @xmath0-averaged velocity profile @xmath131 of a newtonian oil in a six - bladed vane - in - cup geometry ( @xmath28 cm ) for @xmath41 ranging from 1 to 9 rpm ; the vertical dashed line shows the radius of the vane ; the dotted line is the theoretical profile for a rigid body rotation ( for @xmath132 ) ; the solid lines are the theoretical profiles for a newtonian fluid in couette geometries of radii , from right to left : ( i ) @xmath28 cm , ( ii ) @xmath133 cm , and ( iii ) @xmath134 cm corresponding to the @xcite theory in an infinite medium.,title="fig:",width=298 ] in fig . [ figure_mean_velocity_vane]a we observe that the velocity profiles in the gap of a couette geometry are , as expected , in perfect agreement with the theory for a newtonian flow ( eq . [ equation_velocity_couette ] ) . this first observation can be seen as a validation of the measurement technique . in the vane - in - cup geometry ( fig . [ figure_mean_velocity_vane]b ) , we first note that the @xmath0-averaged dimensionless azimuthal velocity profiles @xmath131 measured for several rotational velocities @xmath41 are superposed , as expected from the linear behavior of the material . we also remark that the material between the blades rotates as a rigid body only up to @xmath135 cm , indicating that the shear flow enters deeply the region between the blades ( the vane radius is 4.02 cm ) . the whole limit between the sheared and the unsheared material in the ( @xmath136 ) plane will be determined in sec . [ section_results][section_oil][section_theta_profiles ] ( fig . [ figure_temporal_profiles]b ) . we finally observe that the theoretical velocity profile for a newtonian fluid in a couette geometry of radius equal to that of the vane lies above the data , as expected from the literature . this is also consistent with the observation that the shear flow enters the region between the vane blades . in order to test the couette analogy , we have chosen to plot the @xmath0-averaged strain rate @xmath137 vs. the radius @xmath37 in fig . [ figure_mean_gradient_vane ] . this allows us to distinguish more clearly the difference between the experimental and theoretical flow properties than would the velocity profiles , because the velocity profile always tends to the same limit ( @xmath138 ) at the outer cylinder whereas the strain rate profile does not . note that velocity measurements could not be performed close to the blades , which explains why strain rate data are missing from 4 to 4.2 cm . -averaged strain rate @xmath137 vs. radius @xmath37 for a newtonian oil sheared at 1 rpm in a six - bladed vane - in - cup geometry . the vertical dashed line shows the radius of the vane . the solid lines are the theoretical strain rate profiles for a newtonian fluid in couette geometries of radii : ( i ) @xmath28 cm ( light grey ) , ( ii ) @xmath133 cm ( black ) , and ( iii ) @xmath134 cm ( dark grey ) corresponding to the @xcite theory in a infinite medium.,width=340 ] in fig . [ figure_mean_gradient_vane ] , we first note that @xmath139 is zero up to @xmath140 cm , which corresponds to the limit of the rigid motion of the material ; @xmath137 then increases when @xmath37 tends towards @xmath10 as the material is more and more sheared between the blades . in the gap of the geometry , @xmath139 decreases when @xmath37 increases . as expected , the theoretical strain rate profile for a newtonian material in a couette geometry of radius equal to that of the vane falls well above the data _ at any radius @xmath37 _ ( this was less obvious on the velocity profiles ) . we then observe that the data are well fitted to the theoretical strain rate profile ( eq . [ equation_strainrate_vane ] ) for a newtonian material flowing in an equivalent couette geometry of inner cylinder radius @xmath133 cm ( @xmath141 cm was obtained from a fit of the velocity profile to eq . [ equation_velocity_vane_eq ] ) . this confirms that the @xmath0-averaged strain rate @xmath137 decreases as the inverse squared radius in the gap , in agreement with the couette analogy . from eq . [ equation_torque_rieq ] , we find @xmath142 ( let us recall that we do not need to consider end effects here because we determine the shear rate within the gap , and hence only the contribution to the torque from the material sheared in the gap ) . this value can now be compared to data from the literature . for a six - bladed vane tool in an infinite medium , the @xcite theory would imply a theoretical @xmath143 , which is 8% lower than what we measure , and corresponds to a theoretical `` equivalent radius '' @xmath134 cm when the vane is embedded in a cup of radius @xmath29 cm . [ figure_mean_velocity_vane]b and [ figure_mean_gradient_vane ] show that the flow characteristics predicted with this value of the equivalent radius can be distinguished from our experimental data and fall slightly below the data ( a discrepancy could be expected as @xmath92 is not small in our experiment ) . .ratio @xmath130 between the torque measured when straining a linear medium ( viscous or elastic ) in a vane - in - cup geometry and that measured in a coaxial cylinder geometry of similar dimensions , obtained in various theoretical , numerical and experimental studies of the literature ; only data corrected for ( or free from ) end effects are shown . the number @xmath2 of blades , the cup to vane radius ratio @xmath93 , the shaft radius to vane radius ratio @xmath144 , and the blade thickness to vane radius ratio @xmath145 , are displayed when provided in the manuscripts . the theoretical lower bound computed using variational approaches in sec . [ section_results][section_oil][section_analogy ] is also provided . [ cols="^,^,^,^,^,^,^ " , ] we have gathered experimental and numerical data from the literature where the cup to vane radius ratio @xmath93 is not large in tab . [ tab_torque_reduction ] ; only data corrected for ( or free from ) end effects are shown . first , it should be noted that all torque data obey the theoretical inequalities computed using variational approaches in sec . [ section_results][section_oil][section_analogy ] . however , no clear trends emerge from the comparison of the data . the relative impact of the various geometrical parameters that may affect the flow field , namely the cup to vane radius ratio @xmath93 , the shaft radius to vane radius ratio @xmath144 , and the blade thickness to vane radius ratio @xmath145 , can not be determined at this stage . for example , in very similar geometries , @xcite find a torque ratio @xmath130 close to that of @xcite whereas @xcite find a much lower torque ratio . the only noticeable difference between these two studies ( apart from the numerical method ) is that @xmath144 is higher in @xcite , but our data , with a rather large value of @xmath144 , show different features . we actually note that our study is the only one to report a torque ratio higher than in an infinite medium ; all other data report torque ratios up to 19% lower than expected in an infinite medium . in the general case of a finite vane - in - cup geometry , it thus seems that numerical investigations are still needed , and that , at this stage , a calibration has to be performed to get the geometry factors . we also expect that the bounds obtained using variational approaches in sec . [ section_results][section_oil][section_analogy ] can be improved . to better characterize the flow field , we now study the dependence of the velocity profiles on the angular position @xmath0 . we have performed experiments in which we measure one azimuthal velocity profile per second while the vane tool is rotated at 1 rpm , yielding 10 profiles between two adjacent blades . of a newtonian oil sheared at 1 rpm in a six - bladed vane - in - cup geometry , for various angular positions , @xmath0 , between one blade ( @xmath146 ) and midway between adjacent blades ( @xmath147 ) . the vertical dashed line shows the radius of the vane . the dotted line is the profile for a rigid body rotation ( for @xmath132 ) and the theoretical profile for a newtonian fluid in a couette geometry of radius @xmath10 ( for @xmath148 ) . b ) two - dimensional plot of the limit between rigid motion and shear ( empty circles ) for a newtonian material in the six - bladed vane - in - cup geometry ; the grey rectangles correspond to the blades.,title="fig:",width=328 ] of a newtonian oil sheared at 1 rpm in a six - bladed vane - in - cup geometry , for various angular positions , @xmath0 , between one blade ( @xmath146 ) and midway between adjacent blades ( @xmath147 ) . the vertical dashed line shows the radius of the vane . the dotted line is the profile for a rigid body rotation ( for @xmath132 ) and the theoretical profile for a newtonian fluid in a couette geometry of radius @xmath10 ( for @xmath148 ) . b ) two - dimensional plot of the limit between rigid motion and shear ( empty circles ) for a newtonian material in the six - bladed vane - in - cup geometry ; the grey rectangles correspond to the blades.,title="fig:",width=268 ] in fig . [ figure_temporal_profiles]a , we plot the velocity profiles @xmath149 measured at different angles @xmath0 . we first observe that the velocity profile which starts near from a blade tip ( corresponding to @xmath146by definition ) is very different from the velocity profile in a couette geometry of same radius : it starts with a much steeper slope , which means that the blades tip neighborhoods are regions of important shear as already observed by @xcite . we then observe that , as expected from the @xmath0-averaged velocity profiles , the shear flow enters more and more deeply the region between the blades as @xmath0 tends towards @xmath150(corresponding to midway between two adjacent blades ) ; at this angular position , the rigid rotation stops at @xmath151 cm . from all the velocity profiles , we finally extract a 2d map of the limit @xmath152 between rigid rotation and shear , which is depicted in fig . [ figure_temporal_profiles]b . this provides an idea of the deviation from cylindrical symmetry , and will be compared in the following to the case of yield stress fluids . note that eddies are likely to be present in the `` rigid '' region [ @xcite ] ; however , we did not observe any signature of their existence : they can thus be considered as second - order phenomena . of a newtonian oil sheared at 1 rpm in a six - bladed vane - in - cup geometry , for various angular positions @xmath0 between two adjacent blades ( from @xmath146to @xmath153).,width=340 ] as explained in sec . [ section_display ] , from the @xmath149 measurement and from the material incompressibility , we are able to reconstruct the radial velocity profile @xmath154 ( see fig . [ figure_radial_velocity ] ) . this also allows us to compute the strain rate components @xmath155 and @xmath156 , which are plotted in fig . [ figure_temporal_gradients ] . of course , due to the limited number of profiles between two adjacent blades , this method provides only a rough estimate of these quantities . in addition to their interest for future comparison with models and simulations , these data allow us to evaluate the contribution of the extensional flow to dissipation ; here , in a newtonian medium , the local power density is given by : @xmath157 . ( left ) and @xmath158 ( right ) vs. radius @xmath37 for various angular positions @xmath0 between two adjacent blades ( from @xmath146to @xmath153).,title="fig:",width=274 ] ( left ) and @xmath158 ( right ) vs. radius @xmath37 for various angular positions @xmath0 between two adjacent blades ( from @xmath146to @xmath153).,title="fig:",width=323 ] in fig . [ figure_radial_velocity ] , we first observe that @xmath159 for @xmath146and @xmath147 ; there is thus no extensional flow in these regions of space , as seen in fig . [ figure_temporal_gradients ] . this is actually expected from the fore - aft symmetry of the flow around these angular positions . @xmath160 and its spatial variations ( @xmath161 ) are maximal at @xmath162 . meanwhile , we observe that @xmath1 is maximal near the blades : at @xmath163 it is more than 4 times larger at @xmath146than at @xmath147 . we then find that @xmath1 ( and thus the shear stress @xmath164 ) decreases more rapidly from the blades ( at @xmath146 ) than the @xmath91 scaling of the couette geometry , whereas it does not vary much with @xmath37 midway between adjacent blades ( it even seems to slightly increase with @xmath37 as already observed in simulations by @xcite ) . it is also worth nothing that at @xmath165 , in contrast with what is observed at @xmath163 , the shear stress value is of order two times lower at @xmath146than at @xmath147 . from the whole set of @xmath1 and @xmath161 measurements ( fig . [ figure_temporal_gradients ] ) , we finally find that in regions where @xmath161 is maximal , the contribution of the extensional flow to dissipation is of order 25% . over the whole gap , we then evaluate its average contribution to dissipation to be rather important , of order 5 to 10% . this significant value may be a reason why the torque that has to be exerted to enforce flow is higher than that predicted by @xcite in an infinite medium . the confinement effect induced by a close boundary at a radius @xmath166 likely increases the contribution of the extensional flow to dissipation as compared to the case of an infinite medium ( although other effects may exist , as appears from the comparison of the data of tab . [ tab_torque_reduction ] ) . in this section , we study the flows induced by the vane tool with a yield stress fluid ( a concentrated emulsion ) . we focus on the behavior near the yielding transition , _ i.e. _ on low rotational velocities @xmath41 . -averaged velocity profile @xmath131 of a yield stress fluid ( concentrated emulsion ) in a six - bladed vane - in - cup geometry for @xmath41 ranging from 0.1 to 9 rpm ; the vertical dashed line shows the radius of the vane ; the dotted line is the theoretical profile for a rigid body rotation ( for @xmath132).,width=340 ] in fig . [ figure_average_velocity_yield ] , we plot the @xmath0-averaged azimuthal velocity profiles @xmath59 measured at several @xmath41 values ranging from 0.1 to 9 rpm , corresponding to macroscopic shear rates varying between 0.02 and 2 s@xmath167 . we first observe that flow is localized : the material is sheared only up to a radius @xmath168 . @xmath169 is found to increase as @xmath41 increases . this is a classical feature of flows of yield stress fluids in heterogeneous stress fields . it has been observed in couette geometries [ @xcite ] , where it is attributed to the @xmath91 decrease of the shear stress @xmath164 , which passes below @xmath6 at some @xmath170 at low @xmath41 . in this case , when @xmath41 tends to 0 , @xmath169 tends to @xmath10 and the torque @xmath7 at the inner cylinder tends to @xmath171 . in the vane - in - cup geometry , the same argument holds qualitatively thanks to eq . [ equation_tau_vane ] . it implies that the flow has to stop inside the gap at low @xmath41 . however , in contrast with the case of the couette geometry , as the whole stress field _ a priori _ depends on @xmath0 , this @xmath0-averaged equation does not provide the position of the limit between the sheared and the unsheared material ( which will determined at the end of this section ) . we then observe that , although this effect is less pronounced than with a newtonian material , the shear flow still enters the region between the blades , even at the lowest studied @xmath41 . close examination of the profiles shows that the material trapped between the blades rotates as a rigid body only up to @xmath172 cm at @xmath173 rpm , @xmath174 cm at @xmath175 rpm , and @xmath176 cm at @xmath177 rpm . we recall that @xmath151 cm with a newtonian fluid in the same geometry . of a yield stress fluid ( concentrated emulsion ) sheared at 0.1 rpm in a six - bladed vane - in - cup geometry , for various angular positions @xmath0 between two adjacent blades ( from @xmath146to @xmath153 ) . the vertical dashed line shows the radius of the vane.,width=340 ] as in sec . [ section_results][section_oil][section_theta_profiles ] , to better characterize the flow field , we have performed experiments in which we have measured 10 azimuthal profiles between two adjacent blades at 0.1 rpm . in fig . [ figure_temporal_velocity_yield ] , as for a newtonian fluid , we observe that there is a strong @xmath0-dependence of the velocity profiles . the velocity profile that starts near from a blade tip ( at @xmath146 ) has a much steeper slope than the profile measured midway between adjacent blades ( at @xmath147 ) ; again , this shows that the blade tip neighborhoods are regions of high shear . meanwhile the flow stops at a radius @xmath169 which is larger at @xmath147(4.5 cm ) than at @xmath146(4.3 cm ) . note also that there may be slight fore - aft asymmetry , as sometimes observed with yield stress fluids flows [ @xcite ] , but we did not study this point further . from these velocity profiles , we have reconstructed a 2d map of the flow field ( fig . [ fig_rigid_limit_yield ] ) , indicating both the boundary between the region of rigid body rotation ( between the blades ) and the sheared region , and the boundary between the sheared region and the outer region of fluid at rest ( _ i.e. _ the position where the yield criterion is satisfied ) . flow is found to occur in a layer of complex shape which is far from being cylindrical even at this very low velocity . these observations are in contradiction with the usually accepted picture for yield stress fluid flows at low rates [ @xcite ] , namely that the material contained in the virtual cylinder delimited by the blades rotates as a rigid body , and that it flows uniformly in a thin cylindrical layer near the blades . our results contrast in particular with previous numerical works which showed that the yield surface is cylindrical at low rates for bingham fluids , casson fluids , and herschel - bulkley materials with @xmath178 [ @xcite ] . with apparently similar conditions to those in some of the @xcite simulations , we find an important departure from cylindrical symmetry . this means that further investigation on the exact conditions under which this symmetry can be recovered is still needed . possible difference between our work and that of @xcite is that the blade thickness is zero in this last study . it is particularly striking and counterintuitive that @xmath169 is largest at the angular position ( @xmath147 ) where shear at @xmath10 is smallest ( similar observation was made by @xcite ) . as in sec . [ section_results][section_oil][section_theta_profiles ] , this points out the importance of the extensional flow in this geometry , with @xmath0-dependent normal stress differences which have to be taken into account in the yield criterion , and which thus impact the yield surface . it thus seems that the link between the yield stress @xmath6 and the torque @xmath7 measured at yield with a vane - in - cup geometry is still an open question , although the classical formula probably provides a sufficiently accurate determination of @xmath6 in practice . the same 2d map as above is plotted for @xmath175 rpm in fig . [ fig_rigid_limit_yield ] ; the same phenomena are observed , with enhanced departure from cylindrical symmetry , consistent with the observation that @xmath179 decreases when @xmath41 increases . this result was also unexpected , as simulations find uniform flows for shear - thinning material of index @xmath180 [ @xcite ] ; we would have expected the same phenomenology in a herschel - bulkley material of index @xmath178 ( and thus @xmath179 to tend to @xmath10 when increasing @xmath41 ) . this observation also shows that a couette analogy can hardly be defined for studying the flow properties of such materials in a vane - in - cup geometry because the equivalent couette geometry radius @xmath3 would probably depend also on @xmath41 ( as recently shown by @xcite ) . let us finally note that this departure from cylindrical symmetry has important impact on the migration of particles in a yield stress fluid ( see below ) . in this section , we investigate the behavior of a concentrated suspension of noncolloidal particles in a yield stress fluid ( at a 40% volume fraction ) . a detailed study of their velocity profiles would _ a priori _ present here limited interest : such materials present the same nonlinear macroscopic behavior as the interstitial yield stress fluid , and their rheological properties ( yield stress , consistency ) depend moderately on the particle volume fraction [ @xcite ] . on the other hand , noncolloidal particles in suspensions are known to be prone to shear - induced migration , which leads to volume fraction heterogeneities . this phenomenon is well documented in the case of suspensions in newtonian fluids [ @xcite ] but is still badly known in yield stress fluids ( some studies exist however in viscoelastic fluids [ @xcite ] ) . in the model of @xcite and @xcite , migration is related to shear - induced diffusion of the particles [ @xcite ] . in a wide gap couette geometry , the shear stress heterogeneity is important ( eq . [ equation_tau_couette ] ) ; the shear rate gradients then generate a particle flux towards the low shear zones , which is counterbalanced by a particle flux due to viscosity gradients . a steady state , which results from competition between both fluxes , may then be reached , and is characterized by an excess of particles in the low shear zones of the flow geometry ( near the outer cylinder in a wide - gap couette geometry [ @xcite ] ) . note that there are other models [ @xcite ] in which particle fluxes counterbalance the gradients in the particle normal stresses , and which can be used directly for non - newtonian media . as the development of migration depends on the spatial variations of shear , one may wonder how the azimuthal heterogeneities of shear introduced by the vane tool affect migration ; a related question is that of the relevance of the couette analogy for this phenomenon . in the following , we thus focus on the particle volume fraction distribution evolution when the material is sheared . we first study the behavior at high shear rate , in the absence of shear localization . we shear the suspension in both the standard couette geometry and the vane - in - cup geometry at a rotational velocity @xmath181 rpm . in this first set of experiments , we only study the steady - state of migration . at @xmath181 rpm , this steady - state is reached in less than 30 min ( which corresponds to a macroscopic strain of order 50000 , consistently with strainscale evaluations from data of the literature [ @xcite ] ) . in fig . [ fig_concentration_profile_omega100 ] we plot the steady state volume fraction profiles observed after shearing the suspension at @xmath181 rpm during 1h . rpm in both the couette geometry ( empty circles ) and the vane - in - cup geometry ( squares ) . in the vane - in - cup geometry , the volume fraction profile is determined in a 1 cm thick slice situated exactly between two adjacent blades ( see fig . [ fig_image_vane_omega100]b ) . the inset is a zoom ; the line is a fit of the data measured in the couette geometry to the @xcite model with @xmath182 . b ) @xmath0-averaged azimuthal velocity profile @xmath59 ; the dotted line is the theoretical rigid motion induced by the rotation of the vane tool ; the vertical dashed line shows the radius of the vane.,title="fig:",width=308 ] rpm in both the couette geometry ( empty circles ) and the vane - in - cup geometry ( squares ) . in the vane - in - cup geometry , the volume fraction profile is determined in a 1 cm thick slice situated exactly between two adjacent blades ( see fig . [ fig_image_vane_omega100]b ) . the inset is a zoom ; the line is a fit of the data measured in the couette geometry to the @xcite model with @xmath182 . b ) @xmath0-averaged azimuthal velocity profile @xmath59 ; the dotted line is the theoretical rigid motion induced by the rotation of the vane tool ; the vertical dashed line shows the radius of the vane.,title="fig:",width=289 ] as expected , we first observe that the material is strongly heterogeneous in the couette geometry : the volume fraction varies between 37% near the inner cylinder and 43% near the outer cylinder ( note that the nmr technique we use do not allow quantitative measurements near the walls ) . this heterogeneity is quantitatively similar to that observed in couette flows of newtonian suspensions at a same 40% particle volume fraction [ @xcite ] ; the profiles are actually well fitted to the @xcite model ( see eq . 16 of @xcite ) with a dimensionless diffusion constant @xmath182 which is close to that found by @xcite ( @xmath183 ) , although this model is not expected to hold in non - newtonian suspensions . in the vane - in - cup geometry , the volume fraction profile shows very different features ; note that the profile is measured in a 1 cm thick ( in the azimuthal direction ) slice situated exactly between two adjacent blades ( see fig . [ fig_image_vane_omega100 ] ) . in fig . [ fig_concentration_profile_omega100 ] , we first observe that there is a strong particle depletion in a wide zone between the blades . a homogeneous volume fraction of 40% is observed for radii inferior to 3.1 cm . at a radius @xmath184 cm , there is a strong drop in the volume fraction down to 5% within 1 mm ( corresponding to 4 particle diameters ) . close inspection of the velocity profile fig . [ fig_concentration_profile_omega100 ] shows that this radius @xmath179 corresponds to the transition between rigid motion and shear between the blades . the volume fraction then increases basically linearly with the radius up to a 40.5% volume fraction at a radius @xmath185 cm which is close to the vane radius . the volume fraction then increases only slightly ( between 40.5% and 42.5% ) in the gap of the geometry : the heterogeneity is here much less important than in a standard couette geometry . to get further insight into the new strong depletion phenomenon we have evidenced , we have performed 2d magnetic resonance images of the material . such images provide a qualitative view of the spatial variations of the particle volume fraction as only the liquid phase is imaged . images are coded in grey scales ; a brighter zone contains less particles . in fig . [ fig_image_vane_omega100]b , we first see an image of the homogeneous material . before any shear , as expected , the light intensity is homogeneous in the sample ( intensity variations correspond to noise ) . after a 1h shear at @xmath181 rpm , we observe very bright and thin curves on the , @xmath186 cm ) to the edge of another blade ( at @xmath153 , @xmath186 cm ) , and describes a concave @xmath187 curve whose minimum is @xmath188 cm at @xmath147 . note that as the volume fraction profile is averaged over a slice which is 1 cm thick in the azimuthal direction ( see fig . [ fig_image_vane_omega100]b ) , the fact that we measure a minimum of 5% at @xmath188 cm in the slice probably means that the volume fraction minimum is actually equal to zero in the depletion zone . rpm ( corresponding to a macroscopic strain of order 75000 ) , and ( b ) before any shear . the crosses in fig . [ fig_image_vane_omega100]a correspond to the limit between rigid motion and shear for the newtonian oil of fig . [ figure_temporal_profiles]b . the white rectangle in fig . [ fig_image_vane_omega100]b shows the slice in which the volume fraction profiles of figs . [ fig_concentration_profile_omega100]a and [ fig_concentration_profile_omega1 ] are measured . ( c ) is a zoom of image ( a ) near the edges of a blade . the images are taken in the horizontal plane of the geometry , at middle height of the vane tool , and correspond to vertical averages over 2 cm . the vane tool rotates counterclockwise.,title="fig:",width=453 ] + ( a ) + + rpm ( corresponding to a macroscopic strain of order 75000 ) , and ( b ) before any shear . the crosses in fig . [ fig_image_vane_omega100]a correspond to the limit between rigid motion and shear for the newtonian oil of fig . [ figure_temporal_profiles]b . the white rectangle in fig . [ fig_image_vane_omega100]b shows the slice in which the volume fraction profiles of figs . [ fig_concentration_profile_omega100]a and [ fig_concentration_profile_omega1 ] are measured . ( c ) is a zoom of image ( a ) near the edges of a blade . the images are taken in the horizontal plane of the geometry , at middle height of the vane tool , and correspond to vertical averages over 2 cm . the vane tool rotates counterclockwise.,title="fig:",width=222 ] rpm ( corresponding to a macroscopic strain of order 75000 ) , and ( b ) before any shear . the crosses in fig . [ fig_image_vane_omega100]a correspond to the limit between rigid motion and shear for the newtonian oil of fig . [ figure_temporal_profiles]b . the white rectangle in fig . [ fig_image_vane_omega100]b shows the slice in which the volume fraction profiles of figs . [ fig_concentration_profile_omega100]a and [ fig_concentration_profile_omega1 ] are measured . ( c ) is a zoom of image ( a ) near the edges of a blade . the images are taken in the horizontal plane of the geometry , at middle height of the vane tool , and correspond to vertical averages over 2 cm . the vane tool rotates counterclockwise.,title="fig:",width=223 ] + ( b)(c ) as pointed out above , this curve also likely marks the transition between the unsheared material ( which rotates as a rigid body ) and the sheared material . note in particular the similarity with fig . [ figure_temporal_profiles]b , the data of which are reported in fig . [ fig_image_vane_omega100]a for illustration . a first interpretation of the phenomenon would then simply be that migration is caused by shear and naturally stops at this transition zone . indeed , as shear is maximum near the blades , particles tends to migrate out of this zone ; moreover , there is no source of particle flux from the unsheared zone between the blades to balance the migration towards the outer cylinder . however , this does not explain why the volume fraction drops down to zero : heterogeneities observed at steady - state in the literature are usually moderate and do not lead to zones free of particles . a better understanding of the phenomenon can be gained by zooming on the previous image ( fig.[fig_image_vane_omega100]c ) . we now see that while the depletion phenomenon seems symmetric around both sides of the blades at a macroscopic scale , it is clearly asymmetric at a local scale near the blades and depends on the direction of rotation : depletion is more pronounced at the back of the blade ( note that the vane tool rotates counterclockwise ) . this would mean that the noncolloidal particle trajectories are asymmetric around the blade : a particle that is found at a radius @xmath189 cm just before the blade is necessarily found at a radius slightly higher than 4.02 cm after the blade as there are no particles at @xmath186 cm . this feature is reminiscent of the fore - aft asymmetry that is observed in the bulk of noncolloidal suspensions [ @xcite ] and that leads to their non - newtonian properties [ @xcite ] . it thus seems that , in addition to the shear - induced migration mechanism intrinsic to suspensions , the vane tool induces a specific migration mechanism which has its origin in the direct interactions between the particles and the blades ; this effects leads to the full depletion that is observed at the transition between the sheared and the unsheared material . such direct effect of a flow geometry on migration has also been observed in microchannel flows of colloidal suspensions [ @xcite ] , and also led to full particle depletion . see also @xcite . the kinetics of the phenomenon will be briefly discussed below . the rest of the volume fraction profile results from a complex interplay between shear - induced migration and the fore - aft asymmetry around the blades ; this leads to the rapid increase of the volume fraction between 3.1 cm and 4.02 cm . after 4.02 cm the flow lines do not meet the blade edges , and the phenomenon evidenced above should have basically no effect on the heterogeneity that develops in the gap of the geometry . on the other hand , the mean volume fraction should be slightly higher due to mass conservation ; it is indeed observed to be equal to around 42% . nevertheless , as the mean radial shear rate heterogeneity is basically similar to that observed in a standard couette geometry ( see previous sections ) , we would _ a priori _ expect the heterogeneity to be somehow similar . however , we observe that the volume fraction profile is only slightly heterogeneous : there is less than 5% variation of the volume fraction in the gap , to be compared to the 15% variation observed in the couette geometry . clearly , this means that the couette analogy is irrelevant as regards this phenomenon , and that the details of shear matter . here , the extensional flow that adds to shear may be at the origin of this diminution of migration . a more detailed analysis is out of the scope of this paper . let us now study the behavior at low shear rate . low shear rates are typically imposed with the aim of measuring the yield stress of such materials . starting from a homogeneous suspension at rest , we apply a rotational velocity @xmath175 rpm ( without any preshear ) , and we measure the evolution of the particle volume fraction in time . the corresponding volume fraction profiles are depicted in fig . [ fig_concentration_profile_omega1 ] . rpm measured in the vane - in - cup geometry after different times of shear : 5min , 1h , 14h . the material is homogeneous at the beginning of shear . the inset presents the @xmath0-averaged azimuthal velocity profile @xmath59 measured in the first stages of shear ; the dotted line is the theoretical rigid motion induced by the rotation of the vane tool ; the vertical dashed line shows the radius of the vane.,width=340 ] in fig . [ fig_concentration_profile_omega1 ] , we observe that , although shear is much less important than in the previous experiments , particle depletion also appears between the blades . comparison of the velocity profile and the volume fraction profile shows that depletion also appears between the blades at the transition zone between the sheared and the unsheared materials . this phenomenon appears with a very fast kinetics : the lower volume fraction value in the measurement zone is 36% after only a 5 minute shear ( corresponding to a macroscopic strain of order 50 ) . afterwards , it continues evolving slowly : the minimum observed volume fraction is of order 33% after a 1h shear and of order 32% after a 14h shear ( corresponding to a 10000 macroscopic strain ) . note that the radial position of the minimum value of the volume fraction slightly decreases in time ; it likely corresponds to progressive erosion of the material between the blades ( we did not measure the velocity profiles to check this hypothesis ) . we also note that migration is negligible in the rest of the sheared material as expected from the theory of migration briefly described above ( a larger strain would be needed to observe significant migration ) . nevertheless , we note some particle accumulation ( with a volume fraction value of 43% ) at @xmath169=4.7 cm after a very long time . this corresponds to the yield surface as flow is localized at low velocity ( see velocity profile fig . [ fig_concentration_profile_omega1 ] ) . migration profiles usually result from an equilibrium between various sources of fluxes . on the other hand , the unsheared material does not produce any particle flux while it receives particles from the sheared region . this particle accumulation is thus the signature that the migration phenomenon is indeed active , although not observable on the profile measured in the sheared zone . it is probable that this accumulation process would stop only ( after a very long time ) when there are no more particles in the sheared region . ( b ) is a zoom of image ( a ) between two adjacent blades . the image is taken in the horizontal plane of the geometry , at middle height of the vane tool , and corresponds to a vertical average over 2 cm . the vane tool rotates counterclockwise.,title="fig:",width=298 ] + ( a)(b ) as above , 2d magnetic resonance images of the material provide an insight in the phenomenon . in fig . [ fig_image_vane_omega1 ] , we observe again that particle depletion is enhanced at the rear of the blades ; this confirms that this phenomenon is likely due to direct interactions between the blades and the particles , leading to the asymmetry of the particles trajectory around the blades . this _ a priori _ occurs with any particle whose trajectory is close to the blades , explaining why particle depletion appears so rapidly . there is probably no way to avoid it . note that the images are here much brighter very close to the blades than midway between two adjacent blades ; this would mean that the particle volume fraction is probably close to @xmath190 near the blades , although we observe volume fraction of order 32% between two blades . + finally , let us note that the bright line provides a good idea of the boundary between the sheared material and the material that moves as a rigid body . we see as in sec . [ section_results][section_emulsion ] that this is far from being cylindrical even at this low velocity . we finally present some consequences of this phenomenon . from the above observations , our conclusion is that depletion sets up quickly and is probably unavoidable . then two situations have to be distinguished . if linear viscoelastic properties of a suspension of large particles are measured at rest on the homogeneous material in its solid regime , without any preshear , then these measurements pose no other problem than that of the relevant couette analogy to be used ( see sec . [ section_results][section_oil ] ) . if a yield stress measurement is performed at low imposed rotational velocity , starting from the homogeneous material at rest , then this measurement is likely valid as long as only the peak value or the plateau value at low strain ( of order 1 ) is recorded . on the other hand , any subsequent analysis of the material behavior will _ a priori _ be misleading : irreversible changes have occurred and the material can not be studied anymore . more generally , any measurement performed after a preshear will be incorrect and any flow curve measurement will lead to wrong evaluation of the material properties . in these last cases , the consequence of the new particle depletion phenomenon we have evidenced is a kind of wall slip near the blades , whereas there are no walls . here the `` slip layer '' is made of the ( pure ) interstitial yield stress fluid in a zone close to the blades , as would be observed near a smooth inner cylinder . this contrasts with the common belief that the vane tool prevents slippage . in order to illustrate this feature , we present some results of @xcite : mahaut _ et al . _ performed classical upward / downward shear rate sweeps with a six - bladed vane - in - cup geometry ( @xmath191 cm , @xmath192 cm , @xmath304.5 cm , blade thickness=0.8 mm ) in a pure concentrated emulsion , and in the same emulsion filled with 20% of 140 @xmath17 m ps beads . in these experiments , constant macroscopic shear rates steps increasing from 0.01 to 10 s@xmath167 and then decreasing from 10 to 0.01 s@xmath167 were applied during 30s , and the stationary shear stress was measured for each shear rate value . the results are shown in fig . [ fig_sweep_suspension ] . m ps beads ( filled / open circles ) . figure from @xcite.,width=302 ] while the same curve is observed for the upward / downward shear rate sweeps in the case of the pure emulsion ( as expected for a simple non - thixotropic yield stress fluid ) , the shear stress during the upward shear rate sweep differs from the shear stress during the downward shear rate sweep in the case of the suspension . moreover , any measurement performed on the suspension after this experiment gives a static yield stress equal to the dynamic yield stress observed during the downward sweep . this means that there has been some irreversible change . this irreversible change is actually the particle depletion near the blades we have observed in this paper . as the flow of the suspension is localized near the inner tool at low shear rate , it means that after the first upward sweep that has induced the particle depletion , during the downward shear rate sweep only the pure emulsion created by migration near the blades remains in the sheared layer at sufficiently low rotational velocity . this explains why the same apparent value of the yield stress is found in the suspension during the downward sweep as in the pure emulsion with this experiment . on the other hand , the yield stress at the beginning of the very first upward sweep is that of the suspension as migration has not occurred yet . the conclusion is that the vane tool is probably not suitable to the study of flows of suspensions of large particles .

