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1412.8007

i

to securing communications through the use of information theoretic notions was started by shannon in the 1940 s . in his papers he related fundamental notions , such as entropy , to the secrecy of cryptographic systems @xcite . inspired by the work of shannon , wyner published a paper proving that it was theoretically possible to secure communications solely through the choice of an encoding scheme for a specific channel model @xcite . wyner s security model capitalizes on the eavesdropper receiving a noisier copy of what the intended user receives . in general , for communications security , assumptions on the capabilities of eavesdroppers are required to design systems . in wyner s paper , the presumption is on the channel noise of the eavesdropper . on the other hand , in contemporary cryptography it is assumed that the eavesdropper is subject to certain computational limitations . it is accepted that many people have attempted to break a cryptosystem , and their best efforts to recover plaintext require an infeasible amount of time . in particular , the computational complexity of factoring products of primes is unknown , although it is widely accepted to be a hard problem . thus the only guarantee of the security of these systems is that numerous people have attempted to attack the system and have not succeeded . the question for physical layer security is what circumstances will allow similar conclusions about the eavesdropper s capabilities as in cryptography . in physical layer security , channel noise combined with a special encoder provide the security . thus for wyner s method , how can one ensure that the eavesdropper s channel has specific noise characteristics , thus limiting his / her decoding capabilities ? the goal in this paper is to work with a well - studied channel model , and gradually relax restrictions on the eavesdropper s capabilities . as these relaxations are made , the effect on the security of the system will be evaluated . we will show that if the real channel characteristics deviate even slightly from the assumptions , all guarantees of security are lost . since in a practical system , no assumptions ( either on the intended user s or the eavesdropper s channel ) are verifiable , we can not claim @xmath0 security . the intended users rarely have control over the eavesdropper s access ( especially in the wireless setting ) or the eavesdropper s behavior , so basing a security system on questionable assumptions is risky . on the other hand , wyner s basic idea can be easily combined with cryptographic methods to achieve a secure system based on computationally intractable problems . for example , we can artificially create a channel that is information - theoretically secure under the assumption that the shared key can not be recovered , i.e. , the recovery of the key is computationally intractable . the paper is organized as follows . in section ii , the channel model is presented . the general results for wiretap coding and achieving secrecy are discussed in section iii . section iv quantifies the amount of secrecy lost when the eavesdropper has better access than anticipated . in section v , a shared key cryptosystem is presented from mihaljevic@xcite , that sets the path for a more general method of combining stochastic encoding with computationally intractable problems . the notation for this paper is as follows . random variables will be represented by uppercase letters ( @xmath1 ) , and their instances by lower case letters ( @xmath2 ) . caligraphic uppercase letters will represent the domain of the corresponding random variable ( @xmath3 ) . since we will consider a sequence of codes , @xmath4 , we will use a @xmath5 subscript to denote the corresponding parameters , i.e. , @xmath4 will have rate @xmath6 .

this paper highlights security issues that can arise when incorrect assumptions are made on the capabilities of an eavesdropper . in particular , we analyze a channel model based on a split binary symmetric channel ( bsc ) . corresponding security parameters are chosen based on this channel model , and assumptions on the eavesdroppers capabilities . a gradual relaxation of the restrictions on the eavesdropper s capabilities will be made , and the resulting loss of security will be quantified .

this paper highlights security issues that can arise when incorrect assumptions are made on the capabilities of an eavesdropper . in particular , we analyze a channel model based on a split binary symmetric channel ( bsc ) . corresponding security parameters are chosen based on this channel model , and assumptions on the eavesdroppers capabilities . a gradual relaxation of the restrictions on the eavesdropper s capabilities will be made , and the resulting loss of security will be quantified . an alternative will then be presented that is based on stochastic encoding and creating artificially noisy channels through the usage of private keys . the artificial channel will be constructed through a deterministic process that will be computationally intractable to reverse .

0905.2879

i

the recent surge of interest in hamiltonians which , although non - hermitian , nevertheless have a completely real spectrum began with the pioneering paper of bender and boettcher @xcite , which gave strong numerical and analytical evidence that the spectrum of the class of hamiltonians [ m=1 ] h = p^2 -(ix)^n was completely real and positive for @xmath1 , and attributed this reality to the ( unbroken ) @xmath0 symmetry of the hamiltonian . since then a large number of @xmath0 -symmetric models have been explored ( see , e.g. , @xcite ) , and it was found that the phenomenon is rather general . the natural metric arising in such theories is not positive definite , which precludes a straightforward physical interpretation in terms of probability amplitudes . however , it turns out to be possible to construct @xcite a grading operator @xmath2 , which gives a positive - definite metric @xmath3 . in contrast to standard quantum mechanics , where the metric is the same for any hermitian theory , here the metric is determined in each case by the hamiltonian itself . in the schrdinger wave - function formulation of quantum mechanics , this metric appears explicitly in the calculation of green functions ; however , in the path - integral of functional formulation its role is much more subtle @xcite . the class of hamiltonians ( [ m=1 ] ) can be thought of as a continuation in the exponent of the potential , starting with the harmonic oscillator , @xmath4 . a more general class of hamiltonians @xcite is obtained by continuation off the @xmath5 oscillator : @xmath6 where @xmath7 ; @xmath8 . they include the harmonic oscillator @xmath9 ( @xmath10 , @xmath11 ) , and non - hermitian hamiltonians such as @xmath12 ( @xmath10 , @xmath13 ) , @xmath14 ( @xmath10 , @xmath15 ) and @xmath16 ( @xmath17 , @xmath15 ) . the eigenvalue equation corresponding to ( [ m<>1 ] ) is -_n(x)+x^2m(ix)^_n(x)=e_n(x ) [ sequation ] ( throughout the text , @xmath18 ) , where @xmath19 is required to vanish as @xmath20 . as explained in @xcite , when the total exponent @xmath21 is greater than 4 the boundary condition can no longer be satisfied with @xmath22 real , and one is obliged to analytically continue the eigenvalue equation ( [ sequation ] ) into the complex plane . specifically it should be continued into the lower half @xmath22 plane within a stokes wedge symmetrically placed with respect to the imaginary axis and @xmath16 are in fact non - hermitian and @xmath0-symmetric . ] . when this is done , the energy spectrum turns out to be real , discrete and positive @xcite . a rigorous proof of this property was eventually constructed by dorey et al . @xcite . for reviews of the whole field of non - hermitian hamiltonians see @xcite . in principle it is possible @xcite to relate @xmath23 by a similarity transformation to an equivalent hermitian hamiltonian @xmath24 with the same energy spectrum . however , such a programme is difficult to implement , and an exact form for @xmath24 is available only in very few cases . it should be stressed that , unlike ( [ sequation ] ) , the eigenvalue equation corresponding to @xmath24 can always be solved on the real axis . possible physical applications of these unusual hamiltonians are beginning to emerge . we mention here the quantum brachistochrone " , in which the standard lower bound for the transition time between two states can be circumvented @xcite by a judicious interplay of hermitian and non - hermitian systems . how this could be achieved in practice has been recently discussed in @xcite . in analogue optical situations , where the refractive index plays the role of the potential , pt - symmetric systems have been shown to have unusual and interesting properties @xcite . perhaps surprisingly , little attention has been paid so far to the thermodynamics of such systems . in the present paper we investigate the thermodynamics of the hamiltonians of ( [ m<>1 ] ) , which we hope will act as a template for the investigation of other non - hermitian systems . as far as the quantum partition thermodynamics is concerned we need only calculate the energy levels , on which the partition function depends . the high - temperature limit then probes the classical mechanics of these systems , and we use this to investigate how the classical partition function should be defined , which is not obvious _ a priori_. the paper is organized as follows . in sec . [ spectrum ] we show that the energies @xmath25 of ( [ sequation ] ) can be estimated to a high degree of accuracy , even for small values of @xmath26 , using the wkb approximation including the subleading contribution . in sec . [ qmechanics ] we use the energy levels so determined to evaluate numerically the canonical partition function , which then yields plots illustrating the thermal behavior of the entropy and the specific heat , at low , intermediate and high temperatures . the plots also show how the parameters @xmath27 and @xmath28 affect these quantities . in the high - temperature limit , still using the wkb formula for @xmath25 , we obtain a closed formula for the semiclassical partition function by integration over @xmath26 . this is then used , in sec . [ cmechanics ] , as a tool for investigating how the semiclassical partition function @xmath29 associated with @xmath23 in ( [ m<>1 ] ) should be expressed as a phase - space " integral . in general this must differ from the usual real phase - space integral , which does not converge . the special case @xmath30 ( the wrong - sign quartic oscillator ) is ideal for testing these ideas , because in this case one has an explicit form for the equivalent isospectral hermitian hamiltonian @xmath24 . thus one can start by calculating the semiclassical partition function using the real phase space associated with @xmath24 , and then transform the variables to find the correct integral expression for @xmath29 in terms of the variables appearing in @xmath23 . [ disc ] includes a summary and further discussion .

graphs showing the thermal behavior of the entropy and the specific heat , at all regimes of temperature , are given . to obtain the corresponding classical partition function it turns out to be necessary in general to integrate over a complex phase space " . for the wrong - sign quartic , whose equivalent hermitian hamiltonian is known exactly , it is demonstrated explicitly how this formulation arises , starting from the hermitian case .

this paper investigates the thermodynamics of a large class of non - hermitian , @xmath0-symmetric oscillators , whose energy spectrum is entirely real . the spectrum is estimated by second - order wkb approximation , which turns out to be very accurate even for small quantum numbers , and used to generate the quantum partition function . graphs showing the thermal behavior of the entropy and the specific heat , at all regimes of temperature , are given . to obtain the corresponding classical partition function it turns out to be necessary in general to integrate over a complex phase space " . for the wrong - sign quartic , whose equivalent hermitian hamiltonian is known exactly , it is demonstrated explicitly how this formulation arises , starting from the hermitian case .

1211.6823

c

lhc is expected to confirm if there is a new particle at 125 gev by the end of this year . the likelihood for a new discovery is rather high . nevertheless , whether this new particle is the sm higgs boson is not an easy question to answer . here the scenario of this 125 gev particle produced by vector - boson fusion , instead of gluon fusion as the dominant production mechanism for the standard model higgs boson , is studied in details . by using the forward dijet tagging technique , one can single out the vector - boson fusion mechanism . we studied a number of popular new physics models that have been employed to interpret the observed particle at 125 gev , including fermiophobic higgs boson , the randall - sundrum radion , inert - higgs - doublet model , two - higgs - doublet model , and the mssm . since the inclusive diphoton channel showed an excess over the sm predictions , we first selected the parameter space of each model that can give an inclusive diphoton rate larger than or equal to the sm rate . then , we calculate the exclusive @xmath22 diphoton production rate in vbf for that parameter space . if the diphoton mode excess seen at lhc-7 can be firmly established by the new lhc-8 data , it will be the utmost task to identify the nature of this particle . perhaps , it is simply the sm higgs boson with some level of statistical fluctuation , but it could also be the rs radion @xcite , fermiophobic higgs boson @xcite , the light cp - even higgs boson of the 2hdm @xcite , the higgs boson of the ihdm @xcite , or one of the cp - even higgs bosons in other extensions of the mssm @xcite , all of which can allow an enhancement to the @xmath8 production rate . on the other hand , the vector - boson fusion , as singled out by the dijet tag , provides useful information in helping to differentiate among various models . it is not hard by browsing through fig . [ ratio ] to conclude the following * if a similar rate is seen in inclusive production but no large excess is seen in the exclusive vbf production it would unlikely be a fermiophobic higgs boson . * if a similar rate or excess is seen in inclusive production but some events are seen in exclusive vbf production rate , it would unlikely be the rs radion . * if moderate excess is seen in both inclusive production and exclusive vbf production , it could be the higgs boson of the ihdm , 2hdm , or the mssm . however , if the excess is over 60% it will pose severe challenge to the mssm . it seems easy to rule out either fermiophobic higgs boson or rs radion , providing that we see no large excess or some events in vbf channel , respectively . however , it is still difficult to distinguish the other models when the inclusive and exclusive rates are similar to or slightly larger than the sm values . if the production rate of the diphoton mode at 125 gev lines up with the sm prediction eventually , it is still premature to conclude this is coming from the sm higgs boson . other alternatives in mssm , nmssm , or other susy models can also be mimicking the sm higgs boson , depending on the parameter space of the new physics model . in any case , once the signals at 125 gev are confirmed further studies including all possible decay modes are to be taken into account in order to discriminate these many alternatives beyond the standard model . vector - boson fusion is the next most important production mechanism that must be taken into account to fully identify the newly discovered particle .

, the alternative vector - boson fusion is more sensitive to electroweak symmetry breaking . using the well known dijet - tagging technique to single out the vector - boson fusion mechanism , we investigate potential of vector - boson fusion to discriminate a number of models suggested to give an enhanced inclusive diphoton production rate .

this review is based on the talk presented at the susy 2012 ( beijing ) . the new particle around 125 gev observed at the large hadron collider ( lhc ) is almost consistent with the standard model higgs boson , except that the diphoton decay mode may be excessive . we summarize a number of possibilities . while at the lhc the dominant production mechanism for the higgs boson of the standard model and some other extensions is via the gluon fusion process , the alternative vector - boson fusion is more sensitive to electroweak symmetry breaking . using the well known dijet - tagging technique to single out the vector - boson fusion mechanism , we investigate potential of vector - boson fusion to discriminate a number of models suggested to give an enhanced inclusive diphoton production rate .

1410.2788

i

analysis of the underlying biomolecular solvation is critical when carrying out quantitative descriptions of various important biological processes at the atomic level , such as protein folding and protein ligand bonding , dna recognition , transcription , and translation . from a biological perspective , solvation analysis is concerned with interactions between a solute macromolecule and surrounding solvent ions . from a mathematical perspective , these solute - solvent interactions may be represented via solvation energies with contributions from polar and nonpolar sources . the polar portion arises from electrostatic interactions , which may be represented with the poisson - boltzmann ( pb ) model @xcite . the pb model provides a framework by which to model the distribution of electrostatic potential along the surface of a solute macromolecule within a surrounding solvent with a particular ionic concentration . in the pb model , the pb equation governing electrostatic potentials takes the form of a nonlinear elliptic equation on multiple domains with discontinuous dielectric coefficients across the molecular surface or solute - solvent interface @xcite . the pb equation can not be solved analytically for molecules with complex geometries , only admitting analytical solutions for shapes such as spheres or rods @xcite . however , solving the pb equation numerically also presents significant difficulties because of the discontinuous dielectric coefficients , singularities in the source - term , non - smoothness of the solution , and significant nonlinearity when strong ionic effects are present . recently , a pseudo - transient continuation approach has been proposed for solving the nonlinear pb ( npb ) equation @xcite , which creates a different way to tackle the nonlinear term of the npb equation . in classical finite difference and finite element solutions of the npb equation , a nonlinear algebraic system is typically formed through the discretization of the boundary value problem . a nonlinear relaxation method @xcite or inexact newton method @xcite can be employed to solve such a nonlinear system . in the pseudo - transient continuation approach @xcite , a pseudo - time derivative is added to the npb equation so that one solves an initial - boundary value problem now . the steady state solution of this problem gives rise to the solution to the original boundary value problem . numerically , it is desired that a large time step can be used so that the long time integration can be computed quickly . thus , the efficiency of a pseudo - time npb solver is directly related to its stability , which critically depends on the nonlinear term of the npb equation a hyperbolic sine function that could be exponentially large . several time stepping schemes have been considered for solving the time dependent npb equation . the explicit euler solution is straightforward , but invokes a severe stability constraint @xcite . implicit time integrations have also been studied @xcite , for which care has to be exercised in handling the nonlinear term . in @xcite , a linearization technique based on the first order taylor expansion is proposed so that a linear system is formed at each step of the implicit euler integration . this linearization essentially evaluates the nonlinear term at the previous time instant . similarly , by treating the nonlinear term explicitly , a regularized alternating direction implicit ( adi ) method has been introduced in @xcite . since the thomas algorithm @xcite can be employed to solve the tridiagonal finite difference systems in this time splitting method , the efficiency is greatly improved . however , a very large time increment is still prohibited in these methods , because these implicit schemes are of semi - implicit nature . more recently , we have successfully developed two fully - implicit adi schemes @xcite for solving the time dependent npb equation . the success lies in an analytical integration of the nonlinear term , and the use of a time splitting framework . this completely suppresses the nonlinear instability , so that these fully - implicit adi schemes are unconditionally stable in solving benchmark problems with smooth solutions . however , for the solvation analysis in applications to real biomolecules , these adi schemes are still conditionally stable , probably because the underlying electrostatic potentials are non - smooth . nevertheless , these fully - implicit adi schemes are still found to be quite efficient , due to their high temporal accuracy and much relaxed courant - friedrich - lewy ( cfl ) constraints @xcite . the objective of this paper is to introduce and investigate various new operator splitting methods for solving the time dependent npb equation . the present investigation will be conducted in the same pseudo - transient continuation framework as in @xcite . in particular , in spatial approximation , central finite difference will be employed to discretize the nonhomogeneous diffusion operator , which yields tridiagonal matrices in all dimension - splitting schemes . in temporal approximation , the analytical integration will be carried out for the split nonlinear subsystem . the ultimate goal of this work is to eventually construct unconditionally stable operator splitting methods for solving the npb equation in practical biomolecular applications . in the existing fully - implicit operator splitting npb solvers @xcite , the adi schemes are constructed based on the classical adi schemes @xcite . in the literature , there exists another family of multiplicative operator splitting methods , i.e. , the fractional step methods or locally one - dimensional ( lod ) methods , originally introduced by russian mathematicians @xcite . in the present setup , the adi discretizations can be written as some perturbations of multidimensional discretizations of the implicit methods , such as the crank - nicolson and backward euler . in the proposed lod methods , the similar splitting in alternating directions will be considered , but before the time discretization . in other words , the crank - nicolson and backward euler discretizations will be conducted after the differential equations are split . thus , the discretizations of the lod methods are truly one - dimensional . this is different from the adi methods , in which the right - hand side of the discretized equations contains derivatives from the other directions . comparing with the adi methods , the lod methods tend to be more stable , but have a larger splitting error @xcite . moreover , a previous work on the application of adi and lod schemes to maxwell s equations in isotropic and lossless media found that the lod schemes were approximately 20% computationally less expensive than the adi schemes @xcite . other comparisons of lod schemes and traditional adi schemes as applied to maxwell s equations have also found lower computational costs for the lod methods over adi methods @xcite . this motivates us to develop several lod schemes for solving the time dependent npb equation in this work . besides the adi and lod methods , there exists another family of operator splitting methods , i.e. , the additive operator splitting ( aos ) methods @xcite . in the aos methods , the time integration of each split subsystem can be independently carried out , while in the multiplicative operator splitting methods , the integration of the present fractional step needs the solution from the previous fractional steps . thus , the aos methods are well suited to be implemented in parallel processors . the stability and accuracy of the aos methods have been analyzed in @xcite . the application of additive operator splitting ( aos ) schemes has proved popular for the purposes of nonlinear diffusion filtering for image processing @xcite . the aos schemes are usually efficient and stable for relatively large @xmath0 values , although potentially less accurate than the lod schemes . however , their overall efficiency and simplicity merit further exploration . in the present paper , different formulations and discretizations of the aos methods for solving time dependent npb equation will be considered . previous work in image processing has also explored the properties of schemes combining multiplicative and additive operator splitting , finding higher levels of accuracy with such schemes than with simpler aos methods @xcite . we thus will also explore the construction and application of a multiplicative - additive operator splitting ( maos ) scheme for our current problem . the rest of this paper is organized as follows . in section [ sec.problem ] , we first introduce the physical background of the problem . the pseudo - transient pb model will then be presented . the existing adi schemes will be described and the remaining difficulties are discussed . the proposed operator splitting schemes will then be formulated for solving the time dependent npb equation in section [ sec.method ] . numerical validations of the proposed schemes through benchmark examples with analytical solutions are considered in section [ sec.validation ] , while various benchmark biological systems and subsequent free energy of solvation calculations are presented in section [ sec.application ] . finally , this paper ends with a conclusion .

this work introduces novel unconditionally stable operator splitting methods for solving the time dependent nonlinear poisson - boltzmann ( npb ) equation for the electrostatic analysis of solvated biomolecules . in a pseudo - transient continuation solution of the npb equation , the proposed schemes become much more stable than the adi methods , and some of them are indeed unconditionally stable in dealing with solvated proteins with source singularities and non - smooth solutions . numerically * msc : * 65m06 , 92 - 08 , 92c40 ,

this work introduces novel unconditionally stable operator splitting methods for solving the time dependent nonlinear poisson - boltzmann ( npb ) equation for the electrostatic analysis of solvated biomolecules . in a pseudo - transient continuation solution of the npb equation , a long time integration is needed to reach the steady state . this calls for time stepping schemes that are stable and accurate for large time increments . the existing alternating direction implicit ( adi ) methods for the npb equation are known to be conditionally stable , although being fully implicit . to overcome this difficulty , we propose several new operator splitting schemes , in both multiplicative and additive styles , including locally one - dimensional ( lod ) schemes and additive operator splitting ( aos ) schemes . the nonlinear term is integrated analytically in these schemes , while standard discretizations with finite differences in space and implicit time integrations are used . the proposed schemes become much more stable than the adi methods , and some of them are indeed unconditionally stable in dealing with solvated proteins with source singularities and non - smooth solutions . numerically , the orders of convergence in both space and time are found to be one . nevertheless , the precision in calculating the electrostatic free energy is low , unless a small time increment is used . further accuracy improvements are thus considered , through constructing a richardson extrapolation procedure and a tailored recovery scheme that replaces the fast fourier transform method by the operator splitting method in the vacuum case . after acceleration , the optimized lod method can produce a reliable energy estimate by integrating for a small and fixed number of time steps . since one only needs to solve a tridiagonal linear system in each independent one dimensional process , the overall computation is very efficient . the unconditionally stable lod method scales linearly with respect to the number of atoms in the protein studies , and is over 20 times faster than the conditionally stable adi methods . * keyword : * nonlinear poisson - boltzmann equation ; pseudo - transient continuation approach ; time splitting ; alternating direction implicit ( adi ) ; locally one dimensional ( lod ) ; additive operator splitting ( aos ) ; electrostatic free energy . * msc : * 65m06 , 92 - 08 , 92c40 ,

1410.2788

c

this paper presents the first unconditionally stable numerical scheme for solving the nonlinear poisson - boltzmann ( npb ) equation in a pseudo - transient approach . using this approach , the solution to the npb equation is recovered from the steady state solution to the time dependent pseudo - transient form . however , due to the long time integration of the process , it is necessary to develop numerical schemes that are stable and accurate for large time increments . the alternating direction implicit ( adi ) methods previously developed for solving the time dependent npb equation @xcite are fully implicit , but are still conditionally stable . to construct unconditionally stable solution of the unsteady npb equation , we consider various operator splitting procedures to all five terms of the npb equation , in both multiplicative and additive styles . this gives rise to locally one - dimensional ( lod ) schemes , additive operator splitting ( aos ) schemes , and multiplicative - additive operator splitting ( maos ) scheme . in these schemes , the nonlinear term is analytically integrated , and both implicit euler and crank - nicholson time integrations are formulated . a standard finite difference scheme is utilized for spatial discretization in all schemes . extensive numerical experiments are conducted to verify the unconditional stability and accuracy of the proposed time splitting schemes . one lod scheme is found to outperform other schemes in terms of both stability and accuracy , and is recommended for electrostatic free energy analysis of real proteins . further improvements are introduced to enhance the accuracy and efficiency of this lod scheme for a fast biomolecular simulation . * * stability . * for smooth solution , all proposed time splitting methods should be unconditionally stable , because each individual implicit euler or crank - nicolson time integration with central difference approximation is unconditionally stable . a major task in our numerical experiments is to verify the stability for non - smooth solutions . in case of a simple spherical cavity test , these methods remain unconditionally stable . for real protein systems , only the lodie methods are stable for any @xmath0 . some proposed methods , such as aosie1 , aoscn1 , and lodcn methods , become conditionally stable , while other methods , such as aosie2 , aoscn2 , maos methods , are stable for all @xmath150 . overall , the stability constraints of the proposed time splitting methods are much improved in comparing with the existing adi methods . the lodie method is the most stable method . * * accuracy . * because the charge singularities ( the delta functions ) and the non - smoothness of the solution across the interface @xmath1 are treated in an approximate sense in the present central difference discretization , all numerical schemes achieve roughly the first - order convergence in space . all proposed time splitting methods are of first order accuracy in time , because the underlying time splitting is first order and the discretization error of the implicit euler or crank - nicolson integration is at least first order . however , as shown in protein tests , a very small @xmath0 has to be used in order to produce an accurate estimate of electrostatic free energy . a richardson extrapolation technique and a recovery based on the replacement of the fast fourier transform method by the operator splitting method are proposed to significantly improve the precision in energy calculations . the accelerated lodie method becomes biologically useful , with a large @xmath151 and a stopping time @xmath152 . * * efficiency . * by using central difference discretization , the resulting linear systems in each alternating direction are tridiagonal , and can be efficiently solved via the thomas algorithm @xcite . without the loss of generality , we can assume that the numbers of grid nodes along @xmath39 , @xmath40 and @xmath41 directions are all on the order @xmath153 . then , the linear system in each subsystem of the time splitting procedure has the dimensions @xmath154 . the thomas algorithm solution of such a system has a complexity on the order of @xmath155 , so that the operations for calculating one time step in the proposed time splitting methods are on the order of @xmath156 . since a fixed number of total time steps is used in the lodie solution , the overall complexity of the proposed lodie method is still @xmath156 , making this method very attractive to large protein systems . as demonstrated in our cpu tests , the lodie method scales linearly with respect to the number of atoms of the protein . on average , the unconditionally stable lodie method is over 20 times more efficient than the conditionally stable adi methods for large proteins . it is of great interest to further generalize the proposed time splitting methods by considering other numerical difficulties associated with the npb equation . a regularization procedure to treat the source singularities is under our investigation . the use of a different molecular surface definition will also be examined . the stability proof of the proposed operator splitting methods remains to be an open question , mainly due to the nonlinear hyperbolic sine term . t. lu , p. neittaanmaki , and x .- c . tai , a parallel splitting up method for partial differential equations and its application to navier - stokes equations , _ rairo math . model numer . _ , * 26 * , 673 - 708 , ( 1992 ) . shestakov , j.l . milovich , and a. noy , solution of the nonlinear poisson - boltzmann equation using pseudo - transient continuation and the finite element method , _ j. colloid interface sci . _ , * 247 * , 62 - 79 , ( 2002 ) .

this calls for time stepping schemes that are stable and accurate for large time increments . the existing alternating direction implicit ( adi ) methods for the npb equation are known to be conditionally stable , although being fully implicit . to overcome this difficulty , we propose several new operator splitting schemes , in both multiplicative and additive styles , including locally one - dimensional ( lod ) schemes and additive operator splitting ( aos ) schemes . the nonlinear term is integrated analytically in these schemes , while standard discretizations with finite differences in space and implicit time integrations are used . , the orders of convergence in both space and time are found to be one . nevertheless , the precision in calculating the electrostatic free energy is low , unless a small time increment is used . further accuracy improvements are thus considered , through constructing a richardson extrapolation procedure and a tailored recovery scheme that replaces the fast fourier transform method by the operator splitting method in the vacuum case . after acceleration , the optimized lod method can produce a reliable energy estimate by integrating for a small and fixed number of time steps . since one only needs to solve a tridiagonal linear system in each independent one dimensional process , the overall computation is very efficient . the unconditionally stable lod method scales linearly with respect to the number of atoms in the protein studies , and is over 20 times faster than the conditionally stable adi methods . * keyword : * nonlinear poisson - boltzmann equation ; pseudo - transient continuation approach ; time splitting ; alternating direction implicit ( adi ) ; locally one dimensional ( lod ) ; additive operator splitting ( aos ) ; electrostatic free energy .

this work introduces novel unconditionally stable operator splitting methods for solving the time dependent nonlinear poisson - boltzmann ( npb ) equation for the electrostatic analysis of solvated biomolecules . in a pseudo - transient continuation solution of the npb equation , a long time integration is needed to reach the steady state . this calls for time stepping schemes that are stable and accurate for large time increments . the existing alternating direction implicit ( adi ) methods for the npb equation are known to be conditionally stable , although being fully implicit . to overcome this difficulty , we propose several new operator splitting schemes , in both multiplicative and additive styles , including locally one - dimensional ( lod ) schemes and additive operator splitting ( aos ) schemes . the nonlinear term is integrated analytically in these schemes , while standard discretizations with finite differences in space and implicit time integrations are used . the proposed schemes become much more stable than the adi methods , and some of them are indeed unconditionally stable in dealing with solvated proteins with source singularities and non - smooth solutions . numerically , the orders of convergence in both space and time are found to be one . nevertheless , the precision in calculating the electrostatic free energy is low , unless a small time increment is used . further accuracy improvements are thus considered , through constructing a richardson extrapolation procedure and a tailored recovery scheme that replaces the fast fourier transform method by the operator splitting method in the vacuum case . after acceleration , the optimized lod method can produce a reliable energy estimate by integrating for a small and fixed number of time steps . since one only needs to solve a tridiagonal linear system in each independent one dimensional process , the overall computation is very efficient . the unconditionally stable lod method scales linearly with respect to the number of atoms in the protein studies , and is over 20 times faster than the conditionally stable adi methods . * keyword : * nonlinear poisson - boltzmann equation ; pseudo - transient continuation approach ; time splitting ; alternating direction implicit ( adi ) ; locally one dimensional ( lod ) ; additive operator splitting ( aos ) ; electrostatic free energy . * msc : * 65m06 , 92 - 08 , 92c40 ,

astro-ph0501458

i

the traditional cosmology has been revolutionized by modern sophisticated observation techniques in distant type ia supernovae ( sne ia ) ( e.g. riess et al . 1998 ; schmidt et al . 1998 ; perlmutter et al . 1999 ) , cosmic microwave background ( cmb ) fluctuations ( e.g. bennett et al . 2003 ; spergel et al . 2003 ) , and large - scale structure ( lss ) ( e.g. allen et al . 2003 ; tegmark et al . each type of cosmological data trends to play an unique role in measuring cosmology . in modern cosmology , it has been convincingly suggested that the global mass - energy budget of the universe , and thus its dynamics , is dominated by a dark energy component , and that the currently accelerating universe has once been decelerating ( e.g. , riess et al . the cosmography and the nature of dark energy as well as its evolution with redshift are one of the most important issues in physics and astronomy today . gamma - ray bursts ( grbs ) are the most intense explosions observed so far . they are believed to be detectable up to a very high redshift ( lamb & reichart 2000 ; ciardi & loeb 2000 ; bromm & loeb 2002 ; gou et al . 2004 ) , and their high energy photons are almost immune to dust extinction . these advantages would make grbs an attractive cosmic probe . from the isotropic - equivalent peak luminosity @xmath14variability ( or spectral lag ) relation ( fenimore & ramirez - ruiz 2000 ; norris , marani , & bonnell 2000 ) , the standard energy reservior @xmath1 of grb jets ( frail et al . 2001 ) , the @xmath14 peak energy @xmath2 of the @xmath3 spectrum in the burst frame relation ( lloyd - ronning & petrosian 2002 ; lloyd - ronning & ramirez - ruiz 2002 ; yonetoku et al . 2004 ) , the isotropic - equivalent energy @xmath15 relation ( amati et al . 2002 ) to the beaming - corrected energy @xmath4 relation ( ghirlanda et al . 2004a , ghirlanda relation hereafter ) , grbs are towards more and more standardizable candles . however , these relations in grbs have not been calibrated by a low-@xmath13 grb sample , so one should look for a method which is different from the `` classical hubble diagram '' method in sne ia . the luminosity relations with the variability and spectral lag make grbs a distance indicator in the same sense as cepheids and sne ia , in which an observed light - curve property can yield an apparent distance modulus ( dm ) . schaefer ( 2003 ) considered these two relations for nine bursts with known redshifts and advocated a new cosmographic method ( hereafter method i ) for grbs . in method i , one first calibrates the two relations with the observed sample for a certain cosmology , and then applies the best - fit relations back to the observed sample to obtain a @xmath16 or a probability @xmath17 for this cosmology . similar to the brightness of sne ia , the energy reserviors in grb jets are also clustered , but they are not fine enough for precise cosmology ( bloom et al . amati et al . ( 2002 ) found @xmath18 ( @xmath19 ) relation from 12 _ bepposax _ bursts . the _ hete-2 _ observations confirm this relation and extend it to x - ray flashes ( sakamoto et al . 2004a ; lamb et al . in addition , it also holds within a grb ( liang , dai & wu 2004 ) . the ghirlanda relation is written as @xmath20 , where @xmath21 and @xmath22 are dimensionless parameters . theoretical explanations of this relation include the standard synchrotron mechanism in relativistic shocks ( zhang & mszros 2002 ; dai & lu 2002 ) together with the afterglow jet model , or the emission from off - axis relativistic jets ( yamazaki , ioka & nakamura 2004 ; eichler & levinson 2004 ; levinson & eichler 2005 ) . this relation could also be understood due to comptonization of the thermal radiation flux that is advected from the base of an outflow in the dissipative photosphere model ( e.g. rees & mszros 2005 ) . if these explanations are true , the ghirlanda relation appears to be intrinsic . thus , dai , liang & xu ( 2004 ; dlx04 ) considered the ghirlanda relation for 12 bursts and proposed another cosmographic method ( hereafter method ii ) for grbs . in method ii , one makes marginalizations over the unknown parameters in the ghirlanda relation to obtain a @xmath16 or a probability @xmath17 for a certain cosmology . following schaefer s method , ghirlanda et al . ( 2004b ; gglf04 ) and friedman & bloom ( 2004 ; fb04 ) also investigated the same issue but used different grb data . recently , firmani et al . ( 2005 ; fgga05 ) considered the ghirlanda relation for 15 bursts and proposed a bayesian approach for the cosmological use ( hereafter method iii ) . in method iii , to obtain the probability for a certain cosmology , one considers contributions of all the possible @xmath4 relations associated with their unequal weights . the detailed procedures of the three methods are shown in @xmath23 , which indicate that method iii is the optimized one . as analyzed previously , due to the lack of low-@xmath13 grbs , methods i , ii and iii are different from the `` classic hubble diagram '' method in sne ia . in this paper , we investigate the constraints on cosmological parameters from the observed 17 grbs with different methods . because the present grb sample is a small one , it is necessary to use a large simulated sample , which may be established in the _ swift _ era , to discuss the cosmographic capabilities with different methods . this paper is arranged as follows . in @xmath24 , we describe our analytical methods and data . the results from the observed grb sample are presented in @xmath25 . in @xmath26 , we perform monte carlo simulations and analyze the results from the simulated grb sample . conclusions and discussion are presented in @xmath27 .

three different methods of measuring cosmology with gamma - ray bursts ( grbs ) have been proposed since a relation between the @xmath0-ray energy @xmath1 of a grb jet and the peak energy @xmath2 of the @xmath3 spectrum in the burst frame was reported by ghirlanda and coauthors . in method ii , to calculate the probability for some certain cosmology , contributions of all the possible @xmath4 relations that are best fitted for their corresponding cosmologies are taken into account . with this method to obtain the probability for some cosmology , contributions of all the possible @xmath4 relations associated with their unequal weights are considered . with this method , we obtain an inspiring constraint on the mass density @xmath9 ( @xmath6 ) for a flat universe , and a @xmath10 for the concordance model of @xmath11 .

three different methods of measuring cosmology with gamma - ray bursts ( grbs ) have been proposed since a relation between the @xmath0-ray energy @xmath1 of a grb jet and the peak energy @xmath2 of the @xmath3 spectrum in the burst frame was reported by ghirlanda and coauthors . in method i , to calculate the probability for a favored cosmology , only the contribution of the @xmath4 relation that is already best fitted for this cosmology is considered . we apply this method to a sample of 17 grbs , and obtain the mass density @xmath5 ( @xmath6 ) for a flat @xmath7cdm universe . in method ii , to calculate the probability for some certain cosmology , contributions of all the possible @xmath4 relations that are best fitted for their corresponding cosmologies are taken into account . with this method , we find a constraint on the mass density @xmath8 ( @xmath6 ) for a flat universe . in method iii , to obtain the probability for some cosmology , contributions of all the possible @xmath4 relations associated with their unequal weights are considered . with this method , we obtain an inspiring constraint on the mass density @xmath9 ( @xmath6 ) for a flat universe , and a @xmath10 for the concordance model of @xmath11 . compared with the previous two methods , method iii makes the observed 17 grbs place much more stringent confidence intervals at the same confidence levels . furthermore , we perform a monte carlo simulation and use a larger sample to investigate the cosmographic capabilities of grbs with different methods . we find that , a larger grb sample could be used to effectively measure cosmology , no matter whether the @xmath12 relation is calibrated by low-@xmath13 bursts or not . ongoing observations on grbs in the _ swift _ era are expected to make the cosmological utility of grbs progress from its babyhood into childhood .

nucl-th0307021

i

total ( complete + incomplete ) fusion excitation functions of @xmath0li on @xmath1co and @xmath2bi targets at coulomb barrier energies are obtained using full coupled channels calculations with a new cdcc method of calculating fusion , that has short - range fusion potentials for each fragment separately . the realistic prediction of total fusion cross sections requires the selection of an appropriate fusion model which depends on both the cluster structure of the weakly bound projectile and what the experiment is supposed to measure . the effect of breakup on fusion can be observed in the total fusion excitation function . the breakup enhances the total fusion of @xmath0li at energies just around the barrier , whereas it has very little effect on total fusion at energies well above the barrier . the fusion enhancement factor strongly depends on the decreasing incident energy below the barrier . the fusion enhancement is larger for the reaction with @xmath3li than that with @xmath6li , and it is correlated with the smaller @xmath34-breakup threshold of @xmath3li . the difference between the bound - state structures of @xmath0li does not produce large difference between their total fusion excitation functions . the effect of the @xmath6li ground - state reorientation couplings on total fusion is very weak . a crude estimation reveals that the effect of target excitations on total fusion is weak and similar for @xmath0li . the experimental data for @xmath0li+@xmath1co as well as for @xmath3li+@xmath2bi are well reproduced . the breakup notably causes the difference between the experimental total fusion cross sections of @xmath0li on @xmath1co , but it is not the case for the @xmath2bi target . experiments focused on the deuteron and triton transfer cross sections are important to understand the difference between the total fusion of @xmath0li on @xmath2bi . work is in progress to study @xmath3he induced fusion reactions since low - energy radioactive beams have become available for new experiments in selected facilities @xcite . the authors thank m. dasgupta for providing experimental data in tabulated form . we would also like to acknowledge g.g . adamian , n.v . antonenko and s.j . sanders for a careful reading of the manuscript .

total ( complete + incomplete ) fusion excitation functions of @xmath0li on @xmath1co and @xmath2bi targets around the coulomb barrier are obtained using a new continuum discretized coupled channel ( cdcc ) method of calculating fusion . the effect of breakup on fusion can be observed in the total fusion excitation function . the breakup enhances the total fusion at energies just around the barrier , whereas it hardly affects the total fusion at energies well above the barrier . the difference between the experimental total fusion cross sections for @xmath0li on @xmath1co is notably caused by breakup , but this is not the case for the @xmath2bi target .

total ( complete + incomplete ) fusion excitation functions of @xmath0li on @xmath1co and @xmath2bi targets around the coulomb barrier are obtained using a new continuum discretized coupled channel ( cdcc ) method of calculating fusion . the relative importance of breakup and bound - state structure effects on total fusion is particularly investigated . the effect of breakup on fusion can be observed in the total fusion excitation function . the breakup enhances the total fusion at energies just around the barrier , whereas it hardly affects the total fusion at energies well above the barrier . the difference between the experimental total fusion cross sections for @xmath0li on @xmath1co is notably caused by breakup , but this is not the case for the @xmath2bi target .

0805.0065

i

what is the intrinsic connection between correlated random variables ? how much interaction is necessary to create correlation ? many fruitful efforts have been made to quantify correlation between two random variables . each quantity is justified by the operational questions that it answers . covariance dictates the mean squared error in linear estimation . shannon s mutual information is the descriptive savings from side information in lossless source coding and the additional growth rate of wealth due to side information in investing . gcs and krner s common information @xcite is the number of common random bits that can be extracted from correlated random variables . it is less than mutual information . wyner s common information @xcite is the number of common random bits needed to generate correlated random variables and is greater than mutual information . this work provides a fresh look at two of these quantities mutual information and wyner s common information ( herein simply `` common information '' ) . both are extreme points of the channel simulation problem , introduced as follows : an observer ( _ encoder _ ) of an i.i.d . source @xmath0 describes the sequence to a distant random number generator ( _ decoder _ ) that produces @xmath1 ( see figure [ figure channel simulation ] ) . what is the minimum rate of description needed to achieve a joint distribution that is statistically indistinguishable ( as measured by total variation ) from the distribution induced by putting the source through a memoryless channel ? [ ] [ ] [ 0.8]@xmath2 [ ] [ ] [ 0.8]@xmath3 [ ] [ ] [ 0.8]@xmath4 bits [ ] [ ] [ 0.8]@xmath5 [ ] [ ] [ 0.8]@xmath6 [ ] [ ] [ 1.0]channel simulator : @xmath7 and @xmath8 . the first processor , @xmath9 , observes @xmath10 and the second processor , @xmath8 , generates @xmath11 after receiving a message at rate @xmath12 from @xmath9 . the minimum rate needed is the common entropy of @xmath10 and @xmath11.,title="fig:",width=288 ] channel simulation is a form of random number generation . the variables @xmath2 come from an external source and @xmath6 are generated to be correlated with @xmath2 . the channel simulation is successful if the total variation between the resulting distribution of @xmath13 and the i.i.d . distribution that would result from passing @xmath2 through a memoryless channel is small . this is a strong requirement . it s stricter than the requirement that @xmath13 be jointly typical as in the coordinated action work of cover and permuter @xcite . this total variation requirement means that any hypothesis test that a statistician comes up with to determine whether @xmath2 was passed through a real memoryless channel or the channel simulator will be virtually useless . wyner s result implies that in order to generate @xmath2 and @xmath6 separately as an i.i.d . source pair they must share bits at a rate of at least the common information @xmath14 of the joint distribution . in the channel simulation problem these shared bits come in the form of the description of @xmath2 . however , the `` reverse shannon theorem '' of bennett and shor @xcite suggests that a description rate of the mutual information @xmath15 of the joint distribution is all that is needed to successfully simulate a channel . how can we resolve this apparent contradiction the work of bennett and shor assumes that common random bits , or _ common randomness _ , independent of the source @xmath2 are available to the encoder and decoder . in that setting , the common randomness provides a second connection between the source @xmath2 and output @xmath6 , in addition to the description of @xmath2 . remarkably , even though it is independent from the source @xmath2 , the common randomness assists in generating correlated random numbers and allows for description rates smaller than the common information @xmath14 . in this work , we characterize the tradeoff between the rate of available common randomness and the required description rate for simulating a discrete memoryless channel for a fixed input distribution , as in figure [ figure channel simulation with common randomness ] . indeed , the tradeoff region of section [ section main result ] confirms the two extreme cases . if the encoder and decoder are provided with enough common randomness , sending @xmath15 bits per symbol suffices . on the other hand , in the absence of common randomness one must spend @xmath14 bits per symbol . [ ] [ ] [ 0.8]@xmath2 [ ] [ ] [ 0.8]@xmath3 [ ] [ ] [ 0.8]@xmath16 bits [ ] [ ] [ 0.8]@xmath5 [ ] [ ] [ 0.8]@xmath6 [ ] [ ] [ 1.0]channel simulator : @xmath7 [ ] [ ] [ 0.8]@xmath17 bits and @xmath8 . the first processor , @xmath9 , observes @xmath10 and common randomness independent of @xmath10 at rate @xmath18 . the second processor , @xmath8 , generates @xmath11 based on the common randomness and a message at rate @xmath19 from @xmath9.,title="fig:",width=288 ] this result has implications in cooperative game theory , reminiscent of the framework investigated in @xcite . suppose a team shares the same payoff in a repeated game setting . an opponent tries to anticipate and exploit patterns in the team s combined actions , but a secure line of communication is available to help them coordinate . of course , each player could communicate his randomized actions to the other players , but this is an excessive use of communication . a memoryless channel is a useful way to coordinate their random actions . thus , common information is found in section [ section game theory ] to be the significant quantity in this situation .

two familiar notions of correlation are rediscovered as extreme operating points for simulating a discrete memoryless channel , in which a channel output is generated based only on a description of the channel input . wyner s `` common information '' coincides with the minimum description rate needed . however , when common randomness independent of the input is available , the necessary description rate reduces to shannon s mutual information . this work characterizes the optimal tradeoff between the amount of common randomness used and the required rate of description .

two familiar notions of correlation are rediscovered as extreme operating points for simulating a discrete memoryless channel , in which a channel output is generated based only on a description of the channel input . wyner s `` common information '' coincides with the minimum description rate needed . however , when common randomness independent of the input is available , the necessary description rate reduces to shannon s mutual information . this work characterizes the optimal tradeoff between the amount of common randomness used and the required rate of description .

1407.6565

i

simulations of structure formation in the universe with dark matter only lead us to believe that virialized structures , such as dark matter haloes , possess universal properties that depend only weakly on mass . one such property , most often used , is the spherically averaged density profile that can be approximated by the well - known nfw @xcite formula . however , dark matter haloes are definitely not spherical and their shapes can be approximated by triaxial ellipsoids , with principal axes labelled @xmath1 , @xmath2 , @xmath3 , so that @xmath4 . @xcite reported that on average @xmath5 and @xmath6 . in addition , the longest axis is usually aligned with the closest filament in the neighbouring structure . @xcite showed that the profiles of axis ratios are increasing functions of radius , i.e. their outer parts are more spherical than the inner ones . the inner regions are usually elongated , whereas the outer ones are triaxial or even oblate . another quantity often used to describe the properties of dark matter haloes is the anisotropy parameter @xmath7 @xcite that characterizes the type of orbits dominating in the halo . in general , this parameter is also found to be a function of radius and may depend on mass and environment . for example , @xcite found that the inner parts of simulated cluster - size haloes are characterized by @xmath8 while the outer parts are usually radially biased with @xmath9 ( where @xmath10 is the virial radius ) . although the nearly zero value of the anisotropy parameter in the central parts of simulated haloes is commonly interpreted as a signature of an isotropic velocity distribution , it results from spherical averaging of an axisymmetric and highly anisotropic velocity distribution @xcite . the origin of these properties and the relation between the density distribution , shape and orbital properties of dark matter haloes is still under investigation . one phenomenon that may contribute to the evolution of these properties is the one of orbit instability . @xcite proved that a system consisting entirely of matter streams moving radially is unstable against perturbations of potential . independently , @xcite showed that a system with a radially anisotropic distribution function is unstable . the existence of this kind of instability in an @xmath0-body simulation was demonstrated for the first time by @xcite . he showed that the shape of an initially spherical system , whose particles have only radial component of velocity ( i.e. @xmath11 ) , changes dramatically in the course of the simulation . this type of instability is referred to as the radial orbit instability ( roi ) . @xcite analyzed a finite - size system , whose @xmath12 profile rose from zero in the centre to a given value at the boundary of the system . they decomposed the density and potential into a complete set of functions with the angular part described by spherical harmonics @xmath13 and searched for exponentially growing eigenmodes . the system turned out to be unstable to the @xmath14 mode . moreover , they identified a boundary that separates a system vulnerable to roi . they introduced a global parameter @xmath15 , which for a system without streaming motions of particles amounts to @xmath16 , where @xmath17 is a global anisotropy parameter . the system studied by @xcite turned out to be stable for @xmath18 , i.e. @xmath19 . @xcite analyzed a suite of systems that all had the same density profile but various @xmath12 profiles . they used two families of models : one with @xmath20 const and one with the osipkov - merritt @xcite anisotropy profile : @xmath21 $ ] , where @xmath22 is the so - called anisotropy radius . for constant @xmath23 they found that roi sets on for @xmath24 ( @xmath25 ) . in the case of the second family transition was found for @xmath26 , where @xmath27 is the half - mass radius . for such a model @xmath28 ( @xmath29 ) . therefore , a global value of @xmath30 is not a good indicator of the possibility of the onset of roi . @xcite additionally found that the density profile averaged in spherical shells does not change significantly due to roi , although the final elongations were @xmath31 . most of their models were axisymmetric , only the one composed only of radial orbits was triaxial , with @xmath32 . the stability of anisotropic spherical systems against roi was later investigated also by means of the adiabatic deformation method @xcite , @xmath0-body simulations @xcite and the linear stability analysis @xcite . roi may be connected to the form of the density profiles of cosmological haloes . @xcite showed that for a cold collapse occurring in cosmological setting , if tangential components of gravity were artificially turned off , a halo with the density profile @xmath33 would form , in contrast with normal conditions when a halo with an nfw profile forms . in similar simulations @xcite noted that the haloes formed were elongated , with @xmath12 raising from zero in the centre to unity at the virial radius . one more factor that affects the final shape of the haloes formed from a collapse is the initial virial ratio ( e.g. * ? ? ? @xcite indicated that an initially isotropic core suppresses the onset of roi during cold collapse . an additional stabilizing factor is the presence of a black hole in the centre of the system . it may entirely suppress instability @xcite or even drive partial reduction of elongation @xcite . @xcite found a counterpart of roi in a system that was already triaxial . initially , their system had axis ratios @xmath34 and @xmath35 . during the simulation , the shape has changed to less triaxial and finally @xmath36 . moreover , reduction of the number of box orbits led to the suppression of instability . understanding roi may be crucial for at least two reasons . first , it allows us to place constraints on dynamical models constructed to describe real galaxies . second , it seems that the onset of roi may be of importance in the process of the formation of dark matter haloes , which surround individual galaxies and whole clusters . in this work we study the impact of roi on systems having initially the same nfw density profile , but different anisotropy profiles . our study is inspired by recent developments in the understanding of anisotropy profiles of gravitationally bound systems forming in cosmological context . we focus on dark matter haloes of mass and other properties characteristic of present - day dwarf galaxies . this choice is motivated by the fact that the dynamical time of the systems is relatively short and therefore their evolution may be significant over cosmic time . such systems are presumably old , therefore there was likely enough time for roi to affect them . formation of non - spherical dwarf haloes is also important for testing the reliability of different methods of estimating mass and density profiles of these haloes as such models can be used to generate mock data samples . the paper is organized as follows . in section [ sec_simulations ] we describe the initial conditions used in our simulations and the set - up of the @xmath0-body code . in section [ sec_mass_distribution ] we show how the distribution of matter in the haloes changes due to the occurrence of roi depending of the different anisotropy profiles assumed . in section [ sec_kinematics ] we characterize the influence of roi on halo kinematics , while in section [ sec_individual_orbits ] we focus on orbits of individual particles . the discussion follows in section [ sec_discussion ] and in section [ sec_summary ] we summarize our results .

using @xmath0-body simulations we study the phenomenon of radial orbit instability occurring in dark matter haloes of the size of a dwarf galaxy . we carried out simulations of seven spherical models , with the same standard nfw density profile but different anisotropy profiles of particle orbits . galaxies : dwarf galaxies : fundamental parameters galaxies : kinematics and dynamics cosmology : dark matter

using @xmath0-body simulations we study the phenomenon of radial orbit instability occurring in dark matter haloes of the size of a dwarf galaxy . we carried out simulations of seven spherical models , with the same standard nfw density profile but different anisotropy profiles of particle orbits . four of them underwent instability : two with a constant positive anisotropy , one with an anisotropic core and an isotropic envelope and one with a very small isotropic core and an anisotropic envelope . haloes affected by the instability become approximately axisymmetric and prolate , with the profile of the shortest - to - longest axis ratio increasing with radius . the lower limit for the central value of this axis ratio is 0.3 for an nfw halo . the density profiles of the haloes did not change significantly , whereas the velocity distributions became axisymmetric . the angular momentum modulus rose due to large - amplitude oscillations of its components perpendicular to the symmetry axis of the halo . we also studied orbits of individual particles assigning them to classical orbit families in triaxial potentials . we find that the membership of a given particle in a family depends on its initial angular momentum modulus and its components along the principal axes of matter distribution . galaxies : dwarf galaxies : fundamental parameters galaxies : kinematics and dynamics cosmology : dark matter

1407.6565

c

, for all simulations . the vertical dotted line indicates the radius beyond which the evolution of model c3 is not yet completed . the evolution of model i1 has not finished anywhere . ] all final states of the haloes can be considered biaxial , thus in figure [ fig_comparision_axes_ratios ] we plot the final short - to - long axis ratios for all models , with the ratio defined as @xmath105 . one should notice different areas affected by the instability . the haloes in simulations c1 , i2 and i3 have not undergone roi . in these cases the axis ratios at all radii are consistent with unity within uncertainties from shot noise . first , let us consider models whose initial profile of the anisotropy parameter was constant , i.e. @xmath20const . systems with an isotropic distribution of orbits ( @xmath106 ) , such as model c1 , are stable and roi does not develop in them . the more radial the orbits , i.e. the larger is the initial @xmath23 parameter , the greater is the impact of roi on the shape of the halo . the moment when the configuration of the particles begins to change depends to some extent on the initial anisotropy , whereas the rate of this change depends significantly on @xmath23 . after some time , when the new orbits of particles become stable , the halo reaches its final , approximately axisymmetric shape , with the axis ratios increasing with radius . if we introduce the triaxiality parameter @xmath107 we can quantify the degree of triaxiality in the haloes . the haloes in simulations c2 and c3 have @xmath108 in the region subject to instability , hence we can conclude they are biaxial and prolate . it may seem that they are more triaxial in the centres , but the determination of the axis ratio in the central part of the halo is uncertain . additionally , haloes with a larger initial anisotropy are slightly more triaxial . in both haloes , at the end of the simulation @xmath109 , however only in the very central part of the halo the distribution of orbits is more isotropic than initially . there exists a vast region where @xmath23 is almost equal to its initial value , though the shape of the matter distribution has altered significantly . the models c3 and d had the initial central anisotropy @xmath60 , but for the latter @xmath12 was a decreasing function of radius , approaching the isotropic distribution at large radii . comparing these simulations we conclude that for model d the rate of the evolution was considerably slower and affected a smaller part of the halo . the more isotropic distribution of orbits in the outer part of the halo suppressed the development of the instability : the radius beyond which the halo remained spherical ( @xmath110 kpc ) corresponds to the radius at which the orbits are practically isotropic ( @xmath111 ) . the central axis ratio in simulation d amounts to about 0.4 and in simulation c3 to a little more than @xmath112 . taking into account that for the nfw profile the maximum @xmath60 ( and that even using an increasing profile of @xmath12 with @xmath113 would probably not change the situation much compared to model c3 ) , we can formulate a hypothesis that the minimum central axis ratio that can occur in an nfw halo as a result of roi is about 0.3 . interestingly , it is consistent with the maximum elongation of elliptical galaxies , which are similar to dark matter haloes in a sense of being supported by random motion of their constituents . in the case of elliptical galaxies it is argued that the bending instability prevents the formation of more elongated shapes @xcite . it is thus plausible that the occurrence of this instability halts the development of roi . among haloes which initially had an isotropic distribution of orbits in the centres and anisotropic in the outer parts , only model i1 underwent roi . the remaining two models were stable during the 10 gyr of the simulation . we can not rule out that extending the simulation to a longer period would lead to the occurrence of the instability . then the situation would be similar to the case studied by @xcite who showed that one of the models claimed by @xcite to be stable turns out to be unstable after doubling the simulation time . @xcite argued that for generalized polytropes with a distribution function of the form @xmath114 if @xmath115 then a growing eigenmode is always present , but the growth rate @xmath116 decreases exponentially with @xmath23 , i.e. @xmath117 . hence , in the case of a finite simulation time a given system may seem stable . in our simulations , model i1 appeared stable for a long time before the onset of the instability , so models i2 and i3 might have turned out to be unstable as well if only the simulation had lasted longer . however , there is a major difference between systems with a distribution function whose angular momentum part is given by equation with @xmath62 and generalized polytropes . in the latter case the limit @xmath118 of @xmath119 is not bounded , and according to @xcite and @xcite it is a sufficient condition for roi to occur . in models with @xmath120 the instability took place first in the very centres of the haloes and then spread outwards . in this respect , model i1 was significantly different in a sense that in this case the roi manifested itself first at a considerable distance from the halo centre . a closer inspection revealed that the central part of this halo was not subject to instability , despite the fact that the axis ratios differed from unity . the principal axes of the shape tensor in the central part are not aligned with the principal axes in the outer part . moreover , the value of @xmath23 in the centre began to decrease only after the decrease in the outer part took place . a similar effect should be present in the case of the instability occurring in osipkov - merritt models . unfortunately , the radial dependence of axis ratios was rarely examined in the literature . in the case of @xcite work , the central parts reached @xmath121 , whereas at the radius encompassing 60 per cent of the system mass @xmath122 . @xcite studied the cold collapse of haloes in cosmological setting and for a system with a large isotropic velocity dispersion obtained a spherical nucleus . however , they did not point out that at an average distance from the halo centre @xmath123 . since the outer part of their halo remained spherical , their @xmath124 profile was qualitatively similar to the one obtained in our simulation i1 . the values of @xmath125 , above which the system is unstable against roi , reported in the literature depend on the model and are widely scattered in the interval @xmath126 , which translates to @xmath127 ( see a review by @xcite ) . among our models which underwent roi the one with the smallest @xmath30 is model d , from which we can derive an upper limit for the critical value @xmath128 for the nfw density profile . interestingly , models i2 ( @xmath129 ) and i3 ( @xmath130 ) with a higher value of parameter @xmath131 seemed to be stable . @xcite suggested that a parameter @xmath132 , which is defined in the same way as @xmath131 , but calculated only within the half - mass radius , might be a good indicator of the stability . however , our system d had @xmath133 and was unstable . we note that this value of @xmath134 should not be treated as a new and reliable constraint on the occurrence of roi . moreover , from figure [ fig_comparision_axes_ratios ] it is obvious that the area subject to roi is smaller if the initial distribution of orbits is more isotropic . it seems that there might exist a critical profile @xmath135 ( or , similarly , @xmath136 ) , below which we can not confirm the occurrence of roi , because the @xmath124 and @xmath137 profiles would be indistinguishable from numerical noise ( also present in the profiles for simulation c1 ) . it would not mean that we have found a true critical value ( or profile ) of anisotropy , but only that we reached the limit of the resolution of the numerical results . additionally , @xcite showed that all systems with a distribution function not bounded in the limit of @xmath118 are unstable to roi . such a feature is for example characteristic of _ all _ distribution functions of the form given in equation , for which @xmath138 . therefore , we recommend against using the notion of the global ( or half - mass ) critical value of @xmath131 , as the onset of roi seems to depend predominantly on the shape of the anisotropy parameter profile @xmath12 . final axis ratios obtained in our simulations are similar to those reported by other authors . however , one has to bear in mind that a direct comparison of the final axis ratios is difficult , as we measured _ profiles _ of those ratios , whereas usually only global values are provided . the maximum elongation found by other authors is of the order of @xmath139 ( @xcite ; @xcite ) . @xcite describe all their haloes as having @xmath140 . haloes which form as a result of cold collapse usually have @xmath141 . dark matter haloes from cosmological simulations are typically less elongated and have smaller differences between the inner and outer values of @xmath124 . we suppose that a gradual formation of such a halo , in contrast with the monolithic collapse , may be one of the reasons for the difference . the density profile of our simulated haloes did not change significantly , thus particles did not change their mean distance form the potential centre , but only reconfigured themselves . the decrease of the logarithmic slope @xmath116 in the centre may be a continuation of the effect noticed by @xcite , i.e. the transition from @xmath142 to @xmath143 in the centre of the collapsed halo if the onset of roi was permitted . the anisotropy parameter @xmath23 calculated in spherical shells is definitely an inadequate quantity to describe the velocity distribution of a non - spherical object . the fact that the orbit distribution is tangentially biased in the plane perpendicular to the major axis of the halo is connected to the prevalence of orbits with significant angular momentum ( o , s and i with high initial @xmath144 ) in this region . moreover , when members of the families b , r and the rest of the family i cross this plane , they usually have small radial and large tangential components of the velocity . on the other hand , in the region along the major axis there is much more diversity in the behaviour of the particles , thus the @xmath23 parameter remains almost the same as initially . altogether , it is likely that such a complicated distribution of orbits is not a result of roi but rather an effect of bi- or triaxiality of the potential generated by the mass distribution . a number of authors ( e.g. @xcite ) speculated about the relation between the box orbits and roi . @xcite studied the influence of the @xmath14 perturbation on two - dimensional orbits . they argued that during precession the orbit with a small generalized momentum @xmath145 ( which is in fact the angular momentum ) would be attracted by the bar and if the initial @xmath145 was small enough , the orbit would be caught by the bar . as a result , it would become a two - dimensional equivalent of a box orbit and its @xmath145 would oscillate . we have observed such oscillations for all components of the angular momentum of box orbits and for components @xmath91 and @xmath74 of inner long - axis tubes . analyzing the behaviour of individual particles one can try to understand the development of the instability . if the alignment of particles in the central part of the halo breaks spherical symmetry , particles in outer part of the halo start to move in a triaxial potential . particles with a small @xmath146 which are situated there start to move on orbits belonging to families b and i. contribution of these families to the potential is again non - spherical . therefore , particles from further away once again orbit in a triaxial potential and their trajectories are modified . such a reasoning explains the difference between models c2 and c3 . in the former case there was a smaller number of particles with a small @xmath146 , thus less particles that could have a non - spherical contribution to the density distribution . it explains also why for simulation d the outer part of the halo remained spherical . some of the particles situated there passed to family o and the rest to the others . however , there were enough particles in family o ( which initially had a large @xmath146 ) to balance the influence of families i and b. there is no good answer to the question why in the case of models with constant @xmath23 ( c2 and c3 ) the shells lying further from the centre of the potential are rounder than the ones lying closer to the halo centre . it might be related to the bending instability , whose influence depends on the radius in a non - trivial manner . the size of the area influenced by roi may depend not on _ relative _ parameters , e.g. the ratio of the pericentre distance to the size of the orbit or the ratio of the initial angular momentum to its maximum value at a given distance , but it may depend on _ absolute _ values . particles with a larger mean orbit radius do not pass close to the centre . they also have a larger angular momentum even if it is small compared to @xmath147 . simply put , in order to get to families b and i a small absolute value of @xmath146 is necessary , not relative to @xmath147 .

haloes affected by the instability become approximately axisymmetric and prolate , with the profile of the shortest - to - longest axis ratio increasing with radius . the lower limit for the central value of this axis ratio is 0.3 for an nfw halo . the density profiles of the haloes did not change significantly , whereas the velocity distributions became axisymmetric . we also studied orbits of individual particles assigning them to classical orbit families in triaxial potentials .

using @xmath0-body simulations we study the phenomenon of radial orbit instability occurring in dark matter haloes of the size of a dwarf galaxy . we carried out simulations of seven spherical models , with the same standard nfw density profile but different anisotropy profiles of particle orbits . four of them underwent instability : two with a constant positive anisotropy , one with an anisotropic core and an isotropic envelope and one with a very small isotropic core and an anisotropic envelope . haloes affected by the instability become approximately axisymmetric and prolate , with the profile of the shortest - to - longest axis ratio increasing with radius . the lower limit for the central value of this axis ratio is 0.3 for an nfw halo . the density profiles of the haloes did not change significantly , whereas the velocity distributions became axisymmetric . the angular momentum modulus rose due to large - amplitude oscillations of its components perpendicular to the symmetry axis of the halo . we also studied orbits of individual particles assigning them to classical orbit families in triaxial potentials . we find that the membership of a given particle in a family depends on its initial angular momentum modulus and its components along the principal axes of matter distribution . galaxies : dwarf galaxies : fundamental parameters galaxies : kinematics and dynamics cosmology : dark matter

1407.6565

i

in this paper we examined the impact of roi on the shape of dark matter haloes . for this purpose we performed seven different simulations of haloes with the same nfw density profile of virial radius @xmath148 kpc and concentration @xmath149 . the virial mass of each halo was equal to @xmath150 corresponding in size to haloes of dwarf galaxies obtained in cosmological simulations . however , each model had a different initial radial dependence of the anisotropy parameter @xmath23 . three of them had a constant anisotropy , including an isotropic one . the next model was rather peculiar : it had a strongly anisotropic core but an isotropic envelope . the last three had and increasing @xmath12 profile , similar to haloes obtained in cosmological simulations . they differed in @xmath53 the transition scale between the isotropic core and the anisotropic envelope . the evolution of each halo was followed for 10 gyr using an @xmath0-body code . among all seven haloes , four underwent roi : two with the constant , non - zero anisotropy ( c2 and c3 ) , the only one with the decreasing @xmath23 ( d ) and the one with an increasing @xmath12 and the smallest @xmath53 ( i1 ) . in the three remaining haloes we did not notice any significant evolution of the shape . in all haloes that underwent the instability the final profiles of the axis ratios turned out to depend on radius . with the exception of model i1 , haloes were elongated in the centres and remained spherical in the outer parts . halo i1 was spherical in the centre and had a minimum of the @xmath124 profile at a distance of about 2 kpc from the centre . all haloes became approximately axisymmetric and prolate . the density profiles of the haloes changed only slightly , which means that there were no large scale flows of matter . the profiles of @xmath23 measured in the planes perpendicular to the major axes of the haloes decreased significantly , whereas the ones measured along major axes remained almost unchanged . this indicates that the velocity distribution is axisymmetric . the mean @xmath146 of the haloes increased remarkably , in particular there were few particles with @xmath151 . this is due to large oscillations of the angular momentum components perpendicular to the symmetry axis . the component of the angular momentum along the symmetry axis is conserved with great accuracy . depending on the initial angular momentum , particles eventually join different orbit families . regions of membership are well separated in the planes of the angular momentum components . moreover , regions of different types of contribution to the halo shape also seem to be separable . for a large initial @xmath146 the particle contribution is oblate . particles with a small @xmath146 join the families which make the shape of the halo more prolate . additionally , for small @xmath88 ( component along the later symmetry axis ) orbits are not axisymmetric , thus they contribute to the triaxiality of the halo and this may be related to the fact that the triaxiality increases with the anisotropy of the system . different reactions to the bar - like perturbation arise from different numbers of particles with a given angular momentum that may later join orbit families which make the halo non - spherical . considering the influence of roi on the real dark matter haloes one has to bear in mind a few important issues . first , the infalling matter moves on rather elongated orbits and has small angular momentum relative to the centre of the halo . thus , it is quite likely that roi sets on during the halo growth making it triaxial or prolate . however , in reality haloes accumulate mass continuously , so the situation is different than the one considered in this work . second , it is unlikely that many haloes have a radial orbit distribution in their centre in other words , in simulated haloes we never have @xmath152 significantly above zero . our simulations apply directly to haloes of dwarf galaxy size , but it seems that simple scaling is enough to adapt them to larger objects . one has to remember also that these results refer to isolated haloes . in the case of an interaction of a halo with another object some of the properties discussed above may change .

four of them underwent instability : two with a constant positive anisotropy , one with an anisotropic core and an isotropic envelope and one with a very small isotropic core and an anisotropic envelope . the angular momentum modulus rose due to large - amplitude oscillations of its components perpendicular to the symmetry axis of the halo .

using @xmath0-body simulations we study the phenomenon of radial orbit instability occurring in dark matter haloes of the size of a dwarf galaxy . we carried out simulations of seven spherical models , with the same standard nfw density profile but different anisotropy profiles of particle orbits . four of them underwent instability : two with a constant positive anisotropy , one with an anisotropic core and an isotropic envelope and one with a very small isotropic core and an anisotropic envelope . haloes affected by the instability become approximately axisymmetric and prolate , with the profile of the shortest - to - longest axis ratio increasing with radius . the lower limit for the central value of this axis ratio is 0.3 for an nfw halo . the density profiles of the haloes did not change significantly , whereas the velocity distributions became axisymmetric . the angular momentum modulus rose due to large - amplitude oscillations of its components perpendicular to the symmetry axis of the halo . we also studied orbits of individual particles assigning them to classical orbit families in triaxial potentials . we find that the membership of a given particle in a family depends on its initial angular momentum modulus and its components along the principal axes of matter distribution . galaxies : dwarf galaxies : fundamental parameters galaxies : kinematics and dynamics cosmology : dark matter

1010.1949

i

thousands of coronal mass ejections ( cmes ) have been observed remotely by coronagraphs and hundreds by _ in situ _ instruments since the 1970s ( for a review of cme observations , see , for example and ) . in the past five years , with the launch of spacecraft carrying heliospheric imagers ( _ coriolis _ and the _ solar - terrestrial relations observatory _ ( stereo ) ) , we have witnessed the start of a new era , where cmes can be routinely observed to radial distances as far as 0.5 au with the heliospheric imagers ( his , see ) and sometimes up to earth s orbit . their remote properties can now be compared to _ in situ _ measurements @xcite . to analyze these new measurements , new methods and approximations must be devised . shortly after the launch of _ coriolis _ and stereo , two simple ways to analyze wide angle heliospheric observations were developed : the point - p @xcite and fixed-@xmath3 @xcite approximations . recently , another approximation has also been proposed ( harmonic mean ( hm ) , see ) and these approximations have been completed by other techniques : visual fitting @xcite , fitting to a family of pre - existing simulated ejections @xcite and fitting to known functions of the speed and direction @xcite . these techniques can derive , in addition to the cme speed and position , its average direction of propagation . two other methods have been proposed to analyze simultaneous ( i.e. stereoscopic ) cme observations in the heliosphere , by direct triangulation @xcite or by a `` tangent to a sphere '' method @xcite , to obtain , at all times , the cme position and direction of propagation . heliospheric instruments are planned in a number of future missions , including the _ solar orbiter _ and the _ solar probe_. however , it is possible that there will not be other stereoscopic observations of cmes by heliospheric imagers after the end of the stereo mission . the time period from early 2008 , when the stereo spacecraft separation reached 45@xmath2 to the early 2010 when it reached about @xmath4 is the optimal period to have stereoscopic heliospheric observations . it should be used to validate , test and compare methods to analyze white - light heliospheric observations of cmes . such comparisons between methods was recently performed by between the visual fitting of cor images by and the analytical fitting to a constant direction and velocity by . the theoretical error and bias associated with the manual selection of the elongation data for the method of were also recently quantified in . in the present article , we compare two different stereoscopic heliospheric methods with each other and with fitting methods to study the direction of propagation of cmes . in this article , in section [ mono ] , we propose a new fitting method , similar to that of but based on the model of . we compare theoretically the two methods based on stereoscopic observations proposed by and in section [ stereo ] . in section [ comp ] , we analyse in detail one of the 12 cmes observed simultaneously by the two stereo spacecraft in 2008 and 2009 , before doing a statistical comparison of the methods based on these real analyses . the conclusions of this investigation are drawn in section [ conclusions ] .

this makes it possible to test and compare different analyses techniques . in this article we also compare the results from these two fitting methods with those from two stereoscopic methods , focusing on 12 cmes observed simultaneously by the two stereo spacecraft in 2008 and 2009 .

using data from the heliospheric imagers ( his ) onboard stereo , it is possible to derive the direction of propagation of coronal mass ejections ( cmes ) in addition to their speed with a variety of methods . for cmes observed by both stereo spacecraft , it is possible to derive their direction using simultaneous observations from the twin spacecraft and also , using observations from only one spacecraft with fitting methods . this makes it possible to test and compare different analyses techniques . in this article , we propose a new fitting method based on observations from one spacecraft , which we compare to the commonly used fitting method of . we also compare the results from these two fitting methods with those from two stereoscopic methods , focusing on 12 cmes observed simultaneously by the two stereo spacecraft in 2008 and 2009 . we find evidence that the fitting method of can result in significant errors in the determination of the cme direction when the cme propagates outside of @xmath0 from the sun - spacecraft line . we expect our new fitting method to be better adapted to the analysis of halo or limb cmes with respect to the observing spacecraft . we also find some evidence that direct triangulation in the hi fields - of - view should only be applied to cmes propagating approximatively towards earth ( @xmath1 from the sun - earth line ) . last , we address one of the possible sources of errors of fitting methods : the assumption of radial propagation . using stereoscopic methods , we find that at least seven of the 12 studied cmes had an heliospheric deflection of less than 20@xmath2 as they propagated in the hi fields - of - view , which , we believe , validates this approximation .

1010.1949

c

in this article , we have examined some of the methods used to derive the direction of propagation of coronal mass ejections ( cmes ) from observations by heliospheric imagers . we have focused on four methods : the fitting method of , the triangulation method of , the tangent - to - a - sphere method of and a new fitting method derived in this article . because it is impossible to know the exact direction of propagation of a cme , we have focused our analysis of real data on ejections observed simultaneously by the two stereo spacecraft . for these cmes , it is possible to use the stereoscopic methods and also to compare the direction of propagation based on fitting methods for each of the instruments . overall , we have found a very small or no correlation between the direction obtained from observations by one spacecraft and that obtained from observations by the other spacecraft , and this , both for the fitting method of and for the new method we proposed . however , for four out of 13 cme tracks , it is possible to combine the results of the fit based on the data from each spacecraft within the 95@xmath29 certainty interval to find a well - defined direction . we have addressed two of the three possible sources of error for the fitting method of applied to cmes : i ) the assumption of radial propagation ( absence of heliospheric deflection ) , and ii ) the assumption that the cme is of negligible width ( or that the same part of the cme is always observed ) . we addressed i ) by using stereoscopic methods which can give at all time the cme direction of propagation instead of its average value . stereoscopic methods need to be better tested and validated but for about nine out 13 cmes , we have found reasonable results with the method of and for two cmes with the triangulation method of . for the other two cases , the method of is too noisy and triangulation results in a large underestimation of the cme direction of propagation . in seven of these good cases , we have found no sign of strong heliospheric deflection of cmes , the total deflection being less than 20@xmath2 in the hi field - of - view . this result validates the usage of fitting methods to determine cme direction , since these methods assume no heliospheric deflection . we have proposed a new fitting method which takes into account the cme width . we have found that the assumption of negligible cme width yields worst fit for the method of compared to this new method for cmes propagating outside of @xmath0 from the sun - spacecraft line . _ we believe this new method should be used for halo and limb cmes as seen by the observing spacecraft_. however , both methods can be easily used for all observations and the one with the smallest residual error should be chosen to provide the cme estimated speed and direction on a case - by - case basis . in our analysis of 30 cme tracks , we have found that each fitting method gives a better fit in about half the cases . we have also found that , when a cme is observed to large elongation angles by both stereo spacecraft , the cme direction is best determined using the data from the spacecraft which observed the cme as a halo . this is especially true with the new fitting method . there is a third issue with the two fitting methods : the assumption of constant heliospheric velocity . all the cmes in our sample ( with the exception of the 26 april 2008 with a speed of about 600700 km s@xmath26 ) have speed between 280 and 450 km s@xmath26 and we believe this assumption is approximatively true . this issue is hard to address because of the lack of fast cmes in the past three years . numerical simulations combined with a proper treatment of the thomson scattering @xcite are one of the only ways to address this question of the effect of cme deceleration and we plan to look into this in future research . the research for this manuscript was supported by nsf grant atm-0819653 and nasa grants nnx-07ac13 g and nnx-08aq16 g . soho and stereo are projects of international cooperation between esa and nasa . n. l. would like to thank c. j. davis and j. a. davies from stfc / ral for providing the time - elongation data , and c. mstl , i. i. roussev and a. vourlidas for useful discussions and the anonymous reviewers for their help in improving the manuscript . the secchi data are produced by an international consortium of naval research laboratory , lockheed martin solar and astrophysics lab , and nasa goddard space flight center ( usa ) , rutherford appleton laboratory , and university of birmingham ( uk ) , max - planck - institut fr sonnensystemforschung ( germany ) , centre spatiale de liege ( belgium ) , institut doptique thorique et applique , and institut dastrophysique spatiale ( france ) . soho is a project of international cooperation between esa and nasa , and the soho lasco / eit catalogs are maintained by nasa , the catholic university of america , and the us naval research laboratory ( nrl ) .

using data from the heliospheric imagers ( his ) onboard stereo , it is possible to derive the direction of propagation of coronal mass ejections ( cmes ) in addition to their speed with a variety of methods . for cmes observed by both stereo spacecraft , it is possible to derive their direction using simultaneous observations from the twin spacecraft and also , using observations from only one spacecraft with fitting methods . , we propose a new fitting method based on observations from one spacecraft , which we compare to the commonly used fitting method of . we find evidence that the fitting method of can result in significant errors in the determination of the cme direction when the cme propagates outside of @xmath0 from the sun - spacecraft line . we also find some evidence that direct triangulation in the hi fields - of - view should only be applied to cmes propagating approximatively towards earth ( @xmath1 from the sun - earth line ) . last , we address one of the possible sources of errors of fitting methods : the assumption of radial propagation . using stereoscopic methods , we find that at least seven of the 12 studied cmes had an heliospheric deflection of less than 20@xmath2 as they propagated in the hi fields - of - view , which , we believe , validates this approximation .

using data from the heliospheric imagers ( his ) onboard stereo , it is possible to derive the direction of propagation of coronal mass ejections ( cmes ) in addition to their speed with a variety of methods . for cmes observed by both stereo spacecraft , it is possible to derive their direction using simultaneous observations from the twin spacecraft and also , using observations from only one spacecraft with fitting methods . this makes it possible to test and compare different analyses techniques . in this article , we propose a new fitting method based on observations from one spacecraft , which we compare to the commonly used fitting method of . we also compare the results from these two fitting methods with those from two stereoscopic methods , focusing on 12 cmes observed simultaneously by the two stereo spacecraft in 2008 and 2009 . we find evidence that the fitting method of can result in significant errors in the determination of the cme direction when the cme propagates outside of @xmath0 from the sun - spacecraft line . we expect our new fitting method to be better adapted to the analysis of halo or limb cmes with respect to the observing spacecraft . we also find some evidence that direct triangulation in the hi fields - of - view should only be applied to cmes propagating approximatively towards earth ( @xmath1 from the sun - earth line ) . last , we address one of the possible sources of errors of fitting methods : the assumption of radial propagation . using stereoscopic methods , we find that at least seven of the 12 studied cmes had an heliospheric deflection of less than 20@xmath2 as they propagated in the hi fields - of - view , which , we believe , validates this approximation .

1409.3691

i

coronal mass ejections ( cme ) are large - scale energetic events associated with various manifestations of solar activity ( e.g. , flares , eruptive prominences , shocks ) . the correlation between the kinematics of the cmes with these different forms of solar activity has been , for several decades , a major tool to shed light into the physical mechanisms of cme development . cmes have been frequently observed in white light coronagraph images as having a so called three - part structure , consisting of a bright rim surrounding a dark void which contains a bright core @xcite . the soho / lasco and more recently stereo observations showed that cmes are consistent with a two - dimensional projection of a three - dimensional magnetic flux rope @xcite . the authors concluded that the cavity , seen in white light , can be interpreted as the cross section of an expanded flux rope . @xcite gave arguments implying that at least 40% of the observed cmes have flux - rope structures . in recent years , new prominent results on cme initiation mechanisms and their early development in the low corona have arisen from euv observations with the euv imager of the stereo / secchi telescope ( euvi ; * ? ? ? * ) and from the atmospheric imaging assembly on board the _ solar dynamic observatory _ ( @xmath0/aia ; * ? ? ? * ) . @xcite showed that the cme formation is first characterized by slow , self - similar , expansion of slowly - rising loops , possibly triggered by a rising filament , that leads to the formation of a bubble - shaped structure within about 2 minutes . this is consistent with the transformation , by magnetic reconnection , of loops into a flux rope structure as predicted by several models ( e.g. , * ? ? ? the aia multi - temperature observations have given access to detailed description of a cme namely : i ) the ejection of a plasma blob transforming rapidly into a growing hot flux rope that stretches the upper field lines ; ii ) the appearance of a y - type magnetic configuration at the bottom of the flux - rope , in which a bright thin line ( i.e. , a current sheet , cs ) extends downward ; and iii ) the shrinkage of magnetic field lines observed underneath the cme @xcite . all these above observations are consistent with the cme eruption model proposed by @xcite . this model is based on a flux rope magnetic configuration overlying a photospheric polarity inversion line . this flux rope becomes unstable and erupts building up behind a cs , which convert the surrounding b - field in a new poloidal around the flux rope . in radio , the formation and development of reconnecting cs behind an erupting flux rope was imaged by the nanay radio - heliograph @xcite . cmes are frequently associated with type ii radio bursts which are a signature of a shock formation and propagation in the corona at speeds higher than those of the alfvn speed . these bursts are generated by shocks exciting langmuir waves which decay into radio waves at the local plasma frequency and/or its harmonics ( see e.g. , * ? ? ? a long debate on the physical mechanisms which generate these shocks is still ongoing ( see , e.g. , * ? ? ? * ; * ? ? ? @xcite has led to the conclusion that coronal shocks may be generated by two different mechanisms : blast - waves initiated by the plasma pressure of a flare , and piston driven shocks due to cmes . several statistical studies on the association of cmes with type ii radio bursts can be found in the literature ( see , e.g. , * ? ? ? @xcite have found that 92% of the type ii bursts observed at 109 mhz are associated with cmes and are located near their leading edge . however , the sources of the coronal type ii were often found to be located not in front but on the flanks of cmes , ( see , e.g. , * ? ? ? * ; * ? ? ? ? * ; * ? ? ? coronal type ii bursts were also often observed jointly with the occurrence of euv waves , which are large - scale , bright , wave - like disturbances visible in euv . several authors have recently taken advantage of the high cadence observations and of the simultaneous dual ( or sometimes triple ) view - points obtained with stereo / euvi , @xmath0/aia and probab2/swap @xcite instruments to study the association between cmes and euv waves ( see , e.g. , * ? ? ? * ; * ? ? ? for instance , @xcite found that the development of an euv wave exhibits two phases : a first phase consistent with a wave driven by the expanding flanks of the cme ( e.g. , * ? ? ? * ) , and a second one where the wave propagates freely . however , the physical nature of these waves and their association with type ii bursts is still unclear and no single model can account for the large variety of euv waves observed @xcite . to understand the nature of the shock and its association with cmes , euv waves , and flares , detailed studies of the complex morphology present in radio burst spectra are required . this complex morphology shows up , for instance , under the form of a splitting of the emission bands into two lanes @xcite , or a fragmentation and an abrupt change of their drift rates ( see , e.g. , * ? ? ? * ; * ? ? ? these various morphologies are related to the characteristics of the eruption and to the properties of the surrounding corona in which the shock is propagating . in particular , the electron density and the magnetic field characterize the ambient medium , which then determine the alfvn speed . this characteristic speed is important for the formation of a shock and for the conditions under which the radio burst can be initiated . furthermore , both the coronal density and the magnetic field configuration are crucial to determine the radio burst frequency drift and its duration . while numerous studies have been realized on the origin of the shocks and their association with cmes , there are in fact a very small number of cases for which it has been possible to study such events simultaneously through radio spectra obtained on a large frequency scale , and through radio and euv images obtained with a high enough time resolution to follow their evolution in detail . to contribute to the understanding of when and where the cmes and coronal shocks are produced and how they relate to type ii bursts and euv waves , we study here the complex morphological spectral features of a radio event observed on 06 november 2013 together with imaging euv and radio observations . the november 06 event includes two components , an eruptive jet and a cme , which interact during more than 30 min , and can be considered as physically linked . the magnetic configuration , in which eruptive jets are produced , has already been studied with several magneto - hydrodynamic ( mhd ) numerical simulations ( e.g. * ? ? ? * ; * ? ? ? conversely , eruptive events , such as the 06 november one which was accompanied by a cme , are not frequently described in the literature . the results of the data analysis presented here take advantage from particularly favorable conditions : i ) same field of view on euv and radio instruments ; ii ) joint radio spectral ( 0.5 - 1000 mhz ) and multi - frequency imaging observations ( 150 - 450 mhz ) at high cadence ( better than 1s ) and with an high sensitivity ; iii ) a broad - band frequency spectrogram obtained by the combination of different spectrographs . we identify step by step the causes of the type ii spectral fragmentation in relationship with the cme evolution and the ambient medium . we obtain for each step , without introducing an electronic density model or a mhd simulation , the upstream plasma density , the alfvn mach number for the shock and the magnetic strength . the end of this type ii burst is followed , several minutes later , by a second type ii burst of shorter duration . in the absence of imaging observations , the spectral versus time evolution would have led us to conclude to a reactivation of the original type ii burst . we will show that this is not the case . the paper is organized as follows : section [ sect : joint ] provides first a description of the observations , and then we present the data analysis which mainly includes : i ) a brief overview of the radio event properties ; ii ) the magnetic configuration of the active region and of its environment ; iii a detailed joint euv and radio analysis of the cme and of the associated type ii bursts . section [ sect : shock ] presents the method through which the observations of the first radio type ii burst leads to an estimation of physical parameters such as the alfvn velocity , the density and the magnetic field of the ambient medium . in section [ sect : discussion ] , we discuss what we learnt on : i ) the rle of the eruptive jet and of the ambient medium for setting up the cme ; ii ) the nature of the two shocks , associated with two radio type ii bursts , which occur during the cme progression . the main findings are summarized in section [ sect : conclusions ] .

using multi - wavelength imaging observations , in euv , white light and radio , and radio spectral data over a large frequency range , we analyzed the triggering and development of a complex eruptive event . this one includes two components , an eruptive jet and a cme which interact during more than 30 min , and can be considered as physically linked . the initiation and development of the cme , observed first in euv , does not show usual signatures . in this case , the eruptive jet is the main actor of this event .

using multi - wavelength imaging observations , in euv , white light and radio , and radio spectral data over a large frequency range , we analyzed the triggering and development of a complex eruptive event . this one includes two components , an eruptive jet and a cme which interact during more than 30 min , and can be considered as physically linked . this was an unusual event . the jet is generated above a typical complex magnetic configuration which has been investigated in many former studies related to the build - up of eruptive jets ; this configuration includes fan - field lines originating from a corona null point above a parasitic polarity , which is embedded in one polarity region of large active region ( ar ) . the initiation and development of the cme , observed first in euv , does not show usual signatures . in this case , the eruptive jet is the main actor of this event . the cme appears first as a simple loop system which becomes destabilized by magnetic reconnection between the outer part of the jet and the ambient medium . the progression of the cme is closely associated with the occurrence of two successive types ii bursts from distinct origin . an important part of this study is the first radio type ii burst for which the joint spectral and imaging observations allowed : i ) to follow , step by step , the evolution of the spectrum and of the trajectory of the radio burst , in relationship with the cme evolution ; ii ) to obtain , without introducing an electronic density model , the b - field and the alfvn speed .

1409.3691

i

in the present paper , we have presented an unusual event in which an eruptive jet is involved in the onset of a cme and , then , accompanies its development . first detected in euv , this event appears as a simple loop system rising in the corona , while it is later identified as a cme when observed , in white light , by soho . no euv plasmoid was detected behind the edge of the cme . the aim of this paper was to understand : i ) the role of the eruptive jet and of the ambient medium for setting up this cme ; ii ) the nature of the two shocks associated with two successive type ii bursts , which occur during the cme progression . our main findings are summarized below . \a ) the eruption of the jet marks the beginning of the event ; this jet originates from a coronal null point above a positive parasitic polarity embedded inside the trailing negative part of the active region ( ar ) . the initiation phase occurs when a sudden brightening appears at its base and extends rapidly toward its western neighboring loops . these large scale loops , which connect the two main polarities of the ar , start to shine along their eastern leg . these observations are indicative of the beginning of a destabilization process of the loops caused by their magnetic interaction with the jet structure . \b ) the subsequent eruptive euv and radio manifestations , preceding or accompanying the onset of the cme , occur in the vicinity of the region where the cme le is formed . the idea of a magnetic reconnection process between the outer part of the jet and the ambient medium , is confirmed by the presence of radio type iii bursts . \a ) the first dm type iii burst group , which is followed by two other ones , coincides with the appearance of a bright narrow euv source located above a region of positive polarity . this source persists during several minutes , and subsequent weaker sources are observed in the same region . these observations suggest that the sources , from which the electron beams responsible for the type iii radio bursts originate , result from a magnetic reconnection between the western side of the eruptive jet magnetic field and the field lines anchored in this region of positive polarity . this interpretation is consistent with i ) the sudden appearance , between these two regions , of a bright bridge , particularly well observed by sdo at high temperature ; ii ) the positive polarization of the radio emission ; iii ) the trajectory of the electron beams ( note that the magnetic field lines of positive polarity are not detected by pffs ) . the ascending motion of the cme starts soon after the occurrence of the first group of type iii bursts . \b ) during these dm bursts , two groups of interplanetary type iii bursts are also detected . the electron beams producing these bursts result from the interaction between the eastern side of the jet and the open field lines originating from a region of negative polarity . \c ) the different following observations seem to stress the role of the erupting jet during the cme progression : \a ) its motion is followed by the onset of the first type ii burst . the progressions of the cme and of the burst appear to be closely connected : they follow the same direction and the type - ii burst sources are located above the front edge of the cme . moreover , approximately 1 or 2 minutes later , the source of the type ii burst stops its southward motion and becomes westward oriented , while the cme leading edge becomes also slightly westward oriented . we attribute this effect to the encounter of the eastern edge of the cme with the eruptive jet . let us further remark that : i ) its eastern edge becomes no longer discernible from the jet after their encounter ; ii ) the cme leading edge appears to be split into two parts , its eastern part corresponding in fact to the western branch of the jet , now curved and surrounding the cme . these facts are compatible with the shape of the cme as observed later . \b ) while the cme continues its southward progression , its lateral expansion is limited , on one side by the presence of the eruptive jet , and on the other side by the pressure generated by the coronal hole . this interaction is possibly the cause of the second type ii burst which , during the same period , appears at decameter wavelengths . we note that , 2 hours later , the expansion of the cme , when observed by lasco / c2 , has remained the same . \c ) the last ip bursts , which appear approximately at the time of the approach of the cme with the south pole , probably originate from a magnetic interaction between the cme , or the jet itself , with the open field lines of the polar region . in this study , the cme le and the type ii burst kinematics were compared with ambient coronal characteristics such as the alfvn speed and the b - field , in order to understand the origin of the shock and its progression . these properties were calculated without assuming any model for the coronal density and they were derived from the shock compression ratio ; the latter was obtained from the type ii split lanes , using a method described in @xcite . the cme le showed a fast initial acceleration , and already reached a super - alfvnic speed . this was subsequently followed by the production of a type ii burst with emission lanes split in two bands . the type ii burst also presented a fast initial acceleration leading to a speed faster than the cme le , so that they progressively separate one from the other . a shock can be a blast wave , in which the energy is supplied by a pressure pulse , or it can be driven by a cme , either in a piston - type or in a bow shock scenario @xcite . in the case of a piston shock geometry , the shock moves faster than its driving piston and the medium is confined , since it is not able to stream around the cme @xcite . in our event , as recalled in point c - b above , the lateral expansion of the cme is limited , on one side by the presence of the eruptive jet , and on the other side by the pressure generated by the coronal hole . this confinement , together with the shock propagating faster than the cme le , strongly suggest that the shock has been driven by the cme in a piston - driven mechanism . another observation is in line with this interpretation : the type ii burst sources are located in front of the cme le and undergo the same change as the cme in the propagating direction . the radio observational coverage by the nrh allowed us to resolve the location of the split bands of the type ii burts . we found that the two components were located ahead of the cme le and that the higher frequency lane was positioned behind the lower frequency band . this is in agreement with the @xcite interpretation of the splitting lane emission . in our scenario , the hypothetic shock wave , probably to faint to be detected in euv , is located between the low and hi band position of the splitted lanes . @xcite and @xcite arrived to a similar conclusion , in the study of another dm - metric type ii burst which was also imaged by the nrh .

the jet is generated above a typical complex magnetic configuration which has been investigated in many former studies related to the build - up of eruptive jets ; this configuration includes fan - field lines originating from a corona null point above a parasitic polarity , which is embedded in one polarity region of large active region ( ar ) . the cme appears first as a simple loop system which becomes destabilized by magnetic reconnection between the outer part of the jet and the ambient medium . the progression of the cme is closely associated with the occurrence of two successive types ii bursts from distinct origin .

using multi - wavelength imaging observations , in euv , white light and radio , and radio spectral data over a large frequency range , we analyzed the triggering and development of a complex eruptive event . this one includes two components , an eruptive jet and a cme which interact during more than 30 min , and can be considered as physically linked . this was an unusual event . the jet is generated above a typical complex magnetic configuration which has been investigated in many former studies related to the build - up of eruptive jets ; this configuration includes fan - field lines originating from a corona null point above a parasitic polarity , which is embedded in one polarity region of large active region ( ar ) . the initiation and development of the cme , observed first in euv , does not show usual signatures . in this case , the eruptive jet is the main actor of this event . the cme appears first as a simple loop system which becomes destabilized by magnetic reconnection between the outer part of the jet and the ambient medium . the progression of the cme is closely associated with the occurrence of two successive types ii bursts from distinct origin . an important part of this study is the first radio type ii burst for which the joint spectral and imaging observations allowed : i ) to follow , step by step , the evolution of the spectrum and of the trajectory of the radio burst , in relationship with the cme evolution ; ii ) to obtain , without introducing an electronic density model , the b - field and the alfvn speed .

1409.3691

c

we have presented the formation and development of an unusual cme as described in section 4 and summarized below . the cme resulted from the interaction of an eruptive jet with the surrounding medium . the key points are the overall magnetic structure of the ambient medium and the relative position of the jet in this environment . to our knowledge , it is the first time that such an event has been analyzed in some depth . a cluster of eruptive euv and radio observations , stress the predominant role played by the eruptive jet in the history of this cme : first detected in euv , this event appears as a simple loop system rising in the corona . these loops start to be destabilized by their magnetic interaction with the jet . this early development of the cme does not show the signatures that could be expected from previous observations ( see introduction ) . then , a destabilization process of the loops is caused by magnetic reconnection between the outer part of the jet and the ambient magnetic field . this process occurs in the vicinity of the region where the cme le is formed and when the cme speed is strongly increasing . this is also near this time that the onset of the first type iii burst is observed . this is reminiscent of the break - out model @xcite but with reconnection between closed and open magnetic field . the progression of this cme is later observed in white light , up to a distance of 8 solar radii . two type ii bursts were detected . a distinct origin is identified for the two successive shocks , both associated with the cme development . one of the primary finding of this study is related to the first type ii burst for which the joint spectral and imaging observations allowed us : to conclude , we would like to illustrate , on two specific points , how the data analysis has benefited from particularly favorable conditions : i ) though , the event originated on the solar disk , it was observed by the soho / lasco coronagraph . it allowed us to confirm that this event was a real cme ; ii ) the polarization measurements of the radio type iii bursts was determinant to identify the origin of the dm type three bursts and also showed that electron beams escape along magnetic field lines that were not present in pfss extrapolation . p. zucca is supported by a tcd innovation bursary and acknowledges the cnes for the financial support he received during his stay in lesia , meudon observatory . we thank e. pariat for constructive discussions . we would like to thank the referee for the valuable comments and suggestions . we are also grateful to the sdo team for his open data policy . the soho lasco data used here are produced by a consortium of the naval research laboratory ( usa ) , max - planck - institut fur aeronomie ( germany ) , laboratoire dastronomie spatiale ( france ) , and the university of birmingham ( uk ) . soho is a project of international cooperation between esa and nasa . in france , this work was supported by cnes .

an important part of this study is the first radio type ii burst for which the joint spectral and imaging observations allowed : i ) to follow , step by step , the evolution of the spectrum and of the trajectory of the radio burst , in relationship with the cme evolution ; ii ) to obtain , without introducing an electronic density model , the b - field and the alfvn speed .

using multi - wavelength imaging observations , in euv , white light and radio , and radio spectral data over a large frequency range , we analyzed the triggering and development of a complex eruptive event . this one includes two components , an eruptive jet and a cme which interact during more than 30 min , and can be considered as physically linked . this was an unusual event . the jet is generated above a typical complex magnetic configuration which has been investigated in many former studies related to the build - up of eruptive jets ; this configuration includes fan - field lines originating from a corona null point above a parasitic polarity , which is embedded in one polarity region of large active region ( ar ) . the initiation and development of the cme , observed first in euv , does not show usual signatures . in this case , the eruptive jet is the main actor of this event . the cme appears first as a simple loop system which becomes destabilized by magnetic reconnection between the outer part of the jet and the ambient medium . the progression of the cme is closely associated with the occurrence of two successive types ii bursts from distinct origin . an important part of this study is the first radio type ii burst for which the joint spectral and imaging observations allowed : i ) to follow , step by step , the evolution of the spectrum and of the trajectory of the radio burst , in relationship with the cme evolution ; ii ) to obtain , without introducing an electronic density model , the b - field and the alfvn speed .

astro-ph9904258

i

carbon and oxygen are two of the most abundant elements in the universe and lines from these elements provide valuable plasma diagnostics for almost all classes of cosmic sources . essential for many of these diagnostics are accurate electron - ion recombination rate coefficients , particularly of dielectronic recombination ( dr ) , which for most ions in electron - ionized plasmas is the dominant means of electron capture ( arnaud & rothenflug 1985 ) . producing accurate theoretical dr rate coefficients is , however , theoretically and computationally challenging . in the past , semi - empirical expressions such as the burgess ( 1965 ) formula along with modified versions by burgess & tworkowski ( 1976 ) and merts et al . ( 1976 ) were developed to calculate dr rates . more recently , a number of more sophisticated theoretical approaches have been used to calculate dr , among them single - configuration @xmath0-coupling ( bellantone & hahn 1989 ) , multiconfiguration intermediate - coupling ( pindzola , badnell , & griffin 1990 ) , and multiconfiguration fully - relativistic ( chen 1988 ) techniques , as well as undamped and damped , unified radiative recombination ( rr ) and dr calculations in @xmath0-coupling ( nahar & pradhan 1997 ; nahar 1999 ) . approximations , though , need to be made to make any of these techniques computationally tractable ( hahn 1993 ) . currently , sophisticated dr calculations are non - existent for many ions , and in the absence of anything better , semi - empirical formulae are often still used for plasma modeling . laboratory measurements can be used to test the different theoretical and computational techniques for calculating dr . recently , savin et al . ( 1997 , 1999 ) developed a technique for obtaining rate coefficients from laboratory measurements of dr resonance strengths and energies . they successfully used this technique to derive rates for @xmath2 dr of fe xviii and fe xix and to benchmark existing theoretical calculations . here , we describe this technique in detail for the first time and apply it to recent dr measurements in c v and o viii . kilgus et al . ( 1990 , 1993 ) and mannervik et al . ( 1997 ) have measured the resonance strengths and energies for dr of c v to c iv and o viii to o vii . we use their results to produce dr rate coefficients to benchmark existing c v and o viii dr calculations and to provide rates for use in plasma modeling . in electron - ionized plasmas , lines from heliumlike c v and hydrogenic o viii trace gas at @xmath3 k and @xmath4 k , respectively ( arnaud & rothenflug 1985 ; mazzotta et al . c v and o viii lines have been observed in solar spectra ( doschek & cowan 1984 ) and o viii lines in supernova remnants ( winkler et al . 1981 ) . and with the upcoming launches of _ chandra _ and _ xmm _ and the high - resolution spectrometers aboard , c v and o viii lines are expected to be seen in may other electron - ionized , cosmic sources . using different heavy - ion storage rings , kilgus et al . ( 1993 ) and mannervik et al . ( 1997 ) have measured dr for c v via the capture channels @xmath5 where @xmath6 for the results of kilgus et al . and @xmath7 for the results of mannervik et al . kilgus et al . ( 1990 ) have also measured dr for o viii via the capture channels @xmath8 where @xmath9 . the radiative stabilization of these autoionizing c v and o vii states to bound configurations results in dr . details of the experimental techniques used are given in the references cited . the paper is organized as follows : we describe in section [ sec : methodofcalculation ] how one produces a dr rate coefficient using measured dr resonance strengths and energies . in section [ sec : resultsanddiscussion ] we present the resulting rate coefficients and compare the derived dr rates with published theoretical rates . we also give a simple fitting formula for use in plasma modeling .

using published measurements of dielectronic recombination ( dr ) resonance strengths and energies for c v to c iv and o viii to o vii , we have calculated the dr rate coefficient for these ions . the merts et al . we describe the technique used to obtain dr rate coefficients from laboratory measurements of dr resonance strengths and energies . for use in plasma modeling

using published measurements of dielectronic recombination ( dr ) resonance strengths and energies for c v to c iv and o viii to o vii , we have calculated the dr rate coefficient for these ions . our derived rates are in good agreement with multiconfiguration , intermediate - coupling and multiconfiguration , fully - relativistic calculations as well as with most @xmath0 coupling calculations . our results are not in agreement with the recommended dr rates commonly used for modeling cosmic plasmas . we have used theoretical radiative recombination ( rr ) rates in conjunction with our derived dr rates to produce a total recombination rate for comparison with unified rr+dr calculations in @xmath0 coupling . our results are not in agreement with undamped , unified calculations for c v but are in reasonable agreement with damped , unified calculations for o viii . for c v , the burgess general formula ( gf ) yields a rate which is in very poor agreement with our derived rate . the burgess & tworkowski modification of the gf yields a rate which is also in poor agreement . the merts et al . modification of the gf yields a rate which is in fair agreement . for o viii the gf yields a rate which is in fair agreement with our derived rate . the burgess & tworkowski modification of the gf yields a rate which is in good agreement . and the merts et al . modification yields a rate which is in very poor agreement . these results suggest that for @xmath1 dr it is not possible to know _ a priori _ which formula will yield a rate closer to the true dr rate . we describe the technique used to obtain dr rate coefficients from laboratory measurements of dr resonance strengths and energies . for use in plasma modeling , we also present easy - to - use fitting formulae for the experimentally derived dr rates .

astro-ph9904258

r

in figures [ fig : cv ] and [ fig : oviii ] we present the c v and o viii dr rate coefficients , respectively , derived using the measured resonance strengths and energies of kilgus et al . ( 1990 , 1993 ) and mannervik ( 1997 ) . the unmeasured contribution to the dr rate due to capture into levels where @xmath54 is predicted to be insignificant ( chen 1986 ; pindzola et al . the absolute uncertainties in the derived dr rates are estimated to be @xmath55 which corresponds to the reported absolute experimental uncertainties . existing theoretical dr rates are also shown in figures [ fig : cv ] and [ fig : oviii ] as well as the rr rates of verner & ferland ( 1996 ) . for c v , the single - configuration @xmath0-coupling calculations of bellantone & hahn ( 1986 ) and romanik ( 1988 ) , multiconfiguration intermediate - coupling calculations of badnell , pindzola , & griffin ( 1990 ) , and multiconfiguration fully - relativistic calculations of chen ( 1988 ) are all in good agreement with our experimentally inferred rate . the @xmath0-coupling calculations of younger ( 1983 ) are @xmath56 larger than the experimental rate . the recommended and commonly used dr rate of shull & van steenberg ( 1982 ) peaks at a value @xmath57 larger than ours and has a steeper low @xmath12 behavior . pindzola et al . ( 1990 ) calculated resonance strengths for o viii using intermediate - coupling , multiconfiguration hartree - fock ( mchf ) and intermediate - coupling , multiconfiguration thomas - fermi ( mctf ) techniques . using their mchf results for capture into levels @xmath58 and their mctf results for @xmath59 , as well as the experimental resonance energies , we calculate the corresponding dr rate using equation [ eq : rate2 ] . the resulting rate is in good agreement with our derived rate . the single - configuration @xmath0-coupling rate of bellantone & hahn ( 1986 ) is also in good agreement with the experimental rate , though with decreasing @xmath12 their rate falls off sooner than ours . the recommended and commonly used dr rate of shull & van steenberg ( 1982 ) is @xmath60 larger than our derived rate . not shown in figure [ fig : oviii ] , for reasons of clarity , is the rate of zhdanov ( 1978 ) whose peak rate is @xmath61 times larger than the experimental rate . nahar & pradhan ( 1997 ) and nahar ( 1999 ) present unified rr+dr rates . to compare with their results we add the rr rates of verner & ferland ( 1996 ) to the experimentally derived dr rates . thus we treat rr and dr as independent processes and do not allow for the possibility of interference between the two recombination channels . the validity of this approach is supported by recent theoretical work ( for dr on systems ranging in complexity from c ii and mg ii to u xcii ) which has shown the effect of interferences to be small ( @xcite ) . figures [ fig : cvnah ] and [ fig : oviiinah ] show for c v and o viii , respectively , the unified rr+dr rate of nahar & pradhan and the total rr+dr rate using the derived dr results and the rr results of verner & ferland . for c v , at peak value the undamped , unified rate of nahar & pradhan is @xmath62 larger than our resulting total rr+dr rate . this is consistent with the estimate by pradhan & zhang ( 1997 ) that allowance for radiation damping would reduce the undamped rate by @xmath63 . for o viii , at peak value the damped , unified rate of nahar is @xmath64 larger than our resulting total rr+dr rate . dr rate coefficients are sometimes calculated using the burgess ( 1965 ) general formula ( gf ) or versions of the gf as modified by merts et al . ( 1976 ) and by burgess & tworkowski ( 1976 ) . we have calculated the burgess and merts et al . rates using the formulae as given by cowan ( 1981 ) . we use oscillator strengths and excitation energies from wiese , smith , & glennon ( 1966 ) . shown in figure [ fig : cvburg ] for c v is the merts et al . rate which is in fair agreement with our derived rate , though with decreasing @xmath12 it goes to zero sooner than the experimental rate . also shown in figure [ fig : cvburg ] is the burgess gf rate which is a factor of @xmath65 times larger than the experimental rate . the burgess & tworkowski ( 1976 ) modification of the gf yields a rate @xmath66 larger than our derived rate . this is surprisingly good considering that their modification is meant for dr forming heliumlike , not lithiumlike , ions . figure [ fig : oviiiburg ] shows for o viii the gf rate which is @xmath67 larger than the experimental rate and , considering the expected accuracy of the burgess formula , in fair agreement . the burgess & tworkowski rate is in good agreement . also shown is the merts et al . formula rate which is a factor of @xmath65 smaller than the experimental rate . our c v and o viii results strongly suggest that for @xmath1 dr it is not possible _ a priori _ to know which formula will yield a result closer to the true rate . for use in plasma modeling , we have fit the experimentally derived c v and o viii dr rates using the simple formula ( arnaud & raymond 1992 ) @xmath68 here @xmath69 and @xmath70 are , respectively , the strength and energy parameters for the @xmath71th fitting component . best fit values are listed in table [ tab : fitparameters ] . for c v , the fit is good to better 1% for @xmath72 k. below @xmath73 k , with decreasing @xmath12 the fit goes to zero faster than the derived rate . but this error is insignificant for plasma modeling as the rr rate is @xmath74 orders of magnitude larger than the dr rate at these temperatures . for o viii , the fit is good to better 1% for @xmath75 k. below @xmath76 k , with decreasing @xmath12 the fit goes to zero faster than the derived rate . this error is insignificant for plasma modeling as the rr rate is @xmath77 orders of magnitude larger than the dr rate at these temperatures .

the burgess & tworkowski modification of the gf yields a rate which is also in poor agreement . modification of the gf yields a rate which is in fair agreement . for the burgess & tworkowski modification of the gf yields a rate which is in good agreement . and the merts et al .

using published measurements of dielectronic recombination ( dr ) resonance strengths and energies for c v to c iv and o viii to o vii , we have calculated the dr rate coefficient for these ions . our derived rates are in good agreement with multiconfiguration , intermediate - coupling and multiconfiguration , fully - relativistic calculations as well as with most @xmath0 coupling calculations . our results are not in agreement with the recommended dr rates commonly used for modeling cosmic plasmas . we have used theoretical radiative recombination ( rr ) rates in conjunction with our derived dr rates to produce a total recombination rate for comparison with unified rr+dr calculations in @xmath0 coupling . our results are not in agreement with undamped , unified calculations for c v but are in reasonable agreement with damped , unified calculations for o viii . for c v , the burgess general formula ( gf ) yields a rate which is in very poor agreement with our derived rate . the burgess & tworkowski modification of the gf yields a rate which is also in poor agreement . the merts et al . modification of the gf yields a rate which is in fair agreement . for o viii the gf yields a rate which is in fair agreement with our derived rate . the burgess & tworkowski modification of the gf yields a rate which is in good agreement . and the merts et al . modification yields a rate which is in very poor agreement . these results suggest that for @xmath1 dr it is not possible to know _ a priori _ which formula will yield a rate closer to the true dr rate . we describe the technique used to obtain dr rate coefficients from laboratory measurements of dr resonance strengths and energies . for use in plasma modeling , we also present easy - to - use fitting formulae for the experimentally derived dr rates .

astro-ph9904258

i

we have presented a simple technique for obtaining dr rate coefficients from laboratory measurements of dr resonance strengths and energies . with this technique , we have derived dr rates for c v to c iv and o viii to o vii using published resonance strengths and energies . our derived rates are in good agreement with multiconfiguration , intermediate - coupling and multiconfiguration , fully - relativistic calculations as well as with most @xmath0-coupling calculations . our rates are not in agreement with the recommended dr rates commonly used for astrophysical plasma modeling . we have used theoretical radiative recombination ( rr ) rates in conjunction with our derived dr rates to produce a total recombination rate for comparison with unified rr+dr calculations in @xmath0 coupling . our results are not in agreement with undamped , unified calculations for c v but are in reasonable agreement with damped , unified calculations for o viii . also , neither the burgess general formula , the merts et al . formula , nor the burgess & tworkowski formula consistently yield a rate which is in agreement with our derived rates . this suggests that for @xmath78 dr it is not possible to know _ a priori _ which formula will yield a rate closer to the true dr rate . we have also presented simple fitting formula of the experimentally derived dr rates for use in plasma modeling . the author would like to thank n. r. badnell , m. h. chen , t. w. gorczyca , s. m. kahn , d. a. liedahl , s. n. nahar , and a. wolf for stimulating conversation and for critically reading the manuscript . this work was supported in part by nasa high energy astrophysics x - ray astronomy research and analysis grant nag5 - 5123 . wiese , w. l. , smith , m. w. , & glennon , b. m. 1966 , atomic transition probabilities , volume i hydrogen through neon , national standard reference data series , national bureau of standards 4 ( u. s. government printing office , washington , d.c . )

our derived rates are in good agreement with multiconfiguration , intermediate - coupling and multiconfiguration , fully - relativistic calculations as well as with most @xmath0 coupling calculations . our results are not in agreement with the recommended dr rates commonly used for modeling cosmic plasmas . we have used theoretical radiative recombination ( rr ) rates in conjunction with our derived dr rates to produce a total recombination rate for comparison with unified rr+dr calculations in @xmath0 coupling . our results are not in agreement with undamped , unified calculations for c v but are in reasonable agreement with damped , unified calculations for o viii . for c v , the burgess general formula ( gf ) yields a rate which is in very poor agreement with our derived rate . o viii the gf yields a rate which is in fair agreement with our derived rate . modification yields a rate which is in very poor agreement . these results suggest that for @xmath1 dr it is not possible to know _ a priori _ which formula will yield a rate closer to the true dr rate . , we also present easy - to - use fitting formulae for the experimentally derived dr rates .

using published measurements of dielectronic recombination ( dr ) resonance strengths and energies for c v to c iv and o viii to o vii , we have calculated the dr rate coefficient for these ions . our derived rates are in good agreement with multiconfiguration , intermediate - coupling and multiconfiguration , fully - relativistic calculations as well as with most @xmath0 coupling calculations . our results are not in agreement with the recommended dr rates commonly used for modeling cosmic plasmas . we have used theoretical radiative recombination ( rr ) rates in conjunction with our derived dr rates to produce a total recombination rate for comparison with unified rr+dr calculations in @xmath0 coupling . our results are not in agreement with undamped , unified calculations for c v but are in reasonable agreement with damped , unified calculations for o viii . for c v , the burgess general formula ( gf ) yields a rate which is in very poor agreement with our derived rate . the burgess & tworkowski modification of the gf yields a rate which is also in poor agreement . the merts et al . modification of the gf yields a rate which is in fair agreement . for o viii the gf yields a rate which is in fair agreement with our derived rate . the burgess & tworkowski modification of the gf yields a rate which is in good agreement . and the merts et al . modification yields a rate which is in very poor agreement . these results suggest that for @xmath1 dr it is not possible to know _ a priori _ which formula will yield a rate closer to the true dr rate . we describe the technique used to obtain dr rate coefficients from laboratory measurements of dr resonance strengths and energies . for use in plasma modeling , we also present easy - to - use fitting formulae for the experimentally derived dr rates .

0802.2531

i

we have studied using both the full potential nonorthogonal local orbital minimum basis band structure scheme ( fplo ) and the full - potential screened korringa - kohn - rostoker ( fskkr ) electronic structure methods the electronic , magnetic and gap - related properties of the niysi compounds and have expanded our study also to cover the case of surfaces , interfaces with semiconductors and defects . when y stands for v , the ferromagnetism is not very stable due to the weak v - v interactions and these compounds are not suitable for applications . when y stands for cr or mn , the ferromagnetism is extremely stable leading to very high values of the curie temperature which is predicted to be @xmath0700 k for nicrsi and @xmath01100 k for nimnsi . both nicrsi and nimnsi are half - metallic at their equilibrium lattice constant with large width of the minority - spin gap ( @xmath01 ev ) and integer values of the total spin moment as predicted by the slater pauling rule . the gap is created due to the creation of bonding and antibonding @xmath1-hybrids in the minority - spin band . the width of the gap is marginally affected upon tetragonalization even when we expand or contract the lattice by 5% . nicrsi ( 001 ) surfaces present a high spin - polarization at the fermi level with respect to the nimnsi alloy due to the large intensity of the cr majority - spin density of states ( dos ) at the fermi level . in the case of interfaces with semiconductors with similar lattice parameter ( gap , zns and si ) , ni - based contacts show larger spin - polarization since ni atoms at the interface layer have a more bulk - like environment and in the case of nicrsi interfaces the high cr - dos leads to values of the spin - polarization for the ni - based contacts as high as 90% . finally , we have shown that there are two kind of defects . the defects and atomic swaps involving the cr(mn ) and si atoms lead to a broadening of the bands and the gap is slowly shrinking and for a critical value of the defects - concentration it disappears . ni defects on the other hand lead to a shift of the energy - localized @xmath16 states within the gap and these impurity states completely destroy the half - metallicity . for realistic applications it seems that nicrsi is more suitable with respect to both nimnsi studied here and the well - known and widely studied nimnsb heusler alloy . its curie temperature is smaller than the mn - based alloys but it is still high - enough for applications exceeding considerably the room temperature . moreover the large population of cr majority - spin states at the fermi level ensures the high - spin polarization at the fermi level which is needed for the injection of current in semiconductors . crucial for the operation of devices based on heusler alloys is the prevention of the creation of ni defects , since they induce impurity states within the gap which can couple to interface states and completely destroy the spin - polarization of the current injected into the semiconductor . p. j. webster and k. r. a. ziebeck , in _ alloys and compounds of d - elements with main group elements . _ , edited by h. r. j. wijn , landolt - bornstein , new series , group iii , vol . 19/c ( springer - verlag , berlin 1988 ) .

nicrsi and nimnsi contrary to nivsi are half - metallic at their equilibrium lattice constant exhibiting integer values of the total spin magnetic moment and thus we concentrate on these two alloys . the cr - cr and mn - mn interactions make ferromagnetism extremely stable and the curie temperature exceeds 1000 k for nimnsi . the first - ones which involve the cr(mn ) and si atoms induce states at the edges of the gap which persists for a moderate - concentration of defects .

using state - of - the - art first - principles calculations we study the properties of the ferromagnetic heusler compounds niysi where y stands for v , cr or mn . nicrsi and nimnsi contrary to nivsi are half - metallic at their equilibrium lattice constant exhibiting integer values of the total spin magnetic moment and thus we concentrate on these two alloys . the minority - spin gap has the same characteristics as for the well - known nimnsb alloy being around @xmath01 ev . upon tetragonalization the gap is present in the density of states even for expansion or contraction of the out - of - plane lattice parameter by 5% . the cr - cr and mn - mn interactions make ferromagnetism extremely stable and the curie temperature exceeds 1000 k for nimnsi . surface and interfaces with gap , zns and si semiconductors are not half - metallic but in the case of nicrsi the ni - based contacts present spin - polarization at the fermi level over 90% . finally , we show that there are two cases of defects and atomic - swaps . the first - ones which involve the cr(mn ) and si atoms induce states at the edges of the gap which persists for a moderate - concentration of defects . defects involving ni atoms induce states localized within the gap completely destroying the half - metallicity . based on single - impurity calculations we associate these states to the symmetry of the crystal .