we study the local flow properties of various materials in a vane - in - cup geometry . , we observe that the @xmath0-averaged strain rate component @xmath1 decreases as the inverse squared radius in the gap , in agreement with a couette analogy . , we observe that a thin non - cylindrical slip layer made of the pure interstitial yield stress fluid appears quickly at the interface between the sheared material and the material that moves as a rigid body between the blades . this feature can be attributed to the non - symmetric trajectories of the noncolloidal particles around the edges of the blades .

we study the local flow properties of various materials in a vane - in - cup geometry . we use mri techniques to measure velocities and particle concentrations in flowing newtonian fluid , yield stress fluid , and in a concentrated suspension of noncolloidal particles in a yield stress fluid . in the newtonian fluid , we observe that the @xmath0-averaged strain rate component @xmath1 decreases as the inverse squared radius in the gap , in agreement with a couette analogy . this allows direct comparison ( without end - effect corrections ) of the resistances to shear in vane and couette geometries . here , the mean shear stress in the vane - in - cup geometry is slightly lower than in a couette cell of same dimensions , and a little higher than when the vane is embedded in an infinite medium . we also observe that the flow enters deeply the region between the blades , leading to significant extensional flow . in the yield stress fluid , in contrast with the usually accepted picture based on simulation results from the literature , we find that the layer of material that is sheared near the blades at low velocity is not cylindrical . there is thus a significant extensional component of shear that should be taken into account in the analysis . finally and surprisingly , in the suspension , we observe that a thin non - cylindrical slip layer made of the pure interstitial yield stress fluid appears quickly at the interface between the sheared material and the material that moves as a rigid body between the blades . this feature can be attributed to the non - symmetric trajectories of the noncolloidal particles around the edges of the blades . this new important observation is in sharp contradiction with the common belief that the vane tool prevents slippage , and may preclude the use of the vane tool for studying the flows of pasty materials with large particles .

1306.2041

i

tidal interaction leads to synchronisation and orbital circularisation of close binary stars ( eg . zahn 1977 , hut 1981 ) . it may also result in double star or star - planet systems that undergo close encounters in marginally unbound orbits becoming tidally captured into highly eccentric orbits that then begin to circularise ( eg . press & teukolsky 1977 ) . a process of this kind is believed to account for giant exoplanets in close orbits with periods of a few days ( eg . weidenschilling & marzari 1996 , rasio & ford 1996 ) . the determination of the tidal evolution requires the calculation of the response of the tidally perturbed body . this involves energy and angular momentum exchange between its normal modes and the orbit leading to its evolution . in a companion paper , ivanov et al . ( 2013 ) , subsequently referred to as paper 1 , we developed general procedures for calculating tidal energy and angular momentum exchange rates , for bodies in periodic orbits , that are associated with an identifiable regular spectrum of low frequency rotationally modified gravity modes , for rotating stars with realistic structure . these are likely to give rise to the dominant tidal response in bodies with stratification , where the tidal forcing frequencies significantly exceed the inverse of the convective time scale associated with any convection zone , so that any effective turbulent viscosity is inefficient . this is also expected to be the case for rotating stars , when the dominant tidal forcing frequencies as viewed in the rotating frame exceed twice the rotation frequency with the consequence that inertial modes are not efficiently excited in convective regions . in paper 1 we also gave expressions from which the energy and angular momentum transferred to stellar modes of oscillation as a result of parabolic encounters can be calculated . a process that could lead to tidal captures and also governs the initial phase of orbital circularisation when the orbit is very eccentric ( eg . ivanov & papaloizou 2004 ) . evaluation of the response arising from normal modes requires calculation of mode eigenfrequencies and corresponding overlap integrals that determine the strength of mode coupling with the tidal potential ( eg . press & teukolsky 1977 ) . this procedure was discussed in some detail in paper 1 for the case when the traditional approximation , appropriate for low frequency modes in stratified layers , was adopted . we remark that , as discussed in more detail in paper 1 , tidal phenomena such as energy and angular momentum exchange through parabolic encounters , or orbital evolution in the regime of so - called moderately strong viscosity ( eg . zahn 1977 , goodman @xmath0 dickson 1998 ) , where propagating rotationally modified gravity waves attain short wavelengths , and so are dissipated before reaching boundaries from which they can be reflected , are such that results are independent of the precise specification of the dissipation process . in this regime , the wave dissipation should also occur on a time scale that is significantly longer than the locally excited wave period which will also be characteristic of the time for excitation due to tidal perturbation . in this paper we apply the formalism developed in paper 1 , where only sun - like stars were considered , to calculate the normal modes and their associated overlap integrals for a range of tidal forcing frequencies for two models of a rotating solar mass star with different ages , as well as several models of more massive rotating stars , with different ages . the dependence of these quantities on the existence and extent of convective regions and the transition between convective and radiative regions is elucidated . we also compare results obtained from the normal mode approach of paper 1 to those obtained from direct numerical simulations of parabolic encounters ( eg . papaloizou & ivanov 2010 ) delineating when there is good agreement between the two approaches . our results are then applied to the tidal capture and initial orbital circularisation of giant exoplanets for both prograde and retrograde orbits and also the tidal capture of stars to form binary systems in stellar clusters ( eg . fabian , pringle @xmath0 rees 1975 , press @xmath0 teukolsky 1977 ) . the plan of the paper is as follows . in section 2 we describe the stellar models for which we calculated the quantities that enable their exchange of energy and angular momentum under tidal gravitational perturbation due to a companion to be calculated . these quantities are the overlap integrals and the low frequency rotationally modified @xmath1 mode spectrum and they are discussed in detail in paper 1 . we consider models in the range of @xmath2 with a variety of ages . as indicated in paper 1 , the extent of any convective envelope and/or core plays a significant role in determining the strength of tidal interaction as also does the detailed form of the transition between convective and radiative regions . in section 3 we discuss the properties of the numerically calculated mode spectra and overlap integrals for the stellar models considered . we also derive the rotational splitting coefficients which give the first order shifts of mode eigenfrequencies as a result of stellar rotation . in the non rotating case , the overlap integrals were found to be markedly larger for sun - like stars as compared to either a polytrope with index 3 or more massive models with much less extensive convective regions . this is because of the convective envelope and is expected from the theory developed in paper 1 . the overlap integrals are also calculated for rotating models under the neglect of centrifugal distortion and the adoption of the traditional approximation as indicated in paper 1 . results for angular velocities of rotation in units of the critical rotation rate in the range @xmath3 are presented . we go on to apply our results to evaluate the energy and angular momentum exchanged as a result of a parabolic encounter with a companion . these enable the possibility of tidal capture from unbound orbits to be assessed . in addition the time scale for the initial stages of orbital circularisation to occur for low planetary mass companions is estimated . we compare energy and angular momentum transfers obtained through the normal mode / overlap integral approach to results obtained from solving the encounter problem as an initial value problem numerically ( papaloizou & ivanov 2010 ; ivanov & papaloizou 2011 ) for the full range of rotation rates and for pericentre distances that are not too large to make calculation intractable . both prograde and retrograde encounters are considered . we found that the methods are in good agreement apart from the situation where the system is close to pseudosynchronization . in this case the effective tidal forcing frequencies are comparable to the rotation frequency and inertial modes , not taken into account in the normal mode approach can play a significant role . as the characteristic tidal forcing frequencies are expected to be significantly larger than stellar rotation frequencies , inertial modes are unlikely to be excited in the star during the initial stages of the formation of close in giant planet orbits of hot jupiters. accordingly we do not pursue the issue of inertial modes further in this paper . finally in section 5 we summarize and discuss our results . we remark that as in our earlier work ( ivanov & papaloizou 2011 ) , which considered polytropic models with index , 3 , we find that tidal interaction with the central star is significantly stronger for retrograde orbits and that it could play a significant role in the circularisation process for giant planets , so potentially reducing the amount of potentially destructive energy dissipation in the planetary interior .