1002.3315

i

survival analysis is a commonly - used method for the analysis of failure time such as biological death , mechanical failure , or credit default . within this context , death or failure is also referred to as an event " . survival analysis tries to model time - to - event data , which is usually subject to censoring due to the termination of study . the main goal is to study the dependence of the survival time @xmath0 on covariate variables @xmath1 , where @xmath2 denotes the dimensionality of the covariate space . one common way of achieving this goal is hazard regression , which studies how the conditional hazard function of @xmath0 depends on the covariate @xmath3 , which is defined as @xmath4 according to the definition , the conditional hazard function is nothing but the instantaneous rate of failure at time @xmath5 given a particular value @xmath6 for the covariate @xmath7 . the proportional hazards model is very popular , partially due to its simplicity and its convenience in dealing with censoring . the model assumes that @xmath8 in which @xmath9 is the baseline hazard function and @xmath10 is the covariate effect . note that this model is not uniquely determined in that @xmath11 and @xmath12 give the same model for any @xmath13 . thus one identifiability condition needs to be specified . when the identifiability condition @xmath14 is enforced , the function @xmath9 , the conditional hazard function of @xmath0 given @xmath15 , is called the baseline hazard function . by taking the reparametrization @xmath16 , @xcite introduced the proportional hazards model @xmath17 see @xcite and references therein for more detailed literature on cox s proportional hazards model . here the baseline hazard function @xmath9 is typically completely unspecified and needs to be estimated nonparametrically . a linear model assumption , @xmath18 , may be made , as is done in this paper . here @xmath19 is the regression parameter vector . while conducting survival analysis , we not only need to estimate @xmath20 but also have to estimate the baseline hazard function @xmath9 nonparametrically . interested readers may consult @xcite for more details . recent technological advances have made it possible to collect a huge amount of covariate information such as microarray , proteomic and snp data via bioimaging technology while observing survival information on patients in clinical studies . however it is quite likely that not all available covariates are associated with the clinical outcome such as the survival time . in fact , typically a small fraction of covaraites are associated with the clinical time . this is the notion of sparsity and consequently calls for the identification of important risk factors and at the same time quantifying their risk contributions when we analyze time - to - event data with many predictors . mathematically , it means that we need to identify which @xmath21s are nonzero and also estimate these nonzero @xmath21s . most classical model selection techniques have been extended from linear regression to survival analysis . they include the best - subset selection , stepwise selection , bootstrap procedures @xcite , bayesian variable selection @xcite . please see references therein . similarly , other more modern penalization approaches have been extended as well . @xcite applied the lasso penalty to survival analysis . @xcite considered survival analysis with the scad and other folded concave penalties . @xcite proposed the adaptive lasso penalty while studying time - to - event data . among many other considerations is @xcite . available theory and empirical results show that these penalization approaches work well with a moderate number of covariates . recently we have seen a surge of interest in variable selection with an ultra - high dimensionality . by ultra - high , @xcite meant that the dimensionality grows exponentially in the sample size , i.e. , @xmath22 for some @xmath23 . for ultra - high dimensional linear regression , @xcite proposed sure independence screening ( sis ) based on marginal correlation ranking . asymptotic theory is proved to show that , with high probability , sis keeps all important predictor variables with vanishing false selection rate . an important extension , iterative sis ( isis ) , was also proposed to handle difficult cases such as when some important predictors are marginally uncorrelated with the response . in order to deal with more complex real data , @xcite extended sis and isis to more general loss based models such as generalized linear models , robust regression , and classification and improved some important steps of the original isis . in particular , they proposed the concept of conditional marginal regression and a new variant of the method based on splitting samples . a non - asymptotic theoretical result shows that the splitting based new variant can reduce false discovery rate . although the extension of @xcite covers a wide range of statistical models , it has not been explored whether the iterative sure independence screening method can be extended to hazard regression with censoring event time . in this work , we will focus on cox s proportional hazards model and extend sis and isis accordingly . other extensions of sis include @xcite and @xcite to generalized linear models and nonparametric additive models , in which new insights are provided via elegant mathematical results and carefully designed simulation studies . the rest of the article is organized as follows . section [ sec : cox ] details the cox s proportional hazards model . an overview of variable selection via penalized approach is given in section [ sec : variable - selection - cox ] for cox s proportional hazards model . we extend the sis and isis procedures to cox s model in section [ sec : sis - cox ] . simulation results in section [ sec : simulation ] and real data analysis in section [ sec : realdata ] demonstrate the effectiveness of the proposed sis and isis methods .

recent technological advances have made it possible to collect a huge amount of covariate information such as microarray , proteomic and snp data via bioimaging technology while observing survival information on patients in clinical studies . thus , the same challenge applies in survival analysis in order to understand the association between genomics information and clinical information about the survival time . in this work , we extend the sure screening procedure @xcite to cox s proportional hazards model with an iterative version available . this demonstrates the utility and versatility of the iterative sure independence screening scheme . ,

variable selection in high dimensional space has challenged many contemporary statistical problems from many frontiers of scientific disciplines . recent technological advances have made it possible to collect a huge amount of covariate information such as microarray , proteomic and snp data via bioimaging technology while observing survival information on patients in clinical studies . thus , the same challenge applies in survival analysis in order to understand the association between genomics information and clinical information about the survival time . in this work , we extend the sure screening procedure @xcite to cox s proportional hazards model with an iterative version available . numerical simulation studies have shown encouraging performance of the proposed method in comparison with other techniques such as lasso . this demonstrates the utility and versatility of the iterative sure independence screening scheme . ,

0810.2508

c

we analyzed the constituents stocks of the dow jones industrial average and the standard & poor s 100 index of the nyse stock exchange market . surprisingly , we discovered the data collapse of the histograms of the djia30 price fluctuations and of the s&p100 price fluctuations to the universal non - parametric bramwell - holdsworth - pinton ( bhp ) distribution . since the bhp probability density function appears in several other dissimilar phenomena , our result revealed an universal feature of the stock exchange market .

we analyze the constituents stocks of the dow jones industrial average ( djia30 ) and the standard & poor s 100 index ( s&p100 ) of the nyse stock exchange market . surprisingly , we discover the data collapse of the histograms of the djia30 price fluctuations and of the s&p100 price fluctuations to the universal non - parametric bramwell - holdsworth - pinton ( bhp ) distribution . since the bhp probability density function appears in several other dissimilar phenomena , our result reveals an universal feature of the stock exchange market .

we analyze the constituents stocks of the dow jones industrial average ( djia30 ) and the standard & poor s 100 index ( s&p100 ) of the nyse stock exchange market . surprisingly , we discover the data collapse of the histograms of the djia30 price fluctuations and of the s&p100 price fluctuations to the universal non - parametric bramwell - holdsworth - pinton ( bhp ) distribution . since the bhp probability density function appears in several other dissimilar phenomena , our result reveals an universal feature of the stock exchange market . stock exchange market , universality , econometrics

cond-mat9911351

i

in recent years a significant effort has been devoted to the understanding of glass - forming systems . recent theoretical and numerical results clearly show that the slowing down of the dynamics near the glass transition is strongly connected to the potential energy landscape geometry . the trajectory of the representative point in the configuration space can be viewed as a path in a multidimensional potential energy surface @xcite . the dynamics is therefore strongly influenced by the topography of the potential energy landscape : local minima , barriers heights , basins of attraction an other topological properties all influence the dynamics . the potential energy surface of a super - cooled liquid contains a large number of local minima , called _ inherent structures _ ( is ) by stillinger @xcite . all states that under local energy minimization will flow into the same is define the _ basin _ of the is ( valley ) . with this pictures in mind the time evolution of the system can be seen as the result of two different processes : thermal relaxation into basins ( _ intra - basin _ motion ) and thermally activated potential energy barrier crossing between different basins ( _ inter - basin _ motion ) . when the temperature is lowered down to the order of the critical mode coupling theory ( mct ) temperature @xmath1 the inter - basin motion slows down and the relaxation dynamics is dominated by the slow thermally activated crossing of potential energy barriers @xcite . if the temperature is further reduced the relaxation time eventually becomes of the same order of the observation time and the system falls out of equilibrium since there is not enough time to cross barriers and equilibrate . this define the `` experimental''glass transition temperature @xmath2 . the regime between @xmath1 and @xmath2 can not be described by the mct since it neglects activated processes responsible for barrier crossing . in mct the relaxation time diverges at @xmath1 , leading to @xmath3 , and the dynamics remains confined into a single basin forever . the essential features of mct for glass - forming systems are also common to the high temperature phase of some fully connected spin glass models @xcite , the most well known being the spherical @xmath0-spin spin glass model @xcite . we shall call these models _ mean - field @xmath0-spin - like _ glass models . as a consequence at the critical temperature @xmath1 , called @xmath4 in @xmath0-spin language , an ergodic to non - ergodic transition takes place . below this temperature the system is dynamically confined to a metastable state ( a basin ) @xcite since relaxation to true equilibrium can only take place via activated processes , absent in mean - field models . for these systems , nevertheless , it is known that the true equilibrium transition to a low temperature phase occurs below @xmath4 at the static critical temperature @xmath5 , also denoted by @xmath6 @xcite . this is the analogous of the kauzmann temperature @xmath7 for liquids . the glass transition temperature @xmath2 of real systems sits somewhere in between @xmath5 and @xmath4 . this transition , obviously , can not be reached even on infinite time in mean - field models . despite these difficulties mean - field models , having the clear advantage of being analytically tractable , have been largely used to study the properties of fragile glassy systems , especially between the dynamical temperature @xmath4 and the static temperature @xmath5 . the picture that emerges is however not complete since activated process can not be captured by mean - field models . therefore the relevance of mean - field results for real systems can not be considered completely stated . only recently activated processes in mean - field - like models have been invesigated in extended numerical investigation of _ finite - size _ fully - connected @xmath0-spin - like models @xcite . comparing the results with the observed behavior of super - cooled liquids near @xmath1 we can conclude that , once activated process are allowed , mean - field @xmath0-spin - like models are highly valuable for a deep understanding of the glass transition in real systems . we report the main results obtained for the ising - spin random orthogonal model ( rom ) @xcite , defined by the hamiltonian @xcite , @xmath8 where @xmath9 are @xmath10 ising spin variables , and @xmath11 is a @xmath12 random symmetric orthogonal matrix with @xmath13 . for @xmath14 this model has the same thermodynamic properties of the @xmath0-spin model : a dynamical transition at @xmath15 , with threshold energy per spin @xmath16 , and a static transition at @xmath17 , with critical energy per spin @xmath18 @xcite .

we analyze the properties of the energy landscape of _ finite - size _ fully connected @xmath0-spin - like models whose high temperature phase is described , in the thermodynamic limit , by the schematic mode coupling theory of super - cooled liquids . we show that _ finite - size _ fully connected @xmath0-spin - like models , where activated processes are possible , do exhibit properties typical of real super - cooled liquid when both are near the critical glass transition . our results support the conclusion that fully - connected @xmath0-spin - like models are the natural statistical mechanical models for studying the glass transition in super - cooled liquids . and glass transition , spin - glass , random models pacs : 64.70.pf , 75.10.nr , 61.20.gy , 82.20.wt

we analyze the properties of the energy landscape of _ finite - size _ fully connected @xmath0-spin - like models whose high temperature phase is described , in the thermodynamic limit , by the schematic mode coupling theory of super - cooled liquids . we show that _ finite - size _ fully connected @xmath0-spin - like models , where activated processes are possible , do exhibit properties typical of real super - cooled liquid when both are near the critical glass transition . our results support the conclusion that fully - connected @xmath0-spin - like models are the natural statistical mechanical models for studying the glass transition in super - cooled liquids . and glass transition , spin - glass , random models pacs : 64.70.pf , 75.10.nr , 61.20.gy , 82.20.wt

1210.0323

i

modelling particle acceleration at snrs is one of the main goal to explain the origin of galactic cosmic rays ( crs ) in the context of the so - called _ supernova paradigm _ ( see e.g. * ? ? ? this paradigm requires that snrs are able to accelerate nuclei up to energies as high as a few times @xmath3 gev , converting a fraction @xmath4 of the snr kinetic energy into crs . there is an increasing amount of evidence that shocks in young snrs can indeed reach the required efficiency . unfortunately , all these evidence are indirect and when considered individually can be also explained by other mechanisms that do not require efficient acceleration . a clear example of such an ambiguous situation is represented by @xmath2-ray emission . in the last few years several snrs have been detected both in the gev and in the tev band but , in spite of this increasing amount of data , the question whether this emission is due to hadronic ( through the decay of neutral pions produced in nuclear interactions between accelerated nuclei and the background plasma ) or leptonic processes ( due to inverse compton and/or bremsstrahlung ) is still debated ( see e.g. * ? ? ? * for a general discussion on this topic ) . a possible way to discriminate between the _ leptonic _ ( i.e. inefficient ) and the _ hadronic _ ( i.e. efficient ) scenario is studing the effects that particle acceleration produces at all observable wavelengths , rather that focus the attention only on the @xmath2-ray emission , simultaneously using multiple set of data to constrain the model . here we apply the non - linear diffusive shock acceleration ( nldsa ) theory in order to explain the non - thermal emission and morphological properties of two similar snrs , namely tycho and kepler . tycho , in particular , has been recently detected in @xmath2-rays by fermi - lat @xcite and veritas @xcite , and can be considered one of the most promising object where to test the shock acceleration theory and hence the cr snr connection . we presented a detailed model applyed to tycho in @xcite . kepler , on the other hand , has not been detected in @xmath2-ray band , yet , but it is very similar to tycho in many respects , and we show that the predicted @xmath2-ray spectrum should be detectable by cta .

we apply the non - linear diffusive shock acceleration theory in order to describe the properties of two supernova remnants , sn 1572 ( tycho ) and sn 1604 ( kepler ) . by analyzing the multi - wavelength spectra , we infer that both tycho s and kepler s forward shocks ( fs ) are accelerating protons up to @xmath0 tev , channeling into cosmic rays more than 10 per cent of their kinetic energy . we explain the @xmath2-ray spectrum from the gev up to the tev band as due to pion decay produced in nuclear collisions by accelerated nuclei scattering against the background gas . on the other hand , due to the larger distance , the @xmath2-ray emission from kepler is not detected , being below the sensitivity of the present detectors , but it should be detectable by cta . address = inaf - osservatorio astrofisico di arcetri , l.go e. fermi 5 , i - 50125 firenze , italia address = department of astrophysical sciences , princeton university , princeton , nj 08544 , usa

we apply the non - linear diffusive shock acceleration theory in order to describe the properties of two supernova remnants , sn 1572 ( tycho ) and sn 1604 ( kepler ) . by analyzing the multi - wavelength spectra , we infer that both tycho s and kepler s forward shocks ( fs ) are accelerating protons up to @xmath0 tev , channeling into cosmic rays more than 10 per cent of their kinetic energy . we find that the streaming instability induced by cosmic rays is consistent with the x - ray morphology of the remnants , indicating a very efficient magnetic field amplification ( up to @xmath1 g ) . in the case of tycho we explain the @xmath2-ray spectrum from the gev up to the tev band as due to pion decay produced in nuclear collisions by accelerated nuclei scattering against the background gas . on the other hand , due to the larger distance , the @xmath2-ray emission from kepler is not detected , being below the sensitivity of the present detectors , but it should be detectable by cta . address = inaf - osservatorio astrofisico di arcetri , l.go e. fermi 5 , i - 50125 firenze , italia address = department of astrophysical sciences , princeton university , princeton , nj 08544 , usa

1204.6708

c

in this letter we have calculated the time - like pion - photon transition and em form factors up to nlo in the @xmath0 factorization formalism . the corresponding nlo hard kernels were derived by analytically continuing the space - like ones to the time - like region of the momentum transfer squared @xmath7 . we have identified the @xmath0-dependent internal gluon propagator as the major source for the strong phase of the time - like pion em form factor , which increases with @xmath7 , and approaches an asymptotic value @xcite . the magnitudes of the time - like form factors are larger than those of the space - like ones . it has been realized that the above features are attributed to the inclusion of the parton transverse momenta , and consistent with the tendency implied by the data . it was observed that the nlo corrections in magnitude ( phase ) change the lo leading - twist results by roughly @xmath1 ( @xmath2 ) for the pion transition form factor , and @xmath3 ( @xmath4 ) for the pion em form factor as @xmath139 gev@xmath6 . the stability against radiative corrections justifies the @xmath0 factorization formalism for both time - like form factors at leading twist . therefore , the predictions for strong phases of annihilation contributions to two - body hadronic @xmath8 meson decays in the pqcd approach may be reliable . the framework presented here will have other applications , for example , to the construction of the two - meson wave functions for three - body @xmath8 meson decays . 0.3 cm we thank b. ananthanarayan and i. caprini for useful discussions . the work was supported in part by the national science council of r.o.c . under grant nsc-98 - 2112-m-001 - 015-my3 , and by the national center for theoretical sciences of r.o.c . 99 s. catani , m. ciafaloni and f. hautmann , phys . lett . b * 242 * , 97 ( 1990 ) ; nucl . b * 366 * , 135 ( 1991 ) . collins and r.k . ellis , nucl . b * 360 * , 3 ( 1991 ) . levin , m.g . ryskin , yu.m . shabelskii , and a.g . shuvaev , sov . . phys . * 53 * , 657 ( 1991 ) . j. botts and g. sterman , nucl . b * 325 * , 62 ( 1989 ) . n . li and g. sterman , nucl . b * 381 * , 129 ( 1992 ) . t. huang and q.x . shen , z. phys . c * 50 * , 139 ( 1991 ) ; j.p . ralston and b. pire , phys . lett . * 65 * , 2343 ( 1990 ) . s. nandi and h .- n . li , phys . d * 76 * , 034008 ( 2007 ) . n . li and s. mishima , phys . d * 80 * , 074024 ( 2009 ) . shen , y .- m . wang , and h. zou . d * 83 * , 054029 ( 2011 ) . shen , and y .- m . wang , arxiv:1201.5066 [ hep - ph ] ( 2012 ) . keum , h - n . li , and a.i . sanda , phys . b * 504 * , 6 ( 2001 ) ; phys . d * 63 * , 054008 ( 2001 ) ; y.y . keum and h .- n . li , phys . rev . d * 63 * , 074006 ( 2001 ) ; c.d . lu , k. ukai and m.z . yang , phys . d * 63 * , 074009 ( 2001 ) . chen and h .- n . li , phys . b * 561 * , 258 ( 2003 ) ; phys . d * 70 * , 054006 ( 2004 ) . d. muller et al . , fortschr . physik . * 42 * , 101 ( 1994 ) ; m. diehl , t. gousset , b. pire , and o. teryaev , phys . lett . * 81 * , 1782 ( 1998 ) ; m.v . polyakov , nucl . b555 * , 231 ( 1999 ) . r. jakob , p. kroll and m. raulfs , j. phys . g * 22 * , 45 ( 1996 ) . m. nagashima and h .- n . li , phys . d * 67 * , 034001 ( 2003 ) . d * 64 * , 014019 ( 2001 ) r. jakob and p. kroll , phys . b * 315 * , 463 ( 1993 ) ; b * 319 * , 545 ( 1993 ) . s. j. brodsky , t. huang , and g. p. lepage , slac - pub-2540 ; s.j . brodsky , p. hoyer , c. peterson , and n. sakai , phys . b * 93 * , 451 ( 1980 ) ; s.j . brodsky , c. peterson , and n. sakai , phys . d * 23 * , 2745 ( 1981 ) . u. raha and h. kohyama , phys . d * 82 * , 114012 ( 2010 ) . li , phys . rev . d * 66 * , 094010 ( 2002 ) ; k. ukai and h .- n . li , phys . b * 555 * , 197 ( 2003 ) . d * 52 * , 3958 ( 1995 ) . chen , h. kohyama , k. ohnishi , u. raha , and y .- l . shen , phys . b * 693 * , 102 ( 2010 ) . t. gousset and b. pire , phys . d * 51 * , 15 ( 1995 ) . v. braun , m. gockeler , r. horsley , h. perlt , d. pleiter , et al . d * 74 * , 074501 ( 2006 ) . s.j . brodsky and g.p . lepage , phys . d * 24 * , 1808 ( 1981 ) . bernard aubert et al . d * 74 * , 012002 ( 2006 ) . m. nagashima and h .- n . li , eur . phys . j. c * 40 * , 395 ( 2005 ) . whalley , j. phys . g * 29 * , a1 ( 2003 ) ; j. milana , s. nussinov , and m.g . olsson , phys . lett . * 71 * , 2533 ( 1993 ) ; t.k . pedlar et al . * 95 * , 261803 ( 2005 ) . protopopescu , m. alston - garnjost , a. barbaro - galtieri et al . d * 7 * , 1279 ( 1973 ) . cao , y .- b . dai , and c .- s . huang , eur . j. c * 11 * , 501 ( 1999 ) . t. huang and x .- g . wu , phys . d * 70 * , 093013 ( 2004 ) . t. kurimoto , h .- li , and a. i. sanda , phys . d * 65 * , 014007 ( 2002 ) . a. khodjamirian , r. ruckl , and c. w. winhart , phys . rev . d 58 , 054013 ( 1998 ) . b. ananthanarayan , i. caprini and i. s. imsong , phys . d * 85 * , 096006 ( 2012 ) .

we calculate the time - like pion - photon transition form factor and the pion electromagnetic form factor up to next - to - leading order ( nlo ) of the strong coupling constant in the leading - twist @xmath0 factorization formalism . it is found that the nlo corrections to the magnitude ( phase ) are lower than @xmath1 ( @xmath2 ) for the former , and lower than @xmath3 ( @xmath4 ) for the latter at large invariant mass squared @xmath5 gev@xmath6 of the virtual photons . potential extensions of our formalism to two - body and three - body hadronic @xmath8 meson decays are pointed out .

we calculate the time - like pion - photon transition form factor and the pion electromagnetic form factor up to next - to - leading order ( nlo ) of the strong coupling constant in the leading - twist @xmath0 factorization formalism . it is found that the nlo corrections to the magnitude ( phase ) are lower than @xmath1 ( @xmath2 ) for the former , and lower than @xmath3 ( @xmath4 ) for the latter at large invariant mass squared @xmath5 gev@xmath6 of the virtual photons . the increase of the strong phases with @xmath7 is obtained , consistent with the tendency indicated by experimental data . this behavior is attributed to the inclusion of parton transverse momenta @xmath0 , implying that the @xmath0 factorization is an appropriate framework for analyzing complex time - like form factors . potential extensions of our formalism to two - body and three - body hadronic @xmath8 meson decays are pointed out .

1306.0772

i

the rapidly increasing growth of user - traffic in cellular networks is forcing the need for the deployment of multi - tier heterogeneous networks as well as the development of better analytic methods for quantifying their performance . based on information theoretic arguments , one key performance metric is the signal - to - interference - and - nose - ratio ( sinr ) experienced by a typical user in the network . the sinr is a function of _ propagation processes _ , which incorporate the distance - dependent path - loss function and ( often assumed to be random ) fading and/or shadowing , which we refer to as _ propagation effects_. consequently , results that cast light on the nature of propagation processes ultimately aid in studying the sinr and other useful characteristics of heterogeneous networks . the irregularity of cellular network configurations means that base station positioning is often best assumed to be random , which has motivated the use of models based on stochastic geometry . this assertion has been supported in recent years with tractable models based on the poisson point process yielding accurate solutions @xcite . besides the usual tractability and ` worst - case ' arguments for poisson models , a recent result @xcite has shown that a broad range of network configurations give propagation - based results appearing as though the placement of base stations is a poisson process when sufficiently large log - normal shadowing is incorporated into the model . in this work we present two simple yet very useful results on the invariance and equivalence of network characteristics , such as sinr , that are functions of propagation processes . more precisely , we present a marked poisson model of a random heterogeneous network with the standard power - law path - loss function . under this model , we assume that the propagation process parameters and base station parameters are all random . we present a generalized version of _ propagation ( process ) invariance _ , which shows that propagation processes only depend on one key moment of the random propagation effects and not their distribution . we list how this result has been used previously in the field of communications . building upon the propagation invariance , we then present the main _ network equivalence _ result stating how a general random heterogeneous network model can be immediately replaced with a ` equivalent ' network model with the previously random values , including path - loss exponents , all set to constants . the equivalent ` less random ' model induces the same propagation process and allows for tractable models of multi - tier cellular networks . this network equivalence allows for the comparison of seemingly quite different heterogeneous models by finding their isotropic and , hence , comparable forms . furthermore , we observe for a constant path - loss exponent the isotropic representation reduces simply to a homothecy ( a modification of the constant intensity ) of the original network , which generalizes a previous result showing that the propagation processes only depend on some moment of the emitted power and propagation effects . we illustrate the network equivalence result by giving examples and demonstrating how random path - loss exponents effectively change the network density . we conclude by discussing possible applications such as deriving @xmath0-coverage probability expressions for multi - tier networks in the spirit of @xcite or deriving more general results that allow the replacement of location - dependent networks with more tractable stationary models . gilbert and pollak @xcite derived a classic result showing that a shot noise process , consisting of a sum of functions of poisson points and some random parameter , remains invariant for many different functions and distributions of random parameters . lowen and teich @xcite applied this result to the sum of the power - law functions , akin to the commonly used path - loss function found here , and showed that the sum is independent of the parameter distribution and only relies upon one moment of the random parameter . in the context of sinr of cellular networks , baszczyszyn et al . @xcite observed this invariance characteristic for interference and propagation losses in general ( and not just sums or inteference terms ) , hence the propagation effects are incorporated into the model by only one moment . pinto et al . @xcite independently derived and used a similar result to show that the node degree of secrecy graphs ( based on poisson processes ) is invariant for the distribution of propagation effects . in both papers @xcite , the invariance results are obtained by defining a point process ( which we now call propagation process ) on the positive real line ( a similar process was defined by haenggi @xcite but used for different purposes ) . more specifically , it was shown that this point process is an inhomogeneous poisson point process on the positive real line if the underlying base station configuration forms a homogeneous poisson process . in the context of multi - tier ( heterogeneous ) cellular networks , dhillon et al . @xcite and mukherjee @xcite both derived results for the distribution of the ( downlink ) sinr based on models consisting of independent superpositions of poisson processes with rayleigh fading . madhusudhanan et al . @xcite obtained similar sinr expressions , but derived and used the above propagation invariance result to show that their ( and by extension , the above ) results hold for arbitrary propagation effects . independently , baszczyszyn et al . @xcite used the same argument to derive the sinr - based @xmath0-coverage probability for a single - tier network by first assuming rayleigh fading , then lifting the assumption via propagation invariance . it should be stressed that this approach applies to all results based on functions of propagation processes and not just results involving sums or interference terms . a worthy pursuit would be to list all such results that hold under arbitrary propagation effects , but this is beyond the scope of this paper . our second result involves the equivalence of heterogeneous networks with random parameters , including path - loss exponents . for tractability , the aforementioned multi - tier results all assumed constant path - loss exponents across all tiers . jo et al . @xcite extended this to a model with a different ( but constant ) path - loss exponent on each tier , but only assumed rayleigh fading in their work and examined the sinr based on the base station with the smallest distance to the typical user . also assuming different ( but constant ) path - loss exponents , madhusudhanan et al . @xcite generalized this approach to arbitrary propagation effects by using propagation invariance . for constant ( but different ) parameters across all tiers , they also showed that a multi - tier network is stochastically equivalent to a single - tier network with unity parameters while all the original parameters are incorporated into the density of the ( inhomogeneous poisson ) propagation process . in the context of cellular networks or related fields , we are unaware of work involving random path - loss exponents or equivalence results to the level of generality ( due to more randomized parameters ) presented here .

we consider a general heterogeneous network in which , besides general propagation effects ( shadowing and/or fading ) , individual base stations can have different emitting powers and be subject to different parameters of hata - like path - loss models ( path - loss exponent and constant ) due to , for example , varying antenna heights . these neworks can be replaced with a model where all the previously varying propagation parameters ( including path - loss exponents ) are set to constants while the only trade - off being the introduction of an isotropic base station density . this allows one to perform analytic comparisons of different network models via their isotropic representations . in the case of a constant path - loss exponent , the isotropic representation simplifies to a homogeneous modification of the constant intensity of the original network , thus generalizing a previous result showing that the propagation processes only depend on one moment of the emitted power and propagation effects . we give examples and applications to motivate these results and highlight an interesting observation regarding random path - loss exponents . heterogeneous networks , multi - tier networks , poisson process , shadowing , fading , propagation invariance , stochastic equivalence .

we consider a general heterogeneous network in which , besides general propagation effects ( shadowing and/or fading ) , individual base stations can have different emitting powers and be subject to different parameters of hata - like path - loss models ( path - loss exponent and constant ) due to , for example , varying antenna heights . we assume also that the stations may have varying parameters of , for example , the link layer performance ( sinr threshold , etc ) . by studying the _ propagation processes _ of signals received by the typical user from all antennas marked by the corresponding antenna parameters , we show that seemingly different heterogeneous networks based on poisson point processes can be equivalent from the point of view a typical user . these neworks can be replaced with a model where all the previously varying propagation parameters ( including path - loss exponents ) are set to constants while the only trade - off being the introduction of an isotropic base station density . this allows one to perform analytic comparisons of different network models via their isotropic representations . in the case of a constant path - loss exponent , the isotropic representation simplifies to a homogeneous modification of the constant intensity of the original network , thus generalizing a previous result showing that the propagation processes only depend on one moment of the emitted power and propagation effects . we give examples and applications to motivate these results and highlight an interesting observation regarding random path - loss exponents . heterogeneous networks , multi - tier networks , poisson process , shadowing , fading , propagation invariance , stochastic equivalence .

1211.0682

i

sensor array imaging in a scattering medium is limited because coherent signals recorded at the source - receiver array and coming from a reflector to be imaged are dominated by incoherent signals coming from multiple scattering by the medium . for instance , in a randomly perturbed waveguide , it is known that the field becomes completely incoherent when the propagation distance becomes larger than the equipartition distance , which corresponds to the distance beyond which the source energy has been shared equally among all the propagating modes ( * ? ? ? * chapter 20 ) . as we will see , if the distance between the source - receiver array and the reflector is larger than the equipartition distance , then classical migration of the signals recorded at the array can not give a good image . sources can be expensive or difficult to implement but receivers can be cheap and easy to implement , so an imaging problem in which there are a few sources ( all of them being far from the reflector ) and many receivers ( some of them being close to the reflector ) is of theoretical and practical interest . if there is a unique source far from the reflector ( farther than the equipartition distance ) and if the receiver array is close to the reflector ( closer than the equipartition distance ) , then classical migration of the recorded signals fails again . this was shown is various contexts and we will show it again in the waveguide geometry . however , in such a situation , another kind of migration can be used : from the work devoted to coherent interferometry imaging @xcite and ambient noise imaging @xcite , it is known that migration of cross correlations of noisy signals can be more stable than migration of the signals themselves . the migration of cross correlations of noisy signals recorded by auxiliary passive arrays was proposed by @xcite in geophysical contexts and analyzed recently in randomly scattering open media in @xcite , and we would like to address the same problem in the waveguide geometry . indeed the number of propagating modes is finite in the waveguide geometry so that the statistical behavior of partially coherent fields in random waveguides is very different from the open medium case @xcite . in our paper , we show that , if a receiver array can be placed close to the reflector to be imaged , then the cross correlations of the incoherent signals on this array can be used to image the reflector . we will give a detailed resolution and stability analysis . we will show that the statistical stability requires a broadband source and that good resolution and stability properties do not require the receiver array to span the whole cross section of the waveguide , which is an effect specific to the waveguide geometry . the paper is organized as follows . in section [ sec : prelim ] , we review the mathematical background of the imaging problem in a random waveguide . in section [ sec : imagclas ] we describe and analyze the classical migration functional using the recorded signals and show that it can not give a good image when the propagation distance is beyond the energy equipartition distance . in section [ sec : imagf ] , we introduce the correlation - based imaging functional ; it has two versions which correspond to the time - harmonic case and the broadband case . in section [ sec : resol ] , we analyze the resolution of the proposed imaging functionals . detailed analyses are provided for full aperture and limited aperture arrays . these results are based on the statistical average of the imaging functionals . the variances of these functionals are very important as well because they determine the statistical stability of the imaging functionals . in section [ sec : stabi ] , we study the variances of the imaging functionals . some concluding remarks are listed at the end of the paper .

we consider reflector imaging in a weakly random waveguide . we address the situation in which the source is farther from the reflector to be imaged than the energy equipartition distance , but the receiver array is closer to the reflector to be imaged than the energy equipartition distance . as a consequence , this paper shows that migration of the recorded signals can not give a good image , but an appropriate migration of the cross correlations of the recorded signals can give a very good image . the resolution and stability analysis of this original functional shows that the reflector can be localized with an accuracy of the order of the wavelength even when the receiver array has small aperture , and that broadband sources are necessary to ensure statistical stability , whatever the aperture of the array .

we consider reflector imaging in a weakly random waveguide . we address the situation in which the source is farther from the reflector to be imaged than the energy equipartition distance , but the receiver array is closer to the reflector to be imaged than the energy equipartition distance . as a consequence , the reflector is illuminated by a partially coherent field and the signals recorded by the receiver array are noisy . this paper shows that migration of the recorded signals can not give a good image , but an appropriate migration of the cross correlations of the recorded signals can give a very good image . the resolution and stability analysis of this original functional shows that the reflector can be localized with an accuracy of the order of the wavelength even when the receiver array has small aperture , and that broadband sources are necessary to ensure statistical stability , whatever the aperture of the array .

cond-mat0504754

i

the most interesting features of perfect metallic magnetic multilayer are the oscillatory behavior of bilinear exchange coupling energy between ferromagnets @xcite due to friedel oscillations , and large magnetoresistance in small magnetic fields @xcite . the magnetic structure of adjoining magnetic layers in perfect multilayered structure oscillates between ferro and antiferro - magnetic states with increasing the spacer thickness @xmath1 . disorder in layers contributes to biquadratic exchange coupling . it was shown that fluctuations of thickness of the paramagnetic layer give rise to biquadratic exchange coupling , often leading to non - collinear magnetic ordering @xcite . in ref . the role of scattering of conducting electrons by impurities in metallic magnetic multilayer was studied . it was pointed out that in the case of small ( compared to thickness of the layers ) mean free path of conducting electrons , when average friedel oscillations are exponentially suppressed , the exchange coupling energy due to random friedel oscillations and correlation effects can have biquadratic form . transition to the non - collinear phase in disordered structure with increasing @xmath1 was experimentally observed in ref . . it is established that the magnetoresistance of perfect metallic magnetic multilayered structure is related to spin - depended scattering of conducting electrons at the interfaces between the layers @xcite . in the case of disorder , scattering of conducting electrons by impurities suppresses the effect of spin - dependent scattering on magnetoresistance . moreover , it was theoretically shown that the magnitude of the magnetoresistance decreases exponentially in the case of the current - in - plane ( cip ) geometry , when thickness of the nonmagnetic spacer exceeds the mean free path of conducting electrons @xcite . in the present paper we study the effect of electron - electron interactions on cip conductivity and exchange coupling energy of disordered metallic multilayered structure consisting of two ferromagnetic layers with paramagnetic spacer . we consider the case when mean free path of conducting electrons is smaller than thicknesses of layers . it is known that in the disordered conductors electron - electron interactions result in anomalous contributions to conductivity , thermodynamic quantities and negative magnetoconductivity @xcite . physics behind the effect of electron - electron interactions in disordered conductors is the electron scattering by the random friedel oscillations @xcite . freidel oscillations in magnetic multilayered structure do depend on the angle @xmath2 between directions of magnetization in magnetic layers . the study of this dependence is the subject of this paper . the scattering by freidel oscillations exists in any type of ferromagnetic structure : itinerant ( _ d- _ type ) or localized ( _ f- _ type ) . in what follows , the most relevant factors of disordered magnetic multilayered structure are the characteristic of the disorder - the thouless energy @xmath3 ( @xmath4 is the conducting electron diffusion constant ) , and ferromagnetic splitting of conducting electrons . because of that we consider the model of localized _ s - f _ magnetism that contains these parameters in the most transparent way . we propose that each ferromagnetic layer is described by the homogeneous magnetization , and that directions of magnetizations of different layers make an angle @xmath2 . the conductivity and exchange coupling energy in magnetic multilayered structure are periodic functions of @xmath2 . we show that depending on the ratio of introduced above characteristic energies , the angle @xmath2 dependent contributions of electron - electron interactions experience the @xmath5 periodicity transition . magnitudes of contributions are estimated . we suppose that our results might be relevant to the series of works related to transport properties of mesoscopic ferromagnets with domain walls , where it was experimentally @xcite and theoretically @xcite shown that effects of electron interactions and weak localization are important . we would like to mention that results of this paper complement the theory of electron - electron interactions in disorders conductors @xcite as a study of effect of electron - electron interactions in spatially inhomogeneous effective magnetic field that is imposed by the magnetization in layers .

we consider the effect of electron - electron interactions on the current - in - plane ( cip ) conductivity and exchange coupling energy of a disordered metallic magnetic multilayer . we show that contribution to the cip conductivity and exchange coupling energy as a periodic function of the angle of magnetizations relative orientation experience @xmath0 transition depending on the characteristic energies : ferromagnetic splitting of the conducting electrons and the thouless energy of paramagnetic layer .

we consider the effect of electron - electron interactions on the current - in - plane ( cip ) conductivity and exchange coupling energy of a disordered metallic magnetic multilayer . we analyze its dependence on the value of ferromagnetic splitting of conducting electrons and ferromagnetic layers relative magnetizations orientation . we show that contribution to the cip conductivity and exchange coupling energy as a periodic function of the angle of magnetizations relative orientation experience @xmath0 transition depending on the characteristic energies : ferromagnetic splitting of the conducting electrons and the thouless energy of paramagnetic layer .

1506.06824

i

we consider a partition function defined by @xmath3\prod_{1\leq i < j\leq n } ( \lambda_i-\lambda_j)^2 \ , { \mathrm{d}}^n \lambda . \label{zdef1}\end{aligned}\ ] ] we assume that the potential function @xmath2 is a polynomial : @xmath4 for the integral in ( [ zdef1 ] ) to converge , it is necessary that the polynomial degree @xmath5 is even , and that the parameter @xmath6 is such that the real part of @xmath7 is positive . by replacing the domain of integration @xmath8 with @xmath9 , where @xmath10 is an appropriately chosen contour in the complex plane , it is possible to remove these restrictions @xcite . the partition function in ( [ zdef1 ] ) is the normalization constant for the induced measure on eigenvalues arising from the following probability measure on @xmath11 hermitian matrices : @xmath12\ , { \mathrm{d}}m . \label{matrixmeasure1}\end{aligned}\ ] ] the factor @xmath13 is lebesgue product measure @xmath14 real degrees of freedom of @xmath15 . we are interested in the partition function ( [ zdef1 ] ) because it has a topological expansion whose coefficients are generating functions for a certain kind of embedded graph call a _ map_. letting @xmath16 with the ratio @xmath17 held fixed , we have @xmath18 here @xmath19 is the number of @xmath20-valent vertices of @xmath10 ; that is , vertices at which exactly @xmath20 edges meet . we use @xmath21 to mean that for any @xmath22 , truncating the series after terms of order @xmath23 results in an approximation with error @xmath24 as @xmath25 with @xmath17 . a _ map of genus @xmath26 _ is an equivalence class of labeled graphs embedded in genus @xmath26 compact connected oriented surface . two embedded graphs are equivalent if an orientation preserving homeomorphism of the surface takes the vertices and edges of one to those of the other , preserving labels . a map is equipped with the following labels : each of the map s @xmath27 vertices of each valence @xmath20 has a unique label @xmath28 ; and also for each vertex , one incident edge is marked with an arrow pointing away from that vertex . this marking of edges can be represented as a function @xmath29 from the vertex set to the edge set such that each vertex @xmath2 is incident @xmath30 . the expansion ( [ topexp1 ] ) was used by bessis , itzykson and zuber @xcite . ercolani and mclaughlin @xcite gave a rigorous proof that an expansion of the form ( [ topexp1 ] ) exists , and proved analytical properties of the expansion . in particular , expansions of derivatives of @xmath31 with respect to @xmath26 can be computed by termwise differentiation of the series ( [ topexp1 ] ) . the same is true for differentiation with respect to @xmath32 , but for more complicated reasons ; see section 4.1.3 of @xcite for a proof that this property is equivalent to the string equations . this paper addresses the problem of computing the generating functions @xmath1 , a problem which has been studied by several authors @xcite . these articles give a variety of methods for computing @xmath1 , and yield formulas given in terms of a variety of choices of variables . in this article we focus on _ valence independent _ formulas . formulas of this kind allow derivatives with respect to @xmath32 but forbid explicit dependence on the potential @xmath2 or its parameters @xmath33 . for example we find that @xmath34 where @xmath35 and @xmath36 are defined in equations ( [ rnexpand]-[snexpand ] ) and the notation @xmath37 indicates @xmath38 . other authors assume that the potential @xmath2 is an even function ; this assumption significantly reduces the difficulty of computing @xmath1 , for example with this assumption we have @xmath39 . thus our formula ( [ f1formula ] ) is new and extends formulas given by other authors to the case of an asymmetric potential . the valence independent approach was first used by shirokura @xcite . for the purpose of computing the generating functions @xmath1 , it is difficult to work with the partition function directly . szego s relation ( [ szegorel1 ] ) and the hirota - szego relation ( [ szegorel2 ] ) give two fundamentally different relations between the partition function and recurrence coefficients for a family of orthogonal polynomials : @xmath40 strategies for computing @xmath1 may involve using string equations to compute higher order asymptotics of the recurrence coefficients @xmath41 , then lifting this information to the level of the partition function @xmath42 . for example @xcite uses ( [ szegorel1 ] ) , @xcite uses ( [ szegorel2 ] ) and @xcite uses bleher - its deformation . we will use ( [ szegorel1 ] ) ; the mathematical rigor of our use of this formula was established in section 4.1.4 of @xcite . strategies for computing @xmath1 which are based on loop equations @xcite avoid the recurrence coefficients @xmath43 , but involve computing higher order asymptotics of random matrix correlators . it is also possible to compute @xmath1 directly from the riemann - hilbert problem for orthogonal polynomials @xcite . let us now define the coefficients @xmath44 and explain the string equations which govern them . the monic orthogonal polynomials @xmath45 arise from the following ( non - hermitean ) inner product and orthogonality relation : @xmath46 thus the polynomials @xmath47 can be constructed by the gram - schmidt process . as is well known @xcite , the polynomials satisfy a three term recurrence : @xmath48 this defines the recurrence coefficients @xmath44 . the three term recurrence ( [ threetermrec1 ] ) can be expressed in terms of a jacobi matrix @xmath49 : @xmath50 let @xmath51 be the column vector of all orthogonal polynomials for the potential @xmath2 ; then the three term recurrence can be encoded as a matrix equation @xmath52 following blecher and deao @xcite , we use the string equations @xmath53 a differenced form of these equations was used in @xcite . equation ( [ undiff1 ] ) can be derived as follows . integrating by parts we find that @xmath54 an analogous calculation , but starting with @xmath55 establishes ( [ undiff2 ] ) . we now explain how the continuum limit of string equations can be used to compute the generating functions @xmath1 . the following asymptotic expansions for recurrence coefficients with shifted indices was proven in @xcite : @xmath56 thus we have defined @xmath57 and @xmath58 to be the asymptotic coefficients in the expansions ( [ rnexpand]-[snexpand ] ) . we will use the abbreviations @xmath59 and @xmath60 . inserting these expansion in the string equations gives the continuum limit of the string equations . by extracting terms at order @xmath61 from the continuum limit of string equations , one can solve for @xmath57 and @xmath62 in lower order terms . inserting the expansions ( [ rnexpand]-[snexpand ] ) and the topological expansion ( [ topexp1 ] ) in the szego relation ( [ szegorel1 ] ) , one may solve for @xmath1 in terms of the variables @xmath63 : @xmath64 the constants @xmath65 are bernoulli numbers , and the cumulants @xmath66 are defined by @xmath67 { \widetilde{z}}_g & \log \frac{z}{x } & \frac{z_1}{z } & \frac{z_2}{z}-\frac{z_{1}^2}{2z^2 } & \frac{z_3}{z}-\frac{z_2 z_1}{z^2}+\frac{z_{1}^3}{3z^3 } \end{array}\end{aligned}\ ] ] in @xcite , formula ( [ asymptszegorel1 ] ) was obtained using the euler - maclaurin formula . as was noted in @xcite , further justification is required to make this approach rigorous . a rigorous proof of ( [ asymptszegorel1 ] ) has been given in section 4.2.1 of @xcite . the rest of our paper is organized as follows . in section 2 we prove a theorem concerning the structure of the string equations ; theorem [ str polyn thm ] describes the terms arising in the string equations as a sum of differential operators ( which we call string polynomials ) acting on a residue . the reason that our method results in valence independent formulas is essentially that the string polynomials do not depend on the potential . in section 3 we demonstrate our method by computing @xmath68 . in section 4 we prove a structure theorem for valence independent formulas for @xmath58 and @xmath57 . to compute @xmath1 using formula ( [ asymptszegorel1 ] ) it is necessary to evaluate an indefinite integral with respect to @xmath32 . it turns out that in the cases @xmath69 this integral can be computed in closed form , but we have no proof that this happens for all @xmath70 .

we consider the large @xmath0 expansion of the partition function for the hermitian one - matrix model . it is well known that the coefficients of this expansion are generating functions @xmath1 for a certain kind of graph embedded in a riemann surface . other authors have made a simplifying assumption that the potential @xmath2 is an even function . we present a method for computing @xmath1 in the case that @xmath2 is not an even function . our method is based on the string equations , and yields `` valence independent '' formulas which do not depend explicitly on the potential . we introduce a family of differential operators , the `` string polynomials '' , which make clear the valence independent nature of the string equations . map , random matrix , topological expansion , string equation

we consider the large @xmath0 expansion of the partition function for the hermitian one - matrix model . it is well known that the coefficients of this expansion are generating functions @xmath1 for a certain kind of graph embedded in a riemann surface . other authors have made a simplifying assumption that the potential @xmath2 is an even function . we present a method for computing @xmath1 in the case that @xmath2 is not an even function . our method is based on the string equations , and yields `` valence independent '' formulas which do not depend explicitly on the potential . we introduce a family of differential operators , the `` string polynomials '' , which make clear the valence independent nature of the string equations . map , random matrix , topological expansion , string equation

cs0205070

i

today , very large amounts of information are available in on - line documents . as part of the effort to better organize this information for users , researchers have been actively investigating the problem of automatic text categorization . the bulk of such work has focused on _ topical _ categorization , attempting to sort documents according to their subject matter ( e.g. , sports vs. politics ) . however , recent years have seen rapid growth in on - line discussion groups and review sites ( e.g. , the new york times books web page ) where a crucial characteristic of the posted articles is their _ sentiment _ , or overall opinion towards the subject matter for example , whether a product review is positive or negative . labeling these articles with their sentimentwould provide succinct summaries to readers ; indeed , these labels are part of the appeal and value - add of such sites as www.rottentomatoes.com , which both labels movie reviews that do not contain explicit rating indicators and normalizes the different rating schemes that individual reviewers use . sentimentclassification would also be helpful in business intelligence applications ( e.g. mindfuleye s lexant system ) and recommender systems ( e.g. , , ) , where user input and feedback could be quickly summarized ; indeed , in general , free - form survey responses given in natural language format could be processed using sentimentcategorization . moreover , there are also potential applications to message filtering ; for example , one might be able to use sentimentinformation to recognize and discard `` flames''@xcite . in this paper , we examine the effectiveness of applying machine learning techniques to the sentimentclassification problem . a challenging aspect of this problem that seems to distinguish it from traditional topic - based classification is that while topics are often identifiable by keywords alone , sentimentcan be expressed in a more subtle manner . for example , the sentence `` how could anyone sit through this movie ? '' contains no single word that is obviously negative . ( see section [ sec : discuss ] for more examples ) . thus , sentimentseems to require more _ understanding _ than the usual topic - based classification . so , apart from presenting our results obtained via machine learning techniques , we also analyze the problem to gain a better understanding of how difficult it is .

we consider the problem of classifying documents not by topic , but by overall sentiment , e.g. , determining whether a review is positive or negative . using movie reviews as data , we find that standard machine learning techniques definitively outperform human - produced baselines we conclude by examining factors that make the sentiment classification problem more challenging .

we consider the problem of classifying documents not by topic , but by overall sentiment , e.g. , determining whether a review is positive or negative . using movie reviews as data , we find that standard machine learning techniques definitively outperform human - produced baselines . however , the three machine learning methods we employed ( naive bayes , maximum entropy classification , and support vector machines ) do not perform as well on sentiment classification as on traditional topic - based categorization . we conclude by examining factors that make the sentiment classification problem more challenging .

1403.7867

i

the hypothesis testing theory is a well developed branch of mathematical statistics @xcite . the asymptotic approach allows to find satisfactory solutions in many different situations . the simplest problems , like the testing of two simple hypotheses , have well known solutions . recall that if we fix the first type error and seek the test which maximizes the power , then we obtain immediately ( by neyman - pearson lemma ) the most powerful test based on the likelihood ratio statistic . the case of composite alternative is more difficult to treat and here the asymptotic solution is available in the regular case . it is possible , using , for example , the score function test ( sft ) , to construct the asymptotically ( locally ) most powerful test . moreover , the general likelihood ratio test ( glrt ) and the wald test ( wt ) based on the maximum likelihood estimator are asymptotically most powerful in the same sense . in the non regular cases the situation became much more complex . first of all , there are different non regular ( singular ) situations . moreover , in all these situations , the choice of the asymptotically best test is always an open question . this work is an attempt to study all these situations on the model of inhomogeneous poisson processes . this model is sufficiently simple to allow us to realize the construction of the well known tests ( sft , glrt , wt ) and to verify that these test are asymptotically most powerful also for this model , in the case when it is regular . in the next paper we study the behavior of these tests in the case when the model is singular . the `` evolution of the singularity '' of the intensity function is the following : regular case ( finite fisher information , this paper ) , continuous but not differentiable ( cusp - type singularity , @xcite ) , discontinuous ( jump - type singularity , @xcite ) . in all the three cases we describe the tests analytically . more precisely , we describe the test statistics , the choice of the thresholds and the behavior of the power functions for local alternatives . note that the notion of _ local alternatives _ is different following the type of regularity / singularity . suppose we want to test the simple hypothesis @xmath0 against the one - sided alternative @xmath1 . in the regular case , the local alternatives are usually given by , @xmath2 . in the case of a cusp - type singularity , the local alternatives are introduced by @xmath3 , @xmath2 . as to the case of a jump - type singularity , the local alternatives are @xmath4 , @xmath2 . in all these problems , the most interesting for us question is the comparison of the power functions of different tests . in singular cases , the comparison is done with the help of numerical simulations . the main results concern the limit likelihood ratios in the non - regular situations . let us note , that in many other models of observations ( i.i.d . , time series , diffusion processes etc . ) the likelihood ratios have the same limits as here ( see , for example , @xcite and @xcite ) . therefore , the results presented here are of more universal nature and are valid for any other ( non necessarily poissonian ) model having one of considered here limit likelihood ratios . we recall that @xmath5 is an inhomogeneous poisson process with intensity function @xmath6 , @xmath7 , if @xmath8 and the increments of @xmath9 on disjoint intervals are independent and distributed according to the poisson law @xmath10 in all statistical problems considered in this work , the intensity functions are periodic with some known period @xmath11 and depend on some one - dimensional parameter , that is , @xmath12 . the basic hypothesis and the alternative are always the same : @xmath0 and @xmath13 . the diversity of statements corresponds to different types of regularity / singularity of the function @xmath14 . the case of unknown period @xmath11 needs a special study . the hypothesis testing problems ( or closely related properties of the likelihood ratio ) for inhomogeneous poisson processes were studied by many authors ( see , for example , brown @xcite , kutoyants @xcite , lger and wolfson @xcite , liese and lorz @xcite , sung _ et al . _ @xcite , fazli and kutoyants @xcite , dachian and kutoyants @xcite and the references therein ) . note finally , that the results of this study will appear later in the work @xcite .

we consider the problem of hypothesis testing in the situation when the first hypothesis is simple and the second one is local one - sided composite . _ key words : _ hypothesis testing , inhomogeneous poisson processes , asymptotic theory , composite alternatives , regular situation .

we consider the problem of hypothesis testing in the situation when the first hypothesis is simple and the second one is local one - sided composite . we describe the choice of the thresholds and the power functions of the score function test , of the general likelihood ratio test , of the wald test and of two bayes tests in the situation when the intensity function of the observed inhomogeneous poisson process is smooth with respect to the parameter . it is shown that almost all these tests are asymptotically uniformly most powerful . the results of numerical simulations are presented . msc 2010 classification : 62m02 , 62f03 , 62f05 . _ key words : _ hypothesis testing , inhomogeneous poisson processes , asymptotic theory , composite alternatives , regular situation .

math0503576

i

consider supercritical bond - percolation on @xmath0 , @xmath1 , and the simple random walk on the ( unique ) infinite cluster . in @xcite sidoravicius and sznitman asked the following question : is it true that for a.e . configuration in which the origin belongs to the infinite cluster , the random walk started at the origin exits the infinite symmetric slab @xmath2 through the `` top '' side with probability tending to @xmath3 as @xmath4 ? sidoravicius and sznitman managed to answer their question affirmatively in dimensions @xmath5 but dimensions @xmath6 remained open . in this paper we extend the desired conclusion to all @xmath1 . as in @xcite , we will do so by proving a quenched invariance principle for the paths of the walk . random walk on percolation clusters is only one of many instances of `` statistical mechanics in random media '' that have been recently considered by physicists and mathematicians . other pertinent examples include , e.g. , various diluted spin systems , random copolymers @xcite , spin glasses @xcite , random - graph models @xcite , etc . from this general perspective , the present problem is interesting for at least two reasons : first , a good handle on simple random walk on a given graph is often a prerequisite for the understanding of more complicated processes , e.g. , self - avoiding walk or loop - erased random walk . second , information about the scaling properties of simple random walk on percolation cluster can , in principle , reveal some new important facts about the structure of the infinite cluster and/or its harmonic properties . let us begin developing the mathematical layout of the problem . let @xmath0 be the @xmath7-dimensional hypercubic lattice and let @xmath8 be the set of nearest neighbor edges . we will use @xmath9 to denote a generic edge , @xmath10 to denote the edge between @xmath11 and @xmath12 , and @xmath13 to denote the edges from the origin to its nearest neighbors . let @xmath14 be the space of all percolation configurations @xmath15 . here @xmath16 indicates that the edge @xmath9 is occupied and @xmath17 implies that it is vacant . let @xmath18 be the borel @xmath19-algebra on @xmath20defined using the product topology and let @xmath21 be an i.i.d . measure such that @xmath22 for all @xmath23 . if @xmath24 denotes the event that the site @xmath11 belongs to an infinite self - avoiding path using only occupied bonds in @xmath25 , we write @xmath26 for the set @xmath27 by burton - keane s uniqueness theorem @xcite , the infinite cluster is unique and so @xmath28 is connected with @xmath21-probability one . for each @xmath29 , let @xmath30 be the `` shift by @xmath11 '' defined by @xmath31 . note that @xmath21 is @xmath32-invariant for all @xmath29 . let @xmath33 denote the percolation threshold on @xmath0 defined as the infimum of all @xmath34 s for which @xmath35 . let @xmath36 and , for @xmath37 , define the measure @xmath38 by @xmath39 we will use @xmath40 to denote expectation with respect to @xmath38 . for each configuration @xmath41 , let @xmath42 be the simple random walk on @xmath43 started at the origin . explicitly , @xmath42 is a markov chain with state space @xmath0 , whose distribution @xmath44 is defined by the transition probabilities @xmath45 and @xmath46 with the initial condition @xmath47 thus , at each unit of time , the walk picks a neighbor at random and if the corresponding edge is occupied , the walk moves to this neighbor . if the edge is vacant , the move is suppressed . our main result is that for @xmath38-almost every @xmath41 , the linear interpolation of @xmath48 , properly scaled , converges weakly to brownian motion . for every @xmath49 , let @xmath50,{\mathscr{w } } _ t)$ ] be the space of continuous functions @xmath51\to{\mathbb r}$ ] equipped with the @xmath19-algebra @xmath52 of borel sets relative to the supremum topology . the precise statement is now as follows : [ thm : mainthm ] let @xmath1 , @xmath53 and let @xmath41 . let @xmath42 be the random walk with law @xmath44 and let @xmath54 then for all @xmath49 and for @xmath38-almost every @xmath25 , the law of @xmath55 on @xmath50,{\mathscr{w } } _ t)$ ] converges weakly to the law of an isotropic brownian motion @xmath56 whose diffusion constant , @xmath57 , depends only on the percolation parameter @xmath34 and the dimension @xmath7 . the markov chain @xmath42 represents only one of two natural ways to define a simple random walk on the supercritical percolation cluster . another possibility is that , at each unit of time , the walk moves to a site chosen uniformly at random from the _ accessible _ neighbors , i.e. , the walk takes no pauses . in order to define this process , let @xmath58 be the sequence of stopping times that mark the moments when the walk @xmath42 made a move . explicitly , @xmath59 and @xmath60 using these stopping times which are @xmath44-almost surely finite for all @xmath41we define a new markov chain @xmath61 by @xmath62 it is easy to see that @xmath61 has the desired distribution . indeed , the walk starts at the origin and its transition probabilities are given by @xmath63 a simple modification of the arguments leading to theorem [ thm : mainthm ] allows us to establish a functional central limit theorem for this random walk as well : [ thm:2ndmainthm ] let @xmath1 , @xmath53 and let @xmath41 . let @xmath64 be the random walk defined from @xmath42 as described in and let @xmath65 be the linear interpolation of @xmath66 defined by with @xmath67 replaced by @xmath68 . then for all @xmath49 and for @xmath38-almost every @xmath25 , the law of @xmath69 on @xmath50,{\mathscr{w } } _ t)$ ] converges weakly to the law of an isotropic brownian motion @xmath56 whose diffusion constant , @xmath70 , depends only on the percolation parameter @xmath34 and the dimension @xmath7 . de gennes @xcite , who introduced the problem of random walk on percolation cluster to the physics community , thinks of the walk as the motion of `` an ant in a labyrinth . '' from this perspective , the `` lazy '' walk @xmath48 corresponds to a `` blind '' ant , while the `` agile '' walk @xmath71 represents a `` myopic '' ant . while the character of the scaling limit of the two `` ants '' is the same , there seems to be some distinction in the rate the scaling limit is approached , cf @xcite and references therein . as we will see in the proof , the diffusion constants @xmath72 and @xmath73 are related via @xmath74 , where @xmath75 is the expected degree of the origin normalized by @xmath76 , cf . there is actually yet another way how to `` put '' simple random walk on @xmath28 , and that is to use continuous time . here the corresponding result follows by combining the clt for the `` lazy '' walk with an appropriate renewal theorem for exponential waiting times . the subject of random walk in random environment has a long history ; we refer to , e.g. , @xcite for recent overviews of ( certain parts of ) this field . on general grounds , each random - media problem comes in two distinct flavors : _ quenched _ , corresponding to the situations discussed above where the walk is distributed according to an @xmath25-dependent measure @xmath44 , and _ annealed _ , in which the path distribution of the walk is taken from the averaged measure @xmath77 . under suitable ergodicity assumptions , the annealed problem typically corresponds to the quenched problem averaged over the starting point . yet the distinction is clear : in the annealed setting the slab - exit problem from sect . [ sec1.1 ] is trivial by the symmetries of the averaged measure , while its answer is _ a priori _ very environment - sensitive in the quenched measure . an annealed version of our theorems was proved in the 1980s by de masi _ et al _ @xcite , based on earlier results of kozlov @xcite , kipnis and varadhan @xcite and others in the context of random walk in a field of random conductances . ( the results of @xcite were primarily two - dimensional but , with the help of @xcite , they apply to all @xmath1 ; cf @xcite . ) a number of proofs of quenched invariance principles have appeared in recent years for the cases where an annealed principle was already known . the most relevant paper is that of sidoravicius and sznitman @xcite which established theorem [ thm:2ndmainthm ] for random walk among random conductances in all @xmath78 and , using a very different method , also for random walk on percolation in @xmath5 . ( thus our main theorem is new only in @xmath6 . ) the @xmath5 proof is based on the fact that two independent random walk paths will intersect only very little something hard to generalize to @xmath6 . as this paper shows , the argument for random conductances is somewhat more flexible . another paper of relevance is that of rassoul - agha and sepplinen @xcite where a quenched invariance principle was established for _ directed _ random walks in ( space - time ) random environments . the directed setting offers the possibility to use independence more efficiently every time step the walk enters a new environment but the price to pay for this is the lack of reversibility . the directed nature of the environment also permits consideration of distributions with a drift for which a clt is not even expected to generally hold in the undirected setting ; see @xcite for an example of `` pathologies '' that may arise . finally , there have been been a number of results dealing with harmonic properties of the simple random walk on percolation clusters . grimmett , kesten and zhang @xcite proved via `` electrostatic techniques '' that this random walk is transient in @xmath79 ; extensions concerning the existence of various `` energy flows '' appeared in @xcite . a great amount of effort has been spent on deriving estimates on the heat - kernel i.e . , the probability that the walk is at a particular site after @xmath80 steps . the first such bounds were obtained by heicklen and hoffman @xcite . later mathieu and remy @xcite realized that the right way to approach heat - kernel estimates was through harmonic function theory of the infinite cluster and thus significantly improved the results of @xcite . finally , barlow @xcite obtained , using again harmonic function theory , gaussian upper and lower bounds for the heat kernel . we refer to @xcite for further references concerning this area of research . _ note _ : at the time a preprint version of this paper was first circulated , we learned that mathieu and piatnitski had announced a proof of the same result ( albeit in continuous - time setting ) . their proof , which has in the meantime been posted @xcite , is close in spirit to that of theorem 1.1 of @xcite ; the main tools are poincar inequalities , heat - kernel estimates and homogenization theory . let us outline the main steps of our proof of theorems [ thm : mainthm ] and [ thm:2ndmainthm ] . the principal idea which permeates in various disguises throughout the work of papanicolau and varadhan @xcite , kozlov @xcite , kipnis and varadhan @xcite , de masi _ et al _ @xcite , sidoravicius and sznitman @xcite and others is to consider an embedding of @xmath43 into the euclidean space that makes the corresponding simple random walk a martingale . formally , this is achieved by finding an @xmath81-valued discrete harmonic function on @xmath28 with a linear growth at infinity . the distance between the natural position of a site @xmath82 and its counterpart in this _ harmonic embedding _ is expressed in terms of the so - called _ corrector _ @xmath83 which is a principal object of study in this paper . see fig . [ fig1 ] for an illustration . it is clear that the corrector can be defined in any finite volume by solving an appropriate discrete dirichlet problem ( this is how fig . 1 was drawn ) ; the difficult part is to define the corrector in infinite volume while maintaining the natural ( distributional ) invariance with respect to shifts of the underlying lattice . actually , there is an alternative , probabilistic definition of the corrector , @xmath84 however , the only proof we presently have for the existence of such a limit is by following , rather closely , the constructions from sect . [ sec2.3 ] . once we have the corrector under control , the proof splits into two parts : ( 1 ) proving that the martingale i.e . , the walk on the deformed graph converges to brownian motion and ( 2 ) proving that the deformation of the path caused by the change of embedding is negligible . the latter part ( which is the principal contribution of this work ) amounts to a sublinear bound on the corrector @xmath83 as a function of @xmath11 . here , somewhat unexpectedly , our level of control is considerably better in @xmath85 than in @xmath79 . in particular , our proof in @xmath85 avoids using any of the recent sophisticated discrete - harmonic analyses but , to handle all @xmath1 uniformly , we need to invoke the main result of barlow @xcite . the proof is actually carried out along these lines only for the setting in theorem [ thm : mainthm ] ; theorem [ thm:2ndmainthm ] follows by noting that the time scales of both walks are comparable . here is a summary of the rest of this paper : in sect . [ sec : defcor ] we introduce the aforementioned corrector and prove some of its basic properties . [ sec : erg ] collects the needed facts about ergodic properties of the markov chain `` on environments . '' both sections are based on previously known material ; proofs have been included to make the paper self - contained . the novel parts of the proof sublinear bounds on the corrector appear in sects . [ sec : sec4]-[sec : sublin ] . the actual proofs of our main theorems are carried out in sect . [ sec : invprnp ] . the appendix ( sects . [ appa ] and [ appb ] ) contains the proof of an upper bound for the transition probabilities of our random walk , further discussion and some conjectures .

we consider the simple random walk on the ( unique ) infinite cluster of super - critical bond percolation in @xmath0 with @xmath1 . our analysis is based on the consideration of a harmonic deformation of the infinite cluster on which the random walk becomes a square - integrable martingale . the size of the deformation , expressed by the so called corrector , is estimated by means of ergodicity arguments .

we consider the simple random walk on the ( unique ) infinite cluster of super - critical bond percolation in @xmath0 with @xmath1 . we prove that , for almost every percolation configuration , the path distribution of the walk converges weakly to that of non - degenerate , isotropic brownian motion . our analysis is based on the consideration of a harmonic deformation of the infinite cluster on which the random walk becomes a square - integrable martingale . the size of the deformation , expressed by the so called corrector , is estimated by means of ergodicity arguments . = 1

1201.2853

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the aim of this paper is to introduce and compute a function , called the renormalized energy " , for some specific random point processes that arise in random matrix models , and in this way to associate to each of these processes a unique number , which is expected to measure its disorder " . our renormalized energy " , that we denote @xmath3 , is defined over configurations of points lying either on the real line or on the plane , as the limit as @xmath4 of @xmath5 } \log \left|2\sin \frac{\pi(a_i - a_j ) } n\right| + \log n\qquad \text{in dimension 1},\\ \wc(\{a_i\ } ) & = \frac{1}{2\pi n^2 } \sum_{i\neq j , a_i , a_j \in [ 0,n]^2 } e_n(a_i - a_j ) + \log \frac{n}{2\pi \eta(i)^2}\qquad \text{in dimension 2},\end{aligned}\ ] ] where @xmath6 is an explicit eisenstein series , and @xmath7 is the dedekind eta function . this definition is inspired by that of the renormalized energy " , denoted @xmath8 , introduced by sandier and the second author in @xcite in the case of points in the plane and in @xcite in the case of points on the real line . the definitions for @xmath8 and @xmath3 coincide when the point configuration has some periodicity ( this is where our new definition originates ) , and in that case they amount to computing a sum of pairwise interactions @xmath9 where @xmath10 are the points and @xmath11 is a suitable logarithmic kernel ( the green s function on the underlying torus ) ; however they are not identical in general . we will give more details on the connection in section [ secdefw ] . in @xcite it is shown that in dimension 1 , @xmath8 is bounded below and its minimum is achieved at the perfect lattice @xmath12 . in dimension 2 , the situation is more complex ; it is also shown in @xcite that the minimum of @xmath8 is achieved , but it is only conjectured that this minimum value is achieved at the perfect triangular lattice or abrikosov lattice " according to the terminology of the physics of superconductors ( which was the first main motivation for @xmath8 in @xcite where it was introduced ) . this conjecture is supported by the result that , among configurations of points which form a perfect lattice ( of fixed volume ) , the renormalized energy is minimal if and only if the lattice is the perfect triangular lattice , i.e. with 60@xmath13 angles ( that result is shown in @xcite based on the use of modular functions and results in number theory ) . it is thus natural to think of @xmath8 or @xmath3 as a way to measure the disorder of a configuration of points . with this outlook , in dimension 1 the lattice @xmath12 is the most ordered configuration of points with prescribed density 1 , while in dimension 2 , it is expected to be the triangular lattice ( which is better ordered than any other lattice , say the square lattice ) . in addition , due to its logarithmic nature , @xmath3 has some nice scaling and additive properties , which we believe make it a very good object . a further motivation for choosing to study @xmath3 as opposed to any other total pairwise interaction function is that , as seen in @xcite and @xcite , @xmath8 arises very naturally from the statistical mechanics of coulomb or log gases , which contain as particular cases the ginibre and goe / gue / gse ensembles of random matrices . in @xcite , @xmath8 was introduced and derived in the context of the minimization of the ginzburg - landau model of superconductivity . in @xcite it was derived as a sort of limiting interaction energy for two dimensional coulomb gases , and similarly in @xcite with log gases . these works are based on analysis and energy estimates ( upper and lower bounds ) . both the questions we pursue here and the methods we use are quite different : they aim at obtaining explicit formulas for specific random matrix models . in particular , this is a way to compute some interesting statistics over random matrix eigenvalues , as initiated by dyson - mehta @xcite . we will comment more on this just below . let us now briefly introduce the notion of a random point process . a ( simple ) random point process is a probability measure on the set of all locally finite collections of ( mutually distinct ) points in the space , cf . e.g. @xcite . it can also be viewed as a random measure of the form @xmath14 , with the points @xmath15 distinct and @xmath16 discrete . random point processes are essentially characterized by their @xmath17-point correlation functions " @xmath18 , which give the probability densities of finding @xmath17 points at the locations @xmath19 . we will normalize our processes so that the average number of points per unit volume is always @xmath20 , which is equivalent to @xmath21 . perhaps the most famous random point process is the poisson process , characterized by the facts that the number of points in disjoint subsets are independent , and the number of points in any finite volume subset of the space follows a poisson distribution with parameter equal to the volume of the set with respect to a reference measure . an important class of point processes is that of determinantal point processes , see @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite and references therein . that class is characterized by the fact that the @xmath17-point correlation functions are given by symmetric minors of a ( correlation ) kernel , cf . section [ correl ] . it is easy to see that @xmath22 for the translation invariant poisson process , which means that it is `` too chaotic '' from the point of view of the renormalized energy . let us list the ( stationary ) processes for which we show that @xmath23 provides more meaningful information . we will be interested in one dimension in the @xmath0-sine processes ( @xmath1 ) which arise as the local limit of the law of eigenvalues in random matrix ensembles with orthogonal , unitary , and symplectic symmetry groups ( they are determinantal for @xmath2 and pfaffian otherwise ) . in two dimensions we will examine the ginibre " point process , which is also a determinantal process arising as the local limit of the law of eigenvalues of matrices from the complex ginibre ensemble ( i.e. square matrices with complex gaussian iid entries ) , for further reference , see @xcite ; as well as the random process of zeros of random gaussian analytic functions , often denoted gaf , whose description can be found in @xcite . as our processes are always translation invariant , the @xmath24-point correlation function can always be written in the form @xmath25 for the 2-point _ cluster function _ @xmath26 ( we will come back to this notation in sections [ correl ] and [ sec4 ] ) . the main results we obtain are the following : * for general stationary processes we identify sufficient conditions on the process and its @xmath24-point correlation function @xmath27 for the existence of @xmath28 , and give an explicit formula in terms of @xmath27 which is ( up to constants ) @xmath29 with @xmath30 or @xmath24 according to the dimension . that we check for the above mentioned processes . we expect it to hold for general @xmath0-sine processes but we do not see an _ a priori _ reason for that . it is also not clear to us whether this condition has a physical meaning . ] * we apply this formula to the specific point processes mentioned above . * for the specific point processes above , we explicitly compute the limit of the variance of @xmath31 and obtain that it is @xmath32 . this implies that for such processes , @xmath31 concentrates around its expected value , and converges in probability to @xmath33 as @xmath4 . * we prove that in the class of determinantal point processes with translation invariant kernels in dimensions 1 and 2 , @xmath34 is minimized by the processes whose correlation kernel is the fourier transform of the characteristic function of the ball . a complete physical interpretation of this fact seems to be missing . in dimension 1 the optimization gives the @xmath2 sine process , which can be seen as a heuristic explanation of the fact that this process is the universal local limit of @xmath2 random matrix ensembles . indeed , such a local limit has to be translation invariant and determinantal , and it is natural to expect that it also minimizes an appropriate energy functional . in other dimensions , point processes with such specific kernels called fermi - sphere point processes " appear in @xcite as higher - dimensional analogues of the sine process . for our set of specific processes , we thus show that we can attribute to the process a unique number , which we compute explicitly . whenever these numbers are distinct this implies that the processes are mutually singular ( as measures on the space of point configurations ) . moreover , we check that the processes that are expected to have the highest level of order " or rigidity indeed have a lower value of @xmath35 . for example for the @xmath0-sine processes we find @xmath36 where @xmath37 is the euler constant . these three numbers form a decreasing sequence , as can be expected . in two dimensions , we obtain that the ginibre process has a higher @xmath38 , hence less rigidity , than that of zeros of gaussian analytic functions , in agreement with the results and philosophy of @xcite . the values of @xmath39 for the @xmath1 sine processes above equal twice the thermodynamic `` energy per particle '' or `` mean internal energy '' for the log - gas with infinitely many particles , as obtained by dyson in 1962 ( * ? ? ? * i.ix , iii.vi ) . this is not surprizing as our definition of @xmath31 essentially coincides with that of dyson ( * ? ? ? * i.vi ) once the points on the interval @xmath40 $ ] are identified with points on a circle of same length . furthermore , one can use this fact to infer finer asymptotic properties of @xmath31 as follows ( we are very grateful to peter forrester for the idea ) . if , instead of considering growing windows , one approximates the @xmath0-sine processes by the _ circular ensembles _ of particles on the unit circle with joint probability density @xmath41 , one observes that in rescaled variables , @xmath31 is simply @xmath42 , and its characteristic function can be immediately obtained from selberg s formula for the partition function : @xmath43 see e.g. ( * ? ? ? * section 4.7.2 ) for the formula for @xmath44 . using stirling s formula it is not hard to see that for any @xmath45 and @xmath46 @xmath47 with @xmath48 and the expression of @xmath49 through the partition function @xmath44 coincides with that of the thermodynamic energy per particle . by lvy s continuity theorem this implies the central limit theorem @xmath50 it is natural to conjecture that the same central limit theorem holds for @xmath31 on general @xmath0-sine processes ( constructed in @xcite ) as well , in particular providing asymptotic values @xmath51 and @xmath52 for any @xmath45 . at the moment we do not know how to prove it , although in the @xmath1 cases one may hope to obtain a proof via controlling the asymptotics of moments of @xmath31 through explicit formulas for the correlation functions . in the follow - up paper @xcite , prompted by the wish to analyze experimental data , dyson and mehta looked for a way of approximating the energy per particle , in the case @xmath53 , by averaging a statistic of the form @xmath54 over windows of increasing length in the random matrix spectrum . the concentration requirement of the asymptotically vanishing variance led them to the conclusion that with their choice of @xmath55 , the statistic had to be corrected with further interaction terms ( * ? ? ? * eq . ( 109 ) ) . our renormalized energy @xmath31 seems to be a better solution to dyson - mehta s problem , although one should note that dyson - mehta s statistic is purely local , while @xmath31 involves long range interaction ( between leftmost and rightmost particles in @xmath56 $ ] ) . the paper is organized as follows : in section [ secdefw ] we give the precise definitions of @xmath8 , the context about it and its connection to coulomb energy , from @xcite . this leads us to the definition of @xmath31 . in section [ sec3 ] we compute limits of expectations of @xmath31 : first on the real line and for general processes , then for the @xmath1 sine processes , then in the plane and for general processes , finally for the explicit ginibre and zeros of gaf processes . in section [ optim ] we find minimizers of @xmath57 among determinantal processes with translation - invariant correlation kernels . in section [ sec4 ] we compute the limit variance of @xmath31 for our specific processes ( and show it is @xmath32 ) . in section [ sc : misc ] we gather some miscellaneous computations : the effect on @xmath58 of superposition and decimation of processes and the computation of expectation of @xmath58 for the @xmath2 discrete sine processes . .5 cm * acknowledgements : * we are very grateful to peter forrester for his idea of using circular ensembles for the heuristics above , and also for drawing our attention to @xcite . we also thank the anonymous referee for a careful reading and very interesting comments . a. b. thanks alan edelman for help with numerics and s. s. thanks c. sinan gntrk for helpful discussions related to section [ optim ] . a. b. was partially supported by nsf grant dms-1056390 , s. s. was supported by a euryi award . we also thank the msri for support to attend a workshop where this work was initiated .

we define a renormalized energy " as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line . the definition is inspired by ideas of @xcite . the functional is expected to be a good measure of disorder of a configuration of points . we give certain formulas for its expectation for general stationary random point processes . for the random matrix @xmath0-sine processes on the real line ( @xmath1 ) , and ginibre point process and zeros of gaussian analytic functions process in the plane , we compute the expectation explicitly . we also prove that the @xmath2 sine process minimizes the renormalized energy in the class of determinantal point processes with translation invariant correlation kernels . * keywords : * renormalized energy , random point processes , random matrices , sine processes , ginibre ensemble , zeros of gaussian analytic functions . + * msc classification : * 60g55 , 60g10 , 15b52

we define a renormalized energy " as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line . the definition is inspired by ideas of @xcite . roughly speaking , it is obtained by subtracting two leading terms from the coulomb potential on a growing number of charges . the functional is expected to be a good measure of disorder of a configuration of points . we give certain formulas for its expectation for general stationary random point processes . for the random matrix @xmath0-sine processes on the real line ( @xmath1 ) , and ginibre point process and zeros of gaussian analytic functions process in the plane , we compute the expectation explicitly . moreover , we prove that for these processes the variance of the renormalized energy vanishes , which shows concentration near the expected value . we also prove that the @xmath2 sine process minimizes the renormalized energy in the class of determinantal point processes with translation invariant correlation kernels . * keywords : * renormalized energy , random point processes , random matrices , sine processes , ginibre ensemble , zeros of gaussian analytic functions . + * msc classification : * 60g55 , 60g10 , 15b52

1112.3367

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galaxies are intrinsically complex with multiple components and varied formation histories . this complexity is the primary reason that unravelling the physics of galaxy formation and evolution is so challenging . galaxies are made up of baryons confined to dark matter haloes , and often have multiple distinct kinematic components ( e.g.bulge and/or disc ) . there are complex interactions between the stars , gas , dust , dark matter and super - massive black holes . these can lead to both positive and negative feedback on the formation rate of stars . experimental efforts to address galaxy formation have generally taken two directions . first , galaxy imaging and spectroscopic surveys have progressively moved to higher redshift , in an attempt to directly observe galaxy evolution and formation . this approach has had much success , placing strong constraints on the evolution of the global star formation rate ( e.g. * ? ? ? * ) , unveiling the strong evolution of black hole accretion over most of cosmic time ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , tracing the evolution of galaxy size and morphology ( e.g. * ? ? ? * ) and much more . the second approach has been to expand our view in wavelength rather than cosmic time . the physical processes occurring in galaxies cause emission over the entire range of the electromagnetic spectrum . in order to have a full picture of galaxy formation , a multi - wavelength approach is vital . this has been made more achievable with recent generations of satellites covering the x - ray , ultra - violet , mid- and far - infrared . while the spectral energy distributions of stars tend to peak in the optical or near - infrared , obscuration and reprocessing by dust generates strong mid- and far - infrared emission . young stars ( when not obscured ) are most directly traced in the ultraviolet , while black hole accretion can generate radiation from the radio to x - ray and gamma - ray bands . surveys such as the galaxy and mass assembly ( gama ) survey @xcite and the cosmic evolution survey ( cosmos ; * ? ? ? * ) show the value of this multi - wavelength approach . the third route , and the one that we address in this paper , is to focus on spatially resolving galaxies ; in particular , obtaining spatially resolved spectroscopy . optical spectroscopy allows us to measure a wide range of parameters including current star formation rates ( e.g. via ) , gas phase metallicities , stellar ages , stellar metallicities , black hole accretion rates , ionization structure and extinction due to dust ( e.g. via the balmer decrement ) . the major spectroscopic surveys to date have used a single fibre @xcite or single slit on each object , and so obtain just one measurement of these parameters for each galaxy . moreover , these measurements may not be representative of the galaxy as a whole , but biased , depending on where the aperture is placed . this fundamental problem is addressed by integral field spectrographs ( ifs ) . in the last decade , projects such as sauron @xcite have demonstrated the power of integral field spectroscopy to capture a range of key observables that are simply not available to single - aperture surveys . as well as studying the properties listed above in a spatially - resolved context , obtaining gas and stellar kinematics over an entire galaxy enables us to separate dynamical components , measure dynamical mass , examine the impact of winds and outflows , and discover merging systems via dynamical disturbances . integral field spectroscopy has almost exclusively been limited to single - object instruments , meaning that it is time - consuming to build large samples . the largest current data set , using the sauron system on the william herschel telescope , contain @xmath3 objects ( atlas-3d ; * ? ? ? * ) . the califa project @xcite aims to target 600 objects with the pmas integral field unit ( ifu ) on the calar alto telescope using @xmath4200 nights of telescope time . the only multi - object integral field spectrograph currently available is that on the vlt flames instrument @xcite , which contains 15 ifus , each with 20 spatial elements of size 0.52 arcsec and a total field of view ( fov ) of @xmath5arcsec . this has enabled measurements of the tully - fisher relation at @xmath40.6 as well as a number of other projects . however the small fov of each ifu , combined with the high spectral resolution ( @xmath69000 ) and associated narrow wavelength range limits its applicability for large scale surveys . astrophotonic technology @xcite is now opening the way to new instrumentation that can address the need for highly multiplexed integral field spectroscopy . hexabundles @xcite are optical fibre bundles where the cladding has been stripped from each fibre to a minimum over a short length ( @xmath430 mm ) and the fibres then gently fused together at the input end to provide an ifu ( @xmath41 mm aperture ) with high filling factor . these can then be used in conventional multi - fibre spectrographs . in this paper , we report on the sydney - aao multi - object integral field spectrograph ( sami ) , the first fully operational demonstrator instrument to use hexabundles . sami has 13 ifus that can be positioned anywhere over a 1 degree diameter field of view . in section [ sec : rationale ] , we discuss in detail the scientific rationale for such an instrument , along with some practical considerations regarding sensitivity . in section [ sec : instrument ] , we describe the sami instrument in detail . in section [ sec : comm ] , we outline the observations carried out during the commissioning of the instrument , the results from which are discussed in section [ sec : results ] . our conclusions , and goals for the future , are laid out in section [ sec : conc ] .

we demonstrate a novel technology that combines the power of the multi - object spectrograph with the spatial multiplex advantage of an integral field spectrograph ( ifs ) . each hexabundle comprises 61 lightly fused multimode fibres with reduced cladding and yields a 75 percent filling factor . instrumentation : spectrographs techniques : imaging spectroscopy surveys galaxies : general galaxies : kinematics and dynamics

we demonstrate a novel technology that combines the power of the multi - object spectrograph with the spatial multiplex advantage of an integral field spectrograph ( ifs ) . the sydney - aao multi - object ifs ( sami ) is a prototype wide - field system at the anglo - australian telescope ( aat ) that allows 13 imaging fibre bundles ( `` hexabundles '' ) to be deployed over a 1degree diameter field of view . each hexabundle comprises 61 lightly fused multimode fibres with reduced cladding and yields a 75 percent filling factor . each fibre core diameter subtends 1.6 arcseconds on the sky and each hexabundle has a field of view of 15 arcseconds diameter . the fibres are fed to the flexible aaomega double beam spectrograph , which can be used at a range of spectral resolutions ( @xmath0 170013000 ) over the optical spectrum ( 37009500 ) . we present the first spectroscopic results obtained with sami for a sample of galaxies at @xmath1 . we discuss the prospects of implementing hexabundles at a much higher multiplex over wider fields of view in order to carry out spatially resolved spectroscopic surveys of @xmath2 galaxies . instrumentation : spectrographs techniques : imaging spectroscopy surveys galaxies : general galaxies : kinematics and dynamics

cond-mat0610265

c

in this paper , a mode - coupling theory for the slow dynamics of fluids adsorbed in disordered porous solids made of spherical particles frozen in random positions has been developed . derived by properly taking into account the peculiar structure of the correlations in these systems and by including a contribution which had been forgotten in a previous work @xcite , its equations are found to display many appealing features . for instance , they show universality , in the sense that they do not contain any explicit reference to the precise nature of the random environment in which the fluid evolves . also , they compare favorably with previous mode - coupling equations derived in other contexts , for the residual dynamics in the glassy phase of a bulk fluid ( sec . iii ) or for the equilibrium dynamics of a mean - field spin - glass in a random magnetic field ( appendix [ app.pspin ] ) . thus , from a formal point of view , the theory appears rather satisfactory . nevertheless , a few difficulties remain . first , there is the fact that , in the limit of vanishing fluid - fluid interactions , the present theory does not coincide with the mct which can be derived by assuming from the start that there are no such interactions . second , there is the divergence of the memory kernel for small wavevectors and the resulting spurious long time anomalies @xcite . we do not believe that these issues are really harmful , even if their handling requires ad hoc approximations , but they are worth stressing , since their solutions would probably teach us something on the nature of the approximations underlying the mct scheme and on possible extensions of the theory . for instance , it has been argued by leutheusser that the inclusion of vertex corrections within a kinetic theory approach would solve the second problem , but no operational scheme was proposed for this calculation @xcite . the numerical solution of the mct equations for two simple fluid - matrix models leads to a variety of transition scenarios , which are either discontinuous for dilute matrices or continuous for dense matrices . depending on the model , in the intermediate region where the nature of the transition changes , degenerate or genuine higher - order singularities and glass - glass transition lines are found . another remarkable prediction of the theory is the possibility of a reentry phenomenon for high matrix densities above the localization threshold , which has been interpreted as the signature of a decorrelation process induced by fluid - fluid collisions . before going further , one should note that , strictly speaking , this prediction of the theory can not be correct in the case of hard core fluid - matrix interactions . indeed , as recently confirmed by extensive computer simulations of the lorentz gas @xcite , the localization transition is driven by the percolation transition of the matrix void space , i.e. , localization occurs because , above a certain critical matrix density @xmath186 , the void space only consists of finite disconnected domains . in such a scenario , it is obvious that , whatever the fluid density , it is impossible to have an ergodic system above @xmath186 , since fluid - fluid interactions will never change the geometry of the matrix . this contradiction between the percolation theory and the mct clearly raises the issue of the relation between the two approaches , for which we propose the following simple argument . the mct applied to the problem of the diffusion - localization transition attempts to capture the onset of percolation in an indirect way , by giving an account of the increasingly correlated nature of the fluid - matrix collision events as the threshold is approached . in this respect , one should note that none of the static structure functions on which it is based does show a sensitivity to the phenomenon of percolation . following leutheusser , the theory works at the level of a self - consistent treatment of ring collision processes @xcite . this turns out to be enough to predict a diffusion - localization transition , but , clearly , the infinite sequences of correlated collisions which would really reflect the permanent trapping of the fluid particle in a finite domain above the percolation threshold are missing . from this incomplete characterization of the dynamical processes escorting the percolation phenomenon , it results that the mct diffusion - localization transition is actually an ideal version of the true percolation transition , in the usual sense that the mct predicts ideal glass transitions , and that the theory is not able to detect that , in an exact treatement , the percolation threshold fixes an absolute limit to diffusive behavior . when fluid - fluid collisions come into play at finite fluid densities , this leaves room for the prediction of a reentry phenomenon in contradiction with percolation theory . we believe that it is for the same reason that the mct also misses the fact that , at any matrix density , there is always a non - vanishing probability that particles will be trapped in a finite domain disconnected from the rest of the void space , so that the exploration of the available void space is never completely ergodic @xcite . it is thus clear that the prediction of a reentrant behavior of the ergodicity breaking transition line in the low fluid density domain should not be taken too literally . in fact , a reasonable expectation based on this finding is that , below the localization threshold , but in the regime where transient trapping effects are important , there might be an acceleration of the dynamics due to fluid - fluid collisions . interestingly , such a behavior has already been observed in a computer simulation study of a two dimensional lattice gas model with fixed randomly placed scatterers @xcite . indeed , it was found that , starting from the zero fluid density limit , the diffusion coefficient of a tagged particle first increases with the fluid density . an interpretation in terms of a decorrelation process similar to the one discussed in sec . iv was then proposed and validated by varying the parameters of the model . as a possible source of the difficulties of the theory , one might blame the fact that it works at the level of disorder averaged quantities . indeed , the procedure of averaging over disorder is equivalent to an averaging over the volume of a macroscopic system , an operation in which many microscopic details of the statics and dynamics become blurred . this might confer a mean - field character to the theory , where the contribution of the matrix would actually be taken into account at the level of a diffuse effective localizing potential , with a possible loss of important local constraints . unfortunately , this is a necessary step in order to develop a theory which is comparable in complexity with the one for bulk systems , since it allows one to consider the system as homogeneous . some progress has recently been made on the application of the mct to inhomogeneous situations @xcite , so it should be possible to relax the condition of homogeneity in order to study the dynamics of fluids confined in pores of simple geometry which are often preferred in simulation works , but there is no doubt that the more complex wavevector dependence of the resulting theory will make it harder to obtain numerical solutions of the equations . moreover , beyond this purely technical aspect , the present formulation in terms of disorder averaged quantities has a practical interest as well . indeed , many real porous media are disordered and most experimental techniques measure quantities which are averaged over the volume of a macroscopic sample and thus equivalent to the disorder averages considered by the mct . so , the current theoretical setup seems well suited for direct comparisons with experimental results . for molecular dynamics simulations , however , since rather small systems are usually considered , it might be necessary to explicitly perform the disorder average over a representative sample of matrix configurations before a comparison with the theory can be done . altogether , in spite of the above merely technical issues , we believe that the present mode - coupling theory represents a valuable step towards a better understanding of the slow dynamics of confined glassforming liquids . indeed , it remains rather simple and , since it is a microscopic approach , it allows one to study in detail the effect on the dynamics of changes in the different ingredients of a fluid - matrix model ( fluid - fluid and fluid - matrix interactions , structure of the matrix ) . thus , this provides us with a tool to efficiently and thoroughly explore the phenomenology of dynamics in confinement . this is clearly illustrated by our findings for two very simple systems with pure hard core interactions , which already display new and nontrivial glass transition scenarios . then remains the question of the validation of the theoretical predictions . because the model of the qa mixture is quite simple and the theory makes detailed predictions , molecular dynamics studies should be able to give clear - cut answers . the presently available results look rather encouraging , but more simulation work is definitely needed . it is a pleasure to thank g. tarjus , w. gtze , and w. kob , for useful comments , and f. hfling for a valuable discussion and the communication of unpublished results .

we derive a mode - coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space . numerical solutions for two simple models with pure hard core interactions lead to the prediction of a variety of glass transition scenarios , which are either continuous or discontinuous and include the possibility of higher - order singularities and glass - glass transitions . moreover , a reentry phenomenon is predicted in the low fluid - high matrix density regime and is interpreted as the signature of a decorrelation mechanism by fluid - fluid collisions competing with the localization effect of the solid matrix .

we derive a mode - coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space . its equations display the usual nonlinear structure met in this theoretical framework , except for a linear contribution to the memory kernel which adds to the usual quadratic term . the coupling coefficients involve structural quantities which are specific of fluids evolving in random environments and have expressions which are consistent with those found in related problems . numerical solutions for two simple models with pure hard core interactions lead to the prediction of a variety of glass transition scenarios , which are either continuous or discontinuous and include the possibility of higher - order singularities and glass - glass transitions . the main features of the dynamics in the two most generic cases are reviewed and illustrated with detailed computations . moreover , a reentry phenomenon is predicted in the low fluid - high matrix density regime and is interpreted as the signature of a decorrelation mechanism by fluid - fluid collisions competing with the localization effect of the solid matrix .

nlin0111014

i

the precise quantum signatures of different qualitative types of classical motion and the very definition of chaos in quantum mechanics are still the issues of an unsettled discussion ( see e.g. @xcite ) . due to unitarity of quantum dynamics , quantum chaos can not be defined in the same way as the classical chaos @xcite , namely through the exponential sensitivity on the variation of initial conditions . however , peres @xcite proposed an alternative concept which can be used in classical as well as in quantum mechanics : one can study the stability of quantum motion with respect to a small variation in the hamiltonian , or more generally , a variation of the unitary evolution operator . clearly , in classical mechanics this concept , when applied to individual trajectories ( or to phase space distribution functions as we show below in sect . 4 ) , is equivalent to the sensitivity to initial conditions : integrable systems with regular orbits are stable against small variation in the hamiltonian ( the statement of kam theorem ) , where s for chaotic orbits varying the hamiltonian has a similar effect as varying the initial condition : exponential divergence of two orbits for two nearby chaotic hamiltonians . this paper is devoted to a systematic theoretical study of the stability of a unitary time evolution with respect to small static variations of the unitary propagator . it will be primarily applied to the schr " odinger propagator in quantum dynamics ( sect . 2 and 3 ) , however an alternative application to the stability of classical unitary perron - frobenius evolution will be considered for comparison ( sect . 4 ) . the quantity of the central interest here is the _ fidelity _ of unitary ( quantum ) motion . let us consider a unitary operator @xmath6 being either ( i ) a short - time propagator @xmath7 , or ( ii ) a floquet map @xmath8 of ( periodically time - dependent ) hamiltonian @xmath9 ( @xmath10 ) , or ( iii ) a quantum poincar ' e map or any other quantized symplectic map . in any case a general small perturbation of the unitary operator can be written in the following form @xmath11 where @xmath12 is some self - adjoint operator , @xmath2 is a perturbation strength and @xmath3 is an effective planck constant which is taken out explicitly so that the observable @xmath12 has a well defined classical limit ( e.g. the corresponding weyl symbol ) . the influence of a small perturbation to the unitary evolution is quantitatively described by the overlap @xmath13 measuring the hilbert space distance between the exact and the perturbed time evolution from the same initial pure state @xmath14 , @xmath15 , where _ integer _ @xmath16 is a discrete time ( in units of the period @xmath17 ) . this defines the _ fidelity _ @xmath18 where @xmath19 gives the expectation value in the initial state @xmath20 . more generally , it may be useful to statistically average the fidelity over an ensemble of _ different pure initial states _ @xmath21 appearing with _ probabilities _ @xmath22 . thus we will write the fidelity in terms of a _ statistical density operator _ @xmath23 , namely as eq . ( [ eq : ft ] ) using the conventional statistical expectation value @xmath24 . the theoretical discussion in this paper is fully general , however , we will later apply our theory in the two extreme situations , namely for the ( coherent ) pure initial state @xmath25 , and for the full hilbert space average @xmath26 which is also equivalent to considering a _ random _ pure initial state of maximal information entropy . integer @xmath27 denotes a dimension of the relevant hilbert space which can be written semiclassically by the thomas - fermi rule @xmath28 where @xmath29 is the classical phase - space ( or energy shell ) volume and @xmath30 is the number of ( relevant ) degrees of freedom . the quantity @xmath31 , or its equivalent definitions , have already been discussed in several different contexts in quantum physics . we name just a few , namely those which provided direct motivation for the present work : first , @xmath31 has been proposed by peres @xcite as a measure of the stability of quantum motion . second , @xmath32 is the _ loschmidt echo _ characterizing the _ dynamical irreversibility _ , which has been used e.g. in spin - echo experiments @xcite where one is interested in the overlap between the initial state @xmath20 and an _ echo _ state @xmath33 obtained by composing forward time evolution , imperfect time inversion with a residual ( non - invertible ) interaction described by the operator @xmath34 , and backward time evolution . third , the fidelity has become a standard measure characterizing the loss of phase coherence in the quantum computation @xcite . fourth , it was used to characterize the `` hypersensitivity to perturbations '' in related studies of information theoretic characterization of quantum chaos @xcite , though in a different context of a stochastically time - dependent perturbation . the main result of this paper is a relation of the fidelity to the ergodic properties of quantum dynamics , more precisely to the time autocorrelation function of the generator of perturbation @xmath12 . quantum dynamics of finite and bound systems has always a _ discrete spectrum _ since the effective hilbert space dimension @xmath27 is finite , hence it is _ non - ergodic _ and _ non - mixing _ @xcite : time correlation functions have fluctuating tails of order @xmath35 . in order to reach a genuinely complex quantum motion with a continuous spectrum one has to enforce @xmath36 by considering one of the following two limits : semi - classical limit of effective planck s constant @xmath4 , or thermodynamic limit of number of particles , or number of freedoms @xmath37 . our result is surprising in the sense that it predicts the fidelity to decay slower if the integrated time correlation function is smaller , i.e. if the relaxation process is faster . in particular , for ergodic and sufficiently mixing dynamics ( such that the time integrated autocorrelation function of the perturbation @xmath12 is finite ) the fidelity is found to decay _ exponentially _ on a time - scale @xmath38 , whereas for a ` more regular ' , non - ergodic dynamics with non - vanishing time - averaged correlation functions , the fidelity decay is found to be qualitatively faster with a characteristic time - scale @xmath39 . however , this surprising and apparently counterintuitive result is correctly reconciled with the expected corresponding behavior in the classical limit due to non - trivial non - interchangability of the limits @xmath5 and @xmath4 . in all cases , the relevant time - scale for the decay of fidelity in the semi - classical regime can be explicitly computed in terms of the classical quantities only ( e.g. classical correlation functions ) . the main theoretical predictions are clearly demonstrated on the numerical examples of a kicked top and a pair of coupled kicked tops . furthermore , our theory on fidelity is general and can be applied to any perturbed unitary evolution ; as an example we consider the stability of the classical unitary perron - frobenius ( liouville ) evolution for maps , where we show how ` classical fidelity ' behaves in a qualitatively different way than the quantum fidelity and conforms to the corresponding linearly stable and exponentially unstable behaviors in the respective limiting cases of regular and chaotic dynamics . two short announcements of our theory with applications in the contexts of many - body quantum dynamics and quantum computing have already been reported @xcite . in section 2 , we present a theoretical derivation of the general relation between the fidelity of unitary motion and the correlation decay , discuss qualitatively different regimes of stability in the semiclassical range of small effective @xmath3 and outline the corresponding time - scales . in section 3 , our theoretical predictions are demonstrated in detail by numerical experiments on a quantized kicked top . in addition , we consider also a pair of coupled kicked tops in order to illustrate some dimensionality dependent aspects . in section 4 , we demonstrate the conceptual difference between the stability of classical and quantum unitary evolution by applying our theory to the case of classical ( liouvillian ) unitary evolution of phase space densities . in section 5 , we conclude by pointing to some potentially important applications and implications of our results .

we derive a simple and general relation between the fidelity of quantum motion , characterizing the stability of quantum dynamics with respect to arbitrary static perturbation of the unitary evolution propagator , and the integrated time auto - correlation function of the generator of perturbation . in particular , for non - ergodic and non - mixing dynamics , where asymptotic decay of correlations is absent , a qualitatively different and faster decay of fidelity is predicted on a time scale @xmath0 as opposed to mixing dynamics where the fidelity is found to decay exponentially on a time - scale @xmath1 , where @xmath2 is a strength of perturbation . a detailed discussion of a semi - classical regime of small effective values of planck constant @xmath3 note that the correct and intuitively expected classical stability behavior is recovered in the classical limit @xmath4 , as the two limits @xmath5 and @xmath4 do not commute . in addition we also discuss non - trivial dependence on the number of degrees of freedom . all the theoretical results are clearly demonstrated numerically on a celebrated example of a quantized kicked top . to appear in ( march 2002 )

we derive a simple and general relation between the fidelity of quantum motion , characterizing the stability of quantum dynamics with respect to arbitrary static perturbation of the unitary evolution propagator , and the integrated time auto - correlation function of the generator of perturbation . surprisingly , this relation predicts the slower decay of fidelity the faster decay of correlations is . in particular , for non - ergodic and non - mixing dynamics , where asymptotic decay of correlations is absent , a qualitatively different and faster decay of fidelity is predicted on a time scale @xmath0 as opposed to mixing dynamics where the fidelity is found to decay exponentially on a time - scale @xmath1 , where @xmath2 is a strength of perturbation . a detailed discussion of a semi - classical regime of small effective values of planck constant @xmath3 is given where classical correlation functions can be used to predict quantum fidelity decay . note that the correct and intuitively expected classical stability behavior is recovered in the classical limit @xmath4 , as the two limits @xmath5 and @xmath4 do not commute . in addition we also discuss non - trivial dependence on the number of degrees of freedom . all the theoretical results are clearly demonstrated numerically on a celebrated example of a quantized kicked top . to appear in ( march 2002 )

1403.4364

i

modifying general relativity has been one of the most highlighted fields in gravitational physics in recent years . long distance modification of gravity has been studied extensively so as to explain the current accelerated expansion of the universe ( see , _ e.g. _ , ref . @xcite for a recent review ) . more theoretically , it is interesting to ask the simple question of whether one can consistently modify general relativity to accommodate , _ e.g. _ , massive gravitons @xcite . in many cases , modified theories of gravity can be described , at least effectively , by adding an extra scalar degree of freedom that participates in the dynamics of gravity . the most general lagrangian composed of the metric @xmath3 and a scalar @xmath4 and having second - order field equations will therefore be a powerful tool to study various aspects of modified gravity , and , interestingly , the theory was already constructed forty years ago by horndeski @xcite . recently , the horndeski theory was rediscovered @xcite and shown to be equivalent to the generalized galileon @xcite . while considerable attention has been devoted to cosmological applications of the horndeski theory , black holes in that theory have been less explored so far . in the context of scalar - tensor modification of gravity , one of the central questions to address is whether or not black holes can have scalar hair . it has been proven by hawking that a black hole can not have scalar hair in the brans - dicke theory @xcite . in the traditional scalar - tensor theory where @xmath4 is nonminimally coupled to gravity , the scalar - no - hair theorem was formulated in @xcite ( under the assumption of spherical symmetry ) , and a more general proof was provided recently in @xcite , while the no - hair theorem for a noncanonical scalar field , _ i.e. _ , k - essence , was given in @xcite . it is then natural to ask how those results can be extended to theories whose lagrangian contains second derivatives of @xmath4 . such theories are motivated by the galileon @xcite , for which the equation of motion still remains of second order . for the galileon coupled to gravity , hui and nicolis have shown that static and spherically symmetric black holes can not be surrounded by any nontrivial profile of the scalar field @xcite . the key of the proof of ref . @xcite is shift symmetry of the scalar field , _ i.e. _ , symmetry under @xmath0 , where @xmath5 is a constant , and the regularity of the square of the noether current associated with this symmetry . therefore , the same argument seems to hold for more general scalar - tensor theories with the same symmetry , though there are some loopholes . one loophole can be opened by abandoning the static configuration of @xmath4 and/or relaxing some asymptotic conditions on the metric and @xmath4 , and hairy black hole solutions have thus been constructed explicitly in ref . one can also circumvent the no - hair theorem by tuning the lagrangian @xcite . in light of the former loophole , exact black hole solutions with scalar hair have been found in the theory with nonminimal derivative coupling to the einstein tensor , @xmath6 @xcite . the term @xmath6 has shift symmetry and reflection symmetry , @xmath7 . the goal of this paper is to extend those previous works to go beyond this particular example , giving various exact black hole solutions with scalar hair in a subclass of the horndeski theory possessing shift and reflection symmetries . the theory contains two _ arbitrary _ functions of @xmath2 , and we will provide a variety of solutions without specifying the concrete form of those functions . the paper is organized as follows . in the next section , we present the theory and the black hole ansatz considered in this paper . in secs . 3 and 4 , we give various exact solutions with scalar hair . the regularity of our solutions is discussed in sec . 5 . finally , we conclude in sec .

the theory admits two arbitrary functions of @xmath2 , and our solutions are constructed without specifying the concrete form of the two functions , implying that black hole solutions in specific scalar - tensor theories found in the literature can be extended to a more general class of theories with shift symmetry .

we derive a variety of exact black hole solutions in a subclass of horndeski s scalar - tensor theory possessing shift symmetry , @xmath0 , and reflection symmetry , @xmath1 . the theory admits two arbitrary functions of @xmath2 , and our solutions are constructed without specifying the concrete form of the two functions , implying that black hole solutions in specific scalar - tensor theories found in the literature can be extended to a more general class of theories with shift symmetry . our solutions include a black hole in the presence of an effective cosmological constant , the nariai spacetime , the lifshitz black hole , and other nontrivial solutions , all of which exhibit nonconstant scalar - field profile .

1403.4364

c

in this paper , we have derived a variety of exact black hole solutions in a subclass of horndeski s scalar - tensor theory having shift and reflection symmetries . assuming the time - dependent ansatz for the scalar field @xcite , @xmath181 , and following the method of constructing solutions of ref . @xcite , we have obtained a solution describing a black hole in the presence of a cosmological constant and other nontrivial solutions without fixing the concrete form of the two arbitrary functions in the theory . this was made possible because the solutions we have explored have the key property : @xmath100 const . our solutions circumvent the no - hair theorem because the scalar field itself is not static or it diverges at infinity . note that the action depends only on the derivatives of @xmath4 due to shift symmetry , and as a consequence the spacetime is static and the coordinate invariants constructed from the derivatives of the scalar field are regular . there are a lot of remaining issues to be addressed . one of the basic questions regarding a black hole solution is whether or not it is stable . it would therefore be interesting to study the stability issue by extending the black hole perturbation theory in horndeski s scalar - tensor gravity formulated in the static background @xcite . it would also be worth trying to generalize our solutions to rotating ones as has been done for a conformal scalar field @xcite , or to black holes with a realistic matter distribution , as in ref . @xcite for typical modified gravity theories with a screening mechanism . we primarily focused on @xmath100 const solutions in this paper , even though there could be many interesting solutions with @xmath32-dependent @xmath11 . it would be useful to clarify the phase space of possible solutions and to discuss their phenomenological properties as in refs . the theory we have studied admits superluminal propagations . it is crucial to study whether such superluminal propagations appear around the present black hole background in order to understand their causal structures and the influence of singularities on the region exterior to the horizon . finally , we would like to remark that the euclidean version of the theory ( [ lagrangian ] ) has been used in constructing a mechanism of emergent lorentz signature @xcite . our black hole solutions may help to give an insight about such a novel scenario . we would like to thank christos charmousis and eugeny babichev for pointing out an erroneous statement in the first version of the paper . we also thank hayato motohashi for a comment on the earlier draft . this work was supported in part by jsps grant - in - aid for young scientists ( b ) no . 24740161 ( t.k . ) . the work of n.t . is supported in part by world premier international research center initiative ( wpi initiative ) , mext , japan , and jsps grant - in - aid for scientific research 25@xmath182755 .

we derive a variety of exact black hole solutions in a subclass of horndeski s scalar - tensor theory possessing shift symmetry , @xmath0 , and reflection symmetry , @xmath1 . our solutions include a black hole in the presence of an effective cosmological constant , the nariai spacetime , the lifshitz black hole , and other nontrivial solutions , all of which exhibit nonconstant scalar - field profile .

we derive a variety of exact black hole solutions in a subclass of horndeski s scalar - tensor theory possessing shift symmetry , @xmath0 , and reflection symmetry , @xmath1 . the theory admits two arbitrary functions of @xmath2 , and our solutions are constructed without specifying the concrete form of the two functions , implying that black hole solutions in specific scalar - tensor theories found in the literature can be extended to a more general class of theories with shift symmetry . our solutions include a black hole in the presence of an effective cosmological constant , the nariai spacetime , the lifshitz black hole , and other nontrivial solutions , all of which exhibit nonconstant scalar - field profile .

1511.04443

i

in the local universe , the star formation surface density is determined by the molecular gas surface density ( e.g. larson 1992 ) . recent studies have shown that this relation probably holds at higher redshift ( @xmath15 ) as well ( e.g. tacconi et al . 2013 ; genzel et al . 2015 ) , suggesting that the gas reservoir is the key factor controlling the growth rate of galaxies . in the broader context of galaxy evolution , this has been interpreted as evidence for the equilibrium growth framework in which star formation is regulated by a balance between inflows and outflows ( bouch et al . 2010 ; dav , finlator , & oppenheimer 2012 ; lilly et al . 2013 ; peng & maiolino 2014 ) . in this model , galaxy growth in an integrated sense is driven by the cycle of baryons between galaxies and the halo gas ( dav et al . 2012 ) with the star formation efficiency set by stellar feedback ( hopkins et al . 2014 ) . however , in a resolved sense , exactly how different physical processes couple in different parts of galaxies to regulate star formation and drive structural assembly remains unknown ( dav et al . observationally , significant progress is being made in mapping the molecular gas reservoir and the spatial distribution of star formation of galaxies . molecular gas can now be mapped based on the spatial distribution of co thanks to millimeter arrays such as pdb and alma ( e.g. genzel et al . 2013 ; rybak et al . star formation can be mapped out to @xmath16 using the spatial distribution of the emission line owing to integral field units on ground - based telescopes ( sinfoni , osiris , kmos frster schreiber et al . 2009 ; law et al . 2009 ; wisnioski et al . 2015 ) and the wfc3 grism on hst ( nelson et al . 2012 ; nelson et al . 2013 ) . however , studies of spatially resolved star formation using the emission line suffer from an important systematic uncertainty as they only trace the photons that are not absorbed by dust . the dust attenuation toward star - forming regions is most directly probed using balmer recombination line flux ratios , the balmer decrement : as dust attenuation is wavelength dependent , its effects can be measured by comparing the observed and intrinsic balmer decrements ( e.g. calzetti 1997 ) . on a galaxy - integrated basis , the quantity of dust attenuation toward hii regions ( ) measured using balmer decrements has been shown to increase with increasing stellar mass ( ) , star formation rate ( sfr ) , and attenuation toward the stars ( ) ( calzetti et al . 2000 ; wild et al . 2011 ; momcheva et al . 2013 ; domnguez et al . 2013 ; price et al . 2014 ; reddy et al . 2015 ) . as the stellar mass surface density and the star formation surface density are typically highest in the centers of galaxies , we expect the attenuation to vary within galaxies , such that the dust attenuation is highest in the centers . this is also expected from the fact that both the metallicity and , most importantly , the gas column density increase with decreasing distance from the center ( e.g. bohlin , savage , & drake 1978 ; gilli et al . 2014 ; nelson et al . therefore , in order to tie the global gas reservoir to galactic structural assembly we need to correct the spatially - resolved measurements for the attenuation toward star - forming regions . measuring spatially - resolved balmer decrements is now possible with the wide field camera 3 ( wfc3 ) grism capability on the hubble space telescope , which we employed for the 3d - hst survey ( brammer et al . 2012 ; momcheva et al . 2015 ) . the grism data enable us to create emission line maps for every object in the survey ( see nelson et al . 2012 ; nelson et al . 2013 ; wuyts et al . 2013 ; nelson et al . 2015 ) . in a narrow redshift window ( @xmath17 ) we can map the spatial distribution of both the and emission lines , as they both fall within the g141 wavelength coverage . galaxy - integrated balmer decrements were analyzed in price et al . ( 2014 ) . here we present spatially resolved balmer decrements for galaxies at @xmath0 and derive radial dust gradients . the gradients are measured from deep stacks , using the full 3d - hst dataset . we study radial dust gradients as a function of , and apply these gradients to the observed distributions to obtain spatially - resolved dust - corrected star formation surface density profiles .

we derive average radial gradients in the dust attenuation towards hii regions in 609 galaxies at @xmath0 , using measurements of the balmer decrement out to @xmath1kpc . the balmer decrements are derived from spatially resolved maps of and emission from the 3d - hst survey .

we derive average radial gradients in the dust attenuation towards hii regions in 609 galaxies at @xmath0 , using measurements of the balmer decrement out to @xmath1kpc . the balmer decrements are derived from spatially resolved maps of and emission from the 3d - hst survey . we find that with increasing stellar mass both the normalization and strength of the gradient in dust attenuation increases . galaxies with a mean mass of @xmath2m@xmath3 have little dust attenuation at all radii , whereas galaxies with @xmath4m@xmath3 have @xmath5mag in their central regions . we parameterize this as @xmath6 , with @xmath7 , @xmath8 , @xmath9 in kpc , and @xmath10 the stellar mass in units of @xmath11m@xmath3 . this expression can be used to correct spatially resolved measurements of to radial distributions of star formation . when applied to our data , we find that the star formation rates in the central @xmath12kpc of galaxies in the highest mass bin are @xmath13m@xmath3yr@xmath14 , six times higher than before correction and approximately half of the total star formation rate of these galaxies . if this high central star formation rate is maintained for several gyr , a large fraction of the stars in present - day bulges likely formed in - situ . .

1511.04443

c

using the wfc3 grism to map the distribution of and emission , we constructed the first spatially - resolved maps of the balmer decrement at @xmath65 . these measurements provide stringent constraints on the radial gradients in the dust attenuation toward star forming regions of galaxies , allowing us to derive dust - corrected radial distributions of star formation . we find that the dust attenuation is small ( @xmath66mag ) at all radii in galaxies with @xmath67m@xmath3 . galaxies with higher masses have significant dust attenuation toward their centers . the immediate implication is that the central ( @xmath68kpc ) observed emission of high mass galaxies should not be directly converted to star formation , and the central surface brightness should not be directly converted to stellar mass density . a potential concern in this analysis is that by stacking small galaxies with high attenuation and large galaxies with low attenuation , we could infer a radial dust gradient where on an individual galaxy basis , there is none . to test this , we remove all compact galaxies with sizes more than 0.1 and 0.3dex below the size - mass relation from the stack . in both cases , the qualitative trends remain unchanged meaning the gradients are real , not a byproduct of stacking a heterogeneous sample . another concern is that weighting galaxies by their flux biases the stacks toward galaxies with high and equivalent widths . if galaxies with high equivalent widths have preferentially low dust attenuation , this analysis could underestimate the true dust attenuation at the median mass of the stacks . a straightforward interpretation of our results is that we see the in - situ building of bulges in massive galaxies at @xmath69 . however , a key question is whether this central star formation accounts for a significant fraction of the stars in the central kpc of present - day galaxies . the total amount of stars that are formed in the central kpc can be approximated by @xmath70 with @xmath71 a correction for mass loss due to stellar winds ( see e.g. bruzual & charlot 2003 ) and @xmath72 the duration of the star formation . for @xmath73gyr ( that is , assuming that the current star formation rate is maintained until @xmath74 ) , we find that the total mass that is added is @xmath75 , or @xmath76 of the total mass of the galaxy . if @xmath77gyr the added mass is much less significant . we note that this does not necessarily imply that galaxies are growing outside - in " : this depends on the radial @xmath78 profiles ( szomoru et al . 2013 ) which are driven by gradients in dust and age . this could be tested by deriving mass profiles from the high spatial resolution candels multi - color imaging . in summary , we infer that it is possible that a central mass concentration is built up through in - situ star formation in the highest mass galaxies , but only if the radial distribution of star formation observed at @xmath0 is sustained over several gyr . this can be tested with spatially - resolved absorption maps at lower redshift , which can be created using adaptive optics or the g102 grism on the wfc3 camera . furthermore , high resolution imaging of the molecular gas and of the continuum dust emission with alma can provide direct information on the presence of large amounts of dust in the centers of massive galaxies at these redshifts . finally , with future facilities such as jwst our initial study of averaged spatially - resolved balmer decrements at moderate redshifts can be expanded to higher redshifts and individual galaxies .

galaxies with a mean mass of @xmath2m@xmath3 have little dust attenuation at all radii , whereas galaxies with @xmath4m@xmath3 have @xmath5mag in their central regions . this expression can be used to correct spatially resolved measurements of to radial distributions of star formation . when applied to our data , we find that the star formation rates in the central @xmath12kpc of galaxies in the highest mass bin are @xmath13m@xmath3yr@xmath14 , six times higher than before correction and approximately half of the total star formation rate of these galaxies . if this high central star formation rate is maintained for several gyr , a large fraction of the stars in present - day bulges likely formed in - situ . .

we derive average radial gradients in the dust attenuation towards hii regions in 609 galaxies at @xmath0 , using measurements of the balmer decrement out to @xmath1kpc . the balmer decrements are derived from spatially resolved maps of and emission from the 3d - hst survey . we find that with increasing stellar mass both the normalization and strength of the gradient in dust attenuation increases . galaxies with a mean mass of @xmath2m@xmath3 have little dust attenuation at all radii , whereas galaxies with @xmath4m@xmath3 have @xmath5mag in their central regions . we parameterize this as @xmath6 , with @xmath7 , @xmath8 , @xmath9 in kpc , and @xmath10 the stellar mass in units of @xmath11m@xmath3 . this expression can be used to correct spatially resolved measurements of to radial distributions of star formation . when applied to our data , we find that the star formation rates in the central @xmath12kpc of galaxies in the highest mass bin are @xmath13m@xmath3yr@xmath14 , six times higher than before correction and approximately half of the total star formation rate of these galaxies . if this high central star formation rate is maintained for several gyr , a large fraction of the stars in present - day bulges likely formed in - situ . .