we study the tidal response of rotating solar mass stars , as well as more massive rotating stars , of different ages in the context of tidal captures leading to either giant exoplanets on close in orbits , or the formation of binary systems in star clusters . to do this , we adopt approaches based on normal mode and associated overlap integral evaluation , developed in a companion paper by ivanov et al . , and direct numerical simulation , to evaluate energy and angular momentum exchanges between the orbit and normal modes . , we find that energy transferred to their central stars could play a significant role in the early stages of the circularisation of potential hot jupiters. [ firstpage ] hydrodynamics - celestial mechanics - planetary systems : formation , planet -star interactions , stars : binaries : close , rotation , oscillations

we study the tidal response of rotating solar mass stars , as well as more massive rotating stars , of different ages in the context of tidal captures leading to either giant exoplanets on close in orbits , or the formation of binary systems in star clusters . to do this , we adopt approaches based on normal mode and associated overlap integral evaluation , developed in a companion paper by ivanov et al . , and direct numerical simulation , to evaluate energy and angular momentum exchanges between the orbit and normal modes . the two approaches are found to be in essential agreement apart from when encounters occur near to pseudosynchronization , where the stellar angular velocity and the orbital angular velocity at periastron are approximately matched . we find that the strength of tidal interaction being expressed in dimensionless natural units is significantly weaker for the more massive stars , as compared to the solar mass stars , because of the lack of significant convective envelopes in the former case . on the other hand the interaction is found to be stronger for retrograde as opposed to prograde orbits in all cases . in addition , for a given pericentre distance , tidal interactions also strengthen for more evolved stars on account of their radial expansion . in agreement with previous work based on simplified polytropic models , we find that energy transferred to their central stars could play a significant role in the early stages of the circularisation of potential hot jupiters. [ firstpage ] hydrodynamics - celestial mechanics - planetary systems : formation , planet -star interactions , stars : binaries : close , rotation , oscillations

0902.2908

i

in the pioneering work by bogoliubov @xcite , it was shown that the bose - einstein condensate ( bec ) of weakly interacting bosons has a phonon - type excitation mode . it is now called the bogoliubov mode , which is a nambu - goldstone mode associated with a spontaneous broken u(1 ) symmetry @xcite . this collective mode dominates low - energy properties of bec , so that it is an important key to understand physical properties of bec @xcite . in particular , the existence of bogoliubov phonon is essential for the bose - condensed phase to acquire superfluidity @xcite . since the realization of becs in ultracold atomic gases @xcite , the study of bogoliubov mode has been one of the main issues in cold atom physics @xcite . because of the high degree of controllability , the becs of cold atomic gases offer good opportunities to explore novel properties of bogoliubov excitations . recently , kovrizhin and co - workers @xcite predicted that the bogoliubov mode exhibits striking tunneling properties . they showed that the transmission probability of bogoliubov phonon through a potential barrier increases in the low energy region with decreasing the incident energy . in the low - energy limit , the perfect transmission is realized irrespective of the height of the barrier . this interesting tunneling property of bogoliubov mode is referred to as the _ anomalous tunneling _ @xcite . since their prediction @xcite , the anomalous tunneling has attracted much attention , and has been addressed by many papers @xcite . as the origin of the anomalous tunneling effect , various mechanisms have been proposed , such as quasiresonance scattering @xcite , localized components of bogoliubov mode appearing near the barrier @xcite , and anomalous enhancement of quasiparticle current @xcite . for the perfect transmission in the low - energy limit , the importance of the coincidence of the condensate and excitation wave functions @xcite , as well as supercurrent behavior of low - energy bogoliubov phonons @xcite , has been pointed out . the anomalous tunneling phenomenon was shown to occur even in the supercurrent state @xcite , as well as at finite temperatures @xcite . it has been also studied in the presence of a periodic potential @xcite , as well as a random potential @xcite . it has been also pointed out that similar phenomena to this can be seen in the scattering of bogoliubov phonon by a spherical potential in three dimensions d@xcite , as well as the refraction of bogoliubov phonons @xcite . in this paper , we investigate tunneling properties of bogoliubov phonon in a bec at @xmath0 . in ref . @xcite , we have considered the case when the incident and transmitted bogoliubov phonons feel the same condensate densities on both the right and left of the barrier . in this paper , we extend this previous paper to the case when the condensate density is different between the right and the left of the barrier . as an extreme case , we also deal with the case when the condensate density is absent on one side of the barrier . applying the finite element method to the bogoliubov coupled equations , we numerically calculate the transmission probability and phase shift of bogoliubov phonons . we find that bogoliubov phonons twist the phase of the bec order parameter ( condensate wave function ) due to a back - reaction effect , which leads to the induction of josephson supercurrent . the induced supercurrent is shown to satisfy the josephson relation with respect to the twisted phase when the condensate density is the same on both sides of the barrier . the supercurrent is induced only in the region near the barrier when the condensate has the same densities across the potential barrier . in the case when the condensate density is different between the right and left of the barrier , the supercurrent is also induced in the region far away from the barrier . in addition , the excess quasiparticle current is supplied from the condensate to conserve the total current , so that one obtains the enhancement of the transmission probability of quasiparticle current in the low - energy region . we also show that the supercurrent is induced when one injects free atoms from the outside of condensate . in addition , atoms are shown to evaporate from the surface of superfluid region when bogoliubov excitation propagates toward the superfluid - normal phase boundary . this paper is organized as follows : in sec . [ sec2 ] , we present the model and formalism of the bogoliubov mean - field approximation , as well as the finite element method which we apply for solving the bogoliubov equations . in sec . [ sec3 ] , we study the tunneling of bogoliubov phonons through a rectangular potential barrier . we give a detailed discussion on the origin of the anomalous tunneling and induced josephson supercurrent . in sec . [ sec4 ] , we study the tunneling in the presence of a step potential which yields the different condensate densities across the potential barrier . in sec . [ sec5 ] , we discuss the tunneling of excitations and atoms between superfluid and normal regions .

we find that bogoliubov phonons twist the condensate phase due to a back - reaction effect , which induces the josephson supercurrent . while the total current given by the sum of quasiparticle current and induced supercurrent is conserved , the quasiparticle current flowing through the barrier potential is shown to be remarkably enhanced in the low energy region . when the condensate densities are different between the left and right of the barrier , the excess quasiparticle current , as well as the induced supercurrent , remains finite far away from the barrier . atoms are emitted when the bogoliubov phonons propagate toward the phase boundary from the superfluid region .

we study the tunneling of bogoliubov excitations through a barrier in a bose - einstein condensate . we extend our previous work [ phys . rev . a * 78 * , 013628 ( 2008 ) ] to the case when condensate densities are different between the left and right of the barrier potential . in the framework of the bogoliubov mean - field theory , we calculate the transmission probability and phase shift , as well as the energy flux and quasiparticle current carried by bogoliubov excitations . we find that bogoliubov phonons twist the condensate phase due to a back - reaction effect , which induces the josephson supercurrent . while the total current given by the sum of quasiparticle current and induced supercurrent is conserved , the quasiparticle current flowing through the barrier potential is shown to be remarkably enhanced in the low energy region . when the condensate densities are different between the left and right of the barrier , the excess quasiparticle current , as well as the induced supercurrent , remains finite far away from the barrier . we also consider the tunneling of excitations and atoms through the boundary between the normal and superfluid regions . we show that supercurrent can be generated inside the condensate by injecting free atoms from outside . on the other hand , atoms are emitted when the bogoliubov phonons propagate toward the phase boundary from the superfluid region .

0902.2908

c

to summarize , we have investigated tunneling effects of bogoliubov excitations at @xmath0 . we have extended our previous work to the case when the condensate densities are different on the left and right of the barrier . within the frame work of the bogoliubov theory , we have evaluated the transmission probability , phase shift as well as the energy flux and quasiparticle current carried by bogoliubov excitations . we showed that , while the energy flux is conserved , the quasiparticle current is not conserved . the excess quasiparticle current is actually cancelled out by the counterflow of supercurrent , which is induced by the back - reaction effects of bogoliubov phonons on the condensate . in the case of a rectangular potential barrier , we directly showed that the induced supercurrent satisfies the josephson relation with respect to the twisted phase by bogoliubov phonons . when the condensate has different densities on the left and right of the barrier , the supercurrent is induced in the region far from the barrier potential . we also studied the tunneling of atoms from the normal region to the superfluid region , as well as the tunneling of excitations from the superfluid region to the normal region . in the former case , we showed that supercurrent is induced inside a condensate by injecting free atoms from outside . in the latter case , we found that atoms evaporate from the superfluid - normal state phase boundary , when bogoliubov excitations propagate toward the surface of the superfluid region . we think these results can be of interest for the investigation of bogoliubov mode and its connection to the superfluidity of becs in ultracold atomic gases . we wish to thank i. danshita , s. watabe , d. takahashi , k. kamide , n. yokoshi , s. inouye , f. dalfovo , s. kurihara , and y. kato for stimulating discussions . we acknowledge m. machida , t. suzuki , m. ueda , and t. nikuni for valuable comments . this work was supported by a grant - aid for scientific research from mext , japan and the ctc program of japan .

we extend our previous work [ phys . a * 78 * , 013628 ( 2008 ) ] to the case when condensate densities are different between the left and right of the barrier potential . in the framework of the bogoliubov mean - field theory , we calculate the transmission probability and phase shift , as well as the energy flux and quasiparticle current carried by bogoliubov excitations . we also consider the tunneling of excitations and atoms through the boundary between the normal and superfluid regions . we show that supercurrent can be generated inside the condensate by injecting free atoms from outside . on the other hand ,

we study the tunneling of bogoliubov excitations through a barrier in a bose - einstein condensate . we extend our previous work [ phys . rev . a * 78 * , 013628 ( 2008 ) ] to the case when condensate densities are different between the left and right of the barrier potential . in the framework of the bogoliubov mean - field theory , we calculate the transmission probability and phase shift , as well as the energy flux and quasiparticle current carried by bogoliubov excitations . we find that bogoliubov phonons twist the condensate phase due to a back - reaction effect , which induces the josephson supercurrent . while the total current given by the sum of quasiparticle current and induced supercurrent is conserved , the quasiparticle current flowing through the barrier potential is shown to be remarkably enhanced in the low energy region . when the condensate densities are different between the left and right of the barrier , the excess quasiparticle current , as well as the induced supercurrent , remains finite far away from the barrier . we also consider the tunneling of excitations and atoms through the boundary between the normal and superfluid regions . we show that supercurrent can be generated inside the condensate by injecting free atoms from outside . on the other hand , atoms are emitted when the bogoliubov phonons propagate toward the phase boundary from the superfluid region .

1301.0319

i

as the most commonly observed objects , stars remain at the forefront of astrophysical research . advances in optical detector technology , computer processing power , and data storage capability have enabled new sky surveys ( e.g. , the sloan digital sky survey ; * ? ? ? * ) ; triggered many new optical transient surveys , such as the palomar transient factory @xcite and pan - starrs1 @xcite ; and allowed for space missions ( e.g. , _ kepler _ ; * ? ? ? * ) that continuously monitor more than 100,000 stars . the stellar discoveries from these surveys include revelations about rare stars , unusual explosive outcomes , and remarkably complex binaries . the immediate future holds tremendous promise , as both the space - based survey _ gaia _ @xcite and the ground based large synoptic survey telescope ( lsst ; * ? ? ? * ) come to fruition . these developments have created a new demand for a reliable and publicly available research and education tool in computational stellar astrophysics . we introduced the open source community tool ` mesa ` ( * ? ? ? * hereafter paper i ) to meet these new demands . this first `` instrument '' paper described the design , implementation , and realm of validity of ` mesa ` modules for numerics , microphysics , and macrophysics , and introduced the stellar evolution module , ` mesa ` ` star ` . we presented a multitude of tests and code comparisons that served as our initial verification and demonstrated ` mesa ` ` star ` s initial capabilities . since paper i , ` mesa ` has attracted over 500 registered users , witnessed over 5,000 downloads from http://mesa.sourceforge.net/ , started an annual summer school program , and provided a portal ( http://mesastar.org ) for the community to openly share knowledge ( e.g. , the specific settings for a published ` mesa ` ` star`run ) , codes , and publications . this paper describes the major new ` mesa ` capabilities for modeling giant planets , asteroseismology , and the treatment of rotation and evolution of massive stars . we also describe numerous advances since paper i. these include the incorporation of composition gradients in the determination of convective mixing and additional verification for evolution of intermediate mass stars and the white dwarfs they create . our improvements to ` mesa ` ` star ` for gas giant planets were motivated by the dramatic growth in this field . over 800 exoplanets have been confirmed , and their study has prompted enormous progress in our understanding of the formation and migration of giant planets , and of the importance of factors such as stellar mass @xcite , composition @xcite , and binarity @xcite . puzzles remain , though , both in our solar system and in the studies of the plethora of these newly discovered exoplanets , including the characteristics of the planet - hosting stars and the interiors , atmospheres , surface gravities , temperatures , and compositions of the planets ( e.g. , * ? ? ? * ; * ? ? ? many of these variations can now be numerically explored , as can the incorporation of an inert core in an otherwise regular gas giant and the impact of irradiation . the ability to infer stellar properties ( e.g. , mass , radius , internal state , and rotation ) from measurements of the radial and non - radial oscillation modes has been dramatically improved by two space - based optical telescopes ( convection rotation and planetary transits , _ corot _ ; @xcite and _ kepler _ ; @xcite ) . the high cadences and precision ( often better than ten parts per million ) reveal and accurately measure multitudes of oscillation frequencies for over 10,000 stars , substantially raising the need for accurate and efficient computations of stellar mode frequencies and the resulting eigenfunctions . the intrinsic flexibility of ` mesa ` ` star ` allows for the exploration of model - space required to precisely infer stellar properties from the observed frequencies . an important new addition to ` mesa ` is the incorporation of stellar rotation and magnetic fields in radiative regions . as stars are not solid bodies , they undergo radial differential rotation @xcite and also rotate at different angular velocities at different latitudes @xcite . these rotational shears have a significant impact on the evolution of the stellar magnetic field . despite the resulting 3d nature of magnetism and rotation , the stellar evolution community has come a long way in understanding stars with 1d simulations @xcite , thus motivating our need to fully incorporate rotation within ` mesa ` . the new flexibility in angular momentum transport mechanisms allows for numerical exploration of alternate rotational outcomes should the observations ( e.g. , asteroseismology ) require it . the paper is outlined as follows . section [ s.planets ] describes the new capability of ` mesa ` to evolve models of giant planets , while [ s.astroseismology ] discusses the new asteroseismology capabilities . the ` mesa ` implementation of composition gradients in stellar interiors and their impact on convective mixing is described in [ s.mixing ] . the status of the evolution of intermediate mass stars and the ` mesa ` ` star ` construction and evolution of white dwarfs is described in [ s.agb-wd ] . the new capabilities for evolving rotating stars is described in [ s.rotation ] . the onset of near eddington luminosities and radiation pressure dominance in the envelopes of evolving massive stars has been a challenge for many stellar evolution codes ever since the realization of the iron opacity bump at @xmath1 @xcite . we discuss in [ s.massive ] the resulting improvements for evolving massive stars . this allows for the uninterrupted evolution of rotating massive stars to the onset of core collapse . we conclude in [ s.conclusions ] by highlighting where additional improvements to ` mesa ` are likely to occur in the near future . appendix [ s.input-physics ] describes the many improvements to the physics modules since paper i ; appendix [ s.nuts-and-bolts ] presents `` nuts and bolts '' information on the primary components of evolution calculations ; and appendix [ s.mesasdk ] presents the ` mesa ` software development kit ( ` sdk ` ) . all of our symbols are defined in table [ t.list-of-symbols ] . we denote components of ` mesa ` , such as modules and routines , in courier font , e.g. , ` evolve_star ` . cll @xmath2 & atomic mass number & [ s.chem ] + @xmath3 & mass excess of the @xmath4th isotope & [ s.chem ] + @xmath5 & wind mass loss coefficient & [ s.completing-evolution ] + @xmath6 & day - side flux incident on an irradiated planet & [ sec : irradiation ] + @xmath7 & coulomb coupling parameter & [ s.completing-evolution ] + @xmath4 & specific moment of inertia & [ s.nuts-rotation ] + @xmath8 & opacity & [ s.construction-models ] + @xmath9 & stellar luminosity & [ s.astero ] + @xmath10 & lagrangian mass coordinate & [ s.construction-models ] + @xmath11 & stellar mass & [ s.construction-models ] + @xmath12 & brunt - visl frequency & [ s.ledoux ] + @xmath13 & number density of the @xmath4th isotope & [ s.chem ] + @xmath14 & turbulent viscosity & [ s.nuts-rotation ] + @xmath15 & radial coordinate & [ sec : irradiation ] + @xmath16 & total stellar radius & [ s.construction-models ] + @xmath17 & baryon mass density & [ s.chem ] + @xmath18 & specific entropy & [ s.construction-models ] + @xmath19 & mass column & [ sec : irradiation ] + @xmath20 & depth for heating from irradiation & [ sec : irradiation ] + @xmath21 & optical depth & [ s.completing-evolution ] + @xmath22 & magnitude of changes during a timestep & [ s.timestep-controls ] + @xmath23 & target value for @xmath22 & [ s.timestep-controls ] + @xmath24 & atomic weight & [ s.chem ] + @xmath25 & h mass fraction & [ s.astero ] + @xmath26 & baryon mass fraction of the @xmath4th isotope & [ s.ledoux ] + @xmath27 & he mass fraction & [ s.planets ] + @xmath28 & electrons per baryon ( @xmath29/@xmath30 ) & [ s.chem ] + @xmath31 & abundance of the @xmath4th isotope & [ s.chem ] + @xmath32 & metallicity & [ s.planets ] + @xmath32 & atomic number & [ s.chem ] + @xmath33 & mixing length parameter & [ s.planets-no-core ] + @xmath34 & semiconvection efficiency parameter & [ s.semiconvection ] + @xmath35 & thermohaline efficiency parameter & [ s.thermohaline ] + @xmath36 & smoothing parameter for mlt++ & [ s.superadiabatic ] + @xmath37 & mlt++ parameter used in construction of @xmath36 & [ s.superadiabatic ] + @xmath38 & @xmath39 & [ s.superadiabatic ] + @xmath40 & @xmath41 & [ s.ledoux ] + @xmath42 & @xmath43 & [ s.ledoux ] + @xmath44 & specific heat at constant pressure & [ s.semiconvection ] + @xmath45 & adiabatic sound speed & [ s.astroseismology ] + @xmath46 & large frequency separation of pulsation modes & [ s.astero ] + @xmath47 & overshoot diffusion coefficient & [ s.ledoux ] + @xmath48 & thermohaline diffusion coefficient & [ s.thermohaline ] + @xmath49 & fermi energy at center & [ s.planets-no-core ] + @xmath50 & gravitational heating rate & [ s.completing-evolution ] + @xmath51 & nuclear heating rate & [ s.reactions ] + @xmath52 & neutrino loss rate & [ s.rotation-modifications ] + @xmath53 & convective flux & [ s.massive-evol ] + @xmath54 & convective overshoot parameter & [ s.astero ] + @xmath55 & radiative flux & [ s.massive-evol ] + @xmath56 & reduction factor for @xmath57 & [ s.superadiabatic ] + @xmath58 & @xmath59 & [ s.astroseismology ] + @xmath60 & opacity for thermal radiation orig . in planet & [ sec : irradiation ] + @xmath61 & opacity for irradiation from star & [ sec : irradiation ] + @xmath62 & boltzmann constant & [ s.planets-no-core ] + @xmath63 & accretion luminosity & [ s.compressional ] + @xmath64 & @xmath65 & [ s.superadiabatic ] + @xmath66 & core luminosity & [ s.planets-cores ] + @xmath67 & eddington luminosity & [ s.rotation-mass-loss ] + @xmath68 & log surface gravity & [ s.atmospheres ] + @xmath69 & luminosity at which the onset of convection occurs & [ s.massive-evol ] + @xmath70 & radiative luminosity & [ s.massive-evol ] + @xmath71 & luminosity at which a density inversion occurs & [ s.massive-evol ] + @xmath72 & atomic mass unit & [ s.chem ] + @xmath73 & core mass & [ s.planets-cores ] + @xmath74 & mass - loss rate & [ s.compressional ] + @xmath75 & modeled mass & [ s.mesh-controls ] + @xmath76 & avogadro number & [ s.planets-no-core ] + @xmath77 & adiabatic temperature gradient & [ s.ledoux ] + @xmath78 & ledoux criterion & [ s.semiconvection ] + @xmath79 & radiative temperature gradient & [ s.ledoux ] + @xmath80 & actual temperature gradient & [ s.ledoux ] + @xmath81 & baryon density & [ s.chem ] + @xmath82 & frequency of maximum power & [ s.astero ] + @xmath83 & surface angular velocity & [ s.rotation-mass-loss ] + @xmath84 & angular velocity & [ s.rotation-modifications ] + @xmath85 & surface critical angular velocity & [ s.rotation-mass-loss ] + @xmath86 & central pressure & [ s.construction-models ] + @xmath87 & gas pressure & [ s.compressional ] + @xmath88 & radiation pressure & [ s.compressional ] + @xmath89 & core radius & [ s.planets-cores ] + @xmath90 & central density & [ s.construction-models ] + @xmath91 & pressure scale height & [ s.ledoux ] + @xmath92 & stefan - boltzmann constant & [ s.construction-models ] + @xmath93 & lamb frequency & [ s.astroseismology ] + @xmath94 & superadiabaticity , @xmath95 & [ s.superadiabatic ] + @xmath96 & controls when mlt++ is applied & [ s.superadiabatic ] + @xmath97 & central temperature & [ s.construction-models ] + @xmath98 & effective temperature & [ s.construction-models ] + @xmath99 & numerical timestep & [ s.compressional ] + @xmath100 & thermal ( kelvin - helmholtz ) timescale & [ s.rotation-mass-loss ] + @xmath101 & equatorial velocity & [ s.rotation ] +

we substantially update the capabilities of the open source software package modules for experiments in stellar astrophysics ( ` mesa ` ) , and its one - dimensional stellar evolution module , ` mesa ` ` star ` . improvements in ` mesa ` ` star ` s ability to model the evolution of giant planets now extends its applicability down to masses as low as one - tenth that of jupiter . the dramatic improvement in asteroseismology enabled by the space - based _ kepler _ and _ corot _ missions motivates our full coupling of the adipls adiabatic pulsation code with ` mesa ` ` star ` . we exhibit the evolution of @xmath0 stars through the end of core he burning , the onset of he thermal pulses , and arrival on the white dwarf cooling sequence . we implement diffusion of angular momentum and chemical abundances that enable calculations of rotating - star models , which we compare thoroughly with earlier work . we introduce a new treatment of radiation - dominated envelopes that allows the uninterrupted evolution of massive stars to core collapse . this enables the generation of new sets of supernovae , long gamma - ray burst , and pair - instability progenitor models . we substantially modify the way in which ` mesa ` ` star ` solves the fully coupled stellar structure and composition equations , and we show how this has improved the scaling of ` mesa ` s calculational speed on multi - core processors . updates to the modules for equation of state , opacity , nuclear reaction rates , and atmospheric boundary conditions are also provided . we also highlight a few tools developed by the community for rapid visualization of ` mesa ` ` star ` results .

we substantially update the capabilities of the open source software package modules for experiments in stellar astrophysics ( ` mesa ` ) , and its one - dimensional stellar evolution module , ` mesa ` ` star ` . improvements in ` mesa ` ` star ` s ability to model the evolution of giant planets now extends its applicability down to masses as low as one - tenth that of jupiter . the dramatic improvement in asteroseismology enabled by the space - based _ kepler _ and _ corot _ missions motivates our full coupling of the adipls adiabatic pulsation code with ` mesa ` ` star ` . this also motivates a numerical recasting of the ledoux criterion that is more easily implemented when many nuclei are present at non - negligible abundances . this impacts the way in which ` mesa ` ` star ` calculates semi - convective and thermohaline mixing . we exhibit the evolution of @xmath0 stars through the end of core he burning , the onset of he thermal pulses , and arrival on the white dwarf cooling sequence . we implement diffusion of angular momentum and chemical abundances that enable calculations of rotating - star models , which we compare thoroughly with earlier work . we introduce a new treatment of radiation - dominated envelopes that allows the uninterrupted evolution of massive stars to core collapse . this enables the generation of new sets of supernovae , long gamma - ray burst , and pair - instability progenitor models . we substantially modify the way in which ` mesa ` ` star ` solves the fully coupled stellar structure and composition equations , and we show how this has improved the scaling of ` mesa ` s calculational speed on multi - core processors . updates to the modules for equation of state , opacity , nuclear reaction rates , and atmospheric boundary conditions are also provided . we describe the mesa software development kit ( ` sdk ` ) that packages all the required components needed to form a unified , maintained , and well - validated build environment for ` mesa ` . we also highlight a few tools developed by the community for rapid visualization of ` mesa ` ` star ` results .

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occasionally some of the research results on older topics give excellent insights to the subsequent researches . one of the such works is the recent work on the drifted edward - wilkinson ( ew ) equation @xmath8 with a fixed boundary condition ( fbc ) @xmath9 @xcite . if the diffusion term @xmath10 is ignored in eq . ( [ dew ] ) , one can obtain roughness exponent @xmath11 , growth exponent @xmath12 and dynamic exponent @xmath13 by a scaling argument and some other methods ( [ dew ] ) @xcite . but for periodic boundary condition ( pbc ) , the drift term @xmath14 is irrelevant , and thus eq . ( [ dew ] ) becomes physically equivalent to the normal ew equation @xcite @xmath15 with @xmath16 , @xmath17 , and @xmath18 . in contrast , if fbc instead pbc is imposed , the roughness of surface described by eq . ( [ dew ] ) is exactly proved to show an anomalous behavior with the exponents @xcite , @xmath19 the exact solution for eq . ( [ dew ] ) @xcite gives us an excellent insight to understand the role of the drift term and the boundary condition as a relevant extension of the normal ew equation . the drift term and the diffusion term are crucial for anomalous exponents under fbc @xcite . without the drift term , the maximum time which the roughness is fully developed for the system is order of @xmath20 . if the system is affected by the drift , the time scale that any noise - generated local structure starts from one boundary to the other boundary is @xmath21 . the fluctuation of the surface width is saturated after this time scale . therefore @xmath22 and thus one can get the anomalous exponents ( [ aewx ] ) . in ref . @xcite , local width is numerically studied to test the validity of this physical mechanism . the local width is increased as @xmath23 , with @xmath24 being the position where the width is measured . but the definition of the local width is not physically clear and there is a sort of difficulty to measure @xmath25 for the small system . for last two decades , the stochastic discrete growth models whose dynamical scaling behavior is identical to those of a given continuum growth equation have been used to investigate the dynamical scaling behavior for the corresponding surface roughness @xcite . the stochastic discrete growth model is a powerful tool which simplifies the complicate growth behavior and provides an essential link between theory and experiments . for example , the surface growth which is described by normal ew equation has been studied through the family model @xcite . but no simple growth model which exactly corresponds to the drifted ew equation with fbc has been suggested yet . other existing models can not explain the anomalous behavior of the surface fluctuation which comes from the drift term and fbc in eq . ( [ dew ] ) . first motivation of this paper is thus to make a simple stochastic discrete model which satisfies eq . ( [ dew ] ) with fbc using a stochastic analysis method @xcite . second motivation of this paper is in the explanation of the physical mechanism which causes the anomalous behavior ( [ aewx ] ) by using a height - height correlation function . the height - height correlation function can be easily treated through our handy stochastic discrete model . as mentioned above , the local width @xcite is somewhat unmature physical quantity and has not been widely used for the analysis of surface roughness @xcite . in contrast , height - height correlation function has been extensively used to show the exact dynamic scaling in the surface growth physics @xcite . the height - height correlation function which we will use to analyze the surface with fbc is an average of height differences or of squared height differences between @xmath26 and @xmath27 , where @xmath28 @xmath29 is the distance from a boundary @xmath30 at time @xmath31 . if we know the height - height correlation function between two fixed boundaries , we can get clean and clear information how the saturated surface of whole system is formed . we will measure the height - height correlation function and explain the anomalous behavior ( [ aewx ] ) through it . third motivation of this paper is to suggest about a new type queuing phenomena originated from the analysis of the height - height correlation function . queuing @xcite is a common nonequilibrium phenomenon in nature . it is well established that many driven flow processes belong to the same universality class as kardar - parisi - zhang ( kpz ) type growth of one dimensional interfaces @xcite . for example , a traffic jam @xcite caused by slow and fast bond of the so - called asymmetric simple exclusion process ( asep ) @xcite is related to the faceting on kpz growth . asep breaks translational invariance in many ways . one of them is to retain periodic boundary conditions , but to introduce a defect into the system by modifying the transition rates locally @xcite . by properly chosen injection / removal rates or defect strength , nonequilibrium phase transitions occur between profiles of different shapes and average densities . in our model , we map the fixed boundary condition to a defect which exists on the center of system . the defect site means that the growth at a certain site is impossible or is controlled by a probability @xmath32 which is called a defect strength . that is , the fixed boundary condition @xmath33 is shifted by the mapping @xmath34 to the defect site @xmath35 with the periodic boundary condition . for @xmath36 any deposition or evaporation process at @xmath37 can not occur ( @xmath38 ) , since the strength of the defect is absolutely strong and thus the surface heights can not be freely increased by the defect . if @xmath39 , the deposition or evaporation process at @xmath37 is accepted by @xmath32 and the system with @xmath40 is the same as pbc without the defect . the height - height correlation function of our stochastic discrete model shows lateral asymmetry @xmath41 around the defect , in contrast to kpz - type queuing phenomena or asep which shows up - down symmetry breaking under the transformation @xmath42 . the new queuing phenomena from the drifted ew equation ( [ dew ] ) with a defect is physically different from usual asep or queuing phenomena which is related to the nonlinearity of kpz equation @xcite , because it is from the linearity of the drifted ew equation ( [ dew ] ) . therefore it is very interesting to compare our new queuing phenomena to earlier studied kpz type queuing phenomena . in this paper , we want to investigate new queuing phenomena from the defect and the drift using our stochastic discrete model and apply it to the parking garage model @xcite .

the anomalous behavior of the drifted ew equation with a defect is analyzed . to physically understand the anomalous behavior the height - height correlation functions @xmath1 and @xmath2 . @xmath5 is the same as the anomalous roughness exponent @xmath6 . for the weak defect at which the growth process is partially allowed , we also suggest a new type queuing process based on the asymmetry @xmath7 of the correlation function around the perfect defect .

we suggest a novel stochastic discrete growth model which describes the drifted edward - wilkinson ( ew ) equation @xmath0 . from the stochastic model , the anomalous behavior of the drifted ew equation with a defect is analyzed . to physically understand the anomalous behavior the height - height correlation functions @xmath1 and @xmath2 . the height - height correlation functions follow the power law @xmath3 and @xmath4 with @xmath5 around a perfect defect at which no growth process is allowed . @xmath5 is the same as the anomalous roughness exponent @xmath6 . for the weak defect at which the growth process is partially allowed , the normal ew behavior is recovered . we also suggest a new type queuing process based on the asymmetry @xmath7 of the correlation function around the perfect defect .

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in this paper , we presented a simple stochastic discrete model which describes the drifted ew equation ( [ dew ] ) with a defect . from the simple model , we can easily show the anomalous behavior of the surface fluctuation by the drift and defect . the scaling exponents show the anomalous behavior @xmath6 , @xmath17 , and @xmath13 , only when the defect strength is @xmath36 . the exponents are suddenly changed to normal ew exponents as soon as the defect strength is weakly imposed ( @xmath112 ) . we also measure the height - height correlation functions to characterize the asymmetric interface profile and to explain the exact physical role of the drift term and defect . the height - height correlation functions show that the drift and the perfect defect ( @xmath36 ) makes the asymmetry @xmath167 or @xmath168 . these height - height correlation functions satisfy the power law @xmath3 and @xmath189 with @xmath5 . the height - height correlation function exponents and the roughness exponent have the same value @xmath162 . therefore the saturated surface configuration for drifted ew equation with the defect is solely decided by the defect . the asymmetry of the height - height correlation functions is very unique when compared to the correlation functions for kpz - type growth model with the defect which always shows the symmetry @xmath169 . from this asymmetry we suggest a new queuing process around the defect . , edited by f. family and t. vicsek ( world scientific , singapore , 1991 ) ; a .- barabsi and h. e. stanley , _ fractal concepts in surface growth _ ( cambridge university press , cambridge , 1995 ) ; j. krug , adv . phys . * 46 * , 139 ( 1997 ) ; j. krug and h. spohn , in _ solids far from equilibrium : growth , morphology and defects _ , edited by c. gordreche ( cambridge university press , new york , 1991 ) . m. kardar , g. parisi and y. -c . zhang , phys . lett . * 56 * , 889 ( 1986 ) . c. herring , j. appl . * 21 * , 301 ( 1950 ) ; w. w. mullins , j. appl . * 28 * , 333 ( 1957 ) ; * 30 * , 77 ( 1959 ) . s. majaniemi , t. ala - nissila and j. krug , phys . b * 53 * , 807 ( 1996 ) . f. family , j. phys . a * 19 * l441 ( 1986 ) . s. y. yoon and yup kim , j. korean phys . soc . * 44 * , 538 ( 2004 ) . b. schmittmann and r. k. p. zia , in _ phase transitions and critical phenomena _ vol . 17 , edited by c. domb and j. lebowitz ( academic press , london , 1995 ) ; g. m. schtz , in _ phase transitions and critical phenomena _ vol . 19 , edited by c. domb and j. lebowitz ( academic press , london , 2001 ) . p. meakin , p. ramanlal , l. m. sander and r. c. ball , phys . a * 34 * , 5091 ( 1986 ) ; m. plischke , z. racz and d. liu , phys . b * 35 * , 3485 ( 1987 ) ; j. neergaard and m. den nijs , phys . lett * 74 * , 730 ( 1995 ) . m. myllys , j. maunuksela , j. merikoski , j. timonen , v. k. horvath , m. ha and m. den nijs , phys . e * 68 * , 051103 ( 2003 ) . ; m. ha , j. timonen and m. den nijs , phys . e * 68 * , 056122 ( 2003 ) ; b. derrida , m. r. evans , v. hakim and v. pasquier , j. phys . a * 26 * , 1493 ( 1993 ) m. schreckenberg , a. schadschneider , k. nagel and n. ito , phys . e * 51 * , 2939 ( 1995 ) ; k. nagel , phys . e * 53 * , 4655 ( 1996 ) . s. a. janowsky and j. l. lebowitz , phys . a * 45 * , 618 ( 1992 ) ; b. derrida , m. r. evans and d. mukamel , j. phys . a * 26 * 4911 ( 1993 ) ; b. derrida , e. domany and d. mukamel , j. stat . phys . * 69 * , 667 ( 1992 ) ; s. a. janowsky and j. l. lebowitz , j. stat . phys . * 77 * , 35 ( 1994 ) ; f. j. alexander , z. cheng , s. a. janowsky and j. l. lebowitz , j. stat . phys . * 68 * , 761 ( 1992 ) ; d. kandel and d. mukamel , europhys . lett . * 20 * , 325 ( 1992 ) ; g. schtz , j. stat . phys . * 71 * , 471 ( 1993 ) .

we suggest a novel stochastic discrete growth model which describes the drifted edward - wilkinson ( ew ) equation @xmath0 . from the stochastic model , the height - height correlation functions follow the power law @xmath3 and @xmath4 with @xmath5 around a perfect defect at which no growth process is allowed .

we suggest a novel stochastic discrete growth model which describes the drifted edward - wilkinson ( ew ) equation @xmath0 . from the stochastic model , the anomalous behavior of the drifted ew equation with a defect is analyzed . to physically understand the anomalous behavior the height - height correlation functions @xmath1 and @xmath2 . the height - height correlation functions follow the power law @xmath3 and @xmath4 with @xmath5 around a perfect defect at which no growth process is allowed . @xmath5 is the same as the anomalous roughness exponent @xmath6 . for the weak defect at which the growth process is partially allowed , the normal ew behavior is recovered . we also suggest a new type queuing process based on the asymmetry @xmath7 of the correlation function around the perfect defect .

1604.07915

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we have performed a systematic broadband ( 0.5200 kev ) x - ray spectral analysis of ten local llagns ( with intrinsic 14195 kev luminosities of @xmath363 erg s@xmath2 ) observed with _ suzaku _ and _ swift_/bat . the main conclusions are summarized as follows . 1 . the broadband x - ray spectra can be basically reproduced with an absorbed cut - off power law often accompanied by a reflection component from distant cold matter and a narrow fluorescence iron - k@xmath5 line , and optically - thin thermal emission from the host galaxy . 2 . in all objects , a relativistically blurred reflection component from a standard disk is not required from the spectra . we find the negative correlation between the photon index and eddington ratio . these results are consistent with a picture that an optically - thin riaf is formed at innermost radii in llagns . 3 . applying a torus model by @xcite , we find eight objects showing a significant narrow iron - k@xmath5 emission line have a moderately developed torus with an equatorial column density of @xmath364 or a half opening - angle of @xmath344 . the tori of the two llagns without a narrow iron - k@xmath5 line are likely little developed . 4 . the luminosity ratio between the iron - k@xmath5 line and 1050 kev continuum ( @xmath350 ) has a peak around @xmath353 erg s@xmath2 , from which the average value rapidly declines towards lower luminosities . this result indicates that agn irradiation is not the only key factor that determines the torus structure . low eddington - ratio llagns with @xmath355 show small @xmath350 ratios . we infer that the eddington ratio is a key parameter that affects the torus structure of llagns . 5 . regardless of eddington ratio , our llagns follow the same luminosity correlation between the hard x - ray and mir bands as found for more luminous agns . this implies that other emission mechanisms than agn - heated dust are responsible for the mir emission in low eddington - ratio llagns without developed tori . we thank the referee for the comments , which helped us to improve the quality of the manuscript . we are grateful to c. ricci for kindly providing us with the data . part of this work was financially supported by the grant - in - aid for jsps fellows for young researchers ( t.k ) and for scientific research 26400228 ( yu ) . this research has made use of the nasa/ ipac infrared science archive , which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration .

we systematically analyze the broadband ( 0.5200 kev ) x - ray spectra of hard x - ray ( @xmath0 kev ) selected local low - luminosity active galactic nuclei ( llagns ) observed with _ the overall spectra can be reproduced with an absorbed cut - off power law , often accompanied by reflection components from distant cold matter , and/or optically - thin thermal emission from the host galaxy . in all objects , eight objects show a significant narrow iron - k@xmath5 emission line . comparing their observed equivalent widths with the predictions from the monte - carlo based torus model by @xcite , we constrain the column density in the equatorial plane to be @xmath6 or the torus half opening angle @xmath7 . the luminosity correlation between the hard x - ray and mid - infrared ( mir ) bands of the llagns follows the same one as for more luminous agns . this implies that other mechanisms than agn - heated dust are responsible for the mir emission in low eddington ratio llagns .

we systematically analyze the broadband ( 0.5200 kev ) x - ray spectra of hard x - ray ( @xmath0 kev ) selected local low - luminosity active galactic nuclei ( llagns ) observed with _ suzaku _ and _ swift_/bat . the sample consists of ten llagns detected with _ swift_/bat with intrinsic 14195 kev luminosities smaller than @xmath1 erg s@xmath2 available in the _ suzaku _ archive , covering a wide range of the eddington ratio from @xmath3 to @xmath4 . the overall spectra can be reproduced with an absorbed cut - off power law , often accompanied by reflection components from distant cold matter , and/or optically - thin thermal emission from the host galaxy . in all objects , relativistic reflection components from the innermost disk are not required . eight objects show a significant narrow iron - k@xmath5 emission line . comparing their observed equivalent widths with the predictions from the monte - carlo based torus model by @xcite , we constrain the column density in the equatorial plane to be @xmath6 or the torus half opening angle @xmath7 . we infer that the eddington ratio ( @xmath8 ) is a key parameter that determines the torus structure of llagns : the torus becomes large at @xmath9 , whereas at lower accretion rates it is little developed . the luminosity correlation between the hard x - ray and mid - infrared ( mir ) bands of the llagns follows the same one as for more luminous agns . this implies that other mechanisms than agn - heated dust are responsible for the mir emission in low eddington ratio llagns .