1407.0494

i

@xmath41 is a poor approximation to @xmath36 at all momentum - transfer scales that are either now accessible to experiments involving pion elastic or transition processes , or will become so in the foreseeable future@xcite . predictions of leading - order , leading - twist formulae involving @xmath88 are a misleading guide to interpreting and understanding contemporary experiments . at accessible energy scales a better guide is obtained by using the broad pda described herein in such formulae . this might be adequate for the charged pion s elastic form factor . however , it will probably be necessary to consider higher twist and higher - order corrections in controversial cases such as the @xmath134 transition form factor @xcite . the near agreement for gev@xmath4 in fig.[fig : q2piff2013 ] between the perturbative qcd prediction that uses @xmath135 ( dash - dot curve ) and the new dse result for @xmath2 ( solid curve ) is striking . it highlights that a single dse interaction kernel , essentially determined by one strength parameter , and preserving the one - loop renormalization group behavior of qcd , is very close to unifying the pion s electromagnetic form factor and its valence - quark distribution amplitude . numerous other quantities are also correlated quite closely via a single dse interaction kernel @xcite . moreover , this leading - order , leading - twist qcd prediction , obtained with a pion valence - quark pda evaluated at a scale appropriate to the experiment , underestimates our full computation by merely an approximately uniform 15% on the domain depicted . the small mismatch should be explained by a combination of higher - order , higher - twist corrections to eq . and shortcomings in the rainbow - ladder truncation , which predicts the correct power - law behavior for the form factor but not precisely the right anomalous dimension . hence , as anticipated earlier @xcite ( and expressing a result that can be understood via the behavior of the dressed - quark mass - function @xcite ) , one should expect dominance of hard contributions to the pion form factor for @xmath3gev@xmath4 . notwithstanding this , the normalization of the form factor is fixed by a pion wave - function whose dilation with respect to @xmath41 is a definitive signature of dynamical chiral symmetry breaking . i wish to acknowledge valuable interactions with c. d. roberts and lei chang that made a lot of this work possible . i also wish to thank the organizers of the lightcone 2013 workshop for providing a fine program and a welcoming atmosphere . this work was supported in part by the national science foundation under grant no . nsf - phy-1206187 .

the significant dilation of this pda compared to the known asymptotic pda is a signature of dynamical chiral symmetry breaking ( dcsb ) on the light front . the leading - order , leading - twist perturbative qcd result for @xmath2 underestimates the new dse computation by just 15% on @xmath3gev@xmath4 , in stark contrast with the result obtained using the asymptotic pda .

we describe results for the pion distribution amplitude ( pda ) at the non - perturbative scale 2gev by projecting the poincar - covariant bethe - salpeter wave - function onto the light - front and use it to investigate the ultraviolet behavior of the electromagnetic form factor , @xmath0 , on the entire domain of spacelike @xmath1 . the significant dilation of this pda compared to the known asymptotic pda is a signature of dynamical chiral symmetry breaking ( dcsb ) on the light front . we investigate the transition region of @xmath1 where non - perturbative behavior of constituent - like quarks gives way to the partonic - like behavior of quantum chromodynamics ( qcd ) . the non - perturbative approach is based on the dyson - schwinger equation ( dse ) framework for continuum investigations in qcd . the leading - order , leading - twist perturbative qcd result for @xmath2 underestimates the new dse computation by just 15% on @xmath3gev@xmath4 , in stark contrast with the result obtained using the asymptotic pda .

astro-ph0703095

i

we have presented in this paper the details of the hst acs / wfc cosmos observations and data processing that we used to produce the imaging datasets which form the basis for the majority of the scientific work in the cosmos project . a more general discussion of the hst acs dataset is presented in @xcite . the relative astrometry of all the hst images is accurate to @xmath43 milliarcseconds , with an absolute astrometric accuracy determined fundamentally by the accuracy of the radio reference frame which is @xmath53 milliarcseconds . the images reach a point - source limiting depth ab(f814w ) = 27.2 ( 5@xmath50 ) in a @xmath54 diameter aperture , and have been projected onto output grids of @xmath51/pixel and @xmath22/pixel . the @xmath51/pixel data was drizzled using a gaussian kernel with a fwhm of 40 milliarcseconds , and the average width of the psf in these images is @xmath55 ; these images are optimized for weak lensing studies , and are available as unrotated tiles ( one for each acs orbit ) and also as combined sections oriented with north up , registered to the pixel frame of the ground - based optical datasets . the @xmath22/pixel data was drizzled using a square kernel with a pixfrac of 0.8 and has an average psf width of @xmath56 . this dataset is available in sections that are registered to the pixel frame of the ground - based optical datasets , and is also available as a single monolithic mosaic 100800 pixels on a side ( 80 gb ) . the cosmos hst datasets are publicly available through the web sites for ipac / irsa ( * http://irsa.ipac.caltech.edu/data/cosmos/ * ) and stsci - mast ( * http://archive.stsci.edu/ * ) . irsa also supplies a cutout capability derived from the full field mosaic , which can be made with any field center and size . the hst cosmos treasury program was supported through nasa grant hst - go-09822 . we wish to thank tony roman , denise taylor , and david soderblom for their assistance in planning and scheduling of the extensive cosmos observations . we gratefully acknowledge the contributions of the entire cosmos collaboration consisting of more than 70 scientists . more information on cosmos is available at * http://cosmos.astro.caltech.edu/ * and we acknowledge the services provided by the staff at the nasa ipac / irsa as well as the stsci mast archive in providing online archive and server capabilities for the cosmos datasets . the cosmos science meeting in may 2005 was supported in part by the nsf through grant oise-0456439 . beckwith , s. v. w. , stiavelli , m. , koekemoer , a. m. , caldwell , j. a. r. , ferguson , h. c. , hook , r. , lucas , r. a. , bergeron , l. e. , corbin , m. , jogee , s. , panagia , n. , robberto , m. , royle , p. , somerville , r. s. , sosey , m. 2006 , , 132 , 1729 giavalisco , m. , ferguson , h. c. , koekemoer , a. m. , dickinson , m. , alexander , d. m. , bauer , f. e. , bergeron , j. , biagetti , c. , brandt , w. n. , casertano , s. , cesarsky , c. , chatzichristou , e. , conselice , c. , cristiani , s. , da costa , l. , dahlen , t. , de mello , d. , eisenhardt , p. , erben , t. , fall , s. m. , fassnacht , c. , fosbury , r. , fruchter , a. , gardner , j. p. , grogin , n. , hook , r. n. , hornschemeier , a. e. , idzi , r. , jogee , s. , kretchmer , c. , laidler , v. , lee , k. s. , livio , m. , lucas , r. , madau , p. , mobasher , b. , moustakas , l. a. , nonino , m. , padovani , p. , papovich , c. , park , y. , ravindranath , s. , renzini , a. , richardson , m. , riess , a. , rosati , p. , schirmer , m. , schreier , e. , somerville , r. s. , spinrad , h. , stern , d. , stiavelli , m. , strolger , l. , urry , c. m. , vandame , b. , williams , r. , wolf , c. 2004 , , 600 , 99 rix , h .- w . , barden , m. , beckwith , s. v. w. , bell , e. f. , borch , a. , caldwell , j. a. r. , hussler , b. , jahnke , k. , jogee , s. , mcintosh , d. h. , meisenheimer , k. , peng , c. y. , sanchez , s. f. , somerville , r. s. , wisotzki , l. , wolf , c. 2004 , , 152 , 163 williams , r. e. , blacker , b. , dickinson , m. , dixon , w. v. d. , ferguson , h. c. , fruchter , a. s. , giavalisco , m. , gilliland , r. l. , heyer , i. , katsanis , r. , levay , z. , lucas , r. a. , mcelroy , d. b. , petro , l. , postman , m. , adorf , h .- m . , hook , r. 1996 , , 112 , 1335 williams , r. e. , baum , s. , bergeron , l. e. , bernstein , n. , blacker , b. s. , boyle , b. j. , brown , t. m. , carollo , c. m. , casertano , s. , covarrubias , r. , de mello , d. f. , dickinson , m. e. , espey , b. r. , ferguson , h. c. , fruchter , a. s. , gardner , j. p. , gonnella , a. , hayes , j. , hewett , p. c. , heyer , i. , hook , r. , irwin , m. , jones , d. , kaiser , m. e. , levay , z. , lubenow , a. , lucas , r. a. , mack , j. , mackenty , j. w. , madau , p. , makidon , r. b. , martin , c. l. , mazzuca , l. , mutchler , m. , norris , r. p. , perriello , b. , phillips , m. m. , postman , m. , royle , p. , sahu , k. , savaglio , s. , sherwin , a. , smith , t. e. , stiavelli , m. , suntzeff , n. b. , teplitz , h. i. , van der marel , r. p. , walker , a. r. , weymann , r. j. , wiggs , m. s. , williger , g. m. , wilson , j. , zacharias , n. , zurek , d. r. 2000 , , 120 , 2735 lcc 2003-oct-15 2004-jan-07 & 100 & 42 + 2004-mar-02 2004-may-21 & 280 & 303 + 2004-oct-13 2005-jan-07 & 100 & 103 + 2005-mar-02 2005-may-21 & 280 & 142 + 2005-oct-28 2005-nov-24 & 100 & 2

the median exposure depth across the field is 2028 seconds ( one hst orbit ) , achieving a limiting point - source depth ab(f814w ) = 27.2 ( 5 sigma ) . the final set of images are publicly available through the archive sites at ipac and stsci , along with further documentation on how they were produced .

we describe the details of the _ hubble space telescope ( hst ) advanced camera for surveys / wide field channel ( acs / wfc ) _ observations of the cosmos field , including the data calibration and processing procedures . we obtained a total of 583 orbits of hst acs / wfc imaging in the f814w filter , covering a field that is 1.64 degrees@xmath0 in area , the largest contiguous field ever imaged with hst . the median exposure depth across the field is 2028 seconds ( one hst orbit ) , achieving a limiting point - source depth ab(f814w ) = 27.2 ( 5 sigma ) . we also present details about the astrometric image registration , distortion removal and image combination using multidrizzle , as well as motivating the choice of our final pixel scale ( 30 milliarcseconds per pixel ) , based on the requirements for weak lensing science . the final set of images are publicly available through the archive sites at ipac and stsci , along with further documentation on how they were produced .

1501.05570

i

designing the electromagnetic response of an artificial medium is one of the main target of modern photonics and metamaterial science is probably the most important research field based on such skill . basically the design is made possible by the physical fact that the electromagnetic field , when traveling within a nonhomogeneous medium with sub - wavelength features , is not able to follow its spatial rapidly - varying details so that the field only experiences the effect of an averaged or effective medium . a number of different homogenization approaches have been developed for predicting the effective medium electromagnetic response and they exploit different and suitable approximation schemes . the simplest homogenization technique deals with the retrieval of the effective parameters from the scattering properties of the medium @xcite and it is based on postulating the equivalence between a complex metamaterial array and a uniform slab of same thickness with unknown constitutive parameters . another homogenization technique is the field averaging method which is based on the averaging of the electromagnetic field in a metamaterial unit cell @xcite and , in analogy with the retrieval technique , it is a numerical method for the determination of effective parameters . in addition to numerical methods , mean - field homegenization theories are available where the effective parameters are evaluated from the distribution of the underlying metamaterial inclusions . examples of such techniques are those exploiting lorentz @xcite , clausius - mossotti @xcite , maxwell - garnett @xcite approximations , or based on multipolar expansion @xcite and source - driven approach @xcite . spatial periodicity and rapidly - varying spatial scales are the two basic ingredients of each metamaterial homogenization approach . two different homogenization techniques are obtained by assuming one of these two ingredients and subsequently incorporating the other . therefore , starting from the photonic - crystal description of the structure where the spatial periodicity is fully taken into account , the effective medium response can be extracted in the long wavelength regime @xcite . conversely , the spatial rapidly - varying metamaterial features allows an asymptotic multi - scale analysis of the sample electromagnetic response which combined with the array periodicity yields the effective medium response @xcite . even though the metamaterial inclusions pattering has a spatial scale much smaller than the radiation wavelength , such two scales are generally not so different to allow a description of the effective medium response only comprising effective dielectric permittivity and magnetic permeability tensors . for this reason , the effective medium generally shows an additional nonlocal respose @xcite yielding spatial dispersion . it is well - known that the nonlocal first order contribution ( i.e. containing first order spatial derivatives of the electric field ) is equivalent to a reciprocal bianisotropic response @xcite whereas the second order contribution can be partially interpreted as a correction to the effective magnetic permeability tensor @xcite , a phenomenon which is known as artificial or optical magnetism @xcite . if the effective nonlocality is weak , the effective medium response is adequately described by reciprocal bianisotropic constitutive relations where the chirality tensor accounts for the strength of magnetic and electric polarizations coupling . an efficient way for observing the effect of electromagnetic chirality is considering metamaterials whose underlying constituents pattering exhibits chiral asymmetry , i.e. its mirror image can not be superposed onto it , and theoretical and experimental investigations have been performed both in three - dimensional @xcite and in two - dimensional configurations @xcite . chiral metamaterials have attracted a good deal of attention since they can yield giant optical activity , asymmetric transmission @xcite , repulsive casimir force @xcite , backward waves @xcite and negative refractive index @xcite . in this paper we theoretically investigate the electromagnetic response in the long wavelength regime of a periodic composite medium , whose inclusions are non - magnetic , and we carry out the analysis by including spatial dispersion up to the second order . specifically , by using the ratio @xmath2 between the composite periodicity and the wavelength as an asymptotic expansion parameter , we exploit a general multiscale technique for separating the fast matter scale from the slow radiation one and to extract the average effect of the composite on the electromagnetic field . we fully develop the analysis up to the second order in @xmath2 and we find that the obtained effective medium response has a @xmath3 order reproducing the know results of standard homogenization approaches and @xmath4 and @xmath5 orders accounting for first and second order effective medium nonlocality , respectively . the effective dielectric permittivity tensor ( of rank two ) arising from the zeroth order is obtained by averaging over the metamataterial unit cell specific fast - varying fields satisfying electrostatic - like equations . the main result of the present paper is that this very simple procedure still works for evaluating the two tensors ( of ranks three and four , respectively ) describing effective medium nonlocality up to the second order and the corresponding electrostatic - like equations for the suitable fast - varying fields to be averaged are here derived and discussed . as a consequence we obtain a simple scheme for evaluating the effective medium response up to the second order which is based on solving a small number of poisson equations on the metamaterial unit cell . in particular we obtain a very compact expression for the three - rank tensor describing first order spatial nonlocality which remarkably reveals that it can be evaluated by using the same fast - varying fields appearing in the zeroth order description , thus avoiding the requirement of solving additional electrostatic - like equations . therefore the ensuing procedure for deducing the medium response up to the first order is remarkably simple and compact . for metamaterials with negligible second - order spatial dispersion , we combine the obtained description with the equivalence of first - order spatial dispersion and reciprocal bianisotropic electromagnetic response to obtain a compact and simple expression for the effective medium chirality tensor . using such expression we investigate the impact of the composite patterning symmetry on electromagnetic chirality . specifically we obtain that if the composite does not show chiral asymmetry , i.e. its mirror image can be superposed on it , the effective chiral tensor vanishes with two remarkable exceptions corresponding to the specific cases where the rotation needed to superpose the mirror image onto the structure is either a @xmath0 or @xmath1 rotation around an axis orthogonal to the reflection plane . in these two situations the composite is geometrically achiral and it nonetheless shows electromagnetic chirality whose chiral tensor turns out to be that of pseudo - chiral - omega medium . such general result encompasses in particular the relevant cases of two - dimensional and recently considered one - dimensional metamaterials showing chiral response . as an example admitting full analytical description , we discuss one - dimensional metamaterials whose single chirality parameter is shown to be directly related to the metamaterial dielectric profile by quadratures . the paper is organized as follows . in sec . ii we discuss our approach to the effective medium description of a periodic composite in the long wavelength regime including spatial nonlocality . this is done examining the general multiscale technique in sec . ii.a and applying it to the zeroth , first and second orders in sections ii.b , ii.c and ii.d , respectively . in sec . iii we sum up the results obtained in sec . ii and we stress the simplicity and compactness of the proposed approach . in sec . iv we consider media whose second order contribution to spatial nonlocal response can be neglected and we focus on electromagnetic chirality . specifically in sec . iv.a we adopt the bianisotropic description of the medium to deduce a simple expression for the chirality tensor , in sec . iv.b we examine the relation between geometric and electromagnetic chirality of metamaterials and in sec . iv.c we specialize such general analysis to the cases of two - dimensional and one - dimensional chiral metamaterials . in sec . v we focus on one - dimensional chiral metamaterials and we obtain a closed - form expression for the single parameter ruling electromagnetic chirality of such media . in sec . vi we draw our conclusions .

, we exploit the equivalence of first - order spatial dispersion and reciprocal bianisotropic electromagnetic response to deduce a simple expression for the metamaterial chirality tensor . such an expression allows us to systematically analyze the effect of the composite spatial symmetry properties on electromagnetic chirality . we find that even if a metamaterial is geometrically achiral , i.e. it is indistinguishable from its mirror image , it shows pseudo - chiral - omega electromagnetic chirality if the rotation needed to restore the dielectric profile after the reflection is either a @xmath0 or @xmath1 rotation around an axis orthogonal to the reflection plane . these two symmetric situations encompass two - dimensional and one - dimensional metamaterials with chiral response . as an example admitting full analytical description , we discuss one - dimensional metamaterials whose single chirality parameter is shown to be directly related to the metamaterial dielectric profile by quadratures .

we develop , from first principles , a general and compact formalism for predicting the electromagnetic response of a metamaterial with non - magnetic inclusions in the long wavelength limit , including spatial dispersion up to the second order . specifically , by resorting to a suitable multiscale technique , we show that medium effective permittivity tensor and the first and second order tensors describing spatial dispersion can be evaluated by averaging suitable spatially rapidly - varying fields each satysifing electrostatic - like equations within the metamaterial unit cell . for metamaterials with negligible second - order spatial dispersion , we exploit the equivalence of first - order spatial dispersion and reciprocal bianisotropic electromagnetic response to deduce a simple expression for the metamaterial chirality tensor . such an expression allows us to systematically analyze the effect of the composite spatial symmetry properties on electromagnetic chirality . we find that even if a metamaterial is geometrically achiral , i.e. it is indistinguishable from its mirror image , it shows pseudo - chiral - omega electromagnetic chirality if the rotation needed to restore the dielectric profile after the reflection is either a @xmath0 or @xmath1 rotation around an axis orthogonal to the reflection plane . these two symmetric situations encompass two - dimensional and one - dimensional metamaterials with chiral response . as an example admitting full analytical description , we discuss one - dimensional metamaterials whose single chirality parameter is shown to be directly related to the metamaterial dielectric profile by quadratures .

1501.05570

c

to sum up we have investigated the electromagnetic response of a metamaterial with non - magnetic inclusions by a multiscale analysis and we have included spatial nonlocality up to the second order . the resulting description is very simple and compact since the three tensors characterizing the effective medium response are shown to be averages ( on the unit cell ) of suitable fast - varying fields which , in turn , are obtained from the dielectric distribution by solving a small number of electrostatic equations . if second order nonlocal response can be neglected , the medium response can be recast into the standard bianisotropic form and this has allowed us to obtain a compact expression for the chirality tensor of the effective medium . we have exploited our approach to investigate the relation between geometrical and electromagnetic chirality by proving that the latter is shown , in addition to chiral media , even by an achiral medium whose mirror image can be superposed onto it by means of a @xmath0 or @xmath1 rotation around an axis orthogonal to the reflection plane . we have deduced , as specific relevant examples , the chirality tensor structure of two - dimensional and one - dimensional media and , for the formers , we have obtained a closed form expression for the chirality parameter which can be evaluated from the inclusions dielectric profile by means of quadratures .

we develop , from first principles , a general and compact formalism for predicting the electromagnetic response of a metamaterial with non - magnetic inclusions in the long wavelength limit , including spatial dispersion up to the second order . specifically , by resorting to a suitable multiscale technique ,

we develop , from first principles , a general and compact formalism for predicting the electromagnetic response of a metamaterial with non - magnetic inclusions in the long wavelength limit , including spatial dispersion up to the second order . specifically , by resorting to a suitable multiscale technique , we show that medium effective permittivity tensor and the first and second order tensors describing spatial dispersion can be evaluated by averaging suitable spatially rapidly - varying fields each satysifing electrostatic - like equations within the metamaterial unit cell . for metamaterials with negligible second - order spatial dispersion , we exploit the equivalence of first - order spatial dispersion and reciprocal bianisotropic electromagnetic response to deduce a simple expression for the metamaterial chirality tensor . such an expression allows us to systematically analyze the effect of the composite spatial symmetry properties on electromagnetic chirality . we find that even if a metamaterial is geometrically achiral , i.e. it is indistinguishable from its mirror image , it shows pseudo - chiral - omega electromagnetic chirality if the rotation needed to restore the dielectric profile after the reflection is either a @xmath0 or @xmath1 rotation around an axis orthogonal to the reflection plane . these two symmetric situations encompass two - dimensional and one - dimensional metamaterials with chiral response . as an example admitting full analytical description , we discuss one - dimensional metamaterials whose single chirality parameter is shown to be directly related to the metamaterial dielectric profile by quadratures .

1101.5805

i

as advances in technology allow for the collection and storage of vast databases , there is a growing need for advanced machine learning techniques for speeding up the execution of queries on such large datasets . in this work we focus on the fundamental task of estimating the selectivity , or output size , of a database query , which is a crucial step in a number of query processing tasks such as execution plan optimization and resource allocation in parallel and distributed databases . the task of efficiently obtaining such accurate estimates has been extensively studied in previous work with solutions ranging from storage of pre - computed statistics on the distribution of values in the tables , to online sampling of the databases , and to combinations of the two approaches @xcite . histograms , simple yet powerful statistics of the data in the tables , are the most commonly used solution in practice , thanks to their computational and space efficiency . however , there is an inherent limitation to the accuracy of this approach when estimating the selectivity of queries that involve either multiple tables / columns or correlated data . running the query on freshly sampled data gives more accurate estimates at the cost of delaying the execution of the query while collecting random samples from a disk or other large storage medium and then performing the analysis itself . this approach is therefore usually more expensive than a histogram lookup . our goal in this work is to exploit both the computational efficiency of using pre - collected data and the provable accuracy of estimates obtained by running a query on a properly sized random sample of the database . we apply the statistical concept of vc - dimension @xcite to develop and analyze a novel technique to generate accurate estimates of query selectivity . roughly speaking , the vc - dimension of a collection of indicator functions ( hypotheses ) is a measure of its complexity or expressiveness ( see sect . [ sec : vcdim ] for formal definitions ) . a major theoretical contribution of this work , which is of independent interest , is an explicit bound to the vc - dimension of any class of queries , viewed as indicator functions on the cartesian product of the database tables . in particular , we show that the vc - dimension of a class of queries is a function of the maximum number of boolean , select and join operations in any query in the class , but it is not a function of the number of different queries in the class . by adapting a fundamental result from the vc - dimension theory to the database setting , we develop a method that for any class of queries , defined by its vc - dimension , builds a concise sample of the database , such that with high probability , the execution of _ any _ query in the class on the sample provides an accurate estimate for the selectivity of the query on the original large database . the error probability holds _ simultaneously _ for the selectivity estimate of _ all _ queries in the collection , thus the same sample can be used to evaluate the selectivity of multiple queries , and the sample needs to be refreshed only following major changes in the database . the size of the sample does not depend on the size ( number of tuples ) in the database , just on the complexity of the class of queries we plan to run , measured by its vc - dimension . both the analysis and the experimental results show that accurate selectivity estimates can be obtained using a sample of a surprising small size ( see table [ tab : samplesize ] for concrete values ) , which can then reside in main memory , with the net result of a significant speedup in the execution of queries on the sample . a technical difficulty in applying the vc - dimension results to the database setting is that they assumes the availability of a uniform sample of the cartesian product of all the tables , while in practice it is more efficient to store a sample of each table separately and run the queries on the cartesian product of the samples , which has a different distribution than a sample of the cartesian product of the tables . we develop an efficient procedure for constructing a sample that circumvents this problem ( see sect . [ sec : applications ] ) . we present extensive experimental results that validate our theoretical analysis and demonstrate the advantage of our technique when compared to complex selectivity estimation techniques used in postgresql and the microsoft sql server . the main advantage of our method is that it gives provably accurate predictions for the selectivities of all queries with up to a given complexity ( vc - dimension ) specified by the user before creating the sample , while techniques like multidimensional histograms or join synopses are accurate only for the queries for which they are built . note that we are only concerned with estimating the selectivity of a query , not with approximating the query answer using a sample of the database ( das @xcite presents a survey of the possible solutions to this latter task ) . [ [ outline . ] ] outline . + + + + + + + + the rest of the paper is organized as follows . we review the relevant previous work in sect . [ sec : prevwork ] . in sect . [ sec : prelim ] we formulate the problem and introduce the vapnik - chervonenkis dimension and the related tools we use in developing our results . our main analytical contribution , a bound on the vc dimension of class of queries is presented in sect . [ sec : vcdimqueries ] . the application of these results for selectivity estimation is given in sect . [ sec : applications ] . experiments are presented in sect . [ sec : experiments ] .

we develop a novel method , based on the statistical concept of the _ vapnik - chervonenkis dimension _ , to evaluate the selectivity ( output cardinality ) of sql queries a crucial step in optimizing the execution of large scale database and data - mining operations . the major theoretical contribution of this work , which is of independent interest , is an explicit bound to the vc - dimension of a range space defined by all possible outcomes of a collection ( class ) of queries . we prove that the vc - dimension is a function of the maximum number of boolean operations in the selection predicate and of the maximum number of select and join operations in any individual query in the collection , but it is neither a function of the number of queries in the collection nor of the size ( number of tuples ) of the database . we leverage on this result and develop a method that , given a class of queries , builds a concise random sample of a database , such that with high probability the execution of _ any _ query in the class on the sample provides an accurate estimate for the selectivity of the query on the original large database . the error probability holds _ simultaneously _ for the selectivity estimates of _ all _ queries in the collection , thus the same sample can be used to evaluate the selectivity of multiple queries , and the sample needs to be refreshed only following major changes in the database . the sample representation computed by our method is typically sufficiently small to be stored in main memory . we present extensive experimental results , validating our theoretical analysis and demonstrating the advantage of our technique when compared to complex selectivity estimation techniques used in postgresql and the microsoft sql server .

we develop a novel method , based on the statistical concept of the _ vapnik - chervonenkis dimension _ , to evaluate the selectivity ( output cardinality ) of sql queries a crucial step in optimizing the execution of large scale database and data - mining operations . the major theoretical contribution of this work , which is of independent interest , is an explicit bound to the vc - dimension of a range space defined by all possible outcomes of a collection ( class ) of queries . we prove that the vc - dimension is a function of the maximum number of boolean operations in the selection predicate and of the maximum number of select and join operations in any individual query in the collection , but it is neither a function of the number of queries in the collection nor of the size ( number of tuples ) of the database . we leverage on this result and develop a method that , given a class of queries , builds a concise random sample of a database , such that with high probability the execution of _ any _ query in the class on the sample provides an accurate estimate for the selectivity of the query on the original large database . the error probability holds _ simultaneously _ for the selectivity estimates of _ all _ queries in the collection , thus the same sample can be used to evaluate the selectivity of multiple queries , and the sample needs to be refreshed only following major changes in the database . the sample representation computed by our method is typically sufficiently small to be stored in main memory . we present extensive experimental results , validating our theoretical analysis and demonstrating the advantage of our technique when compared to complex selectivity estimation techniques used in postgresql and the microsoft sql server .

hep-ph9906301

c

we have discussed the pion production via the parametric resonance mechanism within the linear sigma model . in particular , stimulated by the feature of the numerical simulations of the linear sigma model , we focused on the scenario in which classical background oscillations of the sigma model fields are in the @xmath0 direction . assuming small amplitude oscillation which may be natural in the late stage of evolution of dcc , we have shown that one can ignore effects due to nonlinearity and quantum back reactions for sufficiently long time . thanks to this fact , we were able to construct an explicit quantum pion ( and sigma ) state which allows us to calculate the two particle correlations as well as the single particle distributions . our treatment , though under very restrictive assumptions , may be good enough to illuminate characteristic features of the parametric resonance mechanism . we formulated the quantum theory of the system with mathieu instability on a more conventional basis of quantum field theory and clarified the relationship between our and the formalism given by shtanov , traschen and brandenberger @xcite . we have analyzed the computed single particle distributions and clarified the structure of narrow resonances characteristic to the parametric resonance mechanism . we then discussed the two pion correlations as a possible experimental probe for disoriented chiral condensate . since the two pion correlations have unique characteristics , the back - to - back ( in momentum space ) correlations , it must give a clear signature which should merit the experimental hunting of dcc . in particular , it can not be masked by the identical particle interference , the hanbury - brown - twiss effect @xcite . why two particle correlation ? it is certainly far more difficult to measure compared with the multiplicity distributions , on which all the recent experimental search for dcc rely @xcite . the global analysis using multiplicity distributions is powerful if large fractions of events are accompanied by the dcc domain formation . on the other hand , a different strategy is required for hunting if dcc is a rare phenomenon . we have discussed possible origin of the long lasting amplification of low - momentum pion modes in the last section . our discussion can not be a complete one , but we hope that it stimulates the readers interests in this problem . we should mention about the limitation and the drawback in our treatment in this paper . we ignored the quantum back reaction and the instability of @xmath0 meson which should exist in the real world . it is the perfectly legitimate approximation if the amplitudes of background @xmath0 oscillations are really small . however , it is possible that the amplitudes are sometimes large because of the prevailing thermal fluctuations in the initial stage . since we are dealing with the system in which the coupling is really strong , most probably , the peak in the single particle distributions will go away after the quantum back reaction is taken into account . then , the key question is that if anything in our results remain valid after the quantum back reaction is taken into account . we argue that the answer is yes ; it is the characteristic features of the two pion correlations which are discussed in detail in sec . v. we now engage in a computation to verify our expectation . how about the @xmath119 coupling ? it is clear that it also tends to smear out the resonance peaks and , more importantly , may obscure the signature of the back - to - back correlations . again we need more elaborate treatment which includes the instability of @xmath0 to make definitive statement about how much the signature survive in the case with @xmath119 coupling . the formalisms which may be suitable for such analysis have been investigated in detail @xcite . there are also some recent proposals @xcite that the hadronic medium effects may induce the similar back - to - back correlations in momentum space , which would mimic the signature of dcc discussed in this paper . one would hope that it should be possible to find observational features which discriminate these two mechanisms . the task is , however , beyond the scope of this paper . during the long term investigation we benefited from numerous conversations in various stages of this work with masayuki asakawa , dan boyanovsky , berndt mller , krishna rajagopal , and valery rubakov . in particular we thank krishna for his informative and kind correspondences in comparing power spectra obtained by our and their calculations . the research of hm is partly supported by the grant - in - aid for international scientific research no . 09045036 , inter - university cooperative research , and the grant - in - aid for scientific research in priority areas no . 11127213 , ministry of education , science , sports and culture of japan .

classically it is related with the instability in the solutions of the mathieu equation and we explore the quantum aspects of the mechanism . we show that nonlinearities and back reactions can be ignorable for sufficiently long time under the small amplitude approximations of background @xmath0 oscillations , which may be appropriate for the late stage of nonequilibrium phase transition . in particular , two - pion correlations of various charge combinations contain back - to - back correlations which can not be masked by the identical particle interference effect .

we discuss a dynamical mechanism of pion production from disoriented chiral condensates ( dcc ) . it leads to an explosive production of pions via the parametric resonance mechanism , which is similar to the reheating mechanism in inflationary cosmology . classically it is related with the instability in the solutions of the mathieu equation and we explore the quantum aspects of the mechanism . we show that nonlinearities and back reactions can be ignorable for sufficiently long time under the small amplitude approximations of background @xmath0 oscillations , which may be appropriate for the late stage of nonequilibrium phase transition . it allows us to obtain an explicit quantum state of the produced pions and @xmath0 , the squeezed state of bcs type . single particle distributions and two - pion correlation functions are computed within these approximations . the results obtained illuminate the characteristic features of multi - pion states produced through the parametric amplification mechanism . in particular , two - pion correlations of various charge combinations contain back - to - back correlations which can not be masked by the identical particle interference effect . we suggest that the parametric resonance mechanism might be a cause of the long lasting amplification of low momentum modes in linear sigma model simulations . # 1 # 1#1 # 1a^(#1)^ #1a^(#1 )

1510.03541

i

let @xmath1 , @xmath2 or @xmath3 be a bounded connected open set whose boundary @xmath4 is lipschitz . let @xmath5 be a ( small ) nonempty open subset , and assume that @xmath6 . we use the notation @xmath7 , @xmath8 and we denote by @xmath9 the outward unit normal to @xmath10 at any point @xmath11 . bold letters and symbols denote vector - valued functions and spaces ; for instance @xmath12 is the hilbert space of the functions @xmath13 with @xmath14 for all @xmath15 . this work is related to the null controllability problem for the non - stationary stokes system @xmath16 which describes a viscous incompressible fluid flow in the bounded domain @xmath10 . we use as a control function the density of external forces @xmath17 concentrated in the arbitrary subdomain @xmath18 during the time interval @xmath19 ; @xmath20 is the vector field of the fluid velocity , and @xmath21 is the scalar pressure . the real @xmath22 denotes the constant viscosity of the fluid . the symbol @xmath23 stands for the characteristic function of @xmath18 . we introduce the following spaces @xmath24 then , for any @xmath25 , and @xmath26 , there exists exactly one solution @xmath27 of ( [ stokes ] ) with the following regularity : @xmath28;\hvec\right)\cap l^2\left(0 , t;\vvec\right ) , \,\,\pi \in l^2(0,t ; u)\ ] ] ( see @xcite ) . the null controllability problem for ( [ stokes ] ) at time @xmath0 is the following : _ for any @xmath29 , find @xmath30 such that the corresponding solution to satisfies @xmath31 _ the controllability properties of evolution pdes have attracted a lot of works in the last decades : some relevant references are @xcite . in particular , the stokes - and more generally the navier - stokes - system has received a lot of attention : we mention the references @xcite . the following result is proved in @xcite ( see also @xcite ) by the way of carleman estimates . [ th-1 ] the linear system _ ( [ stokes ] ) _ is null - controllable at any time @xmath6 . on the other hand , the ( numerical ) approximation of controls either distributed or located on the boundary for the stokes system has received much less attention , due to the underlying ill - posedness of the approximation . in practice , such approximation is usually addressed in the framework of an optimal control reformulation . precisely , one seeks to minimize the quadratic functional @xmath32 over the non - empty set @xmath33 following @xcite , duality arguments allow to replace this constrained minimization by the unconstrained minimization of its conjugate function @xmath34 defined as @xmath35 over @xmath36 , where @xmath37 solves the adjoint backward stokes system associated with ( [ stokes ] ) : @xmath38 @xmath39 is the hilbert space defined as the completion of any smooth space functions included in @xmath40 for the norm @xmath41 . the control of minimal square - integrable norm is then given by @xmath42 where @xmath43 is associated with the unique minimizer @xmath44 in @xmath39 of @xmath34 ( see @xcite ) . the difficulty , when one wants to approximate such control in any finite dimensional space , that is when one likes to minimize numerically @xmath34 , is that the space @xmath39 is huge , in particular , contains @xmath45 , and even elements that may not be distributions . numerical experiments do suggest that the minimizer @xmath44 is very singular ( we refer to @xcite for a detailed analysis in the close case of the heat equation ) . this phenomenon is independent of the choice of @xmath46 , but is related to the use of dual variables . actually , the equality ( [ null_condition ] ) can be viewed as an equality in a very small space ( due to the strong regularization effect of the heat kernel ) . accordingly , the associated multiplier @xmath47 belong to a large dual space , much larger than @xmath12 , that is hard to represent ( numerically ) in any finite dimensional space . an alternative way of looking at these problems and avoiding the introduction of dual variables has been proposed in @xcite . it is based on the following simple strategy . instead of working all the time with solutions of the underlying state equation , and looking for one that may comply with the final desired state , one considers a suitable class of functions complying with required initial , boundary , final conditions and appropriate regularity , and seeks one of those that is a solution of the state equation . this is in practice accomplished by setting up an error functional defined for all feasible functions , and measuring how far those are from being a solution of the underlying state equation . one advantage of this variational approach is that the way to get closer to a solution of the problem is by minimizing a functional that can not get stuck on local minima because the only critical points of the error turn out to be global minimizers with zero error . therefore a general strategy for approximation consists in using a descent algorithm for this error functional . this approach which has the flavor of a least - squares type method has been employed successfully in our null controllability context for the linear heat equation in @xcite and for an hyperbolic system in @xcite . we apply this approach to the stokes system . in section [ sec2 ] , we describe the ingredients of the variational approach for the system ( [ stokes ] ) and reduce the search of one controlled trajectory for the stokes system to the minimization of the quadratic functional @xmath48 defined by ( [ fonce ] ) over the affine space @xmath49 defined by ( [ spacea ] ) . in section [ sec3 ] , by a general - purpose lemma ( lemma [ basic ] ) , using the very specific structure of the functional @xmath48 , we prove that we may construct minimizing sequences for the error functional @xmath48 that do converge strongly to an extremal point for @xmath48 ( see proposition [ convergence ] ) . section [ sec4 ] , we adapt the argument for the direct problem of the steady navier - stokes system . results of this work were partially announced in the note @xcite .

we discuss the approximation of distributed null controls for partial differential equations . , we mainly focus on the stokes system for which the existence of square - integrable controls have been obtained in _ [ fursikov & imanuvilov , controllability of evolution equations , 1996 ] ) _ via carleman type estimates . we also discuss briefly the direct problem for the steady navier - stokes system .

we discuss the approximation of distributed null controls for partial differential equations . the main purpose is to determine an approximation of controls that drives the solution from a prescribed initial state at the initial time to the zero target at a prescribed final time . as a non trivial example , we mainly focus on the stokes system for which the existence of square - integrable controls have been obtained in _ [ fursikov & imanuvilov , controllability of evolution equations , 1996 ] ) _ via carleman type estimates . we introduce a least - squares formulation of the controllability problem , and we show that it allows the construction of strong convergent sequences of functions toward null controls for the stokes system . the approach consists first in introducing a class of functions satisfying _ a priori _ the boundary conditions in space and time - in particular the null controllability condition at time @xmath0 - , and then finding among this class one element satisfying the system . this second step is done by minimizing a quadratic functional , among the admissible corrector functions of the stokes system . we also discuss briefly the direct problem for the steady navier - stokes system . the method does not make use of any duality arguments and therefore avoid the ill - posedness of dual methods , when parabolic type equation are considered .

astro-ph0608132

i

it is well known that gamma - ray burst ( grb ) afterglow decays as a power - law @xmath1 . the temporal decay index @xmath2 , together with the spectral index , provides us precious information about grb jets and their environment . in the pre - swift era afterglow observations start typically a few hours after a burst . in such a late phase , the decay index is insensitive to the choice of the reference time @xmath0 , and grb trigger time is often used in afterglow modelings . the multi - wavelength observatory swift was launched in nov 2004 . thanks to its fast pointing capabilities swift is disclosing the early afterglow phase . one of unexpected finds by swift is that early x - ray afterglows show a canonical behavior , where light curves include three components : ( 1 ) a steep decay component , ( 2 ) a shallow decay component and ( 3 ) a `` normal '' decay component . on top of this canonical behavior , many events have superimposed x - ray flares ( zhang et al . 2006a ; nousek et al . 2006 ; chincarini et al 2005 ; obrien et al . 2006 ) . the transition from the early steep decay to the shallow decay typically occurs at several hundred seconds , and the timescale is comparable to the duration of rather long grbs . when discussing the early afterglow and its connection to the prompt emission component , the decay index is very sensitive to the reference time @xmath0 one chooses . correctly choosing @xmath0 is therefore essential to derive the right index as well as to interpret each component in the canonical light curve ( piro et al . 2005 ; tagliaferri et al . 2005 ; quimby et al . 2006 ) . tagliaferri et al . ( 2005 ) investigated the first two bursts grb 050126 and grb 050219a which have an x - ray light curve well sampled by the x - ray telescope on board swift . they sought for a possible delay of the afterglow onset by fitting the early x - ray light curves ( the components 1 and 2 which we have discussed above ) with a single power - law model . in both cases , the decaying light curves can be fitted if the onset of the afterglow is shifted to @xmath3 s after the burst trigger with a single power - law . however , while in the case of grb 050126 the light curve does not allow us to clearly state whether a broken power - law modeling is better than a single power - law model , for grb 050219a a broken power - law definitively provides a better fit . in the standard grb model the time shift between the grb trigger and the reference time @xmath0 is expected to be `` small '' . the early steep decay should not be an artifact due to a wrong choice of @xmath0 . lazzati and begelman ( 2006 ) studied forward shock emission , based on a simple energy injection model . their numerical light curves show that measuring times from the beginning of the prompt phase is a good approximation . the early steepening and x - ray flares are likely to be produced by another mechanism ( e.g. internal shocks ; burrows et al . 2005 ; falcone et al . 2006 ; zhang et al . 2006a ; nousek et al . 2006 ; ioka , kobayashi & zhang 2005 ; fan & wei 2005 ) . recently long - lasting soft emission is reported in a short burst grb 050724 ( barthelmy et al . such a soft component was hinted at in the sum of multiple short batste grbs , and it might be the onset of short burst afterglow ( lazzati , ramirez - ruiz & ghisellini 2001 ) . it is therefore of interest to quantitatively examine the @xmath0 issue . in this paper , we study the physics and timescales involved in early afterglow stage , and give more direct and clear arguments for the afterglow slopes . in 2 we study a simple analytic model . in 3 we evaluate light curves of reverse shock emission as well as that of forward shock emission , based on full hydrodynamic calculations . in 4 we address how inhomogeneity of a fireball affects an early afterglow light curve . conclusions and discussion are given in 5 .

we discuss the reference time @xmath0 of afterglow light curves in the context of the standard internal - external shock model . the decay index of early afterglow is very sensitive to the reference time one chooses . in order to understand the nature of early afterglow , it is essential to take a correct reference time . our simple analytic model provides a framework to understand special relativistic effects involved in early afterglow phase . we evaluate light curves of reverse shock emission as well as those of forward shock emission , based on full hydrodynamic calculations .

we discuss the reference time @xmath0 of afterglow light curves in the context of the standard internal - external shock model . the decay index of early afterglow is very sensitive to the reference time one chooses . in order to understand the nature of early afterglow , it is essential to take a correct reference time . our simple analytic model provides a framework to understand special relativistic effects involved in early afterglow phase . we evaluate light curves of reverse shock emission as well as those of forward shock emission , based on full hydrodynamic calculations . we show that the reference time does not shift significantly even in the thick shell case . for external shock emission components , measuring times from the beginning of the prompt emission is a good approximation and it does not cause an early steep decay . in the thin shell case , the energy transfer time from fireball ejecta to ambient medium typically extends to thousands of seconds . this might be related to the shallow decay phases observed in early x - ray afterglow at least for some bursts .

astro-ph0608132

c

we have studied the reference time @xmath0 for the afterglow modeling . although measuring times from the beginning of the prompt emission ( grb trigger ) might cause a slight overestimate of the early afterglow slope in the thick shell case . this choice of @xmath0 gives a reasonable approximation , and it does not induce a very steep decay ( @xmath180 ) like the early steep decay or x - ray flares in the canonical swift x - ray light curve . the leading model to explain the rapid decay and flares in early x - ray afterglow is the internal shock emission . a clear , testable prediction of this model is that the temporal decay index @xmath2 of the tail part should be related to the spectral index @xmath181 by an equation @xmath182 ( kumar & panaitescu 2000 ) . when evaluating the emission decay @xmath183 in the internal shock model , an important difference is that the grb trigger time is no longer special . the reference time @xmath0 should correspond to the onset of each particular spike in the prompt emission or in afterglow ( kobayashi et al . 1997 ; zhang et al . 2006a ; nousek et al . 2006 ; fan & wei 2005 ) . every time when the central engine is re - stared to eject sub - shells , the reference time @xmath0 should be re - set to the reactivation time of the engine . although obrien et al . ( 2006 ) have found that @xmath2 appears to be largely independent of @xmath181 when the bat trigger time is used as @xmath0 , liang et al ( 2006 ) have shown that the relation @xmath182 is more or less satisfied in most cases if @xmath0 is set near the beginning of rising segment of the last pulse of the prompt emission or a corresponding x - ray flare , and if the underlying forward shock emission component is subtracted . swift observations support the internal shock model . the self - consistent internal shock interpretation should be more favorable than the beginning - of - the - afterglow interpretation . the latter can not explain multiple x - ray flares in a single event . such behavior is observed in many swift bursts ( burrows et al . 2005 ; falcone et al . 2006 ; romano et al . 2006 ; obrien et al 2006 ) . usually x - ray flux already begins to decay before x - ray flares appear , and it suggests that the onset of afterglow is prior to the flares . if a large amount of energy is impulsively injected to a fireball during the deceleration , @xmath0 might be re - set to the injection time . however , an afterglow baseline also should shift after a flare ( energy injection ) . this clearly contradicts with observations in which after a flare peak , afteglow decays back to its pre - flare flux level . we can not explain x - ray flares by the shift of @xmath0 associated with large energy injections . swift discovered that a large fraction of x - ray afterglows have a slow decay phase , and it is suggested that energy injection into a blast wave takes place several hundred seconds after the burst . this implies that right after the burst the kinetic energy of a blast wave is very low and in turn the efficiency of internal shock process is extremely high ( zhang et al . 2006a ; nousek et al . 2006 ; ioka et al . 2005 ; granot , knigl & piran 2006 ; zhang et al.2006b ; however see also fan & piran 2006 ) . the round - off forward shock peak in the thin shell case might be a good candidate for the shallow decay phase . however , if we interpret the observed shallow decay as the round - shape of the deceleration phase , the model light curve is shallower than some of the observed ones . it may be because the observed curve is the combination of this round phase and the rapid decay from the grb tail emission ( high latitude ) . equalizing the deceleration time and the shallow phase timescale we obtain the initial lorentz factor @xmath184 where the time dilation effect is taken into account @xmath185 . for a wind environment , we can discuss the @xmath0 issue in a very similar way . the lorentz factor of a shocked shell is constant in both of the thin and thick shell cases during the shock crossing , while the bm blast wave decelerates as @xmath125 ( kobayashi & zhang 2003 ) . the separations are comparable @xmath186 at the deceleration time . measuring times from the beginning of the prompt phase should be a good approximation for events in a wind environment also . since most bursts in a wind environment fall in the thick shell case ( kobayashi , & zhang 2004 ) , and since the deceleration time is comparable to grb duration in the thick shell case , another process ( e.g. refreshed shocks ) rather than the afterglow peak is necessary to explain the shallow decay phase . barthelmy , s.d . 2005 , nature , 438 , 994 blandford , r.d . & mckee , c.f . 1976 , phys , fluids , 19 , 1130 burrows , d . 2005 , science , 309 , 1833 chincarini , g . 2005 , submitted to apj , astro - ph/0506453 falcone , a.d . 2006 , apj , 641 , 1010 fan , y . & piran , t . 2006 , mnras , 369 , 197 fan , y . & wei , d.m . 2005 , mnras , 364 , l42 granot , j.,knigl , a . & piran , t . 2006 , mnras , 370 , 1946 ioka , k.,kobayashi , s.&zhang , b.2005 , apj , 631 , 429 ioka , k.,toma , k.,yamazaki , r.&nakamura , t.2005 , a&a in press , astro - ph/0511749 kobayashi , s . 2000 , apj , 545 , 807 kobayashi , s.,,p.&zhang , b . 2004 , apj , 601 , l13 kobayashi , s.,piran , t.&sari , r . 1997 , apj , 490 , 92 kobayashi , s.,piran , t.&sari , r . 1999 , apj , 513 , 669 kobayashi , s . & sari , r . 2000 , apj , 542 , 819 kobayashi , s . & zhang , b . 2003 , apj , 597 , 455 kumar , p. & panaitescu , a . 2000 , apj , 541 , l51 lazzati , d . & begelman , m.c . 2006 , apj , 641 , 972 lazzati , d.,ramirez - ruiz , e . & ghisellini , g . 2001 , a&a , 379 , l39 liang , e.w . et al . 2006 , apj , 646 , 351 mart , j.m .. & mller , e . 1999 , living rev . relativity , 2 , 3 nakar , e . & piran , t . 2004 , mnras , 353 , 647 nousek , j.a . 2006 , apj , 642 , 389 obrien , p.t . 2006 , apj , 647 , 1213 piro et al . 2005 , apj , 623 , 314 quimby , r.m . 2006 , apj , 640 , 402 romano , p . 2006 , a&a , 450 , 59 sari , r . 1997 , apj , 489 , l37 sari , r . & piran , t.1995 , apj , 455 , l143 sari , r.,piran , t . & narayan , r . 1998 , apj , 497 , l17 tagliaferri , g . 2005 , nature , 436 , 985 waxman , e . 1997 , apj , 491 , l19 zhang , b . 2006a , apj , 642 , 354 zhang , b . 2006b , submitted to apj

measuring times from the beginning of the prompt emission is a good approximation and it does not cause an early steep decay . in the thin shell case , the energy transfer time from fireball ejecta to ambient medium typically extends to thousands of seconds . this might be related to the shallow decay phases observed in early x - ray afterglow at least for some bursts .

we discuss the reference time @xmath0 of afterglow light curves in the context of the standard internal - external shock model . the decay index of early afterglow is very sensitive to the reference time one chooses . in order to understand the nature of early afterglow , it is essential to take a correct reference time . our simple analytic model provides a framework to understand special relativistic effects involved in early afterglow phase . we evaluate light curves of reverse shock emission as well as those of forward shock emission , based on full hydrodynamic calculations . we show that the reference time does not shift significantly even in the thick shell case . for external shock emission components , measuring times from the beginning of the prompt emission is a good approximation and it does not cause an early steep decay . in the thin shell case , the energy transfer time from fireball ejecta to ambient medium typically extends to thousands of seconds . this might be related to the shallow decay phases observed in early x - ray afterglow at least for some bursts .

0712.4231

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topological order of condensed matter system is the cornerstone of topological quantum computation@xcite . the topologically ordered system have degenerated ground states which depend on the topology instead of symmetry . this degeneracy of ground state is robust against any local perturbation due to the gap between ground state and excited states@xcite . an interesting application of topological stablizer quantum codes is implemented in kitaev s toric code model@xcite . a topological color codes with quantum error - correcting capabilities is developed later@xcite , this model removes the need for selective addressing . there are different ways to perform quantum computation in use of topologically ordered states . usually the quantum gate or unitary transformation are implemented by brading quasiparticles . the transversal implementation of quantum gate provides us another way of topological quantum computation without braiding@xcite , in which the stablizer color codes is achieved in a 3-dimensional lattice model . while we focus on the braiding of loop quasiparticles in 3-dimensional spin liquid and chiral spin liuid in this paper . we established the 3-dimenisonal spin liquids by generalizing kitaev s two dimensional spin model . kitaev s spin model on honeycomb lattice has a highly degenerate ground state@xcite . abelian anyons and non - abelian anyons emerge in the background of short range spin liquid . these anyonic excitations obey exotic statistics . quantum computation is based on anyon braiding . during the braiding operation , anyons interact with one another only by encircling a topological nontrivial cycle . a proposal of the experimental operation of anyon braiding in kitaev honeycomb model has been provided by use of ultracold atoms trapped in optical lattices@xcite , however there is some controversal on the details of this experimental proposal@xcite . another most promising candidate of non - abelian anyons may be realized in fractional quantum hall states with @xmath0@xcite . the fractional quantum hall states break parity and time - reversal symmetry since fractional quantum hall occurs in the presence of a strong magnetic field . quantum information is stored in different fusion channels of non - abelian anyons@xcite . for two @xmath1 quasiparticles following fusion rule @xmath2 , if fusion outcome is @xmath3 , we define the qubit as state @xmath4 . when fusion outcome is @xmath5 , the state of the qubit is @xmath6 . we may use @xmath7 antidots at which quasiholes are pinned to construct @xmath8 qubits . non - abelian anyons also arise from other two dimensional systems , such as @xmath9 . in this @xmath10 superconductor , the half - quantum vortices with flux @xmath11 exhibit non - abelian statistics@xcite . spin-@xmath12 chiral spin liquid states proposed by kalmeyer and laughlin possess fractionalized excitations@xcite . this kind of non - abelian anyons appears in 2d solvable spin models which are generalization of kitaev honeycomb model@xcite@xcite . these anyons are point quasiparticles confined in two dimensions . the main disadvantage of two dimensional system is that the expectation value of topological symmetry operators vanishes at finite temperature . this makes the topological memory thermally fragile@xcite@xcite . since most physical materials in nature are three dimensional , anyonic excitations most likely exist in three dimensions . one clue comes from a three dimensional exactly solvable spin model constructed by generalizing kitaev s toric code to cubic lattice@xcite , in which the topological order of its ground state is characterized by string net condensation as well as membrane condensation . the string net and membrane condensation also appear in another exactly solvable spin model@xcite , which is constructed on a general 3-complex embedded in a closed and connected base manifold in three dimension . its ground state degeneracy depends on the homology of the 3-manifold . to establish three dimensional chiral spin liquid , we start from a different way to search for anyons in three dimensions by generalizing kitaev honeycomb lattice model . our interest focuses mainly on nontrivial loop excitations . loops confined in two dimensions have no non - trivial entanglement without cutting each other . it is in three dimensions that loops demonstrate much interesting statistical phenomena without breaking topological constraint . there is a loop braiding group for the statistics of unknotted , unlinked closed strings@xcite . for links consisting of many entangled knots , their non - abelian statistics is closely related to the monodromy matrix in conformal field theory @xcite . quantum loop gas applied to topological quantum computation is under rapid developing@xcite . there were some theoretical investigations on three dimensional chiral spin liquid based on effective field theory@xcite . no exact three dimensional chiral spin liquid is found so far to the authors knowledge . we established a large class of exactly solvable three dimensional spin liquid and chiral spin liquid in this paper . in these models , there is only short - range interaction between neighboring spins . the stable ground states of chiral spin liquid spontaneously break the time reversal symmetry . there exist loop excitations which may serve as basic qubits to store quantum information . loop condensation occurs naturally at ground state . the projection of these three dimensional spin models to @xmath13 plane leads to soluble two dimensional models@xcite which are generalization of kitaev honeycomb model . this projection operation does not keep time reversal symmetry . for example , the exact spin liquid we established on cu-sublattice of crystal green dioptase , which is the crystal structure of a material @xmath14@xcite , projects out the very two dimensional chiral spin model constructed in ref . @xcite . mandal and surendran obtained a different exactly solvable kitaev model in three dimensions@xcite when we finished the research on the spin models in this paper . none of the exact spin models in this paper is identical to mandal and surendran s model . [ honey ] plane . there are two types of elementary plaquettes , plaquette a and plaquette b . plaquette @xmath15 is the shadowed hexagon . plaquette b covers an area of double hexagon , the oriented circles in the blank double hexagon denote the helix chains with different chirality . ( d ) the bonding configuration of the hexagon plaquette.,title="fig:",scaledwidth=45.0% ] the paper is organized as follows : in section ii , we constructed exactly solvable three dimensional spin models on helix - decorated lattice . their ground states are invariant under time reversal transformation . a topological phase transition from gapless phase to gapped phase is observed . in section iii , we established three dimensional chiral spin liquids by doping spins in the helix lattice . their exact ground states break the time reversal symmetry . in section iv , the topological correlation among loops is studied from the point of view of topological quantum field theory and jones polynomial . in section v , non - abelian berry phase of loops is presented . we studied the quantum algebra of loop statistics .

we established a large class of exactly soluble spin liquids and chiral spin liquids on three dimensional helix lattices by introducing kitaev - type s spin coupling . in the chiral spin liquids , we characterize this kind of statistics by non - abelian berry phase and quantum algebra relation .

we established a large class of exactly soluble spin liquids and chiral spin liquids on three dimensional helix lattices by introducing kitaev - type s spin coupling . in the chiral spin liquids , exact stable ground states with spontaneous breaking of the time reversal symmetry are found . the fractionalized loop excitations in both the spin and chiral spin liquids obey non - abelian statistics . we characterize this kind of statistics by non - abelian berry phase and quantum algebra relation . the topological correlation of loops is independent of local order parameter and it measures the intrinsic global quantum entanglement of degenerate ground states .