1003.5929

c

we have theoretically studied the theory of x - ray diffraction from asymmetric - top molecules that are three - dimensionally aligned by elliptically polarized light and have discussed a phase - retrieval method in order to reconstruct molecular structure from the x - ray scattering pattern . the interaction of the gas phase molecules with the laser and x - ray fields was studied in the density matrix formalism . we have assumed rigid rotor molecules . symmetries in the time - dependent hamiltonian and in its solutions as well as in the angular density distribution were exploited and used to improve numerical efficiency . in combination with further computational aspects , a significant enhancement in numerical efficiency has been achieved . a feasibility study of x - ray diffraction from three - dimensionally laser - aligned molecules has been performed using the organic molecule naphthalene . we have linked the degree of alignment to an effective resolution and have studied the impact of x - ray pulse duration and temperature on the diffraction patterns . a phase - retrieval reconstruction was performed on diffraction patterns taken for different effective alignments . the enhancement of incoherent averaging due to imperfect alignment destroys structural information and hinders the recovery of detailed atomic configurations within the molecule . the reconstruction of naphthalene confirms our discussion that the degree of alignment is a good indicator for the achievable resolution in the reconstruction . to decode structures on an atomic length scale , high degree of alignment in all three molecular axes must be achieved . molecules have to be cooled down to a few kelvin or even sub - kelvin temperatures so rotational motion is sufficiently reduced . experiments have shown that it is feasible to cool molecules to 1 k @xcite . to accomplish rotational temperatures well below 1 k is a great challenge and would open the opportunity to image large gas - phase molecules at atomic resolution . the problem of incoherent averaging over a finite range of different orientations has to be further addressed , especially in the case where molecular symmetries do not coincide with the symmetries of the diffraction pattern imposed by alignment . with the ability to detect molecular structure , x - ray scattering from gas phase molecules can be used to study torsion effects and laser - induced deformations that are expected to occur during alignment in the presence of intense laser pulses @xcite . by systematically varying the delay time between pump ( laser ) and probe ( x - ray ) pulse , it is possible to follow molecular motion on an ultrafast time scale . of particular interest is the study of physical and chemical processes in the presence of intense laser fields , which simultaneously provide the required alignment for imaging of reactions with atomic resolution in space and time . we thank cassandra hunt for helpful comments on the manuscript . this work was supported by the office of basic energy sciences , u.s . department of energy under contract no . de - ac02 - 06ch11357 .

we theoretically and numerically analyze x - ray scattering from asymmetric - top molecules three - dimensionally aligned using elliptically polarized laser light . several symmetries in the hamiltonian are identified and exploited to enhance the efficiency of solving the time - dependent schrdinger equation for each rotational state initially populated in a thermal ensemble . using a phase - retrieval algorithm , the feasibility of structure reconstruction from a quasi - adiabatically - aligned sample is illustrated for the organic molecule naphthalene .

we theoretically and numerically analyze x - ray scattering from asymmetric - top molecules three - dimensionally aligned using elliptically polarized laser light . a rigid - rotor model is assumed . the principal axes of the polarizability tensor are assumed to coincide with the principal axes of the moment of inertia tensor . several symmetries in the hamiltonian are identified and exploited to enhance the efficiency of solving the time - dependent schrdinger equation for each rotational state initially populated in a thermal ensemble . using a phase - retrieval algorithm , the feasibility of structure reconstruction from a quasi - adiabatically - aligned sample is illustrated for the organic molecule naphthalene . the spatial resolution achievable strongly depends on the laser parameters , the initial rotational temperature , and the x - ray pulse duration . we demonstrate that for a laser peak intensity of 5 tw/@xmath0 , a laser pulse duration of 100 ps , a rotational temperature of 10 mk , and an x - ray pulse duration of 1 ps , the molecular structure may be probed at a resolution of 1 .

astro-ph0008017

i

extended thermal x - ray emission from the hot ( @xmath0 k ) interstellar medium ( ism ) in giant elliptical galaxies is usually interpreted in terms of a ` cooling flow ' scenario [ see loewenstein for a recent review ] . it implies that radiative cooling of optically thin hot plasma drives a subsonic inflow towards the centre of a potential well formed by the stellar component and a massive dark halo . galactic cooling flows and cooling flows in clusters of galaxies are essentially different owing to a difference in the origin of the two media . the intracluster medium is mostly primordial , cools from its high virial temperature and is accreted by the central galaxy , which provides a focus for the flow . in contrast , the ism in elliptical galaxies is constantly replenished by mass loss from evolved stars . this gas must be thermalized in the galaxy s gravity field and heated to x - ray temperatures from which it may cool down again . thus , in hydrodynamic terms , galactic cooling flows are defined as systems where the mass flux is dominated by source terms as opposed to ` boundary terms ' as in cluster cooling flows @xcite . several potential heat sources have been considered to counterbalance radiative cooling of the hot ism in ellipticals . the energy supplied with normal stellar mass loss is limited by the value of the stellar velocity dispersion and may only provide temperatures a factor of @xmath1 lower than the ism temperatures @xcite . in contrast , gravitational energy liberated in case of gas _ inflow _ would provide too much heat to the central regions [ thomas and references therein ] . heating by supernovae ( sn ) type ia remains a controversial issue . on the one hand , the sn rate is not very well constrained . its value varies from @xmath2 snu , suggested by van den bergh & tammann , the uncertainty being a factor of the order of 1.5 , to @xmath3 snu derived by cappellaro , evans & turatto . is the hubble constant in units of @xmath4 km s@xmath5mpc@xmath5 ; 1 snu = 1 supernova per century per @xmath6 solar bolometric luminosities . ] on the other hand , the low iron content of the diffuse hot gas in ellipticals estimated from high - quality broad band x - ray spectra provided by asca for a single - temperature plasma model @xcite suggests a very low efficiency of ism enrichment by type ia sne . this implies either that the sn rate is lower than @xmath7 snu @xcite or that sn ejecta do not mix with the hot ism @xcite . however , the multi - parametric analysis of x - ray spectra is a complex procedure based on iron l line diagnostic tools , and requires accurate atomic physics data @xcite . the procedure is also model - dependent . using two - temperature multi - phase plasma models buote obtained substantially better spectral fits for the same data sets with iron abundances of @xmath8 solar and relative element abundances fixed at their solar values . his results are consistent with the type ia sn rate being up to a factor of @xmath1 lower than reported by cappellaro et al . . clearly , better quality data are required to determine the type ia sn heating rate more precisely . all of the above mentioned energy sources may be described as being continuously distributed within a galaxy and their local rates depending on the stellar mass density and velocity dispersion , the gas inflow velocity profile , and the shape of the gravitational potential . there is a ` global problem ' @xcite of balancing heating and cooling both in the centre and in the outer regions , since the source terms depend in different ways on physical characteristics which vary with radius . however , empirical scaling laws for ellipticals and the physics of radiative cooling and thermal instability imply certain restrictions on the radial dependences . one possible solution to this problem is a hydrostatic hot gas recycling model @xcite for hot coronae of elliptical galaxies . in the hydrostatic gas configuration all that remains of the gas dynamical equations are the algebraic source terms which balance to zero . in this model two equilibrium conditions are simultaneously satisfied : ( 1 ) the stellar mass loss rate exactly balances the rate that mass cools locally from the flow ( dropout ) and ( 2 ) the rate that thermal energy is radiated away is exactly balanced by the energy input from stars and supernovae . the recycling model can be used as a tool to distinguish between inflow and outflow regimes for a given set of galaxy parameters ( kritsuk , bhringer & mller 1998 ) . periods of sporadic activity can drastically change the thermal state of the ism in the inner ` cooling flow ' region of a cluster or of an elliptical on a time scale of @xmath9 yr . there are numerous observations of an interaction between radio sources and the hot gas both in central cluster galaxies and other ellipticals @xcite . it is this complex central region that is most sensitive to any imbalance in the energy budget of the ism . since the ` thermal ' time scale is shorter there , the core of a few kpc in radius is the first to reach a new equilibrium state corresponding to the current status of heating . high spatial and spectral resolution x - ray observations of these central regions are critical to distinguish among the various heat sources and flow regimes in the core . the response of a cooling flow to energy injection by the central black hole that is fed by the cooling flow was simulated by binney & tabor ( 1995 ) . in their spherically symmetric numerical models the black hole heats the central kiloparsec of the ism as soon as it begins to swallow gas from the ism . the resulting expansion of the heated gas eliminates the cusped density profile and establishes a core that is roughly 2 kpc in radius . after the central heat source has switched off , the core again cools catastrophically within 0.5 gyr . among several limitations of the model ( which include a peculiar feedback mechanism ) the authors particularly note the restriction of spherical symmetry . both the jet and the ensuing convective instabilities can not be properly modelled due to this symmetry restriction . in this paper we analyze the hot gas flow regimes , which develop in elliptical galaxies in response to a small imbalance in the energy budget caused by a global instability of the equilibrium recycling model @xcite . we use multi - dimensional numerical simulations to investigate compact cooling inflows and subsonic convection two alternative saturated nonlinear regimes for a slightly disturbed thermal equilibrium in the core . here , we restrict ourselves to spherically symmetric ( on the average ) convective flows , which have not been studied before . the symmetry restriction will be relaxed in a subsequent paper which more closely addresses the astrophysical aspects of the problem . the analysis presented here provides a basis for a better understanding of more complex convective flows and allows for a direct comparison with one - dimensional models . a short description of our basic model is given in section 2 . section 3 describes the numerical method . the results of numerical experiments are presented in section 4 together with the detailed properties of the inner convective cores . in section 5 we summarize the results and discuss effects to be expected for the dynamical state of the hot gas in ellipticals from a larger imbalance between cooling and heating .

we use hydrodynamic simulations with adaptive grid refinement to study the dependence of hot gas flows in x - ray luminous giant elliptical galaxies on the efficiency of heat supply to the gas . we use an equilibrium hydrostatic recycling model @xcite . we show that a compact cooling inflow develops , if the heating is slightly insufficient to counterbalance radiative cooling of the hot gas in the central few kiloparsecs . we also discuss observational implications of these results .

we use hydrodynamic simulations with adaptive grid refinement to study the dependence of hot gas flows in x - ray luminous giant elliptical galaxies on the efficiency of heat supply to the gas . we consider a number of potential heating mechanisms including type ia supernovae and sporadic nuclear activity of a central super - massive black hole . as a starting point for this research we use an equilibrium hydrostatic recycling model @xcite . we show that a compact cooling inflow develops , if the heating is slightly insufficient to counterbalance radiative cooling of the hot gas in the central few kiloparsecs . an excessive heating in the centre , instead , drives a convectively unstable outflow . we model the onset of the instability and a quasi - steady convective regime in the core of the galaxy in two - dimensions assuming axial symmetry . provided the power of net energy supply in the core is not too high , the convection remains subsonic . the convective pattern is dominated by buoyancy driven large - scale mushroom - like structures . unlike in the case of a cooling inflow , the x - ray surface brightness of an ( on average ) isentropic convective core does not display a sharp maximum at the centre . a hybrid model , which combines a subsonic peripheral cooling inflow with an inner convective core , appears to be stable . we also discuss observational implications of these results . [ firstpage ] hydrodynamics instabilities cooling flows galaxies : ism ism dark matter

astro-ph0008017

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in this paper we have studied hot gas flows originating in the central few kpc of hot galactic coronae in response to a slight energy supply imbalance in a model initially in equilibrium . it is shown that a negative energy budget drives a quasi - steady compact cooling inflow , which is stable to small perturbations . excessive heating creates an isentropic ( on average ) convective core in the vicinity of the galaxy centre . provided the net energy gain in the core is not too high , the convection remains subsonic with typical flow velocities ( both , radial and angular ) of the order of @xmath196kms@xmath5 . the characteristic convective pattern consists of a manifold of mushroom - like structures of different scales . the power spectra of the velocity components are dominated by the largest - scale mushrooms . the emission weighted gas temperature in the core is slightly rising towards the centre . unlike in the case of a cooling inflow , the x - ray surface brightness of a convective core does not display a sharp maximum at the centre . the inner parts of the convective core are dominated by mass supply from evolved stars , while in the colder outer shell mass drop out dominates the mass budget . large - scale mushrooms ( mainly their caps ) can probably be marginally detected by high resolution x - ray images with good photon statistics , as their volume emissivity is about a factor of 2 higher than that of the surrounding gas . we have considered an idealized case with a spherically symmetric heat source and small deviations from ` thermal ' equilibrium near the centre . however , we can extrapolate our results to a more realistic hydrodynamic picture . first , stronger heating in the vicinity of the centre can drive a supersonic convection with velocities in excess of 400kms@xmath5 and produce a much larger ( here 3 - 4kpc ) convective region . second , a type ia sn heating rate which is lower all over the galaxy , and an excessive heating by an agn in the central region will create a hybrid flow with an inner convective core and an outer ` cooling flow ' , which will vanish in convection when the inflow velocity is very subsonic . our preliminary results indicate that such a hybrid dynamic flow can be stable and can last as long as the central source is active . third , a low type ia sn heating rate without extra energy supply near the centre will drive a more extended massive cooling inflow with an even more pronounced central surface brightness peak . it would be harder to turn such a dynamic inflow into an outflow by a strong perturbation ( e.g. , a burst of agn activity , or a merger ) than a weaker compact inflow . finally , we expect that an asymmetric central heat source in excess of the equilibrium value would create bubble(s ) filled with a ( mean ) isentropic convective flow with properties similar to the ones described above . _ chandra _ , _ newton _ and future x - ray missions will teach us more about the hydrodynamics of ` cooling flows ' .

an excessive heating in the centre , instead , drives a convectively unstable outflow . is not too high , the convection remains subsonic . the convective pattern is dominated by buoyancy driven large - scale mushroom - like structures . unlike in the case of a cooling inflow , the x - ray surface brightness of an ( on average ) isentropic convective core does not display a sharp maximum at the centre . a hybrid model , which combines a subsonic peripheral cooling inflow with an inner convective core , appears to be stable .

we use hydrodynamic simulations with adaptive grid refinement to study the dependence of hot gas flows in x - ray luminous giant elliptical galaxies on the efficiency of heat supply to the gas . we consider a number of potential heating mechanisms including type ia supernovae and sporadic nuclear activity of a central super - massive black hole . as a starting point for this research we use an equilibrium hydrostatic recycling model @xcite . we show that a compact cooling inflow develops , if the heating is slightly insufficient to counterbalance radiative cooling of the hot gas in the central few kiloparsecs . an excessive heating in the centre , instead , drives a convectively unstable outflow . we model the onset of the instability and a quasi - steady convective regime in the core of the galaxy in two - dimensions assuming axial symmetry . provided the power of net energy supply in the core is not too high , the convection remains subsonic . the convective pattern is dominated by buoyancy driven large - scale mushroom - like structures . unlike in the case of a cooling inflow , the x - ray surface brightness of an ( on average ) isentropic convective core does not display a sharp maximum at the centre . a hybrid model , which combines a subsonic peripheral cooling inflow with an inner convective core , appears to be stable . we also discuss observational implications of these results . [ firstpage ] hydrodynamics instabilities cooling flows galaxies : ism ism dark matter

1508.03332

i

with advancements in data collection and video recording methods , high - volume datasets of animal groups , such as fish schools @xcite , bird flocks @xcite , and insect and bacterial swarms @xcite , are now ubiquitous . however , analyzing these datasets is still a nontrivial task , even when individual trajectories of all members are available . a desirable step that may ease the experimenter s task of locating events of interest is to identify coarse observables @xcite and behavioral measures @xcite as the group navigates through space . in this context , nonlinear dimensionality reduction ( ndr ) offers a large set of tools to infer properties of such complex multi - agent dynamical systems . traditional dimensionality reduction ( dr ) methods based on linear techniques , such as principal components analysis ( pca ) , have been shown to possess limited accuracy when input data is nonlinear and complex @xcite . dr entails finding the axes of maximum variability @xcite or retaining the distances between points @xcite . multi dimensional scaling ( mds ) with euclidean metric is another dr method which attains low - dimensional representation by retaining the pairwise distance of points in low dimensional representations @xcite . however , euclidean distance calculates the shortest distance between two points on a manifold instead of the genuine manifold distance , which may lead to difficulty of inferring low - dimensional embeddings . the isometric mapping algorithm ( isomap ) resolves the problem associated with mds by preserving the pairwise geodesic distance between points @xcite ; it has recently been used to analyze group properties in collective behavior , such as the level of coordination and fragmentation @xcite . within isomap , however , short - circuiting @xcite created by faulty connections in the neighborhood graph , manifold non - convexity @xcite and holes in the data @xcite can degrade the faithfulness of the reconstructed embedding manifold . diffusion maps @xcite have also been shown to successfully identify coarse observables in collective phenomena @xcite that would otherwise require hit - and - trial guesswork @xcite . beyond isomap and diffusion maps , the potential of other ndr methods to study collective behavior is largely untested . for example , kernel pca ( kpca ) requires the computation of the eigenvectors of the kernel matrix instead of the eigenvectors of the covariance matrix of the data @xcite but this is computationally expensive @xcite . local linear embedding ( lle ) embeds high - dimensional data through global minimization of local linear reconstruction errors @xcite . hessian lle ( hlle ) minimizes the curviness of the higher dimensional manifold by assuming that the low - dimensional embedding is locally isometric @xcite . laplacian eigenmaps ( le ) perform a weighted minimization ( instead of global minimization as in lle ) of the distance between each point and its given nearest neighbors to embed high dimensional data @xcite . iterative ndr approaches have also been recently developed in order to bypass spectral decomposition which is common in most of ndr methods @xcite . curvilinear component analysis ( cca ) employs a self - organized neural network to perform two tasks , namely , vector quantization of submanifolds in the input space and nonlinear projection of quantized vectors onto a low dimensional space @xcite . this method minimizes the distance between the input and output spaces . manifold sculpting ( ms ) transforms data by balancing two opposing heuristics : first , scaling information out of unwanted dimensions , and second , preserving local structure in the data . the ms method , which is robust to sampling issues , iteratively reduces the dimensionality by using a cost function that simulates the relationship among points in a local neighborhoods@xcite . the local spline embedding ( lse ) is another ndr method which embeds the data points using splines that map each local coordinate into a global coordinate of the underlying manifold by minimizing the reconstruction error of the objective function @xcite . this method reduces the dimensionality by solving an eigenvalue problem while the local geometry is exploited by the tangential projection of data . lse assumes that the data is not only unaffected by noise or outliers , but also , sampled from a smooth manifold which ensures the existence of a smooth low dimensional embedding . due to the global perspective of all these methods , none of them provide sufficient control over the mapping from the original high - dimensional dataset to the low - dimensional representation , limiting the analysis in the embedding space . in other words , the low - dimensional coordinates are not immediately perceived as useful , whereby one must correlate the axes of the embedding manifold with selected functions of known observables to deduce their physical meaning @xcite . in this context , a desirable feature of dr that we emphasize here is the regularity in the spatial structure and range of points on the embedding space , despite the presence of noise . with regard to datasets of collective behavior , nonlinear methods have limited use for detailed analysis at the level of the embedding space . this is primarily because the majority of these methods collapse the data onto a lower dimensional space , whose coordinates are not guaranteed to be linear functions of known system variables @xcite . in an idealized simulation of predator induced mobbing @xcite , a form of collective behavior where a group of animals crowd around a moving predator , two degrees of freedom are obvious , namely , the translation of the group and the rotation about the predator ( center of the translating circle ) . this two - dimensional manifold is not immediately perceived by isomap , even for the idealized scenario presented in figure [ fig : predator_mobbing_isomap ] , where a group of twenty individuals rotate about a predator moving at a constant speed about a line bisecting the first quadrant . specifically , the algorithm is unable to locate a distinct elbow in the residual variance vs. dimensionality curve , notwithstanding substantial tweaking of the parameters . thus , the inferred dimensionality is always 1 ( fig . [ fig : predator_mobbing_isomap]b ) . for a two - dimensional embedding ( fig . [ fig : predator_mobbing_isomap]c ) , visual comparison of the relative scale of the axes indicates that the horizontal axis represents a greater translation than the vertical axis . it is likely that the horizontal axis captures the motion of the group along the translating circle . the vertical axis could instead be associated with ( i ) motion about the center of the circle , or ( ii ) noise , which is independent and identically distributed at each time step . the ambiguity in determining the meaning of such direction indicates a drawback of isomap in provide meaningful interpretations of the low - dimensional coordinates . angle ) , axes @xmath0 , @xmath1 generally represent coordinates for the @xmath2-th agent . ( b ) scaled residual variance of candidate low - dimensional embeddings produced by isomap using different nearest neighbor values @xmath3 ( green - circle , brown - square , and black - triangle ) , and ( c ) two - dimensional representation of the data for five nearest neighbors ( black - triangle ) . green and blue crosses mark the start and end points of the trajectory . ] an alternative approach to dr , one that does not require heavy matrix computations or orthogonalization , involves working directly on raw data in the high - dimensional space @xcite . we propose here a method for dr that relies on geodesic rather than euclidean distance and emphasizes manifold regularity . our approach is based on a spline representation of the data that allows us to control the expected manifold regularity . typically , this entails conditioning the data so that the lower dimensions are revealed . for example , in @xcite , raw data is successively clustered through a series of lumping and splitting operations until a faithful classification of points is obtained . in @xcite , one - dimensional parameterized curves are used to summarize the high - dimensional data by using a property called self - consistency , in which points on the final curve coincide with the average of raw data projected on itself . in a similar vein , we construct a pm of the high - dimensional data using cubic smoothing splines . summarizing the data using splines to construct a pm of the data has two advantages : ( i ) it respects the data regularity by enabling access to every point of the dataset , and ( ii ) it gives direct control over the amount of noise rejection in extracting the true embedding through the smoothing parameter . we illustrate the algorithm using the standard swiss roll dataset , typically used in ndr methods . then we validate the method on three different datasets , including an instance of collective behavior similar to that in figure [ fig : predator_mobbing_isomap ] . this paper is organized as follows . section [ sec : algorithm ] describes the three main steps of the algorithm using the swiss roll dataset as an illustrative example . in section [ sec : examples ] , we validate and compare the algorithm on a paraboloid , a swiss roll with high additive noise , and a simulation of collective animal motion . section [ sec : performance ] analyzes the performance of the algorithm by comparing topologies in the original and embedding space as a function of the smoothing parameter , noise intensity , and data density . we conclude in section [ sec : conclusion ] with a discussion of the algorithm performance and ongoing work . individual steps of the algorithm are detailed in [ sec : algorithms ] . computational complexity is discussed in [ sec : complexity ] .