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markov chain monte carlo ( mcmc ) algorithms have proved particularly successful in statistics for investigating posterior distributions in bayesian analysis of complex models ; see , for example , @xcite . almost all mcmc methods are based on the metropolis hastings ( mh ) algorithm which owes much of its success to its tremendous flexibility . however , in order to use the classical mh algorithm , it must be possible to evaluate the target density up to a fixed constant of proportionality . while this is often possible , it is increasingly common for exact pointwise likelihood evaluation to be prohibitively expensive , perhaps due to the sheer size of the data set being analysed . in these situations , classical mh is rendered inapplicable . the _ pseudo - marginal metropolis hastings algorithm _ ( psmmh ) @xcite provides a general recipe for circumventing the need for target density evaluation . instead it is required only to be able to unbiasedly _ estimate _ this density . the target densities in the numerator and denominator of the mh accept / reject ratio are then replaced by their unbiased estimates . remarkably , this yields an algorithm which still has the target as its invariant distribution . one possible choice of algorithm , the _ pseudo - marginal random walk metropolis _ ( psmrwm ) , is popular in practice ( e.g. , @xcite ) because it requires no further information about the target , such as the local gradient or hessian , which are generally more computationally expensive to approximate than the target itself @xcite . broadly speaking , the mixing rate of any psmmh algorithm decreases as the dispersion in the estimation of the target density increases @xcite . in particular , if the target density happens to be substantially over - estimated , then the chain will be overly reluctant to move from that state leading to a long run of successive rejections ( a _ sticky patch _ ) . now , in psmmh algorithms , the target estimate is usually computed using an average of some number , @xmath0 , of approximations ; see sections [ sect.psrwm.intro ] and [ sect.optimising ] . this leads to a trade off , with increasing @xmath0 leading to better mixing of the chain , but also to larger computational expense . we shall consider the problem of optimising @xmath0 . it is well known ( e.g. , @xcite ) that the efficiency of the random - walk metropolis ( rwm ) algorithm varies enormously with the scale of the proposed jumps . small proposed jumps lead to high acceptance rates but little movement across the state space , whereas large proposed jumps lead to low acceptance rates and again to inefficient exploration of the state space . the problem of choosing the optimal scale of the rwm proposal has been tackled for various shapes of target ( e.g. , @xcite ) and has led to the following rule of thumb : choose the scale so that the acceptance rate is approximately @xmath1 . although nearly all of the theoretical results are based upon limiting arguments in high dimension , the rule of thumb appears to be applicable even in relatively low dimensions ( e.g. , @xcite ) . this article focusses on the efficiency of the psmrwm as the dimension of the target density diverges to infinity . for relatively general forms of the target distribution , under the assumption of additive independent noise in the log - target , we obtain ( theorem [ thm.asymp.analysis ] ) expressions for the limiting expected squared jump distance ( esjd ) and asymptotic acceptance rate . esjd is now well established as a pragmatic and useful measure of mixing for mcmc algorithms in many contexts ( see , e.g. , @xcite ) , and is particularly relevant when diffusion limits can be established ; see , for example , the discussion in @xcite . we then prove a diffusion limit for a rescaling of the first component , in the case of a target with independent and identically distributed components ( theorem [ thm.diff.lim ] ) , the efficiency of the algorithm is then given by the speed of this limiting diffusion , which is equivalent to the limiting esjd . we examine the relationship between efficiency , scaling , and the distributional form of the noise , and consider the _ joint _ optimisation of the efficiency of the psmrwm algorithm ( taking computational time into account ) with respect to @xmath0 , and the rwm scale parameter . exact analytical results are obtained ( corollary [ cor.max.gauss ] ) under an assumption of gaussian noise in the estimate of the log - target , with a variance that is inversely proportional to @xmath0 . in this case , we prove that the optimal noise variance is 3.283 , and the corresponding optimal asymptotic acceptance rate is 7.001% , thus extending the previous 23.4% result of @xcite . finally , we illustrate the use of these theoretical results in a simulation study ( section [ sect.sim.study ] ) . consider a state space @xmath2 , and let @xmath3 be a distribution on @xmath4 , whose density ( with respect to lebesgue measure ) will be referred to as @xmath5 . the mh updating scheme provides a very general class of algorithms for obtaining an approximate dependent sample from a target distribution , @xmath3 , by constructing a markov chain with @xmath3 as its limiting distribution . given the current value @xmath6 , a new value @xmath7 is proposed from a pre - specified lebesgue density @xmath8 and is then accepted with probability @xmath9/[\pi(\mathbf{x } ) q ( \mathbf{x},\mathbf{x}^*)]$ ] . if the proposed value is accepted , then it becomes the next current value ; otherwise the current value is left unchanged . the psmmh algorithm @xcite presumes the computational infeasibility of evaluating @xmath5 and uses an approximation @xmath10 that depends on some auxiliary variable , @xmath11 . the auxiliary variable is sampled from some distribution @xmath12 , and the approximation @xmath10 is assumed to satisfy that @xmath13=c\pi ( \mathbf{x})$ ] , for some constant @xmath14 . the value of the constant is irrelevant to all that follows , and so , without loss of generality , we assume that @xmath15 . we also assume that @xmath16 . the psmmh algorithm creates a markov chain with a stationary density ( since @xmath15 ) of @xmath17 which has @xmath5 as its @xmath6 marginal . when a new value , @xmath18 , is proposed via the mh algorithm , a new auxiliary variable , @xmath19 , is proposed from the density @xmath20 . the pair @xmath21 are then jointly accepted or rejected . the acceptance probability for this mh algorithm on @xmath22 is @xmath23 we are thus able to substitute the estimated density for the true density , and still obtain the desired stationary distribution for @xmath6 . note that for symmetric proposals , this simplifies to @xmath24 $ ] . different strategies exist for producing unbiased estimators , for instance , using importance sampling or latent variable representations , as in @xcite , or using particle filters @xcite as in @xcite . we shall illustrate our theory in the context of bayesian analysis of a partially observed markov jump process . pitt et al . @xcite and doucet et al . @xcite examine the efficiency of pseudo - marginal algorithms using bounds on the integrated autocorrelation time ( @xmath25 ) and under the assumptions that the chain is stationary and the distribution of the additive noise in the log - target is independent of @xmath6 ( our assumption [ ass.noise.diff.indep ] ) . under the further assumption that this additive noise is gaussian and the computing time inversely proportional to its variance ( our assumption [ ass.standard.regime ] ) , both articles then seek information on the optimal variance of this additive noise . pitt et al . @xcite consider the ( unrealistic ) case where the metropolis hastings algorithm is an independence sampler which proposes from the desired target distribution for @xmath26 , and obtain an optimal variance of @xmath27 . doucet et al . @xcite consider a general metropolis hastings algorithm and define a parallel hypothetical kernel @xmath28 with the same proposal mechanism as the original kernel , @xmath29 , but where the acceptance rate separates into the product of that of the idealised marginal algorithm ( if the true target were known ) and that of an independence sampler which proposes from the assumed distribution for the noise . this kernel can never be more efficient than the true kernel . upper and lower bounds are obtained for the @xmath25 for @xmath28 in terms of the of @xmath25 of the exact chain and the @xmath25 and a particular lag-1 autocorrelation of the independence sampler on the noise . these bounds are examined under the assumption that the additive noise is gaussian and the optimal variance for the noise is estimated to lie between @xmath27 and @xmath30 . other theoretical properties of pseudo - marginal algorithms are considered in @xcite , which gives qualitative ( geometric and polynomial ergodicity ) results for the method and some results concerning the loss in efficiency caused by having to estimate the target density . in this paper , we follow the standard convention whereby capital letters denote random variables , and lower case letters denote their actual values . bold characters are used to denote vectors or matrices .

we then consider the overall efficiency of the algorithm , in terms of both speed of mixing and computational time . assuming the additive noise is gaussian and is inversely proportional to the number of unbiased estimates that are used , we prove that the algorithm is optimally efficient when the variance of the noise is approximately 3.283 and the acceptance rate is approximately 7.001% . we also find that the optimal scaling is insensitive to the noise and that the optimal variance of the noise is insensitive to the scaling .

we examine the behaviour of the pseudo - marginal random walk metropolis algorithm , where evaluations of the target density for the accept / reject probability are estimated rather than computed precisely . under relatively general conditions on the target distribution , we obtain limiting formulae for the acceptance rate and for the expected squared jump distance , as the dimension of the target approaches infinity , under the assumption that the noise in the estimate of the log - target is additive and is independent of the position . for targets with independent and identically distributed components , we also obtain a limiting diffusion for the first component . we then consider the overall efficiency of the algorithm , in terms of both speed of mixing and computational time . assuming the additive noise is gaussian and is inversely proportional to the number of unbiased estimates that are used , we prove that the algorithm is optimally efficient when the variance of the noise is approximately 3.283 and the acceptance rate is approximately 7.001% . we also find that the optimal scaling is insensitive to the noise and that the optimal variance of the noise is insensitive to the scaling . the theory is illustrated with a simulation study using the particle marginal random walk metropolis . , ,

1309.7209

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we have examined the behaviour of the pseudo - marginal random walk metropolis algorithm in the limit as the dimension of the target infinity , under the assumption that the noise in the estimate of the log - target at a proposed new value , @xmath6 , is additive and independent of @xmath6 . subject to relatively general conditions on the target , limiting forms for the acceptance rate and for the efficiency , in terms of expected squared jump distance ( esjd ) , have been obtained . we examined two different noise distributions ( gaussian and laplace ) , and found that the optimal scaling of the proposal is insensitive to the variance of the noise and to whether the noise has a gaussian or a laplace distribution . we then examined the behaviour of the markov chain on the target , @xmath6 , and the noise , obtaining a limiting diffusion for the first component of a target with independent and identically distributed components . the efficiency function in this case is proportional to the speed of the diffusion , thus further justifying the use of esjd in this context . we identified a `` standard asymptotic regime '' under which the additive noise is gaussian with variance inversely proportional to the number of unbiased estimates that are used . in this regime the efficiency function is especially tractable , and we showed that it is maximised when the acceptance rate is approximately 7.0% and the variance of the gaussian noise is approximately 3.3 . we noted that in this regime the optimal noise variance is also insensitive to the choice of scaling . a detailed simulation study on a lotka volterra markov jump process using a particle filter suggested that in the scenario considered the assumptions of the standard asymptotic regime are reasonable provided the number of particles is not too low . furthermore , whilst the assumption that the distribution of the noise does not depend on the current position is not true , variations in the distribution have a small effect on the distribution of the estimates of the log - target compared with the effect of the noise itself . the optimal scaling was found to be insensitive to the noise variance ( or equivalently the number of particles ) , and the optimal noise variance was relatively insensitive to the choice of scaling . the overall optimal scaling was consistent with the theoretical value obtained ; however the optimal variance was a little lower than the theoretically optimal value . investigations showed that this discrepancy can be explained by the differences between our theoretical measure of efficiency ( esjd ) and empirical measures used in the simulation study ( ess ) . the results from the simulation study suggest that in low dimension a safer option than tuning to a particular variance and acceptance rate might be to take advantage of the insensitivity of the optimal scaling to the variance and vice versa and optimise scaling and variance independently . the diffusion limit provides strong support for the optimisation strategies suggested by the esjd criterion . however , in an ideal world it would be good to show that the sequence of algorithms which achieves the minimal optimal integrated autocorrelation time for a given functional might converge to the optimal diffusion . this is a generic question which is relevant to all diffusion limits for mcmc algorithms , and there are still important open questions regarding the relationships between esjd , diffusion limits , and limiting optimal integrated autocorrelation . in this direction , a recent paper @xcite has shown that diffusion limits can be translated into _ complexity _ results , thus demonstrating that at least the order of magnitude of the number of iterations to `` converge '' can be read off from the diffusion limit . the optimal variance of 3.28 under the standard asymptotic regime is similar to the value of 2.83 obtained in @xcite under the same noise assumptions and for a scenario where the component of the markov chain on @xmath4 mixes infinitely more slowly than the noise component . indeed , as noted in a remark following corollary [ cor.max.gauss ] , 2.83 is ( to two decimal places ) the optimal variance that we obtain when @xmath486 . there are many differences between the approaches in @xcite and this article . for example , we optimise a limiting efficiency for the random walk metropolis with respect to both the scaling and the variance whereas doucet et al . @xcite consider the univariate optimisation of a bound on the efficiency of metropolis hastings kernels which satisfy a positivity condition . that a similar conclusion may be drawn from two very different approaches is encouraging .

we examine the behaviour of the pseudo - marginal random walk metropolis algorithm , where evaluations of the target density for the accept / reject probability are estimated rather than computed precisely . under relatively general conditions on the target distribution , we obtain limiting formulae for the acceptance rate and for the expected squared jump distance , as the dimension of the target approaches infinity , under the assumption that the noise in the estimate of the log - target is additive and is independent of the position . for targets with independent and identically distributed components , we also obtain a limiting diffusion for the first component . the theory is illustrated with a simulation study using the particle marginal random walk metropolis .

we examine the behaviour of the pseudo - marginal random walk metropolis algorithm , where evaluations of the target density for the accept / reject probability are estimated rather than computed precisely . under relatively general conditions on the target distribution , we obtain limiting formulae for the acceptance rate and for the expected squared jump distance , as the dimension of the target approaches infinity , under the assumption that the noise in the estimate of the log - target is additive and is independent of the position . for targets with independent and identically distributed components , we also obtain a limiting diffusion for the first component . we then consider the overall efficiency of the algorithm , in terms of both speed of mixing and computational time . assuming the additive noise is gaussian and is inversely proportional to the number of unbiased estimates that are used , we prove that the algorithm is optimally efficient when the variance of the noise is approximately 3.283 and the acceptance rate is approximately 7.001% . we also find that the optimal scaling is insensitive to the noise and that the optimal variance of the noise is insensitive to the scaling . the theory is illustrated with a simulation study using the particle marginal random walk metropolis . , ,

astro-ph0202174

i

the cosmic microwave background radiation ( cmbr ) provides a light source for exploration of the structure formation history . before the cmbr photons reach the present epoch , they interact with the hot diffuse ionized gas residing in the galaxy clusters over a wide range of redshifts . this process results in subtle changes to the cmbr spectrum due to the inverse compton scattering , the so - called sunyaev - zeldovich ( sz ) effect ( sunyaev & zeldovich , 1972 ; see birkinshaw 1999 and carlstrom et al . 2000 for reviews ) . in the past two decades the detection of sz effects has been reported at an increasing rate ( grego et al . 2000 ; carlstrom et al . 2000 ; joy et al . 2001 ; grego et al . 2001 ) and this effect can therefore provide a realistic powerful probe for cosmological and cluster studies . since the sz flux is not affected by the distance but depends only on the intrinsic thermal energy of hot gases contained in the system , the sz observation , in conjunction with observations of other wavelengths , such as x - ray emitted from intracluster gas , and optical weak lensing measurements , enables us to determine the cosmological parameters by studying the high redshift galaxy clusters . the sz blank sky surveys have been suggested ( bartlett & silk 1994 ; barbosa et al . 1996 ) . several works follow ( bartlett 2000 ; holder et al . 2000 ; da silva et al . 2000 ; kneissl et al . 2001 ; fan & chiueh 2001 ; xue & wu 2001 ) , and have predicted how the sz cluster counts can be related to cosmological parameters . in addition , several next generation interferometric arrays are either under construction or have been proposed , e.g. , ami ( kneissl et al . 2001 ) , sza ( carlstrom et al . 2001 ) , and amiba ( lo et al . 2001 ) . radio point sources or radio galaxies are usually found in the galaxy clusters . therefore , the accuracy of the millimeter to centimeter wavelength observations of the sz effect can be contaminated by the emission from radio sources ( loeb & refregier 1997 ) . below 218 ghz , at which the thermal sz effect becomes null , one measures the sz intensity or flux decrement . the radio sources , however , produce excess emission so that one can underestimate the measured sz decrement , yielding systematic errors in the estimate of cosmological parameters . this confusion has been estimated by cooray et al . ( 1998 , hereafter cghjc ) , who observed toward abell 2218 at 28.5 ghz and concluded that the correction to the hubble constant is less than @xmath7 . in addition to point sources , diffuse cluster radio sources , i.e. halos and relics , ( e.g. , giovannini et al . 1993 ; rttgering et al . 1997 ) also lead to confusion on the cluster sz . with the requirement of accurate sz maps , the radio source subtraction becomes essential for the low brightness ( order of 100 @xmath8jy and mjy ) sz measurements . for this reason , recent sz observations are performed in combination with the measurements of radio sources ( cghjc ; komatsu et al . 1999 ; pointecouteau et al . 2001 ) . while one may remove strong sources as they can be detected above the flux limit , the faint sources below the flux threshold blend with the sz signal , and result in inaccuracy . however , there have not been systematic surveys on the radio sources in high redshift clusters nor systematic surveys at frequencies higher than 30 ghz . in fact , the high - frequency ( e.g. 90 ghz ) radio survey at the mjy flux limit is a formidable task , as the present telescopes are not sufficiently efficient in conducting an unbiased survey with a wide field coverage and high sensitivity . in view of the lack of reliable information for estimating the radio contamination on the sz cluster surveys at high frequencies , such as amiba ( 90 ghz ) , we are motivated to derive an empirical high - frequency cluster radio luminosity function ( crlf ) by synthesizing available low - frequency data ( ledlow & owen 1996 , hereafter lo96 ; slee et al . 1996 , hereafter sra96 , and cghjc ) . unfortunately , the spectral evolution of radio sources is rather uncertain . due to the uncertainties of redshift evolution , it is reasonable , as a first attempt , to adopt a no - evolution hypothesis to evaluate the radio flux in high redshift clusters . in this paper we aim to calculate the expected confusion of high - frequency radio point sources on the cluster sz effect over substantial redshift and cluster mass ranges . in section 2 , we briefly review the formulation of the sz flux . section 3 predicts the high frequency cluster radio luminosity functions ( crlfs ) based on low frequency surveys . the expected high frequency radio flux are calculated in section 4 . finally , the conclusion is given in section 5 . throughout this paper , we use @xmath9 km s@xmath10 mpc@xmath10 , @xmath11 , and @xmath12 .

we examine the expected radio confusion on the thermal sunyaev - zeldovich ( sz ) effect of galaxy clusters at 28.5 ghz and 90 ghz based on the cluster radio luminosity function ( crlf ) at 1.4 ghz . with by contrast , at 90 ghz the confusion is less than @xmath6 for small clusters even at low redshifts .

we examine the expected radio confusion on the thermal sunyaev - zeldovich ( sz ) effect of galaxy clusters at 28.5 ghz and 90 ghz based on the cluster radio luminosity function ( crlf ) at 1.4 ghz . with the observationally determined spectral index ( @xmath0 , where @xmath1 ) distribution , instead of a single average index @xmath2 , we convert the cluster radio luminosity function at 1.4 ghz to the high frequency ones and estimate the total radio flux in a cluster . at 28.5 ghz , radio confusion is up to 10 @xmath3 for small clusters ( @xmath4 ) below redshift @xmath5=1 , with more severe confusion for smaller and lower redshift clusters . by contrast , at 90 ghz the confusion is less than @xmath6 for small clusters even at low redshifts .

1507.02450

i

the non - brownian scaling of the mean squared displacement ( msd ) of a diffusing particle of the power - law form @xcite @xmath5 is a hallmark of a wide range of anomalous diffusion processes @xcite . equation ( [ msd ] ) features the anomalous diffusion coefficient @xmath6 of physical dimension @xmath7 and the anomalous diffusion exponent @xmath1 . depending on its magnitude we distinguish subdiffusion ( @xmath8 ) and superdiffusion ( @xmath9 ) . interest in anomalous diffusion processes was rekindled with the advance of modern spectroscopic methods , in particular , advanced single particle tracking methods @xcite . thus , subdiffusion was observed for the motion of biopolymers and submicron tracer particles in living biological cells @xcite , in complex fluids @xcite , as well as in extensive computer simulations of membranes @xcite or structured systems @xcite , among others @xcite . superdiffusion of tracer particles was observed in living cells due to active motion @xcite . anomalous diffusion processes characterised by the msd ( [ msd ] ) may originate from a variety of distinct physical mechanisms @xcite . these include a power - law statistic of trapping times in the continuous time random walks ( ctrws ) as well as related random energy models @xcite and ctrw variants with correlated jumps @xcite or superimposed environmental noise @xcite . other models include random processes driven by gaussian yet power - law correlated noise such as fractional brownian motion ( fbm ) @xcite or the fractional langevin equation @xcite . closely related to these models is the subdiffusive motion on fractals such as critical percolation clusters @xcite . finally , among the popular anomalous diffusion models we mention heterogeneous diffusion processes with given space dependencies of the diffusion coefficient @xcite as well as processes with explicitly time dependence diffusion coefficients , in particular , the scaled brownian motion ( sbm ) with power - law form @xmath0 analysed in more detail herein @xcite . also combinations of space and time dependent diffusivities were investigated @xcite . space and/or time dependent diffusivities were used to model experimental results for smaller tracer proteins in living cells @xcite and anomalous diffusion in biological tissues @xcite including brain matter @xcite . in particular , sbm was used to describe fluorescence recovery after photobleaching in various settings @xcite as well as anomalous diffusion in various biophysical contexts @xcite . in other branches of physics sbm was used to model turbulent flows observed by richardson @xcite as early as 1952 by batchelor @xcite . moreover , the diffusion of particles in granular gases with relative speed dependent restitution coefficients follow sbm @xcite . we note that in the limiting case @xmath10 the resulting process is ultraslow with a logarithmic growth of the msd @xcite known from processes such as sinai diffusion @xcite , single file motion in ageing environments @xcite , or granular gas diffusion with constant restitution coefficient @xcite . in the following we study the ergodic properties of sbm in the boltzmann - khinchin sense @xcite , finding that even long time averages of physical observables such as the msd do not converge to the corresponding ensemble average @xcite . in particular we compute the ergodicity breaking parameter eb characterising the trajectory - to - trajectory fluctuations of the time averaged msd in the entire range of the scaling exponents @xmath1 , both analytically and from extensive computer simulations . we generalise the results for the ergodic properties of sbm in the presence of ageing , when we start to evaluate the time average the msd a finite time span after the initiation of the system . the paper is organised as follows . in section [ sec - observables ] we summarise the observables computed and provide a brief overview of the basic properties of sbm . in section [ sec - model - simul ] we describe the theoretical concepts and numerical scheme employed in the paper . we present the main results for the eb parameter of non - ageing and ageing sbm in detail in sections [ sec - non - aged ] and [ sec - aged ] . in section [ sec - disc ] we summarise our findings and discuss their possible applications and generalisations .

we compute the ergodicity breaking parameter eb in the entire range of scaling exponents @xmath1 , both analytically and via extensive computer simulations of the stochastic langevin equation . we generalise the analytical and simulations results for the time averaged and ergodic properties of scaled brownian motion in the presence of ageing , that is , when the observation of the system starts only a finite time span after its initiation .

we examine the non - ergodic properties of scaled brownian motion , a non - stationary stochastic process with a time dependent diffusivity of the form @xmath0 . we compute the ergodicity breaking parameter eb in the entire range of scaling exponents @xmath1 , both analytically and via extensive computer simulations of the stochastic langevin equation . we demonstrate that in the limit of long trajectory lengths @xmath2 and short lag times @xmath3 the eb parameter as function of the scaling exponent @xmath1 has no divergence at @xmath4 and present the asymptotes for eb in different limits . we generalise the analytical and simulations results for the time averaged and ergodic properties of scaled brownian motion in the presence of ageing , that is , when the observation of the system starts only a finite time span after its initiation . the approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional brownian motion .

1507.02450

c

we here studied in detail the ergodic properties of sbm with its power - law time dependent diffusivity @xmath0 . in particular , we derived the higher order time averaged moments and obtained the ergodicity breaking parameter of sbm , which quantifies the degree of irreproducibility of time averaged observables of a stochastic process . for the highly non - stationary , out - of - equilibrium sbm process we analysed the eb parameter with respect to the scaling exponent @xmath1 , the lag time @xmath3 , and the trace length @xmath2 . we revealed a non - monotonic dependence @xmath145 . in particular , we showed that there is no divergence at @xmath4 , in contrast to the approximate results of @xcite . we also obtained a peculiar dependence for the eb dependence on the trace length @xmath2 , @xmath146 for @xmath74 and @xmath147 for @xmath73 , in agreement with @xcite . we also obtained analytical and numerical results for eb for ageing sbm as function of the model parameters and the ageing time @xmath35 . our exact analytical results are fully supported by stochastic simulations . we find that over the range @xmath119 and for @xmath20 the eb dependence on the lag time and trace length involves the universal variable @xmath148 , as witnessed by equation ( [ eq - eb - sbm ] ) . for arbitrary lag times and trace lengths the general result for ageing and non - ageing sbm are , however , more complex , see equations ( [ eq - eb - sbm - analyt ] ) and ( [ eq - eq - sbm - final - nominator - aged ] ) these are the main results of the current work . for strongly subdiffusive sbm in the range of exponents @xmath149 the ergodic properties are , in contrast , strongly dependent on the lag time @xmath3 . the correct limit of our exact result ( [ eq - eb - sbm - analyt ] ) was obtained for the eb parameter of ultraslow sbm with @xmath96 and for sbm with exponent @xmath4 . although eb has some additional logarithmic scaling at this point , it reveals no divergence as @xmath4 is approached . we are confident that the strategies for obtaining higher order time averaged moments developed herein will be useful for the analysis of other anomalous diffusion processes , in particular for the analysis of finite time corrections of eb for fractional brownian motion @xcite or for processes with spatially and temporally random diffusivities @xcite . we acknowledge funding from the academy of finland ( suomen akatemia , finland distinguished professorship to rm ) , the deutsche forschungsgemeinschaft ( to agc , ims and ft ) , and the imu berlin einstein foundation ( to avc ) .

we examine the non - ergodic properties of scaled brownian motion , a non - stationary stochastic process with a time dependent diffusivity of the form @xmath0 . the approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional brownian motion .

we examine the non - ergodic properties of scaled brownian motion , a non - stationary stochastic process with a time dependent diffusivity of the form @xmath0 . we compute the ergodicity breaking parameter eb in the entire range of scaling exponents @xmath1 , both analytically and via extensive computer simulations of the stochastic langevin equation . we demonstrate that in the limit of long trajectory lengths @xmath2 and short lag times @xmath3 the eb parameter as function of the scaling exponent @xmath1 has no divergence at @xmath4 and present the asymptotes for eb in different limits . we generalise the analytical and simulations results for the time averaged and ergodic properties of scaled brownian motion in the presence of ageing , that is , when the observation of the system starts only a finite time span after its initiation . the approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional brownian motion .

1502.00775

i

data has been accumulating over the last several years on an increasing number of galaxies in terms of measurements of the bulge velocity dispersion @xmath0 , mass of the central supermassive blackhole ( smbh ) @xmath1 , and the circular velocity , @xmath2 , of the host galaxy ( mcconnell & ma 2013 ; hu 2009 ; graham 2008 ; hu 2008 ; ho 2007 ; courteau et al . 2007 ; pizella et al . 2005 ; baes et al . 2003 ; ferrarese 2002 ; tremaine et al . 2002 ; onken et al 2004 ; peterson et al . 2004 ; nelson et al . 2004 ; merrit and ferrarese 2001 ; bedregal et al . 2006 ; bernardi et al . 2002 ; kronawitter et al . 2000 ; palunas et al . 2000 ; prugniel et al 2001 ; verheijen et al . 2001 ) . with the increase in the number of the galaxies for which @xmath0 , @xmath3 , and @xmath1 have been measured , it is becoming possible to ask , and attempt to answer , questions about the processes that govern the formation of galaxies and their central smbhs , and the symbiotic relationship between an smbh and its host galaxy . one way to approach these issues is to compare observed correlations , or lack thereof , between @xmath2 , @xmath0 , and @xmath1 with theoretical predictions obtained from models of galaxy / smbh formation ( e.g. , di matteo et al . 2008 ; di matteo et al . 2003 ; haehnelt & kauffmann 2000 ; kauffmann & haehnelt 2000 ) . the observed @xmath4 relation is now on a firm basis ( beifiori et al . 2012 ; gultenkin et al . 2009 ; hu 2009 ; graham 2008 ; hu 2008 ; tremaine et al . 2002 ; ferrarese & merritt 2000 ; gebhardt et al . 2000 ) and it points to a common history between the smbh and the spheroidal component of galaxies . moreover , it was recently found that @xmath2 and @xmath0 are correlated ( courteau et al . 2007 ; baes et al . 2003 , ferrarese 2002 ) . however , ho ( 2007 ) by a using a sample of 792 galaxies have shown that the @xmath5 relation has a very large scatter , and it depends on galaxy morphology . ferrares ( 2002 ) investigated the possibility of the masses of the supermassive blackhole being correlated with the total gravitational mass of the host galaxy or the mass of the dark matter halo . the author found a tight correlation between @xmath3 and @xmath0 for a sample of 36 galaxy , and by using the well - known @xmath6 relation , and connecting the mass of the dark matter halo with the circular velocity of the galaxy , report a correlation between the mass of the supermassive blackhole and the circular velocity of the host galaxy . baes et al . ( 2003 ) reported a relation between @xmath1 and @xmath2 . the rationale behind this correlation is that both quantities depend on the mass of the dark matter halo . a heavier halo will result in a deeper potential well that will give rise to a higher @xmath1 , and at the same time lead to a higher @xmath2 . zasov et al . ( 2005 ) , on the other hand , found a very weak correlation between @xmath1 and @xmath3 . however , the @xmath1 values in both baez et al . ( 2003 ) and zasov et al . ( 2005 ) , as well as in ferrarese ( 2002 ) , were obtained from the @xmath4 relation . ho et al . ( 2008 ) report a correlation between @xmath1 and @xmath3 for a sample of active galaxies , where the smbh masses were measured using the virial method ( kaspi et al . 2000 ; greene & ho 2005 ) . more recently , kormendy et al . ( 2011 ) used dynamical @xmath1 measurements to find that @xmath7 relation is very weak in a sample of 25 spiral galaxies . the same result is confirmed in beifiori et al . ( 2012 ) who used a large sample , 105 galaxies , but the used @xmath1 s are a mix of dynamical measurements from gultekin et al . ( 2009a ) and upper limits from beifiori et al . ( 2009 ) , with the upper limits taken as surrogate of black mass . * more recently , sun et al . ( 2013 ) analyzed the @xmath7 relation for 22 galaxies with @xmath2 determined from observations , and came up with a broad relation with large instrinsic scatter . * given the controversy surrounding the @xmath7 relation and its strength , using relations to find blackholes masses will only introduce additional scatter and makes it more difficult to reach firm conclusions for or against a genuine relation . most of the previous studies that have investigated the relation between @xmath1 and the circular velocity did so indirectly since they `` measured '' the smbh masses through the @xmath4 relation for galaxies with measured @xmath2 and @xmath0 . the danger in the indirect approach is that one is at the risk of masking , or leading to , a correlation between @xmath7 through the @xmath8 and @xmath4 , and it necessarily ignores bulge - less spirals with smbhs , further masking the true connection between the smbh and the dark matter halo . the aim of this paper is to present a direct study of the nature of the @xmath9 relation for * 53 * galaxies with dynamically measured @xmath1 . this is the largest sample to date of galaxies that have these two properties available . we also present , as a by - product of our study , the @xmath4 relation based on * 89 * galaxies . we are revisiting the question of the @xmath9 relation with a slightly `` cleaner '' sample of blackhole masses . it is our hope here that by using dynamical @xmath1 s we will be able to probe directly the intrinsic relations between a smbh and the dark matter halo of the host galaxy .

we explore the connection between the central supermassive blackholes ( smbh ) in galaxies and the dark matter halo through the relation between the masses of the smbhs and the maximum circular velocities of the host galaxies , as well as the relationship between stellar velocity dispersion of the spheroidal component and the circular velocity . the only requirement is that the galaxy has a direct measurement of the mass of its smbh and a direct measurement of its circular velocity and its velocity dispersion . previous studies have analyzed the connection between the smbh and dark matter halo through the relationship between the circular velocity and the bulge velocity dispersion , with the assumption that the bulge velocity dispersion stands in for the mass of the smbh , via the well - established smbh mass - bulge velocity dispersion relation . using intermediate relations may be misleading when one is studying them to decipher the active ingredients of galaxy formation and evolution . we believe that our approach will provide a more direct probe of the smbh and the dark matter halo connection .

we explore the connection between the central supermassive blackholes ( smbh ) in galaxies and the dark matter halo through the relation between the masses of the smbhs and the maximum circular velocities of the host galaxies , as well as the relationship between stellar velocity dispersion of the spheroidal component and the circular velocity . our assumption here is that the circular velocity is a proxy for the mass of the dark matter halo . we rely on a heterogeneous sample containing galaxies of all types . the only requirement is that the galaxy has a direct measurement of the mass of its smbh and a direct measurement of its circular velocity and its velocity dispersion . previous studies have analyzed the connection between the smbh and dark matter halo through the relationship between the circular velocity and the bulge velocity dispersion , with the assumption that the bulge velocity dispersion stands in for the mass of the smbh , via the well - established smbh mass - bulge velocity dispersion relation . using intermediate relations may be misleading when one is studying them to decipher the active ingredients of galaxy formation and evolution . we believe that our approach will provide a more direct probe of the smbh and the dark matter halo connection . we find that the correlation between the mass of supermassive blackholes and the circular velocities of the host galaxies is extremely weak , leading us to state the dark matter halo may not play a major role in regulating the blackhole growth in the present universe .

astro-ph9605137

i

understanding the origin and evolution of the fuel supply that feeds quasars and other active galactic nuclei ( agn ) is a key mystery in the astrophysics of these systems . to account for luminosities as high as @xmath2 erg / s the most efficient conceivable process - accretion onto a black hole - requires a mass supply of order one solar mass per year . that matter ( which over the lifetime of the active phase may amount to @xmath3 or more ) must be transported from galactic scales down to the schwarzschild radius of the hole at just a few a.u . evidently this transport mandates an efficient mechanism for disposing of the inflowing material s angular momentum . a partial solution to the problem is provided by invoking the presence of an accretion disk in the immediate vicinity of the hole . although the details are uncertain , viscosity in the disk transports angular momentum outward , and thereby permits mass to flow inward . recent observations by _ asca _ of relativistically broadened iron @xmath4 lines lend strong support to the idea of the existence of both massive black holes and disks in agn ( tanaka et al . 1995 ) . for the purpose of fuelling the hole , however , the disk is unlikely to provide more than a short term reservoir of mass , as models suggest that the disk mass is only a small fraction ( perhaps @xmath5 for a @xmath6 black hole ) of the mass of the hole ( e.g. clarke 1988 ) . even allowing for generous uncertainties in our models of accretion disks , therefore , it seems inevitable that the disk itself must be continually replenished from some further , external , source of mass . two possibilities suggest themselves for the source of this external fuel supply . in the first , the disk could be fed by gas funnelled in from large ( kpc ) galactic scales , perhaps as a consequence of interactions between the agn host galaxy and its neighbours ( hernquist & mihos 1995 ) . this scenario is attractive insomuch as there is undoubtably sufficient mass in gas at those large scales , though whether it can be transported to the sub - parsec scales of the accretion disk efficiently and without forming stars in the process is less clear . as a second possibility , the disk could be resupplied as a consequence of interactions occurring in a dense nuclear star cluster . such clusters are observed in many well - studied nearby galaxies , with the core of m32 exhibiting a central stellar density exceeding @xmath7 ( lauer et al 1992 ; crane et al 1993 ) . clusters of similar or modestly greater ( @xmath8 ) richness then have the potential to be a significant source of agn fuel_if _ a mechanism exists that allows the agn to tap into that supply . disruption of stars in the tidal field of the black hole was suggested by hills ( 1975 ) as a possible way to liberate the gas . disruption occurs when the pericentre @xmath9 of the orbit becomes comparable or smaller than the ` tidal ' radius @xmath10 where @xmath11 is the hole mass ( rees 1988 ) . an attractive prediction of this scenario is that activity should turn off when the central black hole has grown to the point that @xmath12 is comparable to the schwarzschild radius , @xmath13 after which stars are swallowed whole without significant release of radiation . for solar type stars this occurs when the black hole has reached a mass of a few @xmath14 . for the purpose of long - term fuelling of the black hole , however , this mechanism proves inadequate . rapid disruption of stars passing within @xmath12 depletes a region in phase space which is refilled via relaxation of the stars in the central cluster on a timescale @xmath15 yr . this rate is insufficient to provide enough fuel for the most luminous agn ( shields & wheeler 1978 ) . other possibilities that have been assayed include mass loss from stellar winds , which might be enhanced as a result of the agn s ultraviolet or high energy particle flux . a generic problem with such ideas is that gas released throughout the volume of the nuclear star cluster is vulnerable to being expelled by the radiation pressure from the central source . if only a fraction of the liberated mass reaches the disk or black hole then the demands placed on the supply of mass are appropriately aggravated . the interaction between a nuclear star cluster and the accretion flow has been explored for the case of main sequence stars by a number of authors . for such stars collisions with the disk will tend to expel matter out of the disk plane while leaving the star relatively unscathed . this mechanism has been proposed as an origin for the gas producing the broad emission lines seen in agn spectra ( zurek , siemiginowska & colgate 1991 , 1994 ; see addendum in apj xxxx ) . repeated collisions will gradually dissipate the star s orbital energy and in time drag it bodily into the plane of the disk ( syer , clarke & rees 1991 ) . the consequences of stars captured in this fashion , for example for the metallicity of quasar accretion disks , have been extensively investigated ( artymowicz 1993 ; artymowicz , lin & wampler 1993 ) . here , we extend previous studies on star - disk interactions to consider the case of giant stars , with radii typically @xmath16 . the greatly increased geometric area and reduced binding energy suggest that such stars should be susceptible to large - scale stripping of mass on collision with the disk ( zurek , siemiginowska & colgate 1994 ) . within some critical radius @xmath17 collisions will then destroy the star and unbind the envelope mass within the red giant lifetime . the value of @xmath17 will depend on the extent and properties of the disk as well as the velocity and structure of the star , but as we show later it is invariably larger than the radius within which stars are trapped while still on the main sequence . if @xmath17 and the central stellar density are sufficiently large , this mechanism could then provide an important source of fuel for the central black hole . the plan of this paper is as follows . in section 2 we discuss the numerical methods and initial conditions of our calculations . in section 3 we present results of hydrodynamic simulations of the star - disk interaction for a range of stellar velocities @xmath18 , and disk surface densities @xmath19 . our aim is to delineate that portion of the @xmath20 parameter space in which collisions lead to significant envelope loss . in section 4 we then combine the results of our calculations with simple models for the accretion disk and stellar cluster , in order to estimate how much fuel could be provided to the agn by this mechanism . section 5 summarises our results and conclusions .

we explore the role that red giants might play in the fuelling and evolution of active galactic nuclei . due to their large radii and the low binding energy of the stellar envelope , giants are vulnerable to envelope stripping from collisions with the accretion disk . using hydrodynamic simulations we estimate the rate of fuel supply by this mechanism using simple models for the agn disk and central stellar cluster .

we explore the role that red giants might play in the fuelling and evolution of active galactic nuclei . due to their large radii and the low binding energy of the stellar envelope , giants are vulnerable to envelope stripping from collisions with the accretion disk . using hydrodynamic simulations we show that such collisions will typically deposit a substantial fraction of the envelope mass into the disk on each passage . repeated encounters will then lead to the complete destruction of the star save for the dense core . we estimate the rate of fuel supply by this mechanism using simple models for the agn disk and central stellar cluster . if the central stellar density is @xmath0 , then stripping of giants could account for the activity of typical agn provided that the accretion disk extends out to @xmath1 pc . for agn with smaller disks , or clusters of lower central density , giant stripping could supply gas enriched via stellar nucleosynthesis to a disk replenished from some other source . we find that , for typical parameters , this mechanism is able to supply important quantities of gas to the disk at lower stellar densities than previously proposed stellar fuelling models for agn .

1412.5241

c

we have considered the irde model in the non - flat universe . we have derived the analytic solutions for the hubble parameter ( [ hubbleparameter ] ) , the dark energy density ( [ rdes ] ) and matter energy density ( [ rms ] ) . we have also studied astrophysical constraints on this model using the recent observations including snia , bao , cmb anisotropy , and the hubble parameter . we have shown that the allowed parameter range for the fractional energy density of the curvature is @xmath0 @xmath1 @xmath2 @xmath1 @xmath3 for @xmath31 @xmath102 0.15 . the best fit values with @xmath79 error are @xmath103 and @xmath104 with @xmath105 . we have shown that the irde model with a small curvature is allowed by observational constraints . without the interaction , the flat universe is observationally disfavored in this model .

we study astrophysical constraints on this model using the recent observations including the type ia supernovae ( snia ) , the baryon acoustic oscillation ( bao ) , the cosmic microwave background ( cmb ) anisotropy , and the hubble parameter . it is shown that the allowed parameter range for the fractional energy density of the curvature is @xmath0 @xmath1 @xmath2 @xmath1 @xmath3 in the presence of the interactions between dark energy and matter . without the interaction , the flat universe is observationally disfavored in this model .

we extend our previous analysis and consider the interacting holographic ricci dark energy ( irde ) model in non - flat universe . we study astrophysical constraints on this model using the recent observations including the type ia supernovae ( snia ) , the baryon acoustic oscillation ( bao ) , the cosmic microwave background ( cmb ) anisotropy , and the hubble parameter . it is shown that the allowed parameter range for the fractional energy density of the curvature is @xmath0 @xmath1 @xmath2 @xmath1 @xmath3 in the presence of the interactions between dark energy and matter . without the interaction , the flat universe is observationally disfavored in this model .

0709.3980

c

we find that a consistent fit to all the hd 209458b data at secondary eclipse requires that the atmosphere of hd 209458b have a thermal inversion at altitude and a stratosphere . this inversion is caused by the capture of incident optical stellar flux by an extra absorber of currently uncertain origin that resides at low pressures . the irac data of knutson et al . ( 2007c ) can not be fit by the effects of dayside heat redistribution cooling alone . a consequence of stratospheric heating and temperature inversion is the flipping of water absorption features into emission features from the near- to the mid - infrared ( hubeny , burrows , & sudarsky 2003 ; burrows , sudarsky , & hubeny 2006 ) , and this seems to explain all the current hd 209458b data . hence , contrary to the interpretation of richardson et al . ( 2007 ) , the flatness or slight rise of their irs spectrum near @xmath27.8 @xmath0 m ( fig . [ fig1 ] ) in fact supports the presence of abundant atmospheric water , because this region is at the edge of a strong water band in emission . our inference of the presence of water in abundance in the atmosphere of hd 209458b is also consistent with the conclusion of barman ( 2007 ) using transmission spectroscopy . if the extra absorber is in the gas phase , and there is no cloud , then our new models are easily consistent with the low albedo derived by rowe et al . ( 2006,2007 ) . if the extra absorber is a cloud , the cloud particles must have a low scattering albedo and can not be very reflecting . this would seem to rule out forsterite or enstatite clouds , but does not necessarily rule out iron clouds . as shown by hubeny , burrows , & sudarsky ( 2003 ) and burrows , sudarsky , & hubeny ( 2006 ) , strongly irradiated atmospheres can experience a solution bifurcation to an atmosphere with an inversion for which the water features are flipped from absorption to emission . in those papers , the absorber was gas - phase tio / vo , which in equilibrium can exist at low pressures at altitude and not just at high temperatures at depth . if the extra absorber were tio / vo , there would be fewer free parameters , but it was thought that the cold - trap " effect would quickly deplete the upper atmosphere of tio / vo and ensure the default atmospheric solution without an inversion . however , this has not been proven , particularly when atmospheric mass loss is ongoing , as we know to be the case for hd 209458b ( vidal - madjar et al . 2003,2004 ) . the same arguments hold for iron clouds , although since absorption by iron particles is not restricted to the optical , this solution is sub - optimal . one can also speculate that the severe irradiation regime of some close - in egps might create non - equilibrium compounds through photolysis , such as the tholins or polyacetylenes discussed in the more benign contexts of solar - system bodies , that could serve as the extra absorber we deduce exists in the atmosphere of hd 209458b . clearly , what the high - altitude absorber actually is remains to be seen , but one can speculate that its presence is more likely in the atmospheres of the most strongly irradiated egps . most strongly irradiated " actually means is not yet clear , but the flux at the substellar point on hd 209458b is @xmath2@xmath11 erg @xmath12 s@xmath13 . the corresponding numbers for ogle - tr-10b , ogle - tr-56b , ogle - tr-132b , tres-2 , tres-3 , wasp-1b , xo-3b , hat - p-1b , and hd 149026b are higher ( burrows et al . the corresponding number for tres-1 is lower ( @xmath20.43@xmath14 erg @xmath12 s@xmath13 ) and this planet shows good evidence for water in _ absorption _ ( burrows , hubeny , & sudarsky 2005 ) . in addition , the irs spectrum of hd 189733b of grillmair et al . ( 2007 ) seems consistent with a more canonical water absorption feature shortward of @xmath28 @xmath0 m . its substellar flux is @xmath20.47@xmath14 erg @xmath12 s@xmath13 . so , if stellar flux at the planet is an indicator , we may have a handle on which planets reside in the transition region between manifesting water absorption or emission features ( and inversions ) , and where the relative irac 1/irac 2 strengths start to flip . given their substellar fluxes , hd 189733b , xo-1b , xo-2b , and/or wasp-2b may be links . though we find a weak dependence on metallicity , non - equilibrium chemistry and cloud formation may have stronger dependences . therefore , there are still numerous parameters to address . as fig . [ fig1 ] suggests , the planet / star ratios shortward of @xmath24 @xmath0 m are more sensitive to the heat redistribution parameter , p@xmath5 , than the corresponding ratios longward of @xmath28 @xmath0 m . this suggests a shorter - wavelength strategy for designing close - in egp climate diagnostics . in addition , models with inversions significantly boost the mid - infrared fluxes longward of @xmath215 @xmath0 m . this boost is not the only signature of models with dayside stratospheres . since the nightside flux at the same p@xmath5 is unlikely to be much altered by the fact of dayside inversion , if the dayside has such an inversion due to enhanced optical absorption at altitude , the day - night contrasts measured during an orbital traverse by a close - in egp will be larger than expected for a given p@xmath5 . this possibility is relevant when interpreting the 24-@xmath0 m light curve of @xmath15 and b ( harrington et al . perhaps , the large day - night contrast seen in this case does not require a small p@xmath5 . an upper - atmosphere absorber in the optical may simultaneously explain the weaker - than - expected na d feature seen in transit by charbonneau et al . ( 2002 ) ( fortney et al . 2003 ) and the fact that the transit radius measured by richardson et al . ( 2006 ) at 24 @xmath0 m ( 1.26@xmath160.08 r@xmath17 ) is smaller than the corresponding radius in the optical ( 1.32@xmath160.025 r@xmath17 ; knutson et al . in addition , it may help explain why hd 209458b s optical transit radius is as large as it is . finally , the extra absorber may be related to the enhanced opacities for close - in egps discussed in the context of the egp radius models of burrows et al . ( 2007a ) . whatever their actual roles , anomalous optical absorption at altitude and thermal inversions are now insinuating themselves as exciting new components of egp theory . we thank drake deming , bill hubbard , maki hattori , mike cushing , and drew milsom for helpful discussions . this study was supported in part by nasa grants nng04gl22 g and nnx07ag80 g and through the nasa astrobiology institute under cooperative agreement no . can-02-oss-02 issued through the office of space science . burrows , a. , sudarsky , d. , & hubeny , i. 2003 , published in the proceedings of the 14th annual astrophysics conference in maryland the search for other worlds , " eds . s. holt and d. deming , ( aip conference proceedings ) , held in college park , md , october 13 - 14 , 2003 , p. 143 . burrows , a. , hubeny , i. , & sudarsky , d. , 2005 , 625 , l135 burrows , a. , sudarsky , d. & hubeny , i. 2006 , , 650 , 1140 ( astro - ph/0607014 ) burrows , a. , hubeny , i. , budaj , j. , & hubbard , w.b . 2007a , , 661 , 502 burrows , a. , hubeny , i. , & budaj , j. 2007b , in preparation charbonneau , d. , brown , t. m. , noyes , r. w. , & gilliland , r. l. 2002 , , 568 , 377 charbonneau , d. 2005 , , 626 , 523 deming , d. , seager , s. , richardson , l.j . , & harrington , j. , 2005 , nature , 434 , 740 deming , d. , harrington , j. , seager , s. , richardson , l.r . 2006 , , 644 , 560 deming , d. , harrington , j. , laughlin , g. , seager , s. , navarro , s.b . , bowman , w.c . , & horning , k. 2007 , submitted to letters ( arxiv:0707.2778 ) fortney , j.j . , sudarsky , d. , hubeny , i. , cooper , c.s . , hubbard , w.b . , burrows , a. , & lunine , j.i . 2003 , , 589 , 615 fortney , j.j . , marley , m.s . , lodders , k. , saumon , d. , & freedman , r.s . 2005 , , 627 , l69 grillmair , c.j . , charbonneau , d. , burrows , a. , armus , l. , stauffer , j. , meadows , v. , van cleve , j. , & levine , d. 2007 , , 658 , l115 harrington , j. , hansen , b. , luszcz , s. , seager , s. , deming , d. , menou , k. , cho , j. , & richardson , l. 2006 , science , 314 , 623 harrington , j. , luszcz , s. , seager , s. , deming , d. , & richardson , l.j . 2007 , nature , 447 , 691 knutson , h.a . , charbonneau , d. , noyes , r.w . , brown , t.m . , & gilliland , r.l . 2007a , , 655 , 564 knutson , h.a . , charbonneau , d. , allen , l.e . , fortney , j.j . , agol , e. , cowan , n.b . , showman , a.p . , cooper , c.s . , & megeath , s.t . 2007b , nature , 447 , 183 knutson , h.a . , charbonneau , d. , allen , l.e . , torres , g. , burrows , a. , & megeath , s.t . 2007c , submitted to melo , c. , et al . 2006 , , 460 , 251 richardson , l.j . , deming , d. , & seager , s. 2003 , , 597 , 581 richardson , l.j . , harrington , j. , seager , s. , & deming , d. 2006 , , 649 , 1043 richardson , l.j . , deming , d. , horning , k. , seager , s. , & harrington , j. 2007 , nature , 445 , 892 rowe , j.f . , matthews , j.m . , seager , s. , kuschnig , r. , guenther , d.b . , moffat , a.f.j . , rucinski , s.m . , sasselov , d. , walker , g.a.h . , & weiss , w.w . 2006 , , 645 , 1241 ( astro - ph/0603410 ) rowe , j.f . , et al . 2007 , submitted to santos , n.c . , israelian , g. , & mayor , m. 2004 , , 415 , 1153 swain , m. , bouwman , j. , akeson , r. , lawler , s. & beichman , c. 2007 , submitted to letters ( arxiv : astro - ph/0702593 ) tinetti , g. et al . 2007 , nature , 448 , 169 vidal - madjar , a. , lecavelier des etangs , a. , dsert , j .- m . , ballester , g.e . , ferlet , r. , hbrand , g. , & mayor , m. 2003 , nature , 422 , 143

we find that a theoretical fit to all the hd 209458b data at secondary eclipse requires that the dayside atmosphere of hd 209458b have a thermal inversion and a stratosphere . this inversion is caused by the capture of optical stellar flux by an absorber of uncertain origin that resides at altitude . one consequence of stratospheric heating and temperature inversion is the flipping of water absorption features into _ emission _ features from the near- to the mid - infrared and we see evidence of such a water emission feature in the recent hd 209458b irac data of knutson et al . in addition , an upper - atmosphere optical absorber may help explain both the weaker - than - expected na d feature seen in transit and the fact that the transit radius at 24 @xmath0 m is smaller than the corresponding radius in the optical . moreover , it may be a factor in why hd 209458b s optical transit radius is as large as it is . we speculate on the nature of this absorber and the planets whose atmospheres may , or may not , be affected by its presence .

we find that a theoretical fit to all the hd 209458b data at secondary eclipse requires that the dayside atmosphere of hd 209458b have a thermal inversion and a stratosphere . this inversion is caused by the capture of optical stellar flux by an absorber of uncertain origin that resides at altitude . one consequence of stratospheric heating and temperature inversion is the flipping of water absorption features into _ emission _ features from the near- to the mid - infrared and we see evidence of such a water emission feature in the recent hd 209458b irac data of knutson et al . in addition , an upper - atmosphere optical absorber may help explain both the weaker - than - expected na d feature seen in transit and the fact that the transit radius at 24 @xmath0 m is smaller than the corresponding radius in the optical . moreover , it may be a factor in why hd 209458b s optical transit radius is as large as it is . we speculate on the nature of this absorber and the planets whose atmospheres may , or may not , be affected by its presence .