while the existence of low - dimensional embedding manifolds has been shown in patterns of collective motion , the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds . this is mainly due to the necessary spectral decomposition step , which limits control over the mapping from the original high - dimensional space to the embedding space . here , we propose an alternative approach that demands a two - dimensional embedding which topologically summarizes the high - dimensional data . in this sense , our approach is closely related to the construction of one - dimensional principal curves that minimize orthogonal error to data points subject to smoothness constraints . specifically , we construct a two - dimensional principal manifold directly in the high - dimensional space using cubic smoothing splines , and define the embedding coordinates in terms of geodesic distances . thus , the mapping from the high - dimensional data to the manifold is defined in terms of local coordinates . through representative examples , dimensionality reduction , algorithm , collective behavior , dynamical systems

while the existence of low - dimensional embedding manifolds has been shown in patterns of collective motion , the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds . this is mainly due to the necessary spectral decomposition step , which limits control over the mapping from the original high - dimensional space to the embedding space . here , we propose an alternative approach that demands a two - dimensional embedding which topologically summarizes the high - dimensional data . in this sense , our approach is closely related to the construction of one - dimensional principal curves that minimize orthogonal error to data points subject to smoothness constraints . specifically , we construct a two - dimensional principal manifold directly in the high - dimensional space using cubic smoothing splines , and define the embedding coordinates in terms of geodesic distances . thus , the mapping from the high - dimensional data to the manifold is defined in terms of local coordinates . through representative examples , we show that compared to existing nonlinear dimensionality reduction methods , the principal manifold retains the original structure even in noisy and sparse datasets . the principal manifold finding algorithm is applied to configurations obtained from a dynamical system of multiple agents simulating a complex maneuver called predator mobbing , and the resulting two - dimensional embedding is compared with that of a well - established nonlinear dimensionality reduction method . dimensionality reduction , algorithm , collective behavior , dynamical systems

1609.06419

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there is a growing interest from the nanoscience and nanotechnology community of the dirac hamiltonian in condensed matter owing to the emergence of novel materials that mimic the relativistic dirac quantum mechanical behavior . the purpose of this review is to present a unified treatment of dirac hamiltonian in solids and relativistic dirac quantum mechanics from the point of view of energy - band quantum dynamics@xcite coupled with the lattice weyl transformation techniques.@xcite this unified view seems to explicitly emerge in the calculation of the magnetic susceptibility of bismuth and bi - sb alloys.@xcite large diamagnetism in solids has been attributed to interband quantum dynamics,@xcite often giving large @xmath0-factor due to pseudo - spin degrees of freedom and induced magnetic field . these are inherent in interband quantum dynamics . in most cases we are referring to two bands only which could be kramer s degenerate bands.@xcite on the other hand , the classic landau - peierls diamagnetism is purely a single - band dynamical ( orbital ) effect . more recently , fukuyama et al@xcite give a review on diamagnetism of dirac electrons in solids from a theoretical perspective of many - body green s function technique . however , no theoretical calculations were made and compared with the beautiful experiments of wherli@xcite on the diamagnetism of bi - sb alloys . here we employ a theoretical perspective of band dynamics that has a long history even before the time of peierls,@xcite who introduced the peierls phase factor , and wannier who introduced the wannier function.@xcite this band dynamical treatment is generalized to the dirac relativistic quantum mechanics and many - body condensed matter physics.@xcite a detailed calculation@xcite of the diamagnetism of bi - sb alloys using the theory of buot and mcclure@xcite yields outstanding quantitative agreement with experimental results.@xcitewe also give a review of the calculations of the magnetic susceptibility of other systems . firstly , in this section we will give a background on relativistic dirac fermions , the beautiful dirac equation and dirac s declaration of anti - matter and discovery of positrons . we focus on its impact in motivating the development of modern physics , in particular condensed matter physics leading to a plethora of quasiparticle excitations with exotic properties . because of this , condensed matter physics has become a low - energy proving ground on some of theoretical concepts in quantum field theory , high - energy elementary particle physics , and cosmology , where the dirac equation has been extended and consistently deformed in ways exposing novel excitations / quasiparticles in physical systems . in the space - time domain of condensed matter physics , it is interesting that the relativistic dirac - like equation was first recognized in the @xmath1 band theory of bismuth and bi - sb alloys.@xcite this scientific historical event is like a repeat of what has happened in ordinary space - time with the quantum theory of relativistic electrons published in 1928 by dirac@xcite in the form of what is now known as the dirac equation with _ four - component _ fields . the following year , weyl@xcite showed that for massless fermions , a simpler equation would suffice , involving _ two - component _ fields as opposed to the four - component fields of dirac equation . these massless fermions is now known as the weyl spin @xmath2 fermions . about nine years later , in 1937 , majorana@xcite was searching for a real version of the dirac equation which is still lorentz invariant . thus , by imposing reality constraint of the dirac equation , other solutions were obtained by majorana still describing spin @xmath2 fermions , whose outstanding unique property is that they are their own anti - particles . by virtue of the fact that the complex field of the dirac fermions is replaced by real fields , one refers to dirac fermions as consisting of two majorana fermions . thus , majorana fermions are often referred to as half - femions . developments in physics in the early @xmath3th century is not only confined to relativistic fermions but also to relativistic bosons which act as force - fields between particles . these particle - particle interactions are usually mediated by massless bosons such as photons , gluons , and gravitons . however , relativistic massive bosons , the so - called proca particles , mediate the weak interactions between elementary particles . these are , for example , the @xmath4 and @xmath5 spin-@xmath6 heavy vector bosons . twenty five years later after majorana , skyrme@xcite proposed a topological soliton in quantum field theory which is now referred to as skyrmion . then in 1978 , callan et al@xcite proposed another topological objects known as merons . in magnetic systems , skyrmions , merons and bimerons are closely related . thus , whereas weyl demonstrated the existence of massless relativistic spin-@xmath2 fermions , proca@xcite demonstrated in 1936 the existence of massive relativistic spin-@xmath6 bosons . in crystals , phonons are generally classified as the nambu - goldstone modes , but in the interaction between cooper pairs in bcs superconductivity theory no massless phonons are present , only massive plasmalike excitations.@xcitein gauge - field theory of standard model , the proca action is the gauge - fixed version of the stueckelberg action which is a special case of higgs mechanism through which the boson acquires mass . weyl fermions are irreducible representations of the proper lorentz group , they are considered as building blocks of any kind of fermion field . weyl fermions are either right chiral or left chiral but can not have both components . a general fermion field can be described by two weyl fields , one left - chiral and one right - chiral . it is worth mentioning that helicity and chirality coincide for massless fermions . by combining massless weyl - fermion fields of different chiralities , one has not really generated a mass but has created a group - theoretical framework where mass can be allowed in the dirac lagrangian since the mass term must contain two different chiralities . thus , a _ massive _ fermion must have a left - chiral as well as a right - chiral component . surprisingly the above chain of scientific events in ordinary space - time have been followed , although much later experimentally , by corresponding events in the space - time domain of condensed matter systems . although , as early as 1937 , herring@xcite have already theoretically predicted the possibility of weyl points in band theory of solid state physics . in more recent years nielsen and ninomiya@xcite have suggested that excess of particles with a particular chirality were associated with weyl fermions and could be observable in solids . as mentioned before , the explicit form of dirac hamiltonian first appeared in bismuth and bi - sb alloys in a paper by wolff in 1964 upon blount s suggestion.@xcite actually cohen@xcite gave the same form of the hamiltonian of bismuth four years earlier in 1960 , but did not cast into the form of dirac hamiltonian . then , with the discovery of graphene @xcite in 2004 , massless dirac fermions were identified in the energy - band structure at the @xmath7-points of the brillouin zone . the following years are marked with understanding of materials with band structures that are `` topologically '' protected , typically of materials with strong spin - orbit coupling . this understanding have taken roots much earlier from works on quantum hall effect ( qhe ) and quantum spin hall effect ( qshe ) . the term topological refers to a concept whereby there is a ` holographic ' quasiparticle - state structure often localized at boundaries , domain walls or defects , which is topologically protected by the properties of the bulk . this maybe viewed as a sort of _ entanglement _ of the excitation - state with the bulk structure and therefore a _ highly - nonlocal _ property of excitation - state immune to local perturbation.@xcite the pertinent measure of this entanglement is the subject of exploding research activities on the so - called _ topological entanglement entropy_. @xcite indeed , a _ holographic interpretation _ of topological entanglement entopy was given.@xcite this is also known in the literature simply as generalized _ bulk - boundary correspondence_. these years are replete with findings of topological insulators and topological superconductors , based on the realization that band theory must take into account concepts such as chern numbers and berry phases , familiar in quantum field theory of elementary particles , quantum - hall effect , peierls phase of a plaquette , aharonov - bohm effect , and in born - oppenheimer approximations . indeed , theorists are now engaged in the exciting fields of topological field theory ( tft ) and topological band theory ( tbt ) . this attests to the merging of elementary particle physics , cosmology , and condensed matter physics . topological superconductors are simply the analogue of topological insulators . whereas , topological insulators ( ti ) have a bulk band - gap with odd number of _ relativistic dirac fermions _ and gapless modes on the surface , topological superconductors ( tsc ) are certain type of full superconducting gap tsc in the bulk , but due to the inherent particle - hole symmetry , have gapless modes of chargeless _ majorana ` edge ' states _ , also associated with _ andreev bound state _ ( abs)@xcite on its boundaries , interfaces ( e.g. interface between topological insulators and superconductors ) , and defects , supported by the bulk topological invariants . the emergence of topological insulators and superconductors also brought to light two types of quasiparticles properties , namely , ( a ) local or ` trivial ' quasiparticles , and ( b ) nonlocal , ` nontrivial ' or topological quasiparticles , often termed as _ topological charge_. the second type are robust states , these can not be created or removed by any local operators . the topological charge is also called the topological quantum number and is sometimes called the winding number of the solution . the topological quantum numbers are topological invariants associated with topological defects or soliton - type solutions of some set of differential equations modeling a physical system . for example , the first @xmath8d topological insulator was predicted for bi@xmath9-sb@xmath10 system with @xmath11 , where the theoretical band structure calculation predicts the @xmath8d topological insulator phase in bi@xmath12sb@xmath13.@xcite these developments are followed around mid - year of @xmath14 with the experimental discovery of weyl fermions which were identified in the so - called weyl semimetals . specifically , the historic angle - resolved photoemission spectroscopy ( arpes ) experiments performed on ta - as has revealed weyl fermions in the bulk.@xcite likewise , similar experiments on photonic crystal have identified weyl points ( not weyl fermions ) inside the photonic crystal.@xciteweyl points differ from dirac points since the former has two - component wavefunction whereas the later generally has four component wavefunction , e.g. in graphene the @xmath15 points in the brillouin zone end ows the two chiralities for a dirac hamiltonian for graphene . the excitement about the experimental discovery of weyl semimetals has to do with its great potential for ultrafast devices . the absence of backscattering for weyl fermions is related to the so - called klein paradox in quantum electrodynamcis due to conservation of chirality . because of this , weyl fermions can not be localized by random potential scattering in the form of anderson localization@xcite common to massive electrons . moreover , with the eficient electron - hole pairs screening of impurities , mobilities of weyl fermions are expected to be more than order of magnitude higher than the best si transistors . in passing , we could say that the crossing of the bands of different symmetry properties in bi@xmath16-sb@xmath10 alloys @xcite for antimony concentration of @xmath17 might also serves as a weyl semimetal , ignoring questions of topological stability . [ [ the - hunt - for - majorana - fermions ] ] the hunt for majorana fermions + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + on the other hand , the _ experimental _ majorana fermions in solid state systems remains a challenging pursuit , a bit of ` holy grail ' which one can perhaps draw a parallel with the search for higgs particles in high - energy physics.@xcite in conventional condensed matter system , @xmath18 and its hermitian conjugate @xmath19 is a _ physically distinct operator _ that annihilates electron or creates a hole . since particles and antiparticles have opposite conserved charges , a majorana fermion with its own antiparticle is a necessarily uncharged fermion . in his original paper , majorana fermions can have arbitrary spin , so with spin zero it is still a fermion since the majorana annihilation and creation operators still obey the anticommutation rule . for example , a mixture of particles and anti - particles of the form , @xmath20 indicates a chargeless and spinless majorana fermions , often referred to as a _ featureless _ majorana fermions . another form of @xmath21 with equal spin projection , say a triplet or effectively spinless since spin degree of freedom does not have to be accounted for , is also a majorana field operator , @xmath22 . this particular @xmath23-form arises by imposing the majorana condition @xcite on the bogoliubov - de gennes ( bdg ) equation of superconductivity . a conventional quasiparticle in superconductor is a broken cooper pair , an excitation called a bogoliubov quasiparticle and can have spin @xmath2 . it is simply a linear combination of creation and annihilation operators , namely , @xmath24 and @xmath25 , where @xmath26 and @xmath27 are the components of the wavefunction of the bogoliubov - de gennes ( bdg ) equation . the requirement of bogoliubov canonical transformation is that @xmath28 = \big ( a_{\alpha}a_{-\alpha}^{\dagger } + a_{-\alpha}^{\dagger } a_{\alpha}\big)$ ] , therefore we must have @xmath29 and @xmath30 . the particle created by the operator @xmath31 is a fermion , the so - called bogoliubov quasiparticle ( or `` bogoliubon '' ) . it combines the properties of a negatively charged electron and a positively charged hole . indeed , majorana fermion must have a form of superposition of particle and anti - particle . however , the creation and annihilation operators for bogoliubons are still distinct . thus , whereas charge prevents majorana from emerging in a metal , on the other hand _ distinct _ creation and annihilation operators through superposition of electrons and holes with opposite spins is preventing majorana quasiparticles in conventional @xmath32-wave superconductors . if majorana fermion is to appear in the solid state it must therefore be in the form of _ still to be experimetally demonstrated _ nontrivial emergent majorana excitations in real materials . the attention is focused on topological superconductors . after a theoretical demonstration of the existence of majoranas at the ends of a @xmath33-wave pairing kitaev - chain , several theoretical demonstrations for the existence of zero - mode majorana bound states ( mbs ) follow . in kitaev s prediction , inducing some types of superconductivity , known as the proximity effect , would cause the formation of majoranas . these emergent particles are stable ( majorana degenerate bound states ) and do not annihilate each other ( unless the chain or wire is too short ) because they are spatially separated . thus , @xmath33-superconductors provide a natural hunting ground for majoranas . the search for majorana has also pave the way for the _ novel physics of zero modes _ of the extended dirac equation with inhomogeneous mass term that varies with position ( corresponding to the momentum - dependent pairing potential in bdg equation ) , yielding a _ kink - soliton _ solution in @xmath6-d , a _ vortex _ solution in @xmath34-d , and a _ magnetic monopole _ in @xmath8-d . @xcite in condensed matter physics , the experimental search for majorana is focused on exotic superconductors , namely , in triplet @xmath33-wave superconductivity in one dimension ( @xmath6d ) , where mbs are located at both ends of the superconducting wire , and triplet @xmath35-wave superconductivity in two dimensions ( @xmath34d ) where the mbs has been theoretically demonstrated to reside at the core of the vortex at an interface . in triplet @xmath8d superconductors , the mbs is at the core of the ` hedgehog ' configuration . these topological superconductors realize topological phases that support non - abelian exotic excitations at their boundaries and at topological defects ( e.g. , hedgehog configuration ) . most importantly , zero - energy modes localize at the ends of a @xmath6d topological @xmath33-wave superconductor , and bind to vortices in the @xmath34d topological @xmath36-wave superconducting case . these zero - modes are precisely the condensed matter realization of majorana fermions that are now being vigorously pursued . moreover , engineered hererostructures using proximity effect with the @xmath32-wave superconductor , the so - called proximity - induced topological superconductor are correspondingly and vigorously also being pursued . from the technological point of view these topologically - robust majorana excitations are envisaged to implement quantum computing where braiding operation constitutes bits manipulation , analogous to the yang - baxter equations first introduced in statistical mechanics . the majorana number density is limited to an integer ( mode @xmath34 ) , i.e. , @xmath37 and @xmath6 , thus ideally representing a quantum bit . an intrigung proposal is a superconductor - topological insulator - superconductor ( stis ) junction that forms a nonchiral @xmath6d wire for majorana fermions . these ( stis ) junctions can be combined into circuits which allow for the creation , manipulation , and fusion of majorana bound states for topological quantum computation.@xcite there are also proposals for interacting non - abelian anyons as majorana fermions in kitaev s honeycomb lattice model.@xcite indeed , majorana fermions obey non - abelian statistics , since majorana fermions can have arbitrary spin statistics . several groups have experimentally reported detecting majorana fermions . @xcite more recently , a princeton group@xcite , have reported detecting majorana by following kitaev s prediction that , under the correct conditions a majorana fermion bound states would appear at each end of a superconducting wire or kitaev chain . in summary , it is worth emphasizing that condensed matter physics has become the low - energy playground for discovering various quasiparticles and exotic topological excitations , which were mostly first proposed in quantum field theory of elementary particles , namely , dirac fermions , weyl fermions , proca particles , vortices , skyrmions , merons , bimerons and other topologically - protected quasiparticles obeying non - abelian and anyon statistical properties .

wide ranging interest in dirac hamiltomian is due to the emergence of novel materials , namely , graphene , topological insulators and superconductors , the newly - discovered weyl semimetals , and still actively - sought after majorana fermions in real materials . we give a brief review of the relativistic dirac quantum mechanics and its impact in the developments of modern physics . the quantum band dynamics of dirac hamiltonian is crucial in resolving the giant diamagnetism of bismuth and bi - sb alloys . quantitative agreement of the theory with the experiments on bi - sb alloys has been achieved , and physically meaningful contributions to the diamagnetism has been identified .

wide ranging interest in dirac hamiltomian is due to the emergence of novel materials , namely , graphene , topological insulators and superconductors , the newly - discovered weyl semimetals , and still actively - sought after majorana fermions in real materials . we give a brief review of the relativistic dirac quantum mechanics and its impact in the developments of modern physics . the quantum band dynamics of dirac hamiltonian is crucial in resolving the giant diamagnetism of bismuth and bi - sb alloys . quantitative agreement of the theory with the experiments on bi - sb alloys has been achieved , and physically meaningful contributions to the diamagnetism has been identified . we also treat relativistic dirac fermion as an interband dynamics in uniform magnetic fields . for the interacting bloch electrons , the role of translation symmetry for calculating the magnetic susceptibility avoids any approximation to second order in the field . the magnetic susceptibility of hubbard model and those of fermi liquids are readily obtained as limiting cases . the expressions for magnetic susceptibility of dilute nonmagnetic alloys give a firm theoretical foundation of the empirical formulas used in fitting experimental results . for completeness , the magnetic susceptibility of dilute magnetic or kondo alloys is also given for high and low temperature regimes .

1112.4815

c

using adaptive optics imaging at keck , we have discovered a substellar companion to the dusty pleiades star hd 23514 . based on comparison with evolutionary models , we estimate the companion to have a mass of about @xmath26m@xmath33 and temperature @xmath27 k. to our knowledge , hii 1348 and hd 23514 are the only pleiades stars known to have brown dwarf companions @xcite . hd 23514 is one of the dustiest main - sequence stars known to date with @xmath0 . the warm dust present in the system is located within a few au of the primary . in contrast , the companion has a projected separation of @xmath2360 au . at that distance , the companion s gravity is expected to have little influence over the evolution of the warm dust seen around the primary . however , if a tertiary object were present in the system very close to the star , the kozai mechanism can affect its orbit and possibly enhance collisions that generate dust . we thank j. stauffer for useful discussions on the pleiades , r. galicher for the nirc2 coronographic attenuation , and s. yelda for assistance in nirc2 reduction . we thank our anonymous referee for a prompt review and constructive suggestions . the data presented herein were obtained at the w.m . keck observatory , which is operated as a scientific partnership among the california institute of technology , the university of california and the national aeronautics and space administration . the observatory was made possible by the generous financial support of the w.m . keck foundation . the authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of mauna kea has always had within the indigenous hawaiian community . we are most fortunate to have the opportunity to conduct observations from this mountain . this research was supported in part by nasa grants to ucla . lafrenire , d. , jayawardhana , r. , & van kerkwijk , m. h. 2008 , , 689 , l153 lafrenire , d. , jayawardhana , r. , & van kerkwijk , m. h. 2010 , , 719 , 497 lafrenire , d. , jayawardhana , r. , janson , m. , et al . 2011 , , 730 , 42 2006 - 12 - 10 & k@xmath5 & 30 & 2 & 60 & 18 & adi mode , primary saturated + 2006 - 12 - 10 & k@xmath5 & 0.2 & 100 & 20 & 9 & adi mode , secondary not detected + 2006 - 12 - 10 & k@xmath5 & 0.005 & 50 & 0.25 & 12 & adi mode , secondary not detected + 2007 - 10 - 25 & k@xmath5 & 30 & 2 & 60 & 14 & primary saturated + 2007 - 10 - 25 & k@xmath5 & 0.018 & 20 & 0.36 & 8 & secondary not detected + 2007 - 10 - 25 & k@xmath5 & 0.005 & 50 & 0.25 & 6 & secondary not detected + 2008 - 11 - 04 & ks & 20 & 1 & 20 & 8 & primary saturated + 2008 - 11 - 04 & ks & 0.5 & 20 & 10 & 15 & secondary detected in 9/15 frames + 2009 - 11 - 01 & h & 1 & 60 & 60 & 7 & + 2009 - 11 - 02 & ks c600 & 30 & 1 & 30 & 14 & coronographic ; 600 mas diameter spot + 2010 - 10 - 30 & j & 0.053 & 200 & 10.6 & 5 & + 2010 - 10 - 30 & h & 0.053 & 200 & 10.6 & 10 & + 2010 - 10 - 30 & ks & 0.1 & 200 & 20 & 5 & + 2010 - 10 - 30 & ks c800 & 6 & 2 & 12 & 10 & coronographic ; 800 mas diameter spot + 2006 - 12 - 10 & k@xmath5 & 45 & @xmath44 & @xmath45 & @xmath46 & @xmath47 + 2007 - 10 - 25 & k@xmath5 & 25 & @xmath48 & @xmath49 & @xmath50 & @xmath51 + 2008 - 11 - 04 & ks & 20 & @xmath52 & @xmath53 & @xmath54 & @xmath55 + 2009 - 11 - 01 & h & 25 & @xmath56 & @xmath57 & @xmath58 & @xmath59 + 2009 - 11 - 02 & ks c600 & 20 & @xmath60 & @xmath61 & @xmath62 & @xmath63 + 2010 - 10 - 30 & j & 25 & @xmath64 & @xmath65 & @xmath66 & @xmath67 + 2010 - 10 - 30 & h & 25 & @xmath68 & @xmath69 & @xmath70 & @xmath71 + 2010 - 10 - 30 & ks & 25 & @xmath72 & @xmath73 & @xmath74 & @xmath75 + 2010 - 10 - 30 & ks c800 & 25 & @xmath76 & @xmath77 & @xmath78 & @xmath79 + . the uncertainty in these two measurements are comparable to the symbol size and they effectively lie on top of each other in the figure . the black line indicates the relative motion a stationary background source would have throughout these observations with circles denoting the expected location at the time of our observations . we adopt a distance of @xmath19 pc ( see section [ results ] ) . , width=529 ] ) as a function of separation for our 2010 and 2009 coronographic data . limits are computed using the same aperture size by performing aperture photometry on blank regions of the sky in annuli around the primary . the limits are averaged over all frames . companions @xmath211 - 12 magnitudes fainter at ks than the primary could have been detected at separations larger than 1.5 . mass limits in solar masses from the dusty evolutionary model of @xcite are indicated . , width=529 ]

with adaptive optics imaging at keck observatory , we have discovered a substellar companion to the f6 pleiades star hd 23514 , one of the dustiest main - sequence stars known to date ( @xmath0 ) . the 0.06 m@xmath1 late - m secondary has a projected separation of @xmath2360 au .

with adaptive optics imaging at keck observatory , we have discovered a substellar companion to the f6 pleiades star hd 23514 , one of the dustiest main - sequence stars known to date ( @xmath0 ) . this is one of the first brown dwarfs discovered as a companion to a star in the pleiades . the 0.06 m@xmath1 late - m secondary has a projected separation of @xmath2360 au . the scarcity of substellar companions to stellar primaries in the pleiades combined with the extremely dusty environment make this a unique system to study .