1411.0640

i

a point charge with a constant acceleration @xmath0 in its instantaneous rest system follows the relativistic trajectory@xcite @xmath1 the equation relating @xmath2 and @xmath3 is a hyperbola , leading to the common designation of this motion as ` hyperbolic motion ' . the trajectory in eq . ( [ zt ] ) corresponds to a charge that comes to rest at @xmath4 at time @xmath5 after traveling an infinite distance from the infinite past where its speed @xmath61 . the electric field produced by the accelerating charge has been calculated in ref . the field lines show an unusual , non - physical behavior at @xmath7 ( for observation time t=0 ) where they abruptly stop . this is because the retarded position of the charge is outside the past light cone for any @xmath8 . this problem is recognized in @xcite , and they attempt to correct it by introducing truncated hyperbolic motion " , in which the accelerated part of the motion is preceded by motion with a constant velocity . however , their results in figures 3 and 4 of their paper show an unphysical discontinuous behavior for the electric field lines as the charge passes through the transition from constant velocity to accelerated motion . in this paper , we modify the calculation of the electric field lines , resulting in continuous electric field lines that satisfy the appropriate physical constraints . in section 2 of this paper , we summarize the calculation in @xcite of the lienard - wiechert electric field for hyperbolic motion , and agree with their conclusion that the abrupt end of electric field lines at @xmath7 is unphysical . in section 3 , we derive the electric field for the constant velocity phase of the motion and for the accelerated phase from the same standard lienard - wiechert formula , only using different retarded time formulas for the two different situations . consequently , our electric field lines are continuous as the retarded time increases through the transition time between constant velocity and accelerated motion , and our figures 2 and 3 do not show the discontinuous behavior of the corresponding figures 3 and 4 in @xcite . as the transition time approaches negative infinity the constant velocity part of the electric field develops a delta function contribution that has been proposed by others as necessary to preserve gauss s law for the electric field .

the same lienard - wiechert formula holds for the acceleration phase and the constant velocity phase of the charge s motion . the electric field lines are continuous as the retarded time increases through the transition time between constant velocity and accelerated motion . as the transition time approaches negative infinity the electric field develops a delta function contribution that has been introduced by others as necessary to preserve gauss s law for the electric field .

we find the electric field of a point charge in ` truncated hyperbolic motion ' , in which the charge moves at a constant velocity followed by motion with a constant acceleration in its instantaneous rest frame . the same lienard - wiechert formula holds for the acceleration phase and the constant velocity phase of the charge s motion . the only modification is that the formula giving the retarded time is different for the two motions , and the acceleration is zero for the constant velocity motion . the electric field lines are continuous as the retarded time increases through the transition time between constant velocity and accelerated motion . as the transition time approaches negative infinity the electric field develops a delta function contribution that has been introduced by others as necessary to preserve gauss s law for the electric field .

astro-ph0311432

i

we have carried out an analysis of the anisotropy of satellite angular positions with respect to the primary plane . the sample was selected in redshift space from the 2dfgrs and is large enough for studying possible dependencies of anisotropies on both primary and satellite properties . we confirm the existence of the effect first claimed by holmberg , that is , the preference of the satellites to lie near the pole of the primary . we note however that this effect is present up to relative projected separations @xmath7 kpc . we use an anisotropy parameter a suitable to measure the departure from isotropy in the different subsamples analysed . nevertheless , this parameter indicates a lower limit to the real anisotropy , given the contamination by false satellites expected to be uniformly distributed with respect to the primary plane . the deviation from isotropy is detected at least at @xmath51 level for objects with low values of relative velocity @xmath0 km / s while the high velocity subsample is consistent with isotropy . although in principle this effect could be related to different levels of contamination by interlopers , zaritsky 1992 test provides comparable values of contamination in both high and low relative velocity subsamples . by inspection to the luminosity of the primaries , we conclude that the anisotropy of the distribution of satellites around faint primaries shows a high statistical significance ( @xmath87 ) . the most important signal was detected in the sample of satellites corresponding to passive star forming primaries , where the distribution of @xmath24 angles departs from isotropy at the @xmath92 level ; while the opposite behaviour is present in primaries with @xmath93 , for which the a parameter results consistent with zero . moreover , we also notice that the signal is even higher when we raise the eccentricity threshold of the primaries . we also have considered the different spectral types of the satellites , finding the strongest anisotropy for satellites with @xmath94 ( objects with little present day star formation activity ) . we notice that primaries with a low value of @xmath1 in our sample also have satellites with poor star formation activity . the isolation criteria imposed to our sample lowers the probability of including a significant number of elliptical galaxies . thus , most primaries in our sample are expected to be of late type morphology . due to the morphology density relation we expect only 10@xmath95 of our isolated sample of primaries to be ellipticals ( whitmore et al . 1993 ) . we could in principle interpret the holmberg effect as being mainly caused by evolutionary processes . systems dominated by old stellar population objects have formed early , so the physical processes that may have removed satellites near the primary plane have been present for a large time . by contrast , in younger primary and satellite systems , we would expect a larger fraction of objects that have not been accreted yet on to the primary so that they would show an isotropic distribution of satellites . however , as discussed by quinn @xmath9 goodman ( 1986 ) , it may be difficult to produce anisotropies in the distribution of satellites from pure dynamical evolution , specially at large scale @xmath7 kpc . more likely , we suggest that according to abadi et al . ( 2002 ) results , such anisotropies could be the remnants of the formation of the disks of the primaries , where substantial orbital momentum is transfered into primary rotation during the early stages of galaxy formation . thus , the anisotropy effects we detect at large projected separations , could be the relics of such mechanism . we also argue that the significant dependence of the anisotropy effect on the relative velocity between the satellite and the primary could be an important point of disagreement between the results of previous works .

we find a strong statistical evidence of the holmberg effect ( that is a tendency for satellites to avoid regions along the line defined by the primary plane ) within 500 kpc of projected distance to the primary . we explore the dependence of this anisotropy on spectral type ( @xmath1 ) , colours , and luminosities of both primaries and satellites , finding that objects with a low present - day star formation rate present the most significant effect .

we have analysed a sample of satellite and primary galaxies in the 2df galaxy redshift survey . in our study we find a strong statistical evidence of the holmberg effect ( that is a tendency for satellites to avoid regions along the line defined by the primary plane ) within 500 kpc of projected distance to the primary . this effect is present only when we restrict to objects with radial velocity relative to the primary @xmath0 km / s which correspond approximately to the mean of the distribution . we explore the dependence of this anisotropy on spectral type ( @xmath1 ) , colours , and luminosities of both primaries and satellites , finding that objects with a low present - day star formation rate present the most significant effect . cosmology : theory - galaxies : formation - galaxies : evolution .

hep-th0412303

i

iib matrix model @xcite is a candidate of the constructive definition of superstring theory . it is defined by the action @xmath8[a_\mu , a_\nu ] + \frac{1}{2}\bar{\psi}\gamma^\mu[a_\mu,\psi ] \right ) , \label{eq : action}\end{aligned}\ ] ] where @xmath9 and @xmath10 are @xmath11 hermitian matrices . @xmath9 is a ten - dimensional vector and @xmath10 is a ten - dimensional majorana - weyl fermion . one of the important aspects of this model is the dynamical generation of the spacetime and the gauge group . in this model the eigenvalue distribution represents spacetime geometry . from this point of view , if a four - dimensional eigenvalue distribution has smaller free energy than the other configurations , the spacetime will be compactified to four - dimensions . on the other hand the stability of @xmath2 coincident d - branes may indicate the dynamical generation of @xmath12 gauge group . so far , various attempts on this have been made . several such attempts using branched polymer @xcite , complex phase effect @xcite and especially improved mean - field approximation @xcite were successful . in these studies , four - dimensional configurations were found to have smaller free energy . another interesting approach is to compare the free energies on noncommutative backgrounds . in string theory , noncommutative gauge theories on flat or curved backgrounds are realized with constant or nonconstant @xmath13 @xcite . iib matrix model on flat fuzzy space backgrounds can be mapped to noncommutative super yang - mills theory ( ncsym ) @xcite , and the system can be analyzed by perturbative calculations . noncommutative gauge theories on curved manifolds have recently been studied extensively by deforming iib matrix model @xcite . however , flat fuzzy space backgrounds can not be realized as classical solutions at finite @xmath14 . therefore , in order to see the @xmath14-dependences of the free energies , we must study compact noncommutative spaces . fuzzy @xmath15 , @xmath16 and @xmath17 backgrounds have already been studied and @xmath16 has been shown to be stable under certain deformations @xcite . in this paper , we study the free energies of iib matrix model on fuzzy torus backgrounds . the relation to flat fuzzy space is more transparent in the case of the fuzzy torus than in the case of fuzzy sphere . we expand the action of iib matrix model around a fuzzy torus background and sum up all 1pi diagrams . then , we search the minimum of the free energy . especially , we compare @xmath0 and @xmath1 backgrounds . in principle , in order to find the true vacuum , we must calculate free energies on all possible backgrounds and find the minimum . here , however , we consider only fuzzy torus . although fuzzy torus is not a classical solution , however , as we will show later , fuzzy torus locally looks like flat fuzzy space , which is a classical solution . therefore , we expect our calculation captures some qualitative feature of flat fuzzy spaces . if the true vacuum is similar to a flat fuzzy space , we may find some informations such as dimensionality of the spacetime on it . in present study we will see that @xmath0 has smaller free energy than @xmath1 . this implies that if the true vacuum is four - dimensional , it is not a simple noncommutative space considered here . although both fuzzy sphere and fuzzy torus break supersymmetry , the breaking effect is soft and the loop corrections to their free energies almost vanish . this is because their local structures are similar to flat fuzzy spaces . in the case of fuzzy @xmath15 , @xmath16 and @xmath17 , such cancellations have been confirmed to 2-loop level @xcite . for fuzzy torus we can see such cancellation at any loop level . furthermore , in this case the calculations become simpler and we can study larger parameter region . for example , on @xmath1 , we vary the ratio @xmath18 of the noncommutativity parameters of two tori and their ratio @xmath19 of the matrix size . , @xmath20 was studied @xcite . ] we can also see the effect of the global topologies on the free energies by comparing the results for fuzzy tori and fuzzy spheres . on the other hand , fuzzy torus has a few drawbacks . we embed fuzzy @xmath0 into @xmath21 , while fuzzy @xmath15 can be embedded into @xmath22 . therefore , in ten dimensions we can realize only two- and four - dimensional configurations using fuzzy tori ( @xmath0 and @xmath1 ) , while a six - dimensional configuration can be constructed using fuzzy spheres ( @xmath17 ) . in @xcite it is shown that @xmath16 has a smaller free energy than @xmath23 . in our case , such comparison is impossible . we also have subtlety in the perturbative calculation , due to the presence of a few tachyons on fuzzy torus . we will discuss this problem in detail later . the organization of the paper is as follows . in section 2 , we will construct the fuzzy torus backgrounds and show the correspondence between fuzzy torus and flat fuzzy space . in section 3 , we calculate the free energy up to two loop level analytically , and in section 4 , we compare the free energies numerically . in appendices , we show the detail of the calculations . although we are interested in @xmath1 , we will mostly show the feynman diagrams and calculations of @xmath0 as @xmath1 calculations are very lengthy .

we have calculated the free energy up to two loop to compare @xmath0 with @xmath1 in iib matrix model . it turns out that @xmath0 has smaller free energy than @xmath1 . this means that if the true vacuum is four - dimensional , it is not a simple fuzzy space considered here .

we have calculated the free energy up to two loop to compare @xmath0 with @xmath1 in iib matrix model . it turns out that @xmath0 has smaller free energy than @xmath1 . we have also discussed the generation of the gauge group by considering @xmath2-coincident fuzzy tori and found that in this case u(1 ) gauge group is favored . this means that if the true vacuum is four - dimensional , it is not a simple fuzzy space considered here . @xmath3 [ cols= " < " , ] + + + fuzzy torus in matrix model + subrata bal@xmath4 , masanori hanada@xmath5 , hikaru kawai@xmath6 , fukuichiro kubo@xmath7 @xmath4 _ theoretical physics laboratory , riken ( the institute of physical and chemical research ) , + wako , saitama 351 - 0198 , japan _ + @xmath7 _ department of physics , kyoto university , kyoto 606 - 8502 , japan _

1003.4213

i

recent efforts to produce atomic clocks in the optical domain have proven so successful that they are now surpassing the performance of the best frequency standards in the microwave domain @xcite . however , one limitation to further improvements of optical clocks is the performance of ultra - stable lasers , which form the basis for the interrogation of the narrow resonance of an atomic clock @xcite . for this reason , much effort has been devoted to improving ultra - stable references in the optical domain . the best frequency references are generally based on the electromagnetic resonance of a mechanically stable macroscopic element . cryogenic sapphire oscillators ( cso ) have long provided the benchmark in the microwave domain by delivering signals with stabilities in the @xmath1 range . they have also proven to be highly beneficial as the basis for ultra - stable reference frequency dissemination @xcite . with the use of an optical frequency comb , such microwave signals can be multiplied up to the optical domain , but avoiding significant degradation is extremely difficult . the alternative is to rely upon ultra - stable laser sources at optical wavelengths . in a seminal result , an optical signal with a fractional frequency stability of @xmath2 at 1s was achieved by stabilizing lasers to two 24 cm long fabry prot cavities mounted on a large vibration isolation system @xcite . in this paper , we present a fabry prot - based ultra - stable source at infrared wavelengths , extended to the deep ultraviolet for use as an interrogation signal of the @xmath3@xmath4 clock transition in mercury at 265.6 nm @xcite . the fabry prot cavity in our case is designed to be highly immune to environmental perturbations such as temperature fluctuations and vibrations . the design also seeks to minimize the intrinsic performance limitations imposed by the phenomenon of thermal noise through the selection of fused silica for the mirror substrate in the fabry prot cavity . although fused silica has already been shown to give rise to lower levels of thermal noise as compared with ultra - low expansion glass ( ule ) @xcite , this work represents the first attempt to exploit this in a fully - functional optical frequency reference . the resulting ultra - stable signal in the infrared has been subsequently transferred to the ultraviolet regime by two stages of frequency doubling , which should involve only a modest loss of fidelity of the signal @xcite . the resulting system is comparatively cheap and robust and operates indefinitely , without the interruptions typically associated with high - maintenance cryogenic systems . in addition , the system is also linked to the lne - syrte fountain primary frequency standards using an optical frequency comb . by comparison against the standard via this link , we demonstrate a noise level and a stability which are significantly lower than those in the best atomic fountains @xcite . this system therefore provides the means to make absolute frequency measurements of the mercury optical lattice clock limited only by the microwave counterpart .

we have developed an ultra - stable source in the deep ultraviolet , suitable to fulfill the interrogation requirements of a future fully - operational lattice clock based on neutral mercury . at the core of the system prot cavity which is highly impervious to temperature and vibrational perturbations . the mirror substrate is made of fused silica in order to exploit the comparatively low thermal noise limits associated with this material . by stabilizing the frequency of a 1062.6 nm yb - doped fiber laser to the cavity , and including an additional link to lne - syrte s fountain primary frequency standards via an optical frequency comb

we have developed an ultra - stable source in the deep ultraviolet , suitable to fulfill the interrogation requirements of a future fully - operational lattice clock based on neutral mercury . at the core of the system is a fabry prot cavity which is highly impervious to temperature and vibrational perturbations . the mirror substrate is made of fused silica in order to exploit the comparatively low thermal noise limits associated with this material . by stabilizing the frequency of a 1062.6 nm yb - doped fiber laser to the cavity , and including an additional link to lne - syrte s fountain primary frequency standards via an optical frequency comb , we produce a signal which is both stable at the @xmath0 level in fractional terms and referenced to primary frequency standards . the signal is subsequently amplified and frequency - doubled twice to produce several milliwatts of interrogation signal at 265.6 nm in the deep ultraviolet . pacs 06.30.ft 42.62.eh 42.72.bj

1411.3844

i

we undertook a census of central massive black holes in the very nearby universe , targeting specifically low - mass dwarf systems with bh masses in the imbh mass range . using the wise all - sky release source catalog , we examined the ir colors of a sample of known nearby galaxies in order to identify both unobscured and obscured active galactic nuclei . we found that 313 nearby galaxies have wise colors consistent with galaxies containing an agn . of these , eleven lie within a distance of 11 mpc . we estimated the stellar and black hole masses for our nearby galaxy sample and found that activity is detected in stellar masses ranging @xmath47 m@xmath2 and that this activity is due to black holes with masses in the range @xmath3 m@xmath2 . the black hole masses probed here are several orders of magnitude smaller than previously reported for centrally located massive black holes . we examined the stellar mass versus black hole mass relationship in this low galaxy mass regime and found that the relation extends to these low masses . we compare our black hole mass estimates to estimates from the [ oiii ] @xmath535007 line flux and find that the latter method systematically underestimates the black hole masses . these results indicate that central massive black holes are present in low - mass galaxies and in the local universe , and provide new impetus for follow up dynamical studies of quiescent black holes in local dwarf galaxies . alexandroff r. , overzier r.a . , paragi z. , basu - zych a. , heckman t. , kauffmann g. , bourke s. , lobanov a. , ptak a. , schiminovich d. , 2012 , mnras , 423 , 1325 antonucci r. , 1993 , ara&a , 31 , 473 assef r.j . , kochanek c.s . , brodwin m. , et al . , 2010 , apj , 713 , 970 baldwin j.a . , phillips m.m . , terlevich r. , 1981 , pasp , 93 , 5 ballantyne d.r . , draper a.r . , madsen k.k . , rigby j.r . , treister e. , 2011 , apj , 736 , 56 bardeen j.m . , 1970 , nature , 226 , 64 barth a.j . , greene j.e . , ho l.c . , 2008 , aj , 136 , 1179 bender r. , kormendy j. , 2003 , acfp.conf , 262 benson a.j . , 2010 , phr , 495 , 33 booth c.m . , schaye j. , 2009 , mnras , 398 , 53 chilingarian , i.v . , melchior , a .- l . , zolotukhin , i.y . , 2010 , mnras , 405 , 1409 comastri a. , setti g. , zamorani g. , hasinger g. , 1995 , a&a 296 , 1 da cunha e. , charlot s. , elbaz d. , 2008 , mnras , 388 , 1595 degraf c. , di matteo t. , khandai n. , croft r. , 2012 , apj , 755 , ll8 di matteo t. , springel v. , hernquist l. , 2005 , nature , 433 , 604 di matteo t. , colberg j. , springel v. , hernquist l. , sijacki d. , 2008 , apj , 676 , 33 dong x .- b . , et al . , 2012 , apj , 755 , 167 dong x .- b . , et al . , 2007 , apj , 657 , 700 dressler a. , richstone d. , 1988 , apj , 324 , 701 fabian a. c. , 2012 , ara&a , 50 , 455 fan x. , et al . , 2001 , aj , 122 , 2833 ferrarese l. , merritt d. , 2000 , aj , 539 , l9 gebhardt k. , et al . , 2000 , aj , 539 , 13 greene j.e . , ho l.c . , 2007 , apj , 670 , 92 greene j.e . , ho l.c . , 2004 , apj , 610 , 722 griffith r.l . , et al . , 2011 , apj , 736 , l22 hearty t. , fernndez m. , alcal j.m . , covino e. , neuhuser r. , 2000 , a&a , 357 , 681 heckman t.m . , kauffmann g. , brinchmann j. , et al . , 2004 , apj , 613 , 109 heckman t.m . , kauffmann g. , 2011 , sci , 333 , 182 ho l.c . , filippenko a.v . , sargent w.l.w . , 1997 , apjs , 112 , 315 ho l. , kormendy j. , murdin p. , 2000 , eaa .. book , 2365 ishibashi w. , fabian a. c. , 2014 , mnras , 441 , 1474 jia j. , ptak a. , heckman t.m . , overzier r.a . , hornschemeier a. , lamassa s.m . , 2011 , apj , 731 , 55 karachentsev i.d . , makarov d.i . , kaisina e.i . , 2013 , aj , 145 , 101 kauffmann g. , jeckman t.m . , tremonti c. , et al . , 2003 , mnras , 346 , 1055 kewley l.j . , dopita m.a . , sutherland r.s . , heisler c.a . , trevena j. , 2001 , apj , 556 , 221 kewley l.j . , groves b. , kauffmann g. , heckman t. , 2006 , mnras , 372 , 961 khalatyan a. , cattaneo a. , schramm m. , gottlber s. , steinmetz m. , wisotzki l. , 2008 , mnras , 387 , 13 king a. , 2003 , apj , 596 , l27 kormendy j. , ho l.c . , 2013 , ara&a , 51 , 511 kormendy j. , richstone d. , 1995 , ara&a , 33 , 581 lacy m. , et al . , 2004 , apjs , 154 , 166 lacy m. , et al . , 2007 , apj , 669 , 61 lynden - bell d. , 1969 , nature , 223 , 690 lynden - bell d. , rees m.j . , 1971 , mnras , 152 , 461 magorrian j. et al . , 1998 , aj , 15 , 2285 malinen j. , et al . , 2014 , a&a , 563 , 125 marleau f.r . , clancy d. , bianconi m. , 2013 , mnras , 435 , 3085 mateo , m. , 1998 , ara&a , 36 , 435 mcconnachie a.w . , et al . , 2012 , aj , 144 , 4 mcnamara b.r . , nulsen p.e.j . , 2007 , ara&a , 45 , 117 mendel j.t . , simard l. , palmer m. , ellison s.l . , patton d.r . , 2014 , apjs , 210 , 3 merritt d. , ferrarese l. , 2001 , apj , 547 , 140 moran e. , shahinyan k. , sugarman h.r . , vlez d.o . , eracleous m. , 2014 , arxiv:1408.4451v1 mortlock d.j . , et al . , 2011 , nature , 474 , 616 newton r.d.a . , kay s.t . , 2013 , mnras , 434 , 3606 peirani s. , jung , i. , silk , j. , pichon , c. , 2012 , mnras , 427 , 2625 peterson b.m . , somerville r.s . , storchi - bergmann t. , 2010 , iaus , 267 peterson b.m . , 2008 , newar , 52 , 240 power c. , nayakshin s. , king a. , 2011 , mnras , 412 , 269 reines a.e . , plotkin r.m . , russell t.d . , mezcua m. , condon j.j . , sivakoff g.r . , johnson k.e . , 2014 , arxiv:1405.0278v1 reines a.e . , greene j.e . , geha m. , 2013 , apj , 775 , 116 reines a.e . , sivakoff g.r . , johnson k.e . , brogan c.l . , 2011 , nature , 470 , 66 richards g.t . , et al . , 2006 , apjs , 166 , 470 sajina a. , lacy m. , scott d. , 2005 , apj , 621 , 256 salpeter e.e . , 1964 , apj , 140 , 796 satyapal s. , secrest n.j . , mcalpine w. , ellison s.l . , fischer j. , rosenberg j.l . , 2014 , apj , 784 , 113 schawinski k. , 2012 , arxiv , arxiv:1206.2661 seth , a.c . , et al . , 2014 , arxiv:1409.4769v1 sijacki d. , springel v. , di matteo t. , hernquist l. , 2007 , mnras , 380 , 877 silk j. , rees m.j . , 1998 , a&a , 331 , l1 silk j. , mamon g. a. , 2012 , raa , 12 , 917 silk j. , 2013 , apj , 772 , 112 simmons b.d . , lintott c. , schawinski k. , moran e.c . , han a. , kaviraj s. , masters k.l . , urry c.m . , willett k.w . , bamford s.p . , nichol r.c . , 2013 , mnras , 429 , 2199 springel v. , di matteo t. , hernquist l. , 2005 , mnras , 361 , 776 stasinska g. , fernandes r.c . , mateus a. , sodre l. , asari n.v . , 2006 , mnras , 371 , 972 steinhardt c.l . , elvis m. , 2010 , mnras , 402 , 2637 stern d. , et al . , 2012 , apj , 753 , 30 taylor e.n . , 2011 , mnras , 418 , 1587 treister e. , et al . , 2004 , apj , 616 , 123 urry c.m . , padovani p. , 1995 , pasp , 107 , 803 van der marel rp . , cretton n. , de zeeuw p.t . , rix h .- w . , 1998 , apj , 493 , 613 veilleux s. , osterbrock d.e . , 1987 , apjs , 63 , 295 wright e.l . , et al . , 2010 , aj , 140 , 1868 wurster j. , thacker r.j . , 2013 , mnras , 431 , 2513 zeldovich y.b . , novikov i.d . , 1965 , sphd , 9 , 834

we have identified 313 nearby galaxies that display the infrared signature of black hole activity . of these , eleven lie within a distance of 11 mpc . using the wide - field infrared survey explorer ( wise ) all - sky release source catalog , we examine the ir colors of a sample of known nearby dwarf galaxies in order to identify both unobscured ( type 1 ) and obscured ( type 2 ) active galactic nuclei in these low - mass systems . we estimate the stellar and black hole masses for our nearby dwarf galaxy sample and find that activity is detected in galaxies with stellar masses from @xmath0 to @xmath1 m@xmath2 and that this activity is due to black holes with masses in the range @xmath3 m@xmath2 . the black hole masses probed here are several orders of magnitude smaller than previously reported for centrally located massive black holes . we examine the stellar mass versus black hole mass relationship in this low galaxy mass regime , and find that the existing relation extends to these lower masses . these findings indicate that central massive black holes are present in low - mass galaxies and in the local universe . these results provide new impetus for follow up dynamical studies of quiescent black holes in local dwarf galaxies .

we have identified 313 nearby galaxies that display the infrared signature of black hole activity . of these , eleven lie within a distance of 11 mpc . using the wide - field infrared survey explorer ( wise ) all - sky release source catalog , we examine the ir colors of a sample of known nearby dwarf galaxies in order to identify both unobscured ( type 1 ) and obscured ( type 2 ) active galactic nuclei in these low - mass systems . we estimate the stellar and black hole masses for our nearby dwarf galaxy sample and find that activity is detected in galaxies with stellar masses from @xmath0 to @xmath1 m@xmath2 and that this activity is due to black holes with masses in the range @xmath3 m@xmath2 . the black hole masses probed here are several orders of magnitude smaller than previously reported for centrally located massive black holes . we examine the stellar mass versus black hole mass relationship in this low galaxy mass regime , and find that the existing relation extends to these lower masses . these findings indicate that central massive black holes are present in low - mass galaxies and in the local universe . these results provide new impetus for follow up dynamical studies of quiescent black holes in local dwarf galaxies . [ firstpage ] galaxies : general galaxies : seyfert galaxies : active galaxies : dwarfs galaxies : local group galaxies : evolution infrared : galaxies

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we now summarise the implications of these observations for the main models of the formation and stability of spiral structure . no one theory fits all of the observations , but a combination can explain most or all of the features we have observed . this section summarises these conclusions . simple density wave theories ( e.g. lin & shu 1964 , 1966 ) are undermined in three ways . firstly , we do not get the correlation between the fraction of light in the disk and pitch angle which is predicted by lin & shu ( 1964 ) and roberts et al . secondly , lin & shu ( 1964 ) predict that pitch angle should be the same for arms at the same radius within a given galaxy . we find that this is not the case . finally , we have found that the fwhm of arm cross - sections are somewhat narrower than predicted by simple density wave theories . more complicated density wave theories , e.g. modal theory ( bertin et al . 1989a , 1989b ; bertin & lin 1996 ) , are supported by modulation effects that we have found in arm strength as a function of radius , and which appear to be fairly common . bar driven models of spiral structure ( sellwood & sparke 1988 ; sanders & huntley 1976 ) are not supported by our observations , as we find no correlation between arm strength and bar strength , even in the inner part of the disk . tidal effects from near neighbours seem to have some effect . we find that 4 out of 7 galaxies with arm ea greater than @xmath53 have near neighbours whereas only 12 out of 45 galaxies in whole sample have near neighbours . we also find that in the fourier analysis of galaxies with near neighbours , the even low - order modes are dominant , especially the @xmath47 mode . we have also discussed factors affecting star formation in the disks of spiral galaxies . we have found evidence both for and against the large scale shock scenario ( roberts 1969 ) . firstly , we find a correlation between arm contrast and the normalised star formation rate , in agreement with the predictions of the large scale shock scenario . secondly , we find that b - band arms are more loosely wound and narrower than k - band arms , confirming the predictions made by density wave theories ( roberts 1969 ) . however , this can also be interpreted as an extinction effect because dust lies on the trailing edges of arms . finally , and possibly most significantly , we find no correlation between the arm properties of this sample of galaxies and their classified hubble type . combining this with the poor correlation between hubble type and k - band b / d ratio ( paper i ) , it would appear impossible to allocate a hubble type to these galaxies on the basis of these k - band observations , and the morphology of the old stellar population varies surprisingly little between hubble types sa and sd . we speculate that the determining parameter for hubble type is cold gas content , which controls the star formation rate and the distribution of the young stars , which dominate the optical appearance .

we have imaged a sample of 45 face - on spiral galaxies in the k - band , to determine the morphology of the old stellar population , which dominates the mass in the disk . contrary to expectations , no correlation was found between arm pitch angle and hubble type , and combined with previous results this leads us to conclude that the morphology of the old stellar population bears little resemblance to the optical morphology used to classify galaxies . we find that b - band arms lead k - band arms and are narrower than k - band arms , apparently supporting predictions made by the large scale shock scenario , although the effects of dust on b - band images may contribute towards these results .

we have imaged a sample of 45 face - on spiral galaxies in the k - band , to determine the morphology of the old stellar population , which dominates the mass in the disk . the k - band images of the spiral galaxies have been used to calculate different characteristics of the underlying density perturbation such as arm strengths , profiles and cross - sections , and spiral pitch angles . contrary to expectations , no correlation was found between arm pitch angle and hubble type , and combined with previous results this leads us to conclude that the morphology of the old stellar population bears little resemblance to the optical morphology used to classify galaxies . the arm properties of our galaxies seem inconsistent with predictions from the simplest density wave theories , and some observations , such as variations in pitch angle within galaxies , seem hard to reconcile even with more complex modal theories . bars have no detectable effect on arm strengths for the present sample . we have also obtained b - band images of three of the galaxies . for these galaxies we have measured arm cross - sections and strengths , to investigate the effects of disk density perturbations on star formation in spiral disks . we find that b - band arms lead k - band arms and are narrower than k - band arms , apparently supporting predictions made by the large scale shock scenario , although the effects of dust on b - band images may contribute towards these results . galaxies : spiral - galaxies : structure - galaxies : fundamental parameters

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by comparing observations of galaxies in clusters at @xmath7 with those in clusters at @xmath5 , we infer that some environmental effects in clusters have influences on the evolution of the galaxies . @xcite found that clusters at @xmath7 have a high fraction of blue galaxies in comparison with nearby clusters , and subsequent works have confirmed this trend ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? recent observations with the _ hubble space telescope _ ( hst ) revealed details of the blue galaxies . @xcite and @xcite found that most of the blue galaxies are normal spirals with active star formation . on the other hand , observations have shown that the fraction of so galaxies decreases rapidly with redshift in contrast with the normal spirals @xcite . these suggest that the blue normal spirals observed in high redshift clusters evolve into the non - blue so galaxies observed in nearby clusters . in fact , observations show that in distant clusters there are galaxies in post - starburst phase.@xcite . these galaxies may be the ones for which star formation activity is dying down . several mechanisms are proposed that can lead to the color and morphological transformations between galaxy classes in clusters , such as galaxy mergers @xcite , tides by the cluster potential @xcite , and tidal interactions between galaxies @xcite . one of the strongest candidates is the ram - pressure stripping proposed by @xcite . if a cluster galaxy moves through hot intracluster medium ( icm ) , it feels ram - pressure from the icm , which is given by @xmath8 , where @xmath9 is the icm density and @xmath10 is the relative velocity between the galaxy and the icm . if the ram - pressure becomes large enough , the interstellar medium ( ism ) of the galaxy can not be hold by the gravity of the galaxy and is swept away . numerical simulations demonstrate that in a cluster environment , the stripping is likely to occur @xcite . in particular , high - resolution three dimensional numerical simulations show that the ram - pressure stripping is so effective that it removes 100% of the atomic hydrogen content of luminous galaxies within @xmath11 yr @xcite . on the other hand , @xcite investigated the influence of ram - pressure on the star formation activity of a disk galaxy . they found that just before the atomic hydrogen content is stripped , the star formation rate increases at most a factor of 2 , but rapidly decreases on a timescale of @xmath11 yr after the stripping . after the star formation activity , which mainly occurred in the disk , ceases , the galaxy looks like a s0 galaxy in both color and morphology @xcite . hi deficient galaxies and galaxies with no strong emission - lines seen in cluster cores support the theoretical predictions ( e.g. * ? ? ? * ; * ? ? ? although ram - pressure stripping alone does not explain the detailed morphological features of s0 galaxies , such as their large bulge to disk ratios or their conspicuous thick disks @xcite , it may be a principal mechanism of the transformation of spirals with active star formation into s0 galaxies with inactive star formation . however , most of the previous studies dealt with the ram - pressure stripping of a model galaxy in a given cluster with arbitrary initial conditions . moreover , they did not take the evolution of cluster structure into account ; as will be seen in [ sec : model ] , the structure of high - redshift clusters is different from that of nearby clusters even for the same mass . since it affects the icm density , the velocity of the galaxies , and the efficiency of ram - pressure stripping , it must be considered when we compare the theoretical models with observations of high - redshift clusters . in this paper , we investigate ram - pressure stripping in clusters at various redshifts , which grow according to a hierarchical clustering scenario ; the initial position and velocity of galaxies are given by a spherical collapse model of cluster formation . moreover , since a cluster breaks into smaller progenitors as time goes backwards , galaxies in the cluster might have been affected by ram - pressure stripping when they were in the progenitors before the present - day cluster formed . thus , we also consider the ram - pressure stripping of galaxies in these progenitors . since ram - pressure is proportional to the density of icm , the icm distribution of a cluster may be related to the evolution of the cluster galaxies feeling ram - pressure . x - ray observations of nearby clusters show that their icm distributions are generally different from their dark matter distributions . in particular , for low temperature clusters , the distributions of icm are significantly flatter than those of dark matter and the icm fraction in their central regions is small @xcite . a possible explanation of the icm distributions is that the icm has been heated non - gravitationally . in fact , @xcite indicated that the entropy of the icm in the central regions of low - temperature or less massive clusters is higher than can be explained by gravitational collapse alone , although it is not understood what heats the icm ( e.g. supernovae or agn ) and where the icm is heated , that is , outside or inside clusters . heating other than the gravity of a cluster makes the icm distribution flatter and different from the dark matter distribution . thus , we expect that the position where a galaxy suffers from ram - pressure stripping depends on whether the icm of the cluster ( or the gas accreted by the cluster later on ) has been heated non - gravitationally or not . in particular , we expect that the position where ram - pressure stripping occurs is more sensitive to the non - gravitational heating in the past . this is because a cluster breaks into progenitors or less massive clusters as time goes backwards , and because the heat required to explain the observations should have more influence on the icm distributions of the less massive clusters @xcite . therefore , ram - pressure stripping in the progenitors may tell us when the icm of present - day clusters was heated non - gravitationally ; it will be a clue to the heating sources . our paper is organized as follows . in [ sec : model ] we describe our models of the dark matter distribution and the icm distribution within clusters , the ram - pressure stripping of a radially infalling galaxy , and the evolution of cluster progenitors . in [ sec : result ] we give the results of our calculations . we compare them with observations in [ sec : disc ] . conclusions are given in [ sec : conc ] .

we have investigated the ram - pressure stripping of disk galaxies in clusters at various redshifts and in cluster progenitors ; the clusters grow up on a hierarchical clustering scenario . , we find that ram - pressure stripping has more influence on galaxies in more massive clusters . on the other hand , for a given mass , it has more influence on galaxies in the clusters at higher redshifts . while the non - gravitational heating significantly reduces the influence of ram - pressure stripping on galaxies in clusters with mass smaller than @xmath1 , it does not affect the influence in richer clusters . we compare the results with the observations of galaxies in clusters at various redshifts .

we have investigated the ram - pressure stripping of disk galaxies in clusters at various redshifts and in cluster progenitors ; the clusters grow up on a hierarchical clustering scenario . we consider a radially infalling galaxy whose initial position and velocity are given by a spherical collapse model of structure formation . moreover , since observations show that the intracluster medium ( icm ) of nearby clusters is non - gravitationally heated , we study the effect of the non - gravitational heating on the ram - pressure stripping . for a given redshift , we find that ram - pressure stripping has more influence on galaxies in more massive clusters . on the other hand , for a given mass , it has more influence on galaxies in the clusters at higher redshifts . in particular , we predict that in rich clusters at @xmath0 , most of the galaxies are affected by the ram - pressure stripping . while the non - gravitational heating significantly reduces the influence of ram - pressure stripping on galaxies in clusters with mass smaller than @xmath1 , it does not affect the influence in richer clusters . if the icm is heated non - gravitationally at @xmath2 , ram - pressure stripping does not occur at @xmath3 in the progenitors of clusters observed at @xmath4 , because the heat makes the icm fraction of the cluster progenitors small . on the other hand , if the icm is heated non - gravitationally at @xmath5 for the first time , the ram - pressure stripping occurs even at @xmath6 . we compare the results with the observations of galaxies in clusters at various redshifts .

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we have studied ram - pressure stripping of galaxies in clusters and their progenitors . in particular , we pay attention to its dependence on redshift and the mass of clusters . as a model galaxy , we consider a radially infalling disk galaxy ; the initial position and velocity are given by a spherical collapse model of structure formation . since x - ray observations show that the icm of nearby clusters is heated non - gravitationally , we also investigate the effect of the heating on the ram - pressure stripping . our main findings are the following : \1 . for a given redshift , ram - pressure stripping of galaxies is more effective in more massive clusters . this is because the velocity of the radially infalling galaxy increases with the virial mass of the cluster . if ram - pressure stripping transforms spiral galaxies into s0 galaxies , our model is consistent with the observed relation between galaxy populations and cluster luminosities ( or temperatures ) . \2 . for a given mass of clusters , ram - pressure stripping of galaxies in the clusters is more effective at higher redshift . this is because the density of the intracluster medium increases with the redshift . in particular , at @xmath181 , most of the galaxies radially infalling into the centers of rich clusters are affected by ram - pressure stripping . the relatively high fraction of s0 galaxies and the abundance of uv - excess galaxies in rich clusters at @xmath174 may be due to the ram - pressure stripping . the non - gravitational heating reduces the effect of ram - pressure stripping for clusters with @xmath203 at @xmath5 and for those with @xmath204 at @xmath174 . however , for clusters with @xmath205 , it does not have an influence on the effect of ram - pressure stripping . if the icm ( or the gas accreted by a cluster later on ) is heated non - gravitationally at @xmath2 , ram - pressure stripping does not occur in cluster progenitors at @xmath171 , because the heat makes the icm fraction of the cluster progenitors small . on the other hand , if the icm had not been heated non - gravitationally until @xmath5 , ram - pressure stripping occurs even at @xmath6 . i am grateful to t. yamada , m. nagashima , i. tanaka , t. kodama , t. tsuchiya , and d. a. dale for useful discussions and comments . comments from an anonymous referee led to significant improvements in the quality of this paper .

we consider a radially infalling galaxy whose initial position and velocity are given by a spherical collapse model of structure formation . moreover , since observations show that the intracluster medium ( icm ) of nearby clusters is non - gravitationally heated , we study the effect of the non - gravitational heating on the ram - pressure stripping . for a given redshift if the icm is heated non - gravitationally at @xmath2 , ram - pressure stripping does not occur at @xmath3 in the progenitors of clusters observed at @xmath4 , because the heat makes the icm fraction of the cluster progenitors small . on the other hand ,

we have investigated the ram - pressure stripping of disk galaxies in clusters at various redshifts and in cluster progenitors ; the clusters grow up on a hierarchical clustering scenario . we consider a radially infalling galaxy whose initial position and velocity are given by a spherical collapse model of structure formation . moreover , since observations show that the intracluster medium ( icm ) of nearby clusters is non - gravitationally heated , we study the effect of the non - gravitational heating on the ram - pressure stripping . for a given redshift , we find that ram - pressure stripping has more influence on galaxies in more massive clusters . on the other hand , for a given mass , it has more influence on galaxies in the clusters at higher redshifts . in particular , we predict that in rich clusters at @xmath0 , most of the galaxies are affected by the ram - pressure stripping . while the non - gravitational heating significantly reduces the influence of ram - pressure stripping on galaxies in clusters with mass smaller than @xmath1 , it does not affect the influence in richer clusters . if the icm is heated non - gravitationally at @xmath2 , ram - pressure stripping does not occur at @xmath3 in the progenitors of clusters observed at @xmath4 , because the heat makes the icm fraction of the cluster progenitors small . on the other hand , if the icm is heated non - gravitationally at @xmath5 for the first time , the ram - pressure stripping occurs even at @xmath6 . we compare the results with the observations of galaxies in clusters at various redshifts .

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new ccd @xmath0 photometry in the field of the open clusters berkeley26 , czernik27 , melotte72 , ngc2479 and bh37 is reported here . the analysis of the photometric data leads to the following main conclusions : \(i ) once the cluster centres were determined by fitting gaussian distributions to the star counts in the @xmath32 and @xmath33 directions , radial density profiles were produced . \(ii ) cluster cmds cleaned from field star contamination were built by statistically subtracting the number of stars counted in the field cmds . those stars closer in magnitude and colour to the ones in the respective star fields were thus removed . \(iii ) estimates of the cluster ages were obtained for berkeley26 , melotte72 and ngc2479 from both the @xmath42@xmath4 age index and the mai . on the other hand , we outlined possible solutions for cluster fundamental parameters by matching theoretical isochrones , which reasonably reproduce the main cluster features in their cmds . in the case of ngc2479 , the @xmath2 and @xmath3 colour excesses and apparent distance modulus were estimated from the fit of the zams to the colour - colour and magnitude - colour diagrams , respectively .

we indicate possible solutions for the cluster fundamental parameters by matching theoretical isochrones which reasonably reproduce the main cluster features in their cmds . in the case of ngc2479 , the cluster @xmath2 and @xmath3 colour excesses and apparent distance modulus were estimated from the fit of the zero - age main sequence ( zams ) to the colour - colour and colour - magnitude diagrams , respectively . galaxy : open clusters and associations : general - open clusters and associations : individual : berkeley26 - open clusters and associations : individual : czernik27 - open clusters and associations : individual : melotte72 - open clusters and associations : individual : ngc2479 - open clusters and associations : individual : bh37 - galaxy : general - techniques : photometric

we have obtained ccd @xmath0 photometry down to v @xmath1 21.0 for the open clusters berkeley26 , czernik27 , melotte72 , ngc2479 and bh37 . the latter has never been studied before . cluster stellar density profiles were obtained from star counts in appropriate - sized boxes distributed throughout the entire observed fields . based on different measured indices , we estimate the ages of berkeley26 , melotte72 and ngc2479 . on the other hand , we indicate possible solutions for the cluster fundamental parameters by matching theoretical isochrones which reasonably reproduce the main cluster features in their cmds . in the case of ngc2479 , the cluster @xmath2 and @xmath3 colour excesses and apparent distance modulus were estimated from the fit of the zero - age main sequence ( zams ) to the colour - colour and colour - magnitude diagrams , respectively . galaxy : open clusters and associations : general - open clusters and associations : individual : berkeley26 - open clusters and associations : individual : czernik27 - open clusters and associations : individual : melotte72 - open clusters and associations : individual : ngc2479 - open clusters and associations : individual : bh37 - galaxy : general - techniques : photometric

cond-mat9506063

c

we have presented results of the direct numerical calculation of the spectral two point correlation function in metals and at the metal insulator transition . in the metallic regime the results are in very good agreement with the rmt predictions . we have been able to find numerically the altshuler and shklovski regime where the diffusion is power - like . at the metal insulator transition , the short range behavior of the two point correlation function is clearly modified . the short range part of the correlation is weaker and is followed by a power law behavior with an exponent which is consistent with the picture of anomalous diffusion . at the transition , @xmath34 is size independent . this clearly refutes a prediction@xcite that the power law contribution should decrease as @xmath194 . these short range correlations give rise to a non trivial linear term in the spectral rigidity @xmath19 in addition to a power law term which is the signature of the long range correlations . by integration of @xmath34 , we conclude that the prefactor of this linear term may be much smaller than previously anticipated and may even be zero . recently , different models of interpolating ensembles of matrices have been proposed @xcite . our result puts a constraint on the possible choice of ensembles since they should produce a form factor which varies at small times like eq.[kdet ] . acknowledgments : we have benefitted from useful discussions or correspondance with e. hofstetter , v. kravtsov , i. lerner , m.l . mehta and b. shklovski . numerical simulations were performed on the cray computer of idris ( institut du dveloppement et des ressources en informatique scientifique , orsay ) . e. p. wigner , ann . math . * 53 * , 36 ( 1951 ) ; _ ibid _ * 62 * , 548 ( 1955 ) ; _ ibid _ * 65 * , 203 ( 1957 ) ; _ ibid _ * 67 * , 325 ( 1958 ) ; f.j . dyson , j. math . phys . * 3 * , 140 ( 1962 ) ; f.j . dyson and m. l. mehta , j. math . phys . * 4 * , 701 ( 1963 ) ; t. a. brody , j. flores , j. b. french , p. a. mello , a. pandey and s. s. m. wong , rev . 53 * , 385 ( 1981 ) . o.bohigas , in _ chaos and quantum physics . proceedings of the les - houches summer school . session lii _ , ed . by m.j.giannoni et.al ( north holland , amsterdam , 1991 ) , p.91 y.v.fyodorov , phys.rev.lett . * 73 * , 2688 ( 1994 ) y.v.fyodorov , a.d.mirlin , jetp lett . * 60 * ( dec 1994 ) , and submitted to phys.rev.b j. l. pichard et b. shapiro , j. phys . i , france , * 4 * , 623 ( 1994 ) . m. m. moshe , h. neuberger et b. shapiro , phys . lett . * 73 * , 1497 ( 1994 ) . c. m. canali , m. wallin , v. e. kravtsov , preprint 1994 . c. blecken , y. chen et k. a. muttalib , j. phys . * a * : math . * 27 * , l563 ( 1994 ) .

we have studied numerically the spectral correlations in a metallic phase and at the metal - insulator transition . we have calculated directly the two - point correlation function of the density of states @xmath0 . in the metallic phase , june 14 , 1995

we have studied numerically the spectral correlations in a metallic phase and at the metal - insulator transition . we have calculated directly the two - point correlation function of the density of states @xmath0 . in the metallic phase , it is well described by the random matrix theory ( rmt ) . for the first time , we also find numerically the diffusive corrections for the number variance @xmath1 predicted by altshuler and shklovski . at the transition , at small energy scales , @xmath2 starts linearly , with a slope larger than in a metal . at large separations @xmath3 , it is found to decrease as a power law @xmath4 , in good agreement with recent microscopic predictions . at the transition , we have also calculated the form factor @xmath5 , fourier transform of @xmath2 . at large @xmath6 , the number variance contains two terms @xmath7 where @xmath8 is the limit of the form factor for @xmath9 . june 14 , 1995

1404.5883

c

in this paper we studied the dynamical symmetry breaking in models consisting of a fermion field and a self - interacting scalar field with the yukawa interaction between the two fields in the one - loop approximation . we believe that the dynamical symmetry breaking as exhibited by these models can help to analyze similar phenomena in more realistic models . the models are considered in two and four spacetime dimensions . we showed that each models has two phases , one with the preserved symmetry and the other with the broken symmetry . we conclude that both models have a phase transitions as a function of the coupling constants . in four spacetime dimensions , we obtain an analytic expression for the chiral condensate in the limit of a massless scalar field . the two - dimensional case was investigated numerically by solving of the algebraic equation for the scalar field . buividovich , m.n . chernodub , e.v . luschevskaya and m.i . polikarpov , phys . lett . * b682 * , 484 ( 2010 ) ; v.v . braguta , p.v . buividovich , t. kalaydzhyan , s.v . kuznetsov , m.i . polikarpov , arxiv : 1011.3795v3 [ hep - lat ] . d. ebert , n.v . gubina , k.g . klimenko , s.g . kurbanov and v. ch . zhukovsky , phys . rev . * d84 * , 025004 ( 2011 ) ; d. ebert . khunjua , k.g . klimenko and v. ch . zhukovsky , arxiv : 1306.4485v2 [ hep - th ] . g. thooft , nucl . phys . * b75 * , 461 ( 1974 ) ; a. zhitnitsky , phys . rev . * d53 * , 5821 ( 1996 ) ; l.ya . glozman , v.k . sazonov , m. shifman , r.f . wagenbrunn , arxiv : 1201.5814v1 [ hep - th ] ; s. bellucci , e.r . bezerra de mello , a.a . saharian , arxiv : 1312.1686v1[hep - th ] . y. nambu and g. jona - lasinio , phys . rev . * 122 * , 345 ( 1961 ) . gross and a. neveu , phys . rev . * d10 * , 3235 ( 1974 ) . v.g . ksenzov and a.i . romanov , phys . nucl . * 76 * , 534 ( 2013 ) ; arxiv : 1204.3051v2 [ hep - th ] . a.m. polyakov , pisma zh . * 12 * , 381 ( 1970 ) .

we investigate a class of models with a massless fermion and a self - interacting scalar field with the yukawa interaction between these two fields . the models considered are formulated in two and four spacetime dimensions and possess a discrete symmetry . we calculate the chiral condensates are calculated in the one - loop approximation . we show that the models have a phase transitions as a function of the coupling constants .

we investigate a class of models with a massless fermion and a self - interacting scalar field with the yukawa interaction between these two fields . the models considered are formulated in two and four spacetime dimensions and possess a discrete symmetry . we calculate the chiral condensates are calculated in the one - loop approximation . we show that the models have a phase transitions as a function of the coupling constants .

cond-mat0510187

i

recently , in a very interesting paper , zheng _ et al . , _ @xcite have studied the collective directed transport of symmetrically coupled lattices in symmetric periodic potentials . they show that under the action of an external wave , that breaks the spatiotemporal symmetry and introduces inhomogeneities of the lattice , a net unidirectional current can be observed . apparently the current originates from the collaboration of the lattice and the wave ( amplitude , frequency , and phase shifts ) . the study of directed transport of particles is very important in the physics of molecular motors @xcite , vortex dynamics in superconductors @xcite , josephson junction lattices @xcite , nanotechnology @xcite and many other systems . many studies have been dedicated to directed transport in spatiotemporal systems @xcite . these include systems with deterministic ac drives and stochastic forces @xcite . very important are models composed of a symmetrically coupled lattice in a symmetric potential field , which is driven by an external wave @xcite . the equation studied by zheng _ et al . , _ @xcite is the following : @xmath1 this is a frenkel kontorova model driven by the wave @xmath2 . the average current introduced by them @xmath3 was shown to be nonzero for certain values of the parameters of the system . we wish to re - state this problem in terms of the directed motion of solitons . solitons are considered as particles in many systems . moreover , in many systems , the solitons are charge carriers @xcite . so it is very important to study the directed transport of these objects . in the present paper we investigate the generalized klein gordon equation : @xmath4 where @xmath5 , @xmath6 is a symmetric potential with , at least , two minima at @xmath7 , @xmath8 , and a maximum at @xmath9 ( @xmath10 ) ; @xmath11 describes an external wave moving with velocity @xmath12 . both the sine gordon and @xmath13 equations are particular cases of equation ( [ eq2:kg ] ) . the sine gordon equation is a continuous relative of eq . ( [ eq1:fk ] ) . these equations possess important applications in condensed matter physics . for instance , in solid sate physics , they describe domain walls in ferromagnets and ferroelectric materials , dislocations in crystals , charge density waves , interphase boundaries in metal alloys , fluxons in long josephson junctions and josephson transmission lines , etc @xcite . our initial condition will be a kink soliton whose center of mass is situated at rest in the point @xmath14 . we will show that the transport of the soliton by the wave depends on the shape of the wave and the parameters of the system . we will also investigate the stabilization and transport of bubbles using external perturbations in @xmath0systems as the following @xmath15 we will also present the results of real experiments with laser induced bubbles in liquids . the bubbles can be trapped , stabilized and transported by a laser beam of relatively low power . we will show that the directed transport of solitons and bubbles are related . for both phenomena some conditions for the external perturbations must be satisfied .

we investigate generalized soliton bearing systems in the presence of external perturbations . we also investigate the stabilization and transport of bubbles using external perturbations in @xmath0systems . we also present the results of real experiments with laser induced vapor bubbles in liquids .

we investigate generalized soliton bearing systems in the presence of external perturbations . we show the possibility of the transport of solitons using external waves , provided the waveform and its velocity satisfy certain conditions . we also investigate the stabilization and transport of bubbles using external perturbations in @xmath0systems . we also present the results of real experiments with laser induced vapor bubbles in liquids .

hep-ph0510071

r

an essential feature of the @xmath3-classification scheme is to have the static @xmath9 symmetry for light @xmath18 quarks confined inside hadrons . the degree of freedom on the @xmath19-spin , being indispensable for covariant description of spin @xmath20 particles , offers a basis to define the rule of chiral transformation for quark - composite hadrons . since we have the @xmath19-spin degree of freedom , which is discriminated by the eigenvalues of @xmath21 , @xmath22 , in addition to the ordinary @xmath23-spin , the ground states of light - quark @xmath24 mesons are composed of eight @xmath25 multiplets with respective @xmath26 quantum numbers , two pseudoscalars @xmath27 , two scalars @xmath28 , two vectors @xmath29 , and two axial - vectors @xmath30 ( n and e denoting `` normal '' and `` extra '' ) , where each n ( e ) even - parity multiplet is the chiral partner of the corresponding n ( e ) odd - parity multiplet and they form linear representations of the chiral symmetry . since the eigenstates only with the @xmath21-eigenvalue @xmath31 are taken for heavy quarks , we have for heavy - light meson systems two heavy - spin multiplets , @xmath32 and @xmath33 , which are the chiral partner each other , while for heavy - heavy meson systems we have the same @xmath32-spin multiplets as in the conventional nonrelativistic quark model . we try to assign some of the observed mesons to the predicted @xmath24 multiplets , resorting to their @xmath26 quantum numbers and masses . the observed meson data are taken from the particle data group 2004 edition@xcite , except for the following mesons : * @xmath34 . there are several experimental indications of the existence of the @xmath34 reported by the obelix@xcite and lass@xcite collaborations , and others . particle listings and the `` note on the @xmath35 '' in @xcite . ] * @xmath36 . the existence of @xmath36 is claimed in the analysis of the @xmath37 cross section by the snd collaboration@xcite . we accept the existence of these vector mesons as true@xcite . the resulting assignments , though some of them are ambiguous , are shown in table 1 . here we make some comments on these assignments . 1 . the light scalar mesons @xmath38 are assined to the @xmath39-nonet as a chiral partner of the @xmath40-meson @xmath41-nonet . the low - mass vector mesons @xmath42 are assined to the @xmath43-nonet as a chiral partner of the @xmath44-nonet @xmath45 @xmath46 @xmath47 . the axial - vector mesons @xmath48 are assined to the @xmath49-nonet as a chiral partner of the @xmath50-meson @xmath51-nonet . the recent observed mesons @xmath52 are assined to the @xmath33 multiplet as a chiral partner of the @xmath32 multiplet @xmath53@xcite . these newly observed mesons , together with the @xmath23-meson nonet , are the best candidates for the hadronic states with @xmath54 whose existence is expected in the @xmath3 scheme . it is noted that the normal ( n ) and extra ( e ) states with the same @xmath26 generally mix together due to the spontaneous as well as explicit breaking of chiral symmetry and some other mechanism .

address = department of engineering science , junior college funabashi campus , nihon university , funabashi 274 - 8501 , japan address = department of engineering science , junior college funabashi campus , nihon university , funabashi 274 - 8501 , japan address = research institute of science and technology , college of science and technology , nihon university , tokyo 101 - 8308 , japan

we investigate the chiral mass splitting of parity - doubled @xmath0 states for @xmath1 and @xmath2 meson systems in the @xmath3-classification scheme of hadrons , using the linear sigma model to describe the light - quark pseudoscalar and scalar mesons together with the spontaneous breaking of chiral symmetry , and consequently predict the masses of as - yet - unobserved @xmath4 @xmath5 mesons . we also mention some indications of their existence in the recent published data from the belle and babar collaborations . address = department of engineering science , junior college funabashi campus , nihon university , funabashi 274 - 8501 , japan address = department of engineering science , junior college funabashi campus , nihon university , funabashi 274 - 8501 , japan address = research institute of science and technology , college of science and technology , nihon university , tokyo 101 - 8308 , japan

cond-mat0211690

r

we begin our investigation by taking the hubbard-@xmath23 term to be infinitely large that is , to work in the sub - space of states with no double occupation . our hilbert space is thus six - dimensional , and we use the states shown in fig.[basis ] as a basis . we show in fig.[uinf ] the time - dependent number occupation of the four sites at two different values of @xmath46 , in both cases using state @xmath74 as the initial state , and setting the ac frequency to @xmath75 . in fig.[uinf]a @xmath46 has a value of 100.0 , and it can be clearly seen that the electrons perform driven rabi oscillations between the left side of the qd and the right . accordingly , the occupation number of the sites varies continuously between zero and one . in fig.[uinf]b , however , we see that changing the electric potential to a value of @xmath76 produces dramatically different behavior . the occupations of sites a and d only vary slightly from unity , while sites b and c remain essentially empty throughout the time - evolution . only a small amount of charge can transfer per period of the driving field between the left and right sides of the system , producing the small spikes visible in this figure . the amplitude of these features is extremely small , however , indicating that the tunneling between left and right sides has been almost totally destroyed . infinite , @xmath77 and @xmath78 : ( a ) electric potential , e = 100.0 ( b ) e = 115.7 . solid line indicates the occupation of sites a and d , the dotted line the occupation of sites b and c. ] to confirm that cdt is occurring , we present in fig.[uinf_floq ] a comparison of the amplitude of the oscillations of @xmath79 with the quasi - energy spectrum , as a function of the electric potential @xmath46 . similarly to the double qd system , we can see in fig.[uinf_floq]a that the quasi - energies have two different regimes of behavior . the first of these is the weak - field regime , @xmath80 , at which the driving field does not dominate the dynamics . in this regime the quasi - energy spectrum , and correspondingly , the amplitude of oscillations shows little structure . the second regime occurs at strong values of potential , @xmath81 , for which the quasi - energy spectrum clearly shows a sequence of close approaches . in fig.[uinf_floq]c we show an enlargement of one of these approaches which reveals it to be an _ avoided crossing_. employing the perturbative method described in section [ method ] demonstrates that the two quasi - energies involved in these avoided crossings are described by @xmath82 , where @xmath83 is equal to @xmath84 . we may thus again think of @xmath83 as signifying the number of photons the system needs to absorb to overcome the coulomb repulsion between the electrons occupying neighboring sites . the results in fig.[uinf_floq]b and fig.[uinf_floq]d clearly show that the locations of the avoided crossings correspond exactly to quenching of the oscillations in @xmath79 , and so confirm that cdt indeed occurs at these points . infinite , @xmath77 and @xmath78 : circles = exact results , lines = perturbative solution [ @xmath85 . ( b ) amplitude of oscillation of the occupation of site a. ( c ) detail of quasi - energy spectrum , showing an avoided crossing . ( d ) detail of amplitude of oscillations . ] we now take the most general case , and consider the competition between the @xmath51 and @xmath70 terms . setting @xmath51 to a finite value means that the four doubly - occupied basis states are no longer energetically excluded from the dynamics , and accordingly we must take the full ten - dimensional basis set . although it is difficult to obtain precise estimates for the values of parameters of the effective hamiltonian , it is clear that in general @xmath86 . accordingly we choose the parameters @xmath87 to separate the two energy - scales widely for our investigation . we again set the frequency of the ac field to @xmath78 , and in fig.[u160_1]a we show the quasi - energy spectrum obtained by sweeping over the field strength . it is immediately clear from this figure that for electric potentials @xmath53 the form of the spectrum is extremely similar to the infinite-@xmath51 case . performing perturbation theory confirms that , as in the previous case , the behavior of the quasi - energies is given by @xmath82 where @xmath88 . we show in fig.[u160_1]b the amplitude of the oscillations of @xmath79 when the system is initialized in state @xmath74 , which demonstrates that at the locations of the avoided crossings the tunneling parallel to the field is again quenched . and @xmath89 , @xmath78 : circles = exact results , lines = perturbative solution [ @xmath90 . ( b ) amplitude of oscillation of the occupation of site a , with ( 6 ) as the initial state . ] when the electric potential exceeds the value of @xmath51 , however , new structure appears in the quasi - energy spectrum . a group of four quasi - energies , that for weaker fields cluster around zero , become `` excited '' and make a sequence of avoided crossings as the field strength is increased . perturbation theory predicts that these high - field quasi - energies are given by @xmath91 , where @xmath92 , and thus these avoided crossings arise when the absorption of @xmath93 photons equates to the electrostatic energy difference between the two electrons being on neighboring sites , and doubly - occupying one site . this then indicates that this structure arises from the coupling of the ac field to the doubly - occupied states . to probe this phenomenon , we time - evolve the system from an initial state consisting of _ two _ electrons occupying site a. in fig.[u160_2]b it can be seen that for electric potentials weaker than @xmath51 the amplitude of the oscillations in @xmath79 remains small , and shows little dependence on the field . as the potential exceeds @xmath51 , this picture changes , and the ac field drives large oscillations in @xmath79 , and in fact mainly forces charge to oscillate between sites a and b. at the high - field avoided crossings , however , the tunneling between a and b is suppressed , which shuts down this process . instead , the only time - evolution that the system can perform consists of _ undriven _ rabi oscillations between sites a and d , perpendicular to the field . as these oscillations are undriven they have a much longer time - scale than the forced dynamics , and thus during the interval over which we evolve the system the occupation of a only changes by a small amount , producing the very sharp minima visible in fig.[u160_2]b , centered on the roots of @xmath94 . and @xmath89 , @xmath78 : circles = exact results , lines = perturbative solution [ @xmath95 . ( b ) amplitude of oscillation of the occupation of site a , with site a doubly - occupied as the initial state . ] as the tunneling perpendicular to the field is undriven , it is straightforward to evaluate the time evolution of the initial state , if we assume that the left side of the qd is completely decoupled from the right side . the occupation of sites a and d is then given by : @xmath96 where @xmath97 . in fig.[decohere ] we display the occupations of sites a and d as a function of time , for two values of electric potential . at the first value , @xmath98 , tunneling between the left and right sides of the qd is not quenched , and accordingly the occupation of the two sites varies rapidly between zero and two as the electrons are driven by the ac field around the system . the second value , @xmath99 , corresponds to the first high - field avoided crossing . it can be clearly seen that the charge oscillates between sites a and b , with a frequency of @xmath100 . these rabi oscillations are damped , however , indicating that the isolation between the left and right sides of the qd is not perfect . in this sense we can regard the two sites @xmath101 and @xmath102 as providing an environment , causing the quantum system composed of sites a and d to slowly decohere in time . when the tunneling between the left and right sides of the qd is strong , for example at @xmath98 , this decoherence occurs very rapidly . by moving to an avoided crossing , however , and suppressing the tunneling , the rate of mixing between the two sides of the qd can be considerably reduced , and is just limited by the separation in energy between the two quasi - energies . tuning the parameters of the driving field therefore gives us a simple and controllable way to investigate how a two - electron wavefunction can decohere in a qd . and @xmath89 system for @xmath78 : ( a ) electric potential , e = 200.0 ( no cdt ) ( b ) e = 185.8 ( cdt ) . thick solid line indicates the occupation of site a , the thick dotted line the occupation of site d. dotted lines in ( b ) show the rabi oscillations of the isolated two - site system , eq.[rabi ] . ]

the schrdinger equation in time reveals that for certain values of the strength and frequency of the field the tunneling between the dots can be destroyed , thus allowing the correlated two - electron states to be manipulated . we then consider the case of confining the electrons to a single two - dimensional quantum dot in the limit of low particle - density . in this system , we investigate how the ac field can drive the dynamics of the wigner states @xcite . as before , we find that the ac field can be used to control the tunneling between various charge configurations , and we relate this to the presence of avoided crossings in the floquet quasi - energy spectrum . these results hold out the exciting possibility of using ac fields to control the time evolution of entangled states in mesoscopic devices , which has great relevance to the rapidly advancing field of quantum information processing .

we investigate the dynamics of interacting electrons confined to two types of quantum dot system , when driven by an external ac field . we first consider a system of two electrons confined to a pair of coupled quantum dots @xcite by using an effective two - site model of hubbard - type . numerically integrating the schrdinger equation in time reveals that for certain values of the strength and frequency of the field the tunneling between the dots can be destroyed , thus allowing the correlated two - electron states to be manipulated . we then show how floquet theory @xcite can be used to predict the field parameters at which this effect occurs . we then consider the case of confining the electrons to a single two - dimensional quantum dot in the limit of low particle - density . in this system the electrons form strongly correlated states termed wigner molecules , in which the coulomb interaction causes them to become highly localised in space . again using an effective model of hubbard - type , we investigate how the ac field can drive the dynamics of the wigner states @xcite . as before , we find that the ac field can be used to control the tunneling between various charge configurations , and we relate this to the presence of avoided crossings in the floquet quasi - energy spectrum . these results hold out the exciting possibility of using ac fields to control the time evolution of entangled states in mesoscopic devices , which has great relevance to the rapidly advancing field of quantum information processing .

cond-mat0211690

c

in this work we have studied the interplay between coulomb interactions and an ac driving field in two different configurations of qds . for the case of the double qd system we have found that the system presents two different types of behavior , depending on whether the driving field dominates the interaction energy . for weak driving , we have found the surprising result that a suitable ac field can nonetheless freeze the time - evolution of a doubly - occupied qd _ despite _ the coulomb interaction , and that this can be understood by means of an effective two - level model . at high field strengths the system is only driven strongly by the field at frequencies for which an integer number of quanta , @xmath83 , is equal to the interaction energy . when this condition is satisfied cdt is again able to occur at certain well - defined parameters of the field , and by using floquet theory we have shown that these points correspond to the roots of @xmath103 . strong electronic correlations allowed us to use an effective lattice model of just four sites to treat the square qd , by taking advantage of the natural discretization of the system in a wigner molecule state . in the effective model , the inter - electron coulomb interaction is described by two parameters , @xmath51 and @xmath70 , and the dynamics of the system consists essentially of tunneling from corner to corner , along the perimeter of the qd . we find again that when the frequency of the driving field is in resonance with the coulomb gap ( that is , @xmath104 or @xmath105 ) charge is able to circulate freely around the system , except at sharply defined field strengths at which tunneling parallel to the field is destroyed . floquet theory again proved an excellent tool to understand this behavior , and revealed that these points correspond to the roots of @xmath94 . we have thus shown that ac - fields may not only be used as a spectroscopic tools to probe the electronic structure of qd systems , but can also be used to dynamically control the time - evolution of the system . possible applications of cdt range from stabilising the leakage of trapped electrons in physical realisations of quantum bits , to acting as `` electron tweezers '' by destroying or restoring tunneling between regions of a mesoscopic device . the tunability of the cdt effect , and its ability to discriminate between doubly - occupied and singly - occupied states , make it an excellent means for rapid manipulation of the dynamics of strongly correlated electrons in mesoscopic systems .

we investigate the dynamics of interacting electrons confined to two types of quantum dot system , when driven by an external ac field . the electrons form strongly correlated states termed wigner molecules , in which the coulomb interaction causes them to become highly localised in space . again using an effective model of hubbard - type

we investigate the dynamics of interacting electrons confined to two types of quantum dot system , when driven by an external ac field . we first consider a system of two electrons confined to a pair of coupled quantum dots @xcite by using an effective two - site model of hubbard - type . numerically integrating the schrdinger equation in time reveals that for certain values of the strength and frequency of the field the tunneling between the dots can be destroyed , thus allowing the correlated two - electron states to be manipulated . we then show how floquet theory @xcite can be used to predict the field parameters at which this effect occurs . we then consider the case of confining the electrons to a single two - dimensional quantum dot in the limit of low particle - density . in this system the electrons form strongly correlated states termed wigner molecules , in which the coulomb interaction causes them to become highly localised in space . again using an effective model of hubbard - type , we investigate how the ac field can drive the dynamics of the wigner states @xcite . as before , we find that the ac field can be used to control the tunneling between various charge configurations , and we relate this to the presence of avoided crossings in the floquet quasi - energy spectrum . these results hold out the exciting possibility of using ac fields to control the time evolution of entangled states in mesoscopic devices , which has great relevance to the rapidly advancing field of quantum information processing .