1610.00925

i

the neon - sodium cycle of hydrogen burning ( nena cycle ) converts hydrogen to helium through a chain of proton induced reactions involving neon and sodium isotopes . the nena cycle contributes negligibly to the energy budget , but it is of great importance for stellar nucleosynthesis , because it affects the abundances of the elements between @xmath9ne and @xmath10al @xcite . predicting the abundances of nena cycle elements in different astrophysical objects has become highly topical since the discovery of the anticorrelation between sodium and oxygen abundances in red giant stars of globular clusters ( * ? ? ? * a review ) . in principle , material showing such a na - o anticorrelation may be produced by hydrogen burning when the temperature is so high that not only the cno cycle , but also the nena cycle is activated @xcite . in order to explain how such material can be brought to the stellar surface where it can be detected , mainly one scenario is invoked : pollution of the interstellar medium with the ashes of hydrogen burning from a previous generation of stars . several candidates have been proposed for such a pollution : intermediate - mass asymptotic giant branch ( agb ) stars or super agb stars @xcite , fast rotating massive stars @xcite , supermassive stars @xcite , massive stars in close binary systems @xcite , stellar collisions @xcite , and classical novae @xcite . a detailed understanding of the nuclear physics of the nena cycle is needed in order to sharpen quantitative predictions for the nucleosynthetic output of these objects , which , in turn , are necessary to evaluate their respective impact on the na - o anticorrelation @xcite . the @xmath0ne(p,@xmath1)@xmath2na reaction is the most uncertain reaction of the cycle @xcite . the uncertainty is due to a large number of predicted but hitherto unobserved resonances at proton energies refers to the proton beam energy in the laboratory system , @xmath11 to the center - of - mass energy , and @xmath8 to the excitation energy in the @xmath2na nucleus . ] below 400 kev @xcite , and to a number of observed but poorly constrained resonances at 400 - 1300kev @xcite , see fig . [ fig : ls ] for a partial level scheme of @xmath2na including the astrophysically relevant resonances . the resonances above 400 kev have been studied several times before , most recently at the 3mv tandetron of helmholtz - zentrum dresden - rossendorf ( hzdr ) ( * ? ? ? * and references therein ) . for the resonances below 400 kev , however , data are scarce . the @xmath2na states between @xmath8 = 8822 - 9171 kev have been studied with indirect techniques @xcite , but in many cases the spin and parity assignments to those levels are uncertain and their @xmath1 decay modes are poorly known , if at all . direct @xcite and indirect @xcite experiments have been performed to derive the strength of @xmath0ne(p,@xmath1)@xmath2na resonances below 400 kev , but both approaches only provided upper limits ( tab . [ tab : wg_trr ] ) . moreover , three states at @xmath8 = 8862 , 8894 and 9000 kev have been reported as tentative in an indirect measurement @xcite . ( color online ) partial level scheme of @xmath2na , level energies taken from @xcite . the @xmath12-value and the resonance energies in the laboratory system of the @xmath0ne(p,@xmath1)@xmath2na reaction are also shown . the resonances highlighted in red have been studied at luna ( * ? ? ? * and present work ) . the resonances shown in blue have recently been investigated at hzdr @xcite . on the right side of the plot , relevant energy ranges are given for three astrophysical scenarios.,width=264 ] the upper limits for the unobserved resonances are treated differently in the literature . in the nacre compilation @xcite , usually 1/10 of the upper limit is adopted as value , with an error bar from zero to the full upper limit . in the iliadis / starlib compilation @xcite , several unobserved resonances were completely excluded from consideration , therefore also the uncertainty stemming from these cases was left out @xcite . for the other resonances , iliadis / starlib adopted a monte carlo sampling technique . as a result of the different treatment of the unobserved resonances between nacre , on the one hand , and iliadis / starlib , on the other hand , the difference between the adopted rates in the two compilations is as high as a factor of 700 at a temperature of 0.08 gk @xcite . sensitivity studies focusing on nucleosynthesis in agb stars experiencing hot bottom burning ( hbb ) @xcite and on classical novae explosions @xcite show how the uncertainty in the @xmath0ne(p,@xmath1)@xmath2na rate affects the abundances of the nuclides between @xmath9ne and @xmath10al , leading to abundance variations as high as two orders of magnitude . in order to clarify the situation of the @xmath0ne(p,@xmath1)@xmath2na resonances below 400 kev , a new direct experiment has been performed deep underground at the laboratory for underground nuclear astrophysics ( luna ) @xcite . the present data on the @xmath13 = 156.2 , 189.5 and 259.7 kev resonances has been published in abbreviated form @xcite . here , full details of the experiment and data analysis are given , together with the decay branching ratios of the newly observed resonances . the thermonuclear reaction rate is given both in tabular and parameterized forms for use in stellar evolution codes . the present work is organized as follows . the experimental method and the setup are described in sec . [ sec : experiment ] . section [ sec : results ] discusses the data analysis technique . the results obtained for each of the resonances investigated are shown in secs . [ subsec:156]-[subsec : ul ] . the astrophysical reaction rate and a brief discussion are given in sec . [ sec : astro ] .

* background : * the @xmath0ne(p,@xmath1)@xmath2na reaction is the most uncertain process in the neon - sodium cycle of hydrogen burning . at temperatures relevant for nucleosynthesis in asymptotic giant branch stars and classical novae , its uncertainty is mainly due to a large number of predicted but hitherto unobserved resonances at low energy . * purpose : * a new direct study of low energy @xmath0ne(p,@xmath1)@xmath2na resonances has been performed at the laboratory for underground nuclear astrophysics ( luna ) , in the gran sasso national laboratory , italy . = 8943.5 , 8975.3 , and 9042.4 kev excitation energy corresponding to the new resonances , the @xmath1-decay branching ratios have been precisely measured . experimental upper limits have been derived that are significantly more stringent than the upper limits reported in the literature . * conclusions : * based on the present experimental data and also previous literature data , an updated thermonuclear reaction rate is provided in tabular and parametric form . the new reaction rate is significantly higher than previous evaluations at temperatures of 0.08 - 0.3 gk .

* background : * the @xmath0ne(p,@xmath1)@xmath2na reaction is the most uncertain process in the neon - sodium cycle of hydrogen burning . at temperatures relevant for nucleosynthesis in asymptotic giant branch stars and classical novae , its uncertainty is mainly due to a large number of predicted but hitherto unobserved resonances at low energy . * purpose : * a new direct study of low energy @xmath0ne(p,@xmath1)@xmath2na resonances has been performed at the laboratory for underground nuclear astrophysics ( luna ) , in the gran sasso national laboratory , italy . * method : * the proton capture on @xmath0ne was investigated in direct kinematics , delivering an intense proton beam to a @xmath0ne gas target . @xmath1 rays were detected with two high - purity germanium detectors enclosed in a copper and lead shielding suppressing environmental radioactivity . * results : * three resonances at 156.2 kev ( @xmath3 = ( 1.48@xmath40.10)@xmath510@xmath6 ev ) , 189.5 kev ( @xmath3 = ( 1.87@xmath40.06)@xmath510@xmath7 ev ) and 259.7 kev ( @xmath3 = ( 6.89@xmath40.16)@xmath510@xmath7 ev ) proton beam energy , respectively , have been observed for the first time . for the levels at @xmath8 = 8943.5 , 8975.3 , and 9042.4 kev excitation energy corresponding to the new resonances , the @xmath1-decay branching ratios have been precisely measured . three additional , tentative resonances at 71 , 105 and 215 kev proton beam energy , respectively , were not observed here . for the strengths of these resonances , experimental upper limits have been derived that are significantly more stringent than the upper limits reported in the literature . * conclusions : * based on the present experimental data and also previous literature data , an updated thermonuclear reaction rate is provided in tabular and parametric form . the new reaction rate is significantly higher than previous evaluations at temperatures of 0.08 - 0.3 gk .

1610.00925

r

the experiment has been conducted at the luna 400 kv accelerator @xcite , deep underground at the gran sasso national laboratories ( lngs ) , operated by the italian national institute for nuclear physics ( infn ) . owing to its deep underground location , luna affords a uniquely low background @xcite , allowing to investigate proton capture on @xmath0ne with unprecedented sensitivity @xcite . a proton beam with a typical intensity of 200 @xmath14a was delivered to a differentially pumped , windowless gas target ( * ? ? ? * for details ) . the target chamber was filled with 1.5 mbar of neon gas , enriched to 99.9@xmath15 in @xmath0ne . a recirculation and purification system collected the gas exhaust from the pumping stages , removed possible contaminants through a chemical getter and finally recycled the gas to the target chamber , keeping the purity of @xmath0ne constant throughout the measurements . the beam entered the target chamber through a water cooled copper collimator ( denoted ap1 in fig . [ fig : chamber ] ) of 4.3 cm length and 0.7 cm diameter and was stopped on the hot side of a beam calorimeter , used to measure the beam intensity with 1@xmath15 precision @xcite . the gas density as a function of the position inside the chamber and the beam heating correction have been studied in details @xcite , giving the areal number density of the target atoms with an overall uncertainty of 1.3@xmath15 . the possible presence of an air contamination in the gas was checked periodically using the intense @xmath16n(p,@xmath1)@xmath17o resonance at @xmath13 = 278 kev . the nitrogen level in the gas was always found to be below 0.1@xmath15 . emitted @xmath1 rays were detected by two high - purity germanium ( hpge ) detectors ( fig . [ fig : chamber ] ) : one , of 90@xmath15 relative efficiency @xcite , was mounted on top of the target chamber and was collimated at 90@xmath18 ( ge90 ) . the other , of 135@xmath15 relative efficiency , was mounted below the target chamber and collimated at 55@xmath18 ( ge55 ) . both detectors were enclosed in a copper and lead shield of 15 - 25 cm thickness , absorbing @xmath1 rays from the decay of environmental radioactive isotopes @xcite . two independent data acquisition systems were used in parallel : one with a 100 mhz , 14-bit caen n1728b digital adc providing list mode data and the other with a standard analog signal amplification chain and 16k channel histogramming ortec 919e adc unit . the detection efficiency for @xmath1-ray energies between 478 and 1836 kev was measured with point - like @xmath19cs , @xmath20co and @xmath21y activity standards from physikalisch - technische bundesanstalt , calibrated with @xmath22 error , and one @xmath23be radioactive source produced at mta atomki ( hungary ) and calibrated with @xmath24 uncertainty . by moving each of the radioactive sources , in turn , along the beam axis , the peak detection efficiency was measured as a function of the distance from the ap1 collimator ( see the left panel of fig . [ fig : efficiency ] for the efficiency profile at @xmath25 = 478kev , measured with the @xmath23be source ) . the shape of the profile is dominated by the collimation geometry . for both detectors , the efficiency profile is maximal at a distance @xmath26 = 6.2 cm from ap1 ( fig.[fig : efficiency ] , left panel ) . the efficiency curve as a function of @xmath1-ray energy was then extended up to @xmath25 = 6791 kev using the well - known @xmath16n(p,@xmath1)@xmath17o resonance at @xmath13 = 278 kev @xcite ( @xmath8 = 7556 kev ) . this resonance de - excites either directly to the ground state or to one of the excited states at 5180 , 6172 , and 6791 kev . each of these three states , in turn , decays with 100@xmath15 probability directly to the ground state . in the cascade via the 6172 kev ( 6792 kev ) level , a 1384 kev ( 765 kev ) @xmath1 ray is emitted , lying in the energy range where the efficiency can be determined using radioactive sources . this allows to determine the efficiency for 6 mev @xmath1 rays using a relative approach : the efficiency at 1384 kev ( 765 kev ) is derived from the fit of the radioactive sources data , then the efficiency at higher energies was calculated normalizing the 6172 kev ( 6791 kev ) counting rate to the counting rate of the 1384 kev ( 765 kev ) peak . given the short beam - detectors distance , true coincidence summing had to be taken into account in the evaluation of the detection efficiency . the summing - out correction @xcite depends both on the full - energy peak efficiency and on the total detection efficiency . a geant4 @xcite simulation of the setup was used to determine the peak - to - total ratio and to infer the total detection efficiency for @xmath20co , @xmath21y and @xmath16n(p,@xmath1)@xmath17o @xmath1 rays . the summing out correction was always between 0.028 and 0.040 , depending on @xmath1-ray energies . a conservative uncertainty of @xmath27 on the summing - out correction was adopted . [ fig : efficiency ] ( right ) shows the full - energy peak efficiency as a function of the @xmath1-ray energy , measured at 6.2 cm from the ap1 collimator . fits of the efficiency curves with second - order polynomials in the double - logarithmic plane @xcite are also shown , together with the fit residuals . the total uncertainty on the detection efficiency determined through the fit functions in fig . [ fig : efficiency ] is always at the 1 - 2@xmath15 level . further details on the experimental setup , and on the data analysis , can be found in thesis works @xcite .

* method : * the proton capture on @xmath0ne was investigated in direct kinematics , delivering an intense proton beam to a @xmath0ne gas target . @xmath1 rays were detected with two high - purity germanium detectors enclosed in a copper and lead shielding suppressing environmental radioactivity .

* background : * the @xmath0ne(p,@xmath1)@xmath2na reaction is the most uncertain process in the neon - sodium cycle of hydrogen burning . at temperatures relevant for nucleosynthesis in asymptotic giant branch stars and classical novae , its uncertainty is mainly due to a large number of predicted but hitherto unobserved resonances at low energy . * purpose : * a new direct study of low energy @xmath0ne(p,@xmath1)@xmath2na resonances has been performed at the laboratory for underground nuclear astrophysics ( luna ) , in the gran sasso national laboratory , italy . * method : * the proton capture on @xmath0ne was investigated in direct kinematics , delivering an intense proton beam to a @xmath0ne gas target . @xmath1 rays were detected with two high - purity germanium detectors enclosed in a copper and lead shielding suppressing environmental radioactivity . * results : * three resonances at 156.2 kev ( @xmath3 = ( 1.48@xmath40.10)@xmath510@xmath6 ev ) , 189.5 kev ( @xmath3 = ( 1.87@xmath40.06)@xmath510@xmath7 ev ) and 259.7 kev ( @xmath3 = ( 6.89@xmath40.16)@xmath510@xmath7 ev ) proton beam energy , respectively , have been observed for the first time . for the levels at @xmath8 = 8943.5 , 8975.3 , and 9042.4 kev excitation energy corresponding to the new resonances , the @xmath1-decay branching ratios have been precisely measured . three additional , tentative resonances at 71 , 105 and 215 kev proton beam energy , respectively , were not observed here . for the strengths of these resonances , experimental upper limits have been derived that are significantly more stringent than the upper limits reported in the literature . * conclusions : * based on the present experimental data and also previous literature data , an updated thermonuclear reaction rate is provided in tabular and parametric form . the new reaction rate is significantly higher than previous evaluations at temperatures of 0.08 - 0.3 gk .