1610.00390

i

the thermal hall effect ( the ) is a heat analog of the hall effect , namely , the heat current flows perpendicular to a temperature gradient when the time - reversal symmetry is broken . recently , the the has been experimentally studied in ferromagnetic metals @xcite , ferromagnetic insulators @xcite , and frustrated magnets in a magnetic field @xcite . in ferromagnetic metals @xcite , the the is utilized in order to investigate effects of inelastic scattering on the anomalous hall effect ( ahe ) . according to the wiedemann - franz law , the lorenz ratio @xmath1 coincides with the universal lorenz number @xmath2 at @xmath3 , but decreases as temperature increases and inelastic scattering dominates elastic scattering . here @xmath4 and @xmath5 are the electric and thermal ( hall ) conductivities , respectively , and @xmath0 is temperature . therefore the lorenz ratio is a quantitative indicator of inelastic scattering . in ferromagnetic insulators @xcite and frustrated magnets @xcite , the the is a powerful probe of chargeless spin excitations . further experimental progress in the the is expected in the future . theoretically , it is difficult to calculate the thermal hall conductivity owing to the fundamental reasons below . first , the kubo formula is justified by introducing luttinger s gravitational potential since a temperature gradient is not mechanical but statistical force @xcite . second , the heat magnetization correction to the kubo formula is necessary because the heat current as well as the density matrix is perturbed by a gravitational potential @xcite . once the berry - phase formula has been established @xcite , we can easily calculate the thermal hall conductivity in the clean noninteracting limit . however , as mentioned above , it is highly desired to calculate the thermal hall conductivity in disordered or interacting systems . the formula derived in the celebrated paper by smrka and steda , who first pointed out the necessity of the magnetization correction , can be applied to generic disordered systems in principle @xcite , but not easily in practice . practically , we take into account disorder or interactions by a perturbation theory , e.g. , feynman diagrams . in this context , the ordinary hall effect in disordered metals was studied with feynman diagrams @xcite . recently , we found a gravitational vector potential by gauging the time translation symmetry and derived the keldysh formalism in curved spacetime @xcite . with this formalism , we can calculate the kubo formula and the heat magnetization in disordered or interacting systems within a perturbation theory . in this paper , we first apply the keldysh formalism in curved spacetime to a three - dimensional disordered weyl ferromagnet , which is known to exhibit the ahe . the main purpose is to show the wiedemann - franz law by a practical perturbation theory with respect to the impurity strength . we take nonmagnetic impurities into account within the self - consistent @xmath0-matrix approximation and calculate @xmath4 and @xmath6 on an equal footing . we begin with brief reviews of gauging the time translation symmetry and the keldysh formalism in curved spacetime . the details of calculation are given in appendices . this paper serves as the first step towards a unified theory of the ahe at finite temperature , in which we should take into account both disorder and interactions . before going to the main part , let us review some theoretical aspects of the ahe @xcite . the ahe occurs in ferromagnets with spin - orbit coupling . in the first microscopic theory by karplus and luttinger @xcite , the ahe was attributed to the anomalous velocity , which is now understood as the berry curvature @xcite . since this mechanism works in the absence of disorder and depends only on the band structure , leading to @xmath7 , it is called the intrinsic mechanism . soon later , it was revealed that the skew scattering , i.e. , the antisymmetric part of the transition probability due to disorder , also gives rise to the ahe @xcite . an important consequence of the skew - scattering mechanism is @xmath8 . another mechanism due to disorder was proposed by berger @xcite . this side - jump mechanism results in @xmath7 , which is the same as the intrinsic mechanism . the most systematic way to deal with all these mechanisms on an equal footing is based on the keldysh formalism @xcite . one important advantage of this formalism is that we can go beyond a finite - order perturbation theory with respect to the impurity strength with preserving the gauge invariance . by using this formalism , some authors investigated a two - dimensional disordered rashba ferromagnet within the self - consistent @xmath0-matrix approximation and found the crossover between the superclean and moderately dirty regimes , where the skew - scattering and intrinsic contributions are dominant , respectively @xcite . we also note that the nontrivial scaling relation @xmath9 was found in the dirty regime @xcite . let us also review three - dimensional weyl semimetals @xcite which we investigate in this paper . weyl semimetals have pairs of weyl nodes at which two bands touch each other . typically , weyl semimetals are realized from dirac semimetals by breaking the time - reversal @xcite or inversion symmetry @xcite . in particular , weyl semimetals without the time - reversal symmetry exhibit the ahe @xcite . when the fermi level is sufficiently close to weyl nodes , the ahe is purely intrinsic @xcite , which results from chiral anomaly @xcite . on the other hand , when the fermi level is away from weyl nodes , the extrinsic mechanisms due to disorder can be relevant . in this paper , we mean such doped weyl semimetals without the time - reversal symmetry by weyl ferromagnets because we are interested in both the extrinsic and intrinsic mechanisms of the ahe and the . although the the in weyl ferromagnets was studied with the semiclassical boltzmann theory @xcite , we go beyond the relaxation time approximation used in the literature . hereafter we assign the latin ( @xmath10 ) and greek ( @xmath11 ) alphabets to locally flat and global coordinates , respectively . we follow the einstein convention , which implies summation over the spacetime dimension @xmath12 when an index appears twice in a single term . the minkowski metric is taken as @xmath13 . the planck constant and the charge are denoted by @xmath14 and @xmath15 , respectively , and the speed of light and the boltzmann constant are put to @xmath16 . the upper or lower signs in equations correspond to boson or fermion .

in particular , we calculate the anomalous thermal hall conductivity , which consists of the kubo formula and the heat magnetization , without relying on the wiedemann - franz law . we take nonmagnetic impurities into account within the self - consistent @xmath0-matrix approximation and reproduce the wiedemann - franz law for the extrinsic fermi - surface and intrinsic fermi - sea terms , respectively . this is the first step towards a unified theory of the anomalous hall effect at finite temperature , where we should take into account both disorder and interactions .

we investigate the electric and thermal transport properties in a disordered weyl ferromagnet on an equal footing by using the keldysh formalism in curved spacetime . in particular , we calculate the anomalous thermal hall conductivity , which consists of the kubo formula and the heat magnetization , without relying on the wiedemann - franz law . we take nonmagnetic impurities into account within the self - consistent @xmath0-matrix approximation and reproduce the wiedemann - franz law for the extrinsic fermi - surface and intrinsic fermi - sea terms , respectively . this is the first step towards a unified theory of the anomalous hall effect at finite temperature , where we should take into account both disorder and interactions .

1201.2511

i

observational data coming from the type ia supernovae ( sneia ) surveys , large scale structure ( lss ) , and cosmic microwave background ( cmb ) anisotropy spectrum indicate that the expansion of our present universe is accelerating rather than slowing down @xcite . this cosmic acceleration can not be explained by the four known fundamental interactions in the standard models , which is the greatest challenge today in the modern physics . the proposals that have been put forward to explain this observed phenomenon can basically be classified into two categories . one is to assume that in the framework of einstein s general relativity ( gr ) , an exotic component with negative pressure called dark energy ( de ) is necessary to explain this observed phenomena . for a good review on the dynamics of different de models see @xcite and references therein . another alternative to account for the current accelerating cosmic expansion is to modify gr theory . the well - known modified gravity theories are , for examples , @xmath4 theory , scalar - tensor theory ( including brans - dicke theory ) , braneworld scenarios ( such as dgp , rsi and rsii ) , @xmath5 theory ( @xmath6 is the gauss - bonett term ) , hoava - lifshitz theory , modified newtonian dynamics ( mond ) , and so forth . for some relevant reviews see @xcite . recently , a new modified gravity theory namely the so - called @xmath0 theory @xcite-@xcite was proposed to describe the present accelerating expansion of the universe without resorting to de . it is a generalization of the teleparallel gravity ( tg ) @xcite by replacing the so - called torsion scalar @xmath3 with @xmath0 . tg was originally developed by einstein in an attempt of unifying gravity and electromagnetism . the basic variables in tg are tetrad fields @xmath7 , where the weitzenbock connection rather than the levi - civita connection was used to define the covariant derivative . as a result , the spacetime has no curvature but contains torsion . a vector @xmath8 in tg is parallel transported along a curve if its projection @xmath9 remains constant , this is the so - called teleparallelism . the main advantage of @xmath0 theory is that its field equations are the second order which are remarkably simpler than the fourth order equations of @xmath4 theory @xcite . the other interesting issue in modern cosmology is the thermodynamical description of the accelerating universe driven by de or modified gravity . it was shown that by applying the first law of thermodynamics ( clausius relation ) @xmath10 to the apparent horizon @xmath11 , the friedmann equation in the einstein gravity can be derived if we take the hawking temperature @xmath12 and the entropy @xmath13 on the apparent horizon , where @xmath14 is the area of the horizon @xcite . here , @xmath15 is the amount of energy flow through the fixed apparent horizon . the equivalence between the first law of thermodynamics and the friedmann equation was also found for gravity with gauss - bonnet term , the lovelock gravity theory and the braneworld scenarios @xcite . note that in the thermodynamics of the apparent horizon in the einstein gravity , the geometric entropy is assumed to be proportional to its horizon area , @xmath13 @xcite . however , this definition is changed for other modified gravity theories . for instance , the geometric entropy in @xmath4 gravity is given by @xmath16 @xcite , where the subscript @xmath17 denotes a derivative with respect to the curvature scalar r. in @xmath0 gravity , it was shown that when @xmath18 is small , the first law of black hole thermodynamics is satisfied approximatively and the entropy of horizon is @xmath19 @xcite , where the subscript @xmath3 denotes a derivative with respect to the torsion scalar @xmath3 . besides examining the validity of the thermodynamical interpretation of gravity by expressing the gravitational field equations into the first law of thermodynamics in different spacetimes , it is also of great interest to investigate the validity of the generalized second law ( gsl ) of thermodynamics in the accelerating universe @xcite-@xcite . the gsl of thermodynamics like the first law is an accepted principle in physics . here , our aim is to investigate the gsl of thermodynamics in the framework of @xmath0 gravity for a spatially flat friedmann - robertson - walker ( frw ) universe filled with the pressureless matter . to do this , in section 2 , we briefly review the @xmath0 gravity . in section 3 , we investigate the gsl of thermodynamics on the dynamical apparent horizon with the hawking temperature . in section 4 , for two viable @xmath0 models we first calculate the effective equation of state and deceleration parameters . then , the null and strong energy conditions are investigated . also the viability of both models is checked by cosmography . finally , the validity of the gsl is examined . section 5 is devoted to conclusions .

we investigate the validity of the generalized second law ( gsl ) of gravitational thermodynamics in the framework of @xmath0 modified teleparallel gravity . but in the future , the gsl is violated for the special ranges of the torsion scalar @xmath3 . = 16truecm = 23truecm = -1.3truecm = -2truecm = 1.20 cm = 1.60 cm * keywords : * cosmology of theories beyond the sm , modified gravity

we investigate the validity of the generalized second law ( gsl ) of gravitational thermodynamics in the framework of @xmath0 modified teleparallel gravity . we consider a spatially flat frw universe containing only the pressureless matter . the boundary of the universe is assumed to be enclosed by the hubble horizon . for two viable @xmath0 models containing @xmath1 and @xmath2 , we first calculate the effective equation of state and deceleration parameters . then , we investigate the null and strong energy conditions and conclude that a sudden future singularity appears in both models . furthermore , using a cosmographic analysis we check the viability of two models . finally , we examine the validity of the gsl and find that for both models it is satisfied from the early times to the present epoch . but in the future , the gsl is violated for the special ranges of the torsion scalar @xmath3 . = 16truecm = 23truecm = -1.3truecm = -2truecm = 1.20 cm = 1.60 cm * keywords : * cosmology of theories beyond the sm , modified gravity

0808.2813

c

the interplay between the evolution of bhs and the hierarchical build - up of galaxies appears as scaling relations between the masses of bhs and global properties of their hosts such as the bh mass vs. bulge velocity dispersion - the @xmath126 relation and the bh mass vs. bulge luminosity @xmath127 relation . the low bh mass end of this relation has recently been probed by ferrarese et al . ( 2006 ) in an acs survey of the virgo cluster galaxies . they find that galaxies brighter than @xmath128 host a supermassive central bh whereas fainter galaxies host a central nucleus , referred to as a central massive object ( cmo ) . ferrarese et al . report that a common @xmath129 relation leads smoothly down from the scaling relations observed for more more massive galaxies . extrapolating observed scaling relations to higher bh masses to the umbh range , we predict that these are likely hosted by the massive , high luminosity , central galaxies in clusters with large velocity dispersions . the velocity dispersion function of early - type galaxies measured from the sdss points to the existence of a high velocity dispersion tail with @xmath130 ( bernardi et al . if the observed scaling relations extend to the higher mass end as well , these early - types are the most likely hosts for umbhs . recent simulation work that follows the merger history of cluster scale dark matter halos and the growth of bhs hosted in them by yoo et al.(2007 ) also predict the existence of a rare population of local umbhs . however , theoretical arguments suggest that there may be an upper limit to the mass of a bh that can grow in a given galactic nucleus hosted in a dark matter halo of a given spin . clearly the issue of the existence of umbhs is intimately linked to the efficiency of galaxy formation and the formation of the largest , most luminous and massive galaxies in the universe . possible explanations for the tight correlation observed between the velocity dispersion of the spheroid and black hole mass involve a range of self - regulated feedback prescriptions . an estimate of the upper limits on the black hole mass that can assemble in the most massive spheroids can be derived for all these models and they all point to the existence of umbhs . in this paper , we have argued that while rare umbhs likely exist , there is nevertheless an upper limit of @xmath131 for the mass of bhs that inhabit galactic nuclei in the universe . we first show that our current understanding of the accretion history and mass build up of black holes allows and implies the existence of umbhs locally . this is primarily driven by new work that predicts the formation of massive black hole seeds at high redshift ( lodato & natarajan 2007 ) and their subsequent evolution ( volonteri , lodato & natarajan 2008 ) . starting with massive seeds and following their build - up through hierarchical merging in the context of structure formation in a cold dark matter dominated universe , we show that a viable pathway to the formation of umbhs exists . there is also compelling evidence from the observed evolution of x - ray agn for the existence of a local umbh population . convolving the observed x - ray lf s of agn , with a simple accretion model , the mass function of black holes at @xmath1 is estimated . mimic - ing the effect of self - regulation processes that impose an upper limit to bh masses and incorporating this into the x - ray agn lf we find that the observed umbh mass function at @xmath1 is reproduced . this self - regulation limited growth is implemented by steepening the high luminosity end of the agn lf at the bright end . we estimate the abundance of umbhs to be @xmath132 at @xmath1 . the key prediction of our model is that the slope of the @xmath4 relation likely evolves with redshift at the high mass end . probing this is observationally challenging at the present time but there are several bright , massive early - type galaxies that are promising host candidates from the sdss survey as well as a survey of bright central galaxies of nearby clusters . observational detection of umbhs will provide key insights into the physics of galaxy formation and black hole assembly in the universe .

we show that there are three strong lines of argument that predicate the existence of umbhs : ( i ) expected as a natural extension of the observed black hole mass bulge luminosity relation , when extrapolated to the bulge luminosities of bright central galaxies in clusters ; ( ii ) new predictions for the mass function of seed black holes at high redshifts predict that growth via accretion or merger - induced accretion inevitably leads to the existence of rare umbhs at late times ; ( iii ) the local mass function of black holes computed from the observed x - ray luminosity functions of active galactic nuclei predict the existence of a high mass tail in the black hole mass function at @xmath1 . this consistent picture also predicts that the slope of the @xmath2-@xmath3 relation will evolve with redshift at the high mass end . models of self - regulation that explain the co - evolution of the stellar component and nuclear black holes naturally provide such an upper limit . the combination of multi - wavelength constraints predicts the existence of umbhs and simultaneously provides an upper limit to their masses . the typical hosts for these local umbhs are likely the bright , central cluster galaxies in the nearby universe .

we make a case for the existence for ultra - massive black holes ( umbhs ) in the universe , but argue that there exists a likely upper limit to black hole masses of the order of @xmath0 . we show that there are three strong lines of argument that predicate the existence of umbhs : ( i ) expected as a natural extension of the observed black hole mass bulge luminosity relation , when extrapolated to the bulge luminosities of bright central galaxies in clusters ; ( ii ) new predictions for the mass function of seed black holes at high redshifts predict that growth via accretion or merger - induced accretion inevitably leads to the existence of rare umbhs at late times ; ( iii ) the local mass function of black holes computed from the observed x - ray luminosity functions of active galactic nuclei predict the existence of a high mass tail in the black hole mass function at @xmath1 . consistency between the optical and x - ray census of the local black hole mass function requires an upper limit to black hole masses . this consistent picture also predicts that the slope of the @xmath2-@xmath3 relation will evolve with redshift at the high mass end . models of self - regulation that explain the co - evolution of the stellar component and nuclear black holes naturally provide such an upper limit . the combination of multi - wavelength constraints predicts the existence of umbhs and simultaneously provides an upper limit to their masses . the typical hosts for these local umbhs are likely the bright , central cluster galaxies in the nearby universe . galaxies : evolution , active , nuclei . x - rays : galaxies .

hep-ex0212051

i

experimental data on inclusive @xmath4 meson semileptonic decays can in principle provide a very precise method to determine the cabibbo - kobayashi - maskawa ( ckm ) quark mixing parameter @xmath12 @xcite . a crucial theoretical input is the hadronic matrix element needed to express the measured semileptonic width in terms of @xmath12 . the heavy quark expansion ( hqe ) @xcite is a qcd - based approach to inclusive processes that casts perturbative and non - perturbative corrections to the partonic width as power series expansions . an underlying assumption of this approach is quark - hadron duality . it is important to quantify the uncertainties induced by the neglected higher order terms in the non - perturbative expansion , as well as the uncertainty introduced by possible duality violations , in order to achieve a full understanding of the theoretical errors and be able to ascertain the true uncertainty on @xmath12 . the only strategy proposed so far to gather further insight is to measure several quantities predicted in this framework . a precise measurement of the lepton spectrum is an important element of this program and is the key result presented in this paper . the theoretical expression for the inclusive semileptonic width for @xmath17 ( @xmath18 or @xmath19 ) through @xmath20 in the non - perturbative expansion and @xmath21 in the perturbative one is given by @xcite _ sl & = & 0.3689 , [ vcbf ] where @xmath22 is the one - loop qcd beta function and @xmath23 is the number of relevant flavors and the form factors @xmath24 , @xmath25 , @xmath26 , @xmath27 , @xmath28 , and @xmath29 are the parameters of the @xmath10 terms in the non - perturbative expansion . these @xmath10 form factors are expected , from dimensional arguments , to be of the order @xmath30 , and thus they are generally assumed to be @xmath31 gev@xmath32 . in addition , @xmath33 is expected to be positive from the vacuum - saturation approximation @xcite . furthermore , as gremm and kapustin have noted @xcite , the @xmath34-@xmath4 and @xmath35-@xmath36 mass splittings impose the constraint @xmath37 where @xmath38 and @xmath39 represent the beauty and charm quark masses , respectively ; @xmath40^{(3/\beta_0)}$ ] and @xmath41 represents the vector - pseudoscalar meson splitting in the beauty ( charm ) sector . the parameter @xmath42 @xcite is related to the expectation value of the operator corresponding to the kinetic energy of the @xmath14 quark inside the @xmath4 meson : @xmath43 where @xmath44 denotes the 4-velocity of the heavy hadron and @xmath45 is the quark field in the heavy quark effective theory . the parameter @xmath46 @xcite is the expectation value of the leading chromomagnetic operator that breaks the heavy quark spin symmetry . it is formally defined as @xmath47 where @xmath48 is the heavy quark field and @xmath49 is the @xmath4 meson state . the value of @xmath50 is determined from the @xmath51 mass difference to be @xmath52 gev@xmath9 . the quantity @xmath53 is related to the @xmath14-quark pole mass @xmath38 @xcite through the expression @xmath54 where @xmath55 is the spin - averaged @xmath56 mass ( @xmath57 gev/@xmath16 ) . a similar relationship holds between the @xmath3-quark mass @xmath39 and the spin - averaged charm meson mass ( @xmath58 gev/@xmath16 ) . the shape of the lepton momentum spectrum in @xmath17 decays can be used to measure the hqe parameters @xmath42 and @xmath53 , through its energy moments , which are also predicted in the heavy quark expansion . we choose to study truncated moments of the lepton spectrum , with a momentum cut of @xmath59 gev/@xmath3 in the @xmath4 meson rest frame . this choice decreases the sensitivity of our measurement to the secondary leptons from the cascade decays ( @xmath60 ) . we extract the hqe parameters @xmath61 and @xmath62 from measurements of two moments originally suggested by gremm _ _ : is first introduced as r@xmath63 . ] @xmath64 @xmath65 the theoretical expressions for these moments r@xmath66 @xcite are evaluated by integrating the dominant @xmath67 component of the lepton spectrum . in addition , the small contribution coming from charmless semileptonic decays @xmath68 is included by adding the contribution from @xmath69 , scaled by @xmath70 @xcite . we determine these two moments from the measured lepton spectrum in @xmath71 and insert them in the theoretical expressions to extract the two parameters @xmath72 and @xmath73 . we have previously published experimental determinations of @xmath73 and @xmath62 obtained by studying the @xmath74 spectrum in @xmath75 @xcite and the first moment of the mass @xmath76 of the hadronic system recoiling against the @xmath77 pair in @xmath78 decays @xcite . we compare our results to these measurements . in recent years , increasing attention has been focused on `` short - range masses , '' preferred by some authors as they are not affected by renormalon ambiguities @xcite . in particular , the so - called 1s @xmath14-quark mass , , defined as one half of the energy of the 1s @xmath79 state calculated in perturbation theory , has been extracted from @xmath80(1s ) resonance data @xcite . the mass has been shown to have remarkably well - behaved perturbative relations to other physical quantities such as the hadronic matrix element governing the @xmath81 semileptonic width @xcite . using the formalism developed by bauer and trott @xcite , we have used the spectral moments @xmath82 and @xmath83 to determine . these authors also explore different lepton energy moments , by varying the exponent of the energy in the integrands and the lower limits of integration . in particular , they identify several moments that provide constraints for and @xmath72 that are less sensitive to higher order terms in the non - perturbative expansion . we study four such moments defined as @xmath84 @xmath85 @xmath86 @xmath87 the values of @xmath73 and @xmath62 determined with the latter set of constraints have different relative weights of the experimental and theoretical uncertainties and thus provide complementary information . finally , bauer and trott identify moments that are insensitive to and @xmath72 . they suggest that a comparison between theoretical evaluations of these `` duality moments '' and their experimental values may provide useful constraints on possible quark - hadron duality violations in semileptonic processes . we report our measurement of two such duality moments " , defined as @xmath88 and @xmath89 this measurement , together with new emerging experimental information @xcite , may eventually lead to a more complete assessment of our present understanding of inclusive semileptonic decays .

we use these moments to determine non - perturbative parameters governing the semileptonic width . the theoretical constraints used are evaluated through order @xmath10 in the non - perturbative expansion and @xmath11 in the perturbative expansion . we use these parameters to extract @xmath12 from the world average of the semileptonic width and find @xmath13 . in addition , we extract the short range @xmath14-quark mass = ( @xmath15 ) gev/@xmath16 . finally , we discuss the implications of our measurements for the theoretical understanding of inclusive semileptonic processes .

we measure the primary lepton momentum spectrum in @xmath0 decays , for p@xmath1 @xmath2 1.5 gev/@xmath3 in the @xmath4 rest frame . from this , we calculate various moments of the spectrum . in particular , we find @xmath5 and @xmath6 gev . we use these moments to determine non - perturbative parameters governing the semileptonic width . in particular , we extract the heavy quark expansion parameters @xmath7 ) gev and @xmath8 ) gev@xmath9 . the theoretical constraints used are evaluated through order @xmath10 in the non - perturbative expansion and @xmath11 in the perturbative expansion . we use these parameters to extract @xmath12 from the world average of the semileptonic width and find @xmath13 . in addition , we extract the short range @xmath14-quark mass = ( @xmath15 ) gev/@xmath16 . finally , we discuss the implications of our measurements for the theoretical understanding of inclusive semileptonic processes .

hep-ex0212051

c

we have measured the lepton momentum spectra in @xmath124 ( @xmath125 and @xmath102 ) for p @xmath2 1.5 gev/@xmath3 in the b rest frame . from these , we determine the spectral moments r@xmath120 , r@xmath121 , r@xmath126 , r@xmath127 , r@xmath128 , r@xmath129 , d@xmath130 and d@xmath131 . using the moments r@xmath120 and r@xmath121 we extract the hqe parameters @xmath132 ) gev and @xmath133 ) gev@xmath9 . these results imply that the pole mass @xmath134 ) gev/@xmath16 . the short range mass @xmath135 is found to be ( @xmath136 ) gev/@xmath16 . we obtain @xmath137 . finally , an extensive study of different spectral moments shows good agreement between independent determinations of the hqe parameters .

we measure the primary lepton momentum spectrum in @xmath0 decays , for p@xmath1 @xmath2 1.5 gev/@xmath3 in the @xmath4 rest frame . from this , we calculate various moments of the spectrum . in particular , we find @xmath5 and @xmath6 gev . in particular , we extract the heavy quark expansion parameters @xmath7 ) gev and @xmath8 ) gev@xmath9 .

we measure the primary lepton momentum spectrum in @xmath0 decays , for p@xmath1 @xmath2 1.5 gev/@xmath3 in the @xmath4 rest frame . from this , we calculate various moments of the spectrum . in particular , we find @xmath5 and @xmath6 gev . we use these moments to determine non - perturbative parameters governing the semileptonic width . in particular , we extract the heavy quark expansion parameters @xmath7 ) gev and @xmath8 ) gev@xmath9 . the theoretical constraints used are evaluated through order @xmath10 in the non - perturbative expansion and @xmath11 in the perturbative expansion . we use these parameters to extract @xmath12 from the world average of the semileptonic width and find @xmath13 . in addition , we extract the short range @xmath14-quark mass = ( @xmath15 ) gev/@xmath16 . finally , we discuss the implications of our measurements for the theoretical understanding of inclusive semileptonic processes .

cond-mat0512496

i

we performed low - bias stm imaging on underdoped sc bi2212 crystals , and confirmed that the nondispersive @xmath3 electronic charge order appears within the pairing gap at @xmath11 . the present nondispersive charge order is consistent with the findings in the ldos maps for the sc state of bi2212 by howald _ et al . _ and for the pseudogap state ( @xmath10 ) by vershinin _ et al . _ @xcite howald _ et al . _ have claimed that the nondispersive charge order results from the formation of the stripe order , though this scenario does not so straightforwardly explain why the observation of the @xmath3 charge order is restricted to within the pairing gap.@xcite the appearance of the charge order within the pairing gap is not inconsistent with the models of pair density waves , electronic supersolids , paired - hole wigner crystallization , or the coexistence of multi - type sc and spin density wave.@xcite on the other hand , vershinin _ et al . _ have claimed that the nondispersive @xmath9 charge order at @xmath10 is a hidden order of the electron system in the pseudogap state ( @xmath10).@xcite in that case , the observation that the nondispersive charge order survives even in the sc state means that the hidden order of the pseudogap state will remain essentially unchanged down to below @xmath5 . it is urgently desired to elucidate how the charge order in the pseudogap state ( @xmath10 ) evolves into the nondispersive one in the superconducting state . we pointed out the possibility that the sample dependence of the nondispersive @xmath3 charge order can be understood qualitatively from the standpoint of the pinning picture , which indicates that the @xmath3 charge order will be dynamical in itself and pinned down over regions with effective pinning centers . the dynamical @xmath3 charge order is a possible candidate for the hidden order in the pseudogap regime of pure bulk crystals with no effective pinning centers . we also pointed out that the pairing gap of samples exhibiting more intense , pinned @xmath3 charge order is spatially more inhomogeneous . the inhomogeneous gap structure can be attributable to incoherent electronic ( quasiparticle ) states around the antinodes , where the pseudogap develops at @xmath10 . the electronic ( quasiparticle ) states will be largely modified there by randomness associated with the pinning potential of the @xmath3 charge order . thanks to useful discussions for professor f. j. ohkawa , professor z. teanovi and professor k. maki . this work was supported in part by grant - in - aid for scientific research and the 21st century coe program `` topological science and technology '' from the ministry of education , culture , sports , science and technology of japan .

we performed stm / sts measurements on underdoped bi2212 crystals with doping levels @xmath0 , @xmath1 and @xmath2 to examine the nature of the nondispersive @xmath3 charge order in the superconducting state at @xmath4 . we point out the possibility that the @xmath3 charge order will be dynamical in itself , and pinned down over regions with effective pinning centers .

we performed stm / sts measurements on underdoped bi2212 crystals with doping levels @xmath0 , @xmath1 and @xmath2 to examine the nature of the nondispersive @xmath3 charge order in the superconducting state at @xmath4 . the charge order appears conspicuously within the pairing gap , and low doping tends to favor the charge order . we point out the possibility that the @xmath3 charge order will be dynamical in itself , and pinned down over regions with effective pinning centers . the pinned @xmath3 charge order is closely related to the spatially inhomogeneous pairing gap structure , which has often been reported in sts measurements on high-@xmath5 cuprates .

astro-ph0405031

i

bar - driven gas flows have been proposed to explain the high star formation rates in the nuclei of some starburst galaxies @xcite . star formation is predicted to be enhanced in regions with little shear and/or weak or no shocks , i.e. , where the velocity gradients are small . these regions are predicted to be found , and in some cases are observed , at the bar ends , along the leading edges of the bar , and at locations within a nuclear ring or spiral . molecular gas concentrations often appear in these areas , in particular at so - called `` twin peaks '' near the contact points between the dust lanes of the bar and the nuclear ring @xcite . high resolution images of the molecular gas in the archetypal starburst galaxy ngc 253 suggest that a similar ring of clouds may exist around its nucleus . specifically , the position - velocity diagram ( pvd ) shows a hole near the center @xcite , though this feature does not unambiguously indicate the presence of a ring @xcite . from cs observations , @xcite suggest that much of the dense , star - forming gas in the nucleus of ngc 253 lies in a ring associated with so - called @xmath1 orbits , which are small , elongated orbits perpendicular to the bar @xcite . similarly , @xcite conclude from the pvds of and sio emission in ngc 253 that the dense gas also follows these orbits . the ratio of hcn and co intensities , an indicator of density , is also elevated 5@xmath2 on either side of the nucleus along the major axis @xcite . indeed , dense gas in the face - on galaxy ngc 6951 appears to follow the @xmath1 orbits closely @xcite , but the low declination and high inclination of ngc 253 ( @xmath3 , * ? ? ? * ) have hindered similar analysis . previous high resolution maps of gas emission from ngc 253 either did not trace the bulk of the molecular gas , i. e. , they were most sensitive to dense , shocked or ionized gas @xcite , or they lacked the spatial resolution to isolate individual cloud complexes and their kinematics @xcite . further , since the first co interferometer map of ngc 253 by @xcite , new images have been made of the stellar and dust distributions @xcite and optically thin gas traced by @xcite . @xcite have also analyzed the co velocity field at high resolution , and with the submillimeter array now operational , interferometric maps of dense and warm gas traced by co and other lines are certainly imminent . given these new and anticipated data , it is appropriate to reexamine the properties of the molecular gas in ngc 253 but on the spatial scales of individual giant molecular clouds ( @xmath4 pc ) . to this end , we imaged the co emission from ngc 253 with the nobeyama millemeter array . to place any new work in the proper context will require this relied - upon tracer of the bulk of the star - forming gas in galaxies . we compare these data to high resolution hcn and maps @xcite to infer the properties of the molecular clouds and compare them to the kinematics and dust distribution to test how the bar in ngc 253 may drive the central starburst .

we present @xmath0 resolution interferometry of co emission from the starburst galaxy ngc 253 . the high spatial resolution of these new data , in combination with recent high resolution maps of , hcn and near - infrared emission , allow us for the first time to link unambiguously the gas properties in the central starburst of ngc 253 with its bar dynamics . two distinct kinematic features are evident from the co map and position - velocity diagram : a group of clouds rotating as a solid body about the kinematic center of the galaxy , and a more extended gas component associated with the near - infrared bar . we model the line intensities of co , hcn and to infer the physical conditions of the gas in the nucleus of ngc 253 . this result is similar to observations of the face - on , twin - peaks galaxy ngc 6951 , and is consistent with models of starburst generation due to gas inflow along a bar .

we present @xmath0 resolution interferometry of co emission from the starburst galaxy ngc 253 . the high spatial resolution of these new data , in combination with recent high resolution maps of , hcn and near - infrared emission , allow us for the first time to link unambiguously the gas properties in the central starburst of ngc 253 with its bar dynamics . we confirm that the star formation results from bar - driven gas flows as seen in `` twin peaks '' galaxies . two distinct kinematic features are evident from the co map and position - velocity diagram : a group of clouds rotating as a solid body about the kinematic center of the galaxy , and a more extended gas component associated with the near - infrared bar . we model the line intensities of co , hcn and to infer the physical conditions of the gas in the nucleus of ngc 253 . the results indicate increased volume densities around the radio nucleus in a twin - peaks morphology . compared with the co kinematics , the gas densities appear highest near the radius of a likely inner linblad resonance , and slightly lead the bar minor axis . this result is similar to observations of the face - on , twin - peaks galaxy ngc 6951 , and is consistent with models of starburst generation due to gas inflow along a bar . # 1

astro-ph0110417

r

figure 1 shows the spatial distributions of all of the local group dark matter halos , the high - velocity clouds ( without distance constraints ; see below ) , and the compact high - velocity clouds in galactic coordinates . the dark matter halos show a clear bias in their distribution towards m31 and the local group anti - barycenter region . this bias in the distribution is independent of the size and mass of the halos , however , in terms of distance , it only appears beyond @xmath0500 kpc of the milky way ( see figure 2 ) . the distribution of cataloged hvcs shown in the middle panel of figure 1 , excludes those hvcs which have distance determinations . direct distance determinations have been made to several of the larger high velocity complexes which place them within approximately 10 kpc of the galaxy ( e.g. complex a , m , and we ; wakker 2001 ) , and the stream and leading arm originated from the interaction of the magellanic clouds with the milky way and are at distances within 100 kpc . we can also exclude those complexes which are bright in h@xmath3 emission ( e.g. complex l , gcp ( the smith cloud ) , and c ) , as this emission would not have been detected at distances greater than 100 kpc ( e.g. bland hawthorn & maloney 1999 ) , unless associated with an active star forming region . there are excesses of hvcs in the same general directions as the halos , but the extreme overabundance in the direction of m31 is not present . furthermore , the distance determination methods have not uniformly sampled the sky , and this bias in the hvc distribution may disappear with future observations . the chvcs shown in the bottom panel of figure 1 are clustered , but clearly show a different distribution to the local group halos . rrc object & # & mean @xmath26 + hvcs ( without distance constraints ) & 469 & -49 + chvcs ( compact hvcs ) & 215 & -57 + all dark matter halos & 2135 & -66 + halos outside of 300 kpc & 1530 & -69 + halos within 500 kpc & 584 & -27 + halos with m@xmath27 & 624 & -63 + figure 2 shows the spatial distributions of only those local group halos at least 300 kpc from both m31 and the galaxy ( top ) , within 500 kpc of the galaxy ( middle ) , and those halos with dark matter masses @xmath28 . the bias in the spatial distribution of the halos is not evident within 500 kpc of the galaxy . the beginning of an asymmetric distribution is seen between 500 and 800 kpc in this simulation . since the simulation places the center of m31 at 1100 kpc , rather than the observed distance of 700 kpc ( freedman & madore 1990 ) , the actual bias in the distribution could appear somewhat closer . the asymmetric distribution of halos remains in both the @xmath29 300 kpc and @xmath30 cases , but the total number of objects is greatly decreased ( see table 1 ) . the velocity distributions of all of the dark matter halos , hvcs without distance constraints , and chvcs are shown in terms of galactic longitude ( @xmath31 ) and local group standard of rest velocity ( @xmath26 ) in figure 3 . their mean lgsr velocities are tabulated in table 1 . there is no obvious position - velocity relationship between the populations of clouds and the local group halos . a wide range of velocities about m31 is shown in the simulation , as is a clear bias for negative @xmath26 s ( i.e. infall ) . the hvc and chvc velocity distributions are limited by confusion with galactic emission between @xmath32 + /- this is evident in the hvc distribution shown in the middle panel of figure 3 , with the hvcs clustering about a sinusoidal gap in the distribution . both the hvcs and chvcs show a preference for negative velocities in the local group reference frame . the chvcs show a tendency towards more positive velocities at @xmath33 and negative velocities at @xmath34 , with the largest range of velocities about @xmath35 . the panels of fig . 4 show the velocity distributions of the selected groups of halos shown in fig . the velocity distribution of the local group halos within 500 kpc is fairly uniform , as is the spatial distribution , with a mean @xmath17 the same magnitude more positive than the hvcs ( @xmath36 ) as the other halo populations are more negative . the population of halos with m@xmath37 appears as a thinned version of the velocity distribution of all of the halos . those halos over 300 kpc from m31 and the galaxy have a similar thinned distribution , but there is less scatter and less extreme velocities in the direction of m31 . though it is difficult to infer a mass distribution of the hvcs and chvcs due to their unknown distances ( m@xmath38 d@xmath39 ) , we can infer a flux distribution of the halos using their masses and distances and assuming a certain percentage of gas is associated with the dark matter . if the halos contain 1% of their dark matter mass in neutral hydrogen , their total hi fluxes are directly comparable to those of the hvcs and chvcs , as shown in figure 5 . note that some of the plots have different values on both axes . the projected flux distribution of all of the dark matter halos is shown in the bottom left panel of figure 5 by the solid points . the slope is -1.5 , which is the same as that of the hvcs shown in the upper left panel , but the number of halos in each flux bin is much higher . the upper right panel shows that both the total number of chvcs and the slope of the flux distribution ( @xmath40 ) is different from that of the halos . the selected populations of halos discussed above are shown in the bottom two panels of figure 5 . halos outside of 300 kpc from the galaxy and m31 are represented by the dashed line in the bottom left panel . the total number of clouds is again somewhat higher than that of the hvcs and the slope is steeper , like the chvcs . the flux distribution of those halos with m@xmath27 ( @xmath41 ; solid points in the bottom right panel ) and those halos within 500 kpc of the galaxy ( @xmath42 ; dashed line in the bottom right panel ) are the most comparable to the hvcs in terms of total number and slope . the size distribution of the halos is another property which can be compared to the hvcs if one assumes that the gas and dark matter are coupled . these plots will be shown in a future paper . figure 5 also shows that even if the local group halos are not hvcs or chvcs , they should have been detected by the recent large area hi surveys if they contain @xmath01% of their dark matter mass in neutral hydrogen . for instance , hipass covers over half of the sky and the velocities of the local group galaxies with a completeness level of @xmath43 jy , and the wakker catalog reaches fluxes of @xmath44 jy ( wakker & van woerden 1991 ) . therefore , considering the entire population of halos ( 2135 total ) , almost all of them would have been detected if they contain 1% or greater of their dark matter mass in . by applying cuts in halo distance or mass , the number of halos which should have been detected is in closer agreement with the number of hvcs without lowering m@xmath8 to below 1% m@xmath45 .

the @xmath02000 leftover satellites in the simulation have dark matter masses which range between 0.5 to 10 @xmath1 , sizes between 3 to 30 kpc , and distances between 100 kpc and 2 mpc . the dark matter halos show a clear bias in their distribution towards m31 and to a lesser extent towards the local group anti - barycenter . if the local group halos contain @xmath01% of their dark matter mass in neutral hydrogen they should have been easily detected by the current surveys . the only objects detected with the potential to be the local group halos are the high - velocity clouds . here the spatial , kinematic , and flux properties of the clouds and dark matter halos are compared . several different subsets of halos which may be more likely to contain neutral hydrogen are investigated , and the hvcs are found to have some similar properties to those halos within 500 kpc of the galaxy and those halos with dark matter masses @xmath2 . # 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in

we present a comparison of the leftover satellites at z=0 in a cold dark matter dominated simulation of the formation of the local group to the distribution of observed neutral hydrogen high - velocity clouds and compact high - velocity clouds . the @xmath02000 leftover satellites in the simulation have dark matter masses which range between 0.5 to 10 @xmath1 , sizes between 3 to 30 kpc , and distances between 100 kpc and 2 mpc . the dark matter halos show a clear bias in their distribution towards m31 and to a lesser extent towards the local group anti - barycenter . if the local group halos contain @xmath01% of their dark matter mass in neutral hydrogen they should have been easily detected by the current surveys . the only objects detected with the potential to be the local group halos are the high - velocity clouds . here the spatial , kinematic , and flux properties of the clouds and dark matter halos are compared . several different subsets of halos which may be more likely to contain neutral hydrogen are investigated , and the hvcs are found to have some similar properties to those halos within 500 kpc of the galaxy and those halos with dark matter masses @xmath2 . the compact high - velocity clouds do not show similar properties to the halos . # 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in

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there does not appear to be a close correlation between the entire population of dark matter halos in this standard cold dark matter local group simulation and the high - velocity clouds and compact high - velocity clouds . however , when cuts are made in distance or mass , the remaining halos show properties which could be argued are consistent with those of the hvcs without distance constraints . the compact hvcs do not show similar properties to the dark matter halos . the justification behind the halo cuts are summarized below . for greater than 300 kpc from m31 and the galaxy , it is possible that the neutral hydrogen gas would not survive outside of a particular distance from these galaxies . this could be due to either ram pressure or tidal stripping effects ( e.g. quilis & moore 2001 ) , or ionizing radiation escaping from the galaxy ( e.g. bland - hawthorn & maloney 1999 ) . the cut which requires the halos associated with neutral hydrogen gas be within 500 kpc , is based on the idea that the is only able to condense within a certain radius of the galaxy ( e.g. oort 1970 ) . finally , the choice of only those halos with dark matter masses above @xmath46 having neutral gas associated with them comes from cdm simulations which include reionization at @xmath47 ( e.g. gnedin 2000 ) . the increase in temperature of the gas during reionization suppresses the formation of low mass satellites due to a reduction in gas mass via the expulsion of already accreted gas and the suppression of further accretion . the primary difference between these sub - populations of halos and the entire population is a reduction in the total number , but there are also differences in the flux distributions and within 500 kpc there is certainly a more uniform spatial and kinematic distribution . considering the distance determinations which have been made to some of the larger high velocity complexes and the search for hvcs in other groups which have not found extragalactic hi clouds without stars down to m@xmath8 levels of @xmath48 ( e.g. zwaan 2001 ) , the possibility of the hvcs being the dark matter halos within a certain radius of the milky way seems the most likely possibility . if the nearby halos are represented by hvcs , are the further away halos represented by the lower column density ly@xmath3 absorbers which have been detected in other groups ( e.g. penton , shull & stocke 2000 ) ? it is difficult to find these low column density systems within the local group due to the the damping wings of the galaxy s ly@xmath3 and to some extent ly@xmath49 absorption lines obscuring those velocities . the detection of these systems through other absorption lines may be possible in some cases ( e.g. @xmath50 ) , and may have already been detected along some sightlines ( e.g. sembach et al . evidence for a link between hvcs and these few absorption line detections of lower column density high velocity gas lies in their spatial and kinematic relationship . therefore , if this gas is related to the ly@xmath3 absorbers , one might expect to detect higher column density systems akin to hvcs in the vicinity of some of the low - redshift ly@xmath3 absorber systems . the flux distribution plots of the halos , presented in the bottom two panels of figure 5 , put strong constraints on the amount of neutral hydrogen the halos can have . hipass and other hvc surveys cover the velocities of all of the local group galaxies down to flux levels of 2 - 5 jy . figure 5 shows that the majority of the halos should have been detected if they contain at least 1% of their dark matter mass in . since only @xmath51 local group galaxies have been detected in , there is an obvious need to look towards other objects . the number of hvcs and chvcs is also too low to agree with the number of halos that should have been detected , unless one applies distance and/or mass cuts ( see figure 5 and table 1 ) . no other candidate `` missing satellites '' have been detected in in the local group , so either the hvcs are a population of the missing satellites , or the majority of the dark matter halos contain @xmath52% of their dark matter mass in .

we present a comparison of the leftover satellites at z=0 in a cold dark matter dominated simulation of the formation of the local group to the distribution of observed neutral hydrogen high - velocity clouds and compact high - velocity clouds . the compact high - velocity clouds do not show similar properties to the halos .

we present a comparison of the leftover satellites at z=0 in a cold dark matter dominated simulation of the formation of the local group to the distribution of observed neutral hydrogen high - velocity clouds and compact high - velocity clouds . the @xmath02000 leftover satellites in the simulation have dark matter masses which range between 0.5 to 10 @xmath1 , sizes between 3 to 30 kpc , and distances between 100 kpc and 2 mpc . the dark matter halos show a clear bias in their distribution towards m31 and to a lesser extent towards the local group anti - barycenter . if the local group halos contain @xmath01% of their dark matter mass in neutral hydrogen they should have been easily detected by the current surveys . the only objects detected with the potential to be the local group halos are the high - velocity clouds . here the spatial , kinematic , and flux properties of the clouds and dark matter halos are compared . several different subsets of halos which may be more likely to contain neutral hydrogen are investigated , and the hvcs are found to have some similar properties to those halos within 500 kpc of the galaxy and those halos with dark matter masses @xmath2 . the compact high - velocity clouds do not show similar properties to the halos . # 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in

1210.7998

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the fundamental atmospheric ( effective temperature , surface gravity , and metallicity ) and physical ( mass and age ) parameters of stars provide the major observational foundation for chemo - dynamical studies of the milky way and other galaxies in the local group . with the dawn of large spectroscopic surveys to study individual stars , such as segue @xcite , rave @xcite , gaia - eso @xcite , and hermes @xcite , these parameters are used to infer the characteristics of different populations of stars that comprise the milky way . stellar parameters determined by spectroscopic methods are of a key importance . the only way to accurately measure metallicity is through spectroscopy , which thus underlies photometric calibrations ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , while high - resolution spectroscopy is also used to correct the low - resolution results ( e.g. , * ? ? ? the atmospheric parameters can all be estimated from a spectrum in a consistent and efficient way . this also avoids the problem of reddening inherent in photometry since spectroscopic parameters are not sensitive to reddening . the spectroscopic parameters can then be used alone or in combination with photometric information to fit individual stars to theoretical isochrones or evolutionary tracks to determine the stellar mass , age , and distance of a star . a common method for deriving the spectroscopic atmospheric parameters is to use the information from fe and fe absorption lines under the assumption of hydrostatic equilibrium ( he ) and local thermodynamic equilibrium ( lte ) . many previous studies have used some variation of this technique ( e.g. , ionisation or excitation equilibrium ) to determine the stellar atmospheric parameters and abundances , and henceforth distances and kinematics , of fgk stars in the milky way . for example , some have used this procedure to estimate the effective temperature , surface gravity , and metallicity of a star ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , while others use photometric estimates of effective temperature in combination with the ionisation equilibrium of the abundance of iron in lte to estimate surface gravity and metallicity ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . however , both observational ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) and theoretical evidence ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) suggest that systematic biases are present within such analyses due to the breakdown of the assumption of lte . more recently , @xcite and @xcite quantified the effects of non - local thermodynamic equilibrium ( nlte ) on the determination of surface gravity and metallicity , revealing very substantial systematic biases in the estimates at low metallicity and/or surface gravity . it is therefore extremely important to develop sophisticated methods , which reconcile these effects in order to derive accurate spectroscopic parameters . this is the first in a series of papers , in which we develop new , robust methods to determine the fundamental parameters of fgk stars and then apply these techniques to large stellar samples to study the chemical and dynamical properties of the different stellar populations of the milky way . in this work , we utilise the sample of stars selected from the rave survey originally published in ( * ? ? ? * hereafter r11 ) to formulate the methodology to derive very accurate atmospheric parameters . we consider several temperature scales and show that the balmer line method is the most reliable among the different methods presently available . further , we have developed the necessary tools to apply on - the - fly nlte corrections to fe lines , utilising the grid described in @xcite . we verify our method using a sample of standard stars with interferometric estimates of effective temperature and/or _ hipparcos _ parallaxes . we then perform a comprehensive comparison to standard 1d , lte techniques for the spectral analysis of stars , finding significant systematic biases .

we present a comprehensive analysis of different techniques available for the spectroscopic analysis of fgk stars , and provide a recommended methodology which efficiently estimates accurate stellar atmospheric parameters for large samples of stars . we further investigate several temperature scales , finding that estimates from balmer line measurements provide the most accurate effective temperatures at all metallicites . this has large implications for the study of the stellar populations in the milky way . [ firstpage ] stars : abundances stars : late - type stars : population ii

we present a comprehensive analysis of different techniques available for the spectroscopic analysis of fgk stars , and provide a recommended methodology which efficiently estimates accurate stellar atmospheric parameters for large samples of stars . our analysis includes a simultaneous equivalent width analysis of fe and fe spectral lines , and for the first time , utilises on - the - fly nlte corrections of individual fe lines . we further investigate several temperature scales , finding that estimates from balmer line measurements provide the most accurate effective temperatures at all metallicites . we apply our analysis to a large sample of both dwarf and giant stars selected from the rave survey . we then show that the difference between parameters determined by our method and that by standard 1d lte excitation - ionisation balance of fe reveals substantial systematic biases : up to @xmath0 k in effective temperature , @xmath1 dex in surface gravity , and @xmath2 dex in metallicity for stars with @xmath3 . this has large implications for the study of the stellar populations in the milky way . [ firstpage ] stars : abundances stars : late - type stars : population ii

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in this work , we explore several available methods to determine effective temperature , surface gravity , and metallicity for late - type stars . the methods include excitation and ionization balance of fe lines in lte and nlte , semi - empirically calibrated photometry ( r11 ) , and the infra - red flux method ( irfm ) . applying these methods to the large set of high - resolution spectra of metal - poor fgk stars selected from the rave survey , we then devise a new efficient strategy which provides robust estimates of their atmospheric parameters . the principal components of our method are ( i ) balmer lines to determine effective temperatures , ( ii ) nlte ionization balance of fe to determine @xmath17 and @xmath18 , and ( iii ) restriction of the fe lines to that with the lower level excitation potential greater than 2 ev to minimize the influence of 3d effects @xcite . a comparison of the new nlte - opt stellar parameters to that obtained from the widely - used method of 1d lte excitation - ionization of fe , lte - fe , reveals significant _ systematic biases _ in the latter . the difference between the nlte - opt and lte - fe parameters systematically increase with decreasing metallicity , and can be quite large for the metal - poor stars : from 200 to 400 k in @xmath16 , 0.5 to 1.5 dex in @xmath17 , and 0.1 to 0.5 dex in @xmath18 . these systematic trends are largely influenced by the difference in the estimate of the stellar effective temperature , and thus , a reliable effective temperature scale , such as the balmer scale , is of critical importance in any spectral parameter analysis . however , a disparity between the abundance of iron from fe and fe lines still remains . it is therefore necessary to include the nlte effects in fe lines to eliminate this discrepancy . the implications of the very large differences between the nlte - opt and lte - fe estimates of atmospheric parameters extend beyond that of just the characterisation of stars by their surface parameters and abundance analyses . spectroscopically derived parameters are often used to derive other fundamental stellar parameters such as mass , age and distance through comparison to stellar evolution models . the placement of a star along a given model will be largely influenced by the method used to determine the stellar parameters . for example , distance scales will change , which could affect the abundance gradients measured in the milky way ( e.g. , r11 ) , as well as the controversial identification of different components in the mw halo @xcite . we explore this in greater detail in the next paper of this series @xcite .

we apply our analysis to a large sample of both dwarf and giant stars selected from the rave survey . we then show that the difference between parameters determined by our method and that by standard 1d lte excitation - ionisation balance of fe reveals substantial systematic biases : up to @xmath0 k in effective temperature , @xmath1 dex in surface gravity , and @xmath2 dex in metallicity for stars with @xmath3 .

we present a comprehensive analysis of different techniques available for the spectroscopic analysis of fgk stars , and provide a recommended methodology which efficiently estimates accurate stellar atmospheric parameters for large samples of stars . our analysis includes a simultaneous equivalent width analysis of fe and fe spectral lines , and for the first time , utilises on - the - fly nlte corrections of individual fe lines . we further investigate several temperature scales , finding that estimates from balmer line measurements provide the most accurate effective temperatures at all metallicites . we apply our analysis to a large sample of both dwarf and giant stars selected from the rave survey . we then show that the difference between parameters determined by our method and that by standard 1d lte excitation - ionisation balance of fe reveals substantial systematic biases : up to @xmath0 k in effective temperature , @xmath1 dex in surface gravity , and @xmath2 dex in metallicity for stars with @xmath3 . this has large implications for the study of the stellar populations in the milky way . [ firstpage ] stars : abundances stars : late - type stars : population ii

1004.4500

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the field of single - molecule electronics