1610.00925

r

for each resonance studied here , as a first step a run was performed at the beam energy where the maximum yield was expected according to the literature resonance energy , the beam energy loss and the efficiency profile of the detectors . if a signal was observed , a resonance scan was performed , changing the beam energy in 1 - 2 kev energy steps and measuring the yield of the @xmath25 = 440 kev transition from the first excited state to the ground state of @xmath2na . finally , a long run was performed at the beam energy where the maximal yield was observed , aiming for a statistical uncertainty below 10@xmath15 for each detector . the branching ratio @xmath28 for each transition @xmath29 was then derived using the following relationship : @xmath30 where @xmath31 is the number of counts observed for each @xmath1 line and @xmath32 its peak detection efficiency . as the @xmath1-ray spectra were always dominated by the resonance under study , the contribution from possible unobserved transitions was assumed to be negligible in the branching ratio analysis . only one detector , ge55 , was used for the branching ratios determination . the second order legendre polynomial vanishes at 55@xmath33 , minimizing possible angular distribution effects . in order to determine the energy of the three newly discovered resonances , each resonance scan was compared to the efficiency profile measured with the @xmath34be source . the maxima of the efficiency profile and of the resonance scan are expected to be in the same position along the target chamber , because the two @xmath1-ray energies are very close by ( @xmath35=478kev for @xmath34be , and @xmath35=440kev for the resonance scan ) . the resonance energies were then calculated using the relationship : @xmath36 where : * @xmath13 is the proton energy corresponding to the maximum in the yield profile of the resonance , * @xmath29 is the distance between the place of the efficiency maximum ( fig.[fig : efficiency ] ) and the right edge of the ap1 collimator ( fig.[fig : chamber ] ) , * @xmath37 is the effective length of the ap1 collimator ( fig.[fig : chamber ] ) , * @xmath38 is the proton energy loss per unit length in neon gas , and * @xmath39@xmath40 @xmath41 0.5kev is a correction introduced to account for the proton energy loss in the tube that connects the first pumping stage with the target chamber @xcite . the uncertainty of @xmath42 was estimated taking into account the systematic uncertainty on the proton beam energy ( 0.3kev @xcite ) and on the proton energy loss in neon gas ( 1.7% @xcite ) . the overall uncertainty is two to three times smaller than the uncertainty reported in the literature @xcite . the results on the resonance energies are shown in table [ tab : res_en ] , together with a comparison with previously reported values @xcite . the values by jenkins _ @xcite for the excitation energy @xmath8 have been reported with 1kev uncertainty . for comparison , the jenkins @xmath8 data are converted to resonance energies @xmath42 using the @xmath12-value of the @xmath0ne(p,@xmath1)@xmath2na reaction , which is precisely known , @xmath12 = ( 8794.11@xmath40.02 ) kev @xcite . also , new recommended excitation energies @xmath8 are computed from the present @xmath42 values ( table [ tab : res_en ] ) . [ tab : res_en ] .resonance energy @xmath42 in kev obtained here ( luna ) , compared to the literature values by iliadis _ _ @xcite and by jenkins _ the values for the excitation energy @xmath8 from the present work ( luna ) and from jenkins _ et al . _ @xcite are also shown . [ cols="^,^,^,^,^",options="header " , ] ( color online ) regions of interest for the 440 kev peak ( pink ) and for the background estimation ( light green lines ) in the spectrum taken on the tentative 215 kev resonance . ] the tentative resonances at 71 , 105 and 215 kev were searched for by setting the beam energy to populate each resonance at the target position where both detectors had maximum efficiency . because of the width of the efficiency plateau , for a given resonance energy @xmath42 this search covers a beam energy range of [ @xmath42 - 2kev;@xmath42 + 2kev ] . the existence of the three excited states corresponding to these states had been reported as tentative in an early @xmath0ne(@xmath43he , d)@xmath2na experiment @xcite . a later study with the same method re - investigated the 71 and 105 kev resonances but could only find upper limits @xcite . the nuclear data sheet lists the existence of all three levels as tentative @xcite . however , for each of the first two levels , corresponding to the 71 and 105 kev resonances , a definitive spin - parity assignment of @xmath44 = 1/2@xmath45 is given @xcite . this value is justified @xcite with the assumption of @xmath46=0 angular momentum transfer in the @xmath0ne(@xmath43he , d)@xmath2na reaction . however , these levels were only tentatively or not at all detected in the two @xmath0ne(@xmath43he , d)@xmath2na experiments @xcite , so the assumed @xmath44 assignment for the 71 and 105 kev resonances @xcite seems speculative and is not followed here . for the tentative 215 kev resonance , no spin - parity assignment is given @xcite . also in the present experiment , none of the three resonances was detected . instead , upper limits for the resonance strengths were derived assuming @xmath47 branching ratio for the 440@xmath480 kev transition from the first excited to the ground state . for the evaluation of the upper limits the rolke method has been used @xcite , which applies the profile likelihood technique in the case of a poisson - distributed signal , taking into account the uncertainty on the background determination . in the present case the background estimate is based on experimental data , i.e. on the number of counts in two spectral regions on the left and on the right side of the 440 kev peak . the background thus has similar uncertainty as the signal , which is why the rolke method is used here . [ fig : ul_spec ] shows the regions of interest adopted for the signal and for the background estimation in the case of the tentative 215 kev resonance . the regions of interest were chosen using spectra from different , observed resonances where the 440 kev peak was clearly in evidence , and then used without change for the tentative resonances . [ tab : wg_trr ] d | c | r | r | r | c & & + & & & & & + & direct & & & & + 29 & - & @xmath492.6@xmath5010@xmath51@xcite & - & @xmath492.6@xmath5010@xmath51 + 37 & - & ( 3.1@xmath41.2)@xmath5010@xmath52@xcite & - & ( 3.1@xmath41.2)@xmath5010@xmath52 + 71 & @xmath493.2@xmath5010@xmath7@xcite & @xmath491.9@xmath5010@xmath53@xcite & @xmath491.5@xmath5010@xmath54 & @xmath491.5@xmath5010@xmath54 & 1.266 + 105 & @xmath490.6@xmath5010@xmath7@xcite & @xmath491.4@xmath5010@xmath6@xcite & @xmath497.6@xmath5010@xmath54 & @xmath497.6@xmath5010@xmath54 & 1.140 + 156.2 & @xmath491.0@xmath5010@xmath7@xcite & ( 9.2@xmath43.7)@xmath5010@xmath54@xcite & ( 1.48@xmath40.09@xmath55@xmath40.04@xmath56)@xmath5010@xmath6 & ( 1.48@xmath40.10)@xmath5010@xmath6 & 1.074 + 189.5 & @xmath492.6@xmath5010@xmath7@xcite & 3.4@xmath5010@xmath7@xcite & ( 1.87@xmath40.03@xmath55@xmath40.05@xmath56)@xmath5010@xmath7 & ( 1.87@xmath40.06)@xmath5010@xmath7 & 1.055 + 215 & @xmath491.4@xmath5010@xmath7@xcite & - & @xmath492.8@xmath5010@xmath57 & @xmath492.8@xmath5010@xmath57 & 1.045 + 259.7 & @xmath492.6@xmath5010@xmath7@xcite & @xmath491.3@xmath5010@xmath6@xcite & ( 6.89@xmath40.07@xmath55@xmath40.15@xmath56)@xmath5010@xmath7 & ( 6.89@xmath40.16)@xmath5010@xmath7 & 1.034 + 291 & @xmath492.2@xmath5010@xmath7@xcite & - & - & @xmath492.2@xmath5010@xmath7 + 323 & @xmath492.2@xmath5010@xmath7@xcite & - & - & @xmath492.2@xmath5010@xmath7 + 334 & @xmath493.0@xmath5010@xmath7@xcite & - & - & @xmath493.0@xmath5010@xmath7 + 369 & - & @xmath496.0@xmath5010@xmath58@xcite & - & @xmath496.0@xmath5010@xmath58 + 394 & - & @xmath496.0@xmath5010@xmath58@xcite & - & @xmath496.0@xmath5010@xmath58 + 436 & 0.079 @xmath4 0.006 @xcite & & - & 0.079 @xmath4 0.006 + 479 & 0.594 @xmath4 0.038 @xcite & & - & 0.594 @xmath4 0.038 + 638.5 & 2.45 @xmath4 0.18 @xcite & - & & 2.45 @xmath4 0.18 + 661 & 0.032 @xmath4 0.015 @xcite & & - & 0.032 @xmath4 0.015 + the present new upper limits are summarized in table [ tab : wg_trr ] . owing to the ultra - low background at luna , the new limits are orders of magnitude lower than the upper limits from the previous direct experiment @xcite . it should be noted that the limits calculated are purely experimental , different from indirect upper limits available from the literature which depend on the spin - parity assumed and on the normalization for spectroscopic factors @xcite .

* results : * three resonances at 156.2 kev ( @xmath3 = ( 1.48@xmath40.10)@xmath510@xmath6 ev ) , 189.5 kev ( @xmath3 = ( 1.87@xmath40.06)@xmath510@xmath7 ev ) and 259.7 kev ( @xmath3 = ( 6.89@xmath40.16)@xmath510@xmath7 ev ) proton beam energy , respectively , have been observed for the first time . for the levels at @xmath8 three additional , tentative resonances at 71 , 105 and 215 kev proton beam energy , respectively , were not observed here . for the strengths of these resonances ,

* background : * the @xmath0ne(p,@xmath1)@xmath2na reaction is the most uncertain process in the neon - sodium cycle of hydrogen burning . at temperatures relevant for nucleosynthesis in asymptotic giant branch stars and classical novae , its uncertainty is mainly due to a large number of predicted but hitherto unobserved resonances at low energy . * purpose : * a new direct study of low energy @xmath0ne(p,@xmath1)@xmath2na resonances has been performed at the laboratory for underground nuclear astrophysics ( luna ) , in the gran sasso national laboratory , italy . * method : * the proton capture on @xmath0ne was investigated in direct kinematics , delivering an intense proton beam to a @xmath0ne gas target . @xmath1 rays were detected with two high - purity germanium detectors enclosed in a copper and lead shielding suppressing environmental radioactivity . * results : * three resonances at 156.2 kev ( @xmath3 = ( 1.48@xmath40.10)@xmath510@xmath6 ev ) , 189.5 kev ( @xmath3 = ( 1.87@xmath40.06)@xmath510@xmath7 ev ) and 259.7 kev ( @xmath3 = ( 6.89@xmath40.16)@xmath510@xmath7 ev ) proton beam energy , respectively , have been observed for the first time . for the levels at @xmath8 = 8943.5 , 8975.3 , and 9042.4 kev excitation energy corresponding to the new resonances , the @xmath1-decay branching ratios have been precisely measured . three additional , tentative resonances at 71 , 105 and 215 kev proton beam energy , respectively , were not observed here . for the strengths of these resonances , experimental upper limits have been derived that are significantly more stringent than the upper limits reported in the literature . * conclusions : * based on the present experimental data and also previous literature data , an updated thermonuclear reaction rate is provided in tabular and parametric form . the new reaction rate is significantly higher than previous evaluations at temperatures of 0.08 - 0.3 gk .

physics0701123

i

many experimental groups are presently working on the formation of ultracold molecules and molecular quantum gases . a very efficient scheme is the photoassociation reaction , where two colliding atoms absorb a photon to make a molecule @xcite ; moreover ultracold photoassociation spectroscopy @xcite is capable of providing deep insight into the properties of long range molecules , cold atomic collisions , or pair correlations in a condensate . theoretical two - body scattering models have been developed to compute the photoassociation rates @xcite , in the framework of a perturbative treatment , adapted to situations where low - intensity cw lasers are employed and many - body effects are negligible . a linear variation of the photoassociation rate as a function of intensity is then predicted . in the work of bohn and julienne @xcite , which develops a semi - analytic theory yielding laser - induced energy shifts and l ine broadening , the departure from this linear behavior is described , the saturation limit at larger laser intensities being evaluated . in a condensate , the two - body model should fail and javanainen and mackie @xcite have developed a many - body theory which predicts a saturation limit occurring at lower intensities and attributed to rogue photodissociation . the search for saturation effects has stimulated several experiments . measurement , by mc kenzie _ et al _ @xcite , of the photoassociation rate in a sodium condensate as a function of laser intensity has shown a linear behavior in the intensity range considered , in agreement with the two - body bohn and julienne estimation , and in contrast with the prediction of javanainen and mackie . for a quantum degenerate lithium atomic gas , measurement @xcite of the intensity dependence of the photoassociation rate has verified both the large value of this rate ( at a temperature @xmath0=600 nk ) and the two - body saturation effect at intensities @xmath1 30 w/@xmath2 . the agreement with theory is considered as reasonable within the present experimental accuracy : the higher value of the measured saturation limit , and the oscillations in the experimental rate in the 30 - 80 w/@xmath2 intensity range should be confirmed by measurements with a smaller error bar . for a non - degenerate gas of cesium atoms , at a temperature of 40 @xmath3k , within an optical dipole trap , saturation limit is reached for intensities above 100 w/@xmath2@xcite , and the experimental values then lay around the theoretical curve : it is not clear whether such oscillations are due to uncertainties or should be attributed to a physical effect . + recently naidon and masnou - seeuws @xcite have developed a time - dependent many - body theory of photoassociation in an atomic bose - einstein condensate , showing that several physical effects depend on pair correlations . they show that the two existing models for the description of such correlations @xcite , differ in their predictions of the photoassociation line shapes at large intensities . precise measurements of the variation of the line shapes as a function of cw laser intensity should therefore give insight into the optimal description of many - body effects . + the aim of the present paper is to anticipate such measurements by revisiting the theoretical treatment of photoassociation line shapes , taking advantage of the efficiency of grid methods @xcite for the numerical description of cold collisions and long range molecules , particularly in cases where several channels are involved . actually , the later methods have been widely used for the computation of photoassociation rates @xcite , since they can determine very precise energies and wave functions , both for bound and for continuum levels . it has been demonstrated that due to their global character , mapped grid methods are ideally suited to precise computation of the perturbations occurring in molecular spectra , such as rb@xmath4@xcite or k@xmath4@xcite singlet - triplet mixing . in such cases , the perturbation of one level of a given series should be attributed to a large number of bound or continuum levels of the other series , and local perturbation treatments are poorly adapted . however , up to know , attempts to compute the photoassociation line shapes via grid methods have not been very efficient @xcite and the interpretation of precise measurements is routinely performed with numerov type approaches @xcite . the present paper is proposing an alternative way of implementing grid methods for the calculation of photoassociation line shapes , energy shifts , and rates . + the paper is organized as follows : the description of the present model is reported in section ii - iv . the link with previous models , such as the bohn and julienne model is discussed in section v , where the various assumptions and approximations are underlined . application to the cases of sodium photoassociation in the experimental conditions of ref . @xcite is presented in section vi . section vii will summaries and discuss the outlook of the method .

a description of photoassociation by cw laser is formulated in the framework of grid methods . the hamiltonian describing one or several bound states coupled to a multiple of continuum manifolds via a radiative field is written in the energy representation and diagonalized . the generality of the treatment allows to compute accurately and efficiently physical properties such as non - linear high - intensity energy shifts , line shapes , and photoassociation rates both for isolated and non - isolated resonances . application is given to sodium photoassociation in the experimental conditions of mc kenzie _ et al _ [ phys . inverted region for the dependency of the rate vs. the intensity and non - symmetric lineshapes were predicted to occur above the saturation limit . comparison with the model of bohn and julienne [ phys .

a description of photoassociation by cw laser is formulated in the framework of grid methods . the hamiltonian describing one or several bound states coupled to a multiple of continuum manifolds via a radiative field is written in the energy representation and diagonalized . the generality of the treatment allows to compute accurately and efficiently physical properties such as non - linear high - intensity energy shifts , line shapes , and photoassociation rates both for isolated and non - isolated resonances . application is given to sodium photoassociation in the experimental conditions of mc kenzie _ et al _ [ phys . . lett . * 88 * , 090403 ( 2002 ) ] . inverted region for the dependency of the rate vs. the intensity and non - symmetric lineshapes were predicted to occur above the saturation limit . comparison with the model of bohn and julienne [ phys . rev . a * 60 * , 414 ( 1999 ) ] is discussed .

quant-ph0605166

i

nonlinear interaction of light in a medium provides a very useful framework to study various nonclassical properties of quantum states of radiation . these nonclassical properties are usually associated with quantum interference and entanglement . the phase space wigner distribution function description of quantum states of light is a powerful tool to investigate such nonclassical effects . with the help of the wigner function one can simply visualize quantum interference . for example , a signature of quantum interference is exhibited in the wigner function by the non - positive values and sub - planck structures @xcite . the non - positive wigner function is a witness of a nonclassicality and monitors a decoherence process of a quantum state , e.g. a photon - added coherent state in the photon - loss channel @xcite , photon - subtracted squeezed state @xcite , gaussian quadrature - entangled single photon subtracted light pulse @xcite , two - photon fock state @xcite , odd photon number states superposition @xcite and coherent states superpositions @xcite . the wigner function has also been used for computing numerically the quantum - mechanical corrections to the classical dynamics of a nanomechanical resonator ( its characteristic pattern , the interference fringes and negative values , served as a signature for a classical to quantum domain transition ) @xcite ; it has been applied in the model of the dynamics of a nanoscale semiconductor laser @xcite , to list only a few examples of its applications . the kerr medium provides one of the simplest nonlinearity for which there exists a simple analytic wigner function @xcite expression . the highly @xmath0 nonlinear systems generated a lot of interest recently due to their applications e.g. to nondemolition measurements @xcite , quantum computing architectures @xcite , single particle detectors @xcite . the well known example of such a medium is an optical fiber . however , the nonlinearity is small in fibers and is often accompanied by other unwanted effects . enhanced kerr nonlinearity was studied in terms of electromagnetically induced transparency @xcite and was observed in bose einstein condensates @xcite and cold atoms @xcite . recent proposals predict obtaining enormous kerr nonlinearity using the purcell effect @xcite , rydberg atoms @xcite , and interaction of a cavity mode with atoms @xcite . the first and last method is predicted to obtain the nonlinearity of nine orders of magnitude higher than natural self - kerr interactions with negligible losses . the significant nonlinearity has also been observed for nanomechanical resonators @xcite . most of the investigations of the wigner function of light have been made for steady state situations . the simplicity of the kerr medium will allow to study the full time - dependent wigner function dynamics with or without a quantum noise . in this paper we present a fokker - planck equation which determines the time evolution of the wigner function in a noisy @xmath0 medium . we solve this equation numerically assuming a coherent state as an initial condition . we discuss first an ideal and then a dissipative kerr medium . the results obtained for the ideal case reveal the quantum nature of the state under evolution . the coherent state , known as the most classical among all the pure states , becomes a non - gaussian squeezed state after some time of interaction with the medium . for some specific times it becomes a finite superposition of other coherent states . an interference pattern with the negative values is clearly visible on the plots of its wigner function . due to the small value of the @xmath0 nonlinearity and losses in optical fibers such phenomena have never been observed for light ; neither for any other system . however , it turns out that not all quantum effects are washed out due to the decoherence . the fokker - planck equation allows for a similar state evolution analysis for any other input state . the paper is organized as follows : in section [ fs ] the fokker - planck equation for the wigner function evolution in a @xmath0 medium is derived from the master equation obtained for a single mode of light density operator . the equation is displayed in a polar coordinates . the decoherence effects : losses and thermal noise are included . the initial and boundary conditions for the wigner function are set . in section [ ss ] the numerical results of the wigner function evolution in a nondissipative @xmath0 medium are introduced and discussed . these results are obtained using three independent methods : computing the fokker - planck equation and the other two equations determining the wigner function directly , which are obtained from its definition . correspondence between the wigner function negative values and zeros of the q - function is noted . in section [ ts ] the influence of the decoherence process on quantum effects such as the interference pattern and the negative values of the wigner function is analyzed . the technical limitations on the use of the fokker - planck equation are discussed . the wigner function sub - planck structure is shown in section [ sub ] . in section [ fos ] the numerical methods used in sections [ ss ] and [ ts ] are compared and discussed . finally some conclusions are presented .

a fokker - planck equation for the wigner function evolution in a noisy kerr medium ( @xmath0 non - linearity ) is presented . we numerically solved this equation taking a coherent state as an initial condition . the dissipation effects are discussed . the results also apply to the description of a nanomechanical resonator with an intrinsic duffing nonlinearity .

a fokker - planck equation for the wigner function evolution in a noisy kerr medium ( @xmath0 non - linearity ) is presented . we numerically solved this equation taking a coherent state as an initial condition . the dissipation effects are discussed . we provide examples of quantum interference , sub - planck phase space structures , and gaussian versus non - gaussian dynamical evolution of the state . the results also apply to the description of a nanomechanical resonator with an intrinsic duffing nonlinearity .

1104.3516

c

we have presented an efficient parallel version of a contact dynamics method in this work , which allows for large - scale granular simulations with almost @xmath0 efficiency . we aimed at the full parallelization of the code with hierarchical domain decomposition and dynamic load balancing , in which the interface area between subdomains is also minimized . the parallel code is hence applicable to a broad range of densities and different simulation conditions . the force calculation in cd is done by an iterative scheme , which shows an instability if more than about half of the contacts are calculated in parallel . the iteration scheme was kept domain - wise sequential while data across the domain boundaries is exchanged after each iteration sweep , ensuring that the iteration is stable for all system sizes . it is known that the cd iterative scheme approaches the solution in a diffusive manner . the diffusion constant is smaller for parallel update , which happens at domain boundaries . however , this overhead is proportional to the square root of the number of processors divided by the number of particles ( in 2d ) , which vanishes for large systems . regarding this as the only impact of the parallelization on the convergence , it must be expected that the efficiency is not affected by modifications at the local level i.e. non - spherical particles , three - dimensional particles , more sophisticated contact laws , etc . of course , those can deteriorate the convergence per se but the parallel version will simply `` inherit '' that . the other point of discussion raised here concerns the choice of the mesh size and adjusting the subdomain borders to it . communication overhead was reduced because between iteration steps not all boundary information is sent but only the relevant part of it . the subdomain wall position is only important if the particle size is not small compared to the system size . for large scale parallel applications this can only be a problem for highly polydisperse systems , for which the cell method for contact detection breaks down anyway . the load balancing is done only at the end of each time step . our investigations show that this happens rarely enough that load balancing overhead and cpu time fluctuations are negligible but often enough to achieve fast load balance . we used a global criterion for stopping the iteration scheme . this ensures that the physical properties of the tested samples do not show any difference compared to the non - parallel version of the code . blocking point - to - point communications were used to transfer data among processors . since our algorithm needs synchronization after each iteration , non - blocking data transfer would not be advantageous . the whole amount of data is transmitted in one single packet , which reduces communication overhead over the pure data . this method introduces parallel contact update at domain boundaries , which induces an iteration number overhead due to the lower diffusivity of the information in parallel update . this overhead vanishes , e.g. with the square root of the processor number over particle number in two dimensions , which is in general negligible . an alternative method would be to use non - blocking communications for the iteration scheme , namely to immediately send a freshly updated contact force in the vicinity of the borders to the corresponding processors , while on the other side this would trigger an interrupt when the other processor immediately updates the received contact data . this prevents the mixture of sequential and parallel update schemes . however , we do not expect that the performance of the method is greatly enhanced by the use of non - blocking communication because the information of each contact force is sent individually and the overhead associated with the increase of the inter - processor communications significantly affects the performance . the last point to discuss concerns the load balancing method . the most exact method would be to consider the number of particles and/or contacts in each subdomain to calculate their new boundaries . practically , this would cause difficulties , since each processor is just aware of particles and contacts within its own borders . the amount of calculations and communications between neighboring processors to place the interface according to the current contact and particle positions would make the load balancing a computationally expensive process . this lead us to balance the load further by dividing the simulation domain according to the current subdomain volumes ( not always proportional to the number of particles and/or contacts ) , which is in fact a control loop with the inherent problems of under- and over - damping .

a fully parallel version of the contact dynamics ( cd ) method is presented in this paper . for large enough systems , @xmath0 efficiency has been demonstrated for up to @xmath1 processors using a hierarchical domain decomposition with dynamic load balancing . the iterative scheme to calculate the contact forces is left domain - wise sequential , with data exchange after each iteration step , which ensures its stability . the number of additional iterations required for convergence by the partially parallel updates at the domain boundaries becomes negligible with increasing number of particles , which allows for an effective parallelization .

a fully parallel version of the contact dynamics ( cd ) method is presented in this paper . for large enough systems , @xmath0 efficiency has been demonstrated for up to @xmath1 processors using a hierarchical domain decomposition with dynamic load balancing . the iterative scheme to calculate the contact forces is left domain - wise sequential , with data exchange after each iteration step , which ensures its stability . the number of additional iterations required for convergence by the partially parallel updates at the domain boundaries becomes negligible with increasing number of particles , which allows for an effective parallelization . compared to the sequential implementation , we found no influence of the parallelization on simulation results . contact dynamics method , granular materials , hierarchical domain decomposition , load balancing , mpi library 45.70.-n , 02.70.-c , 45.10.-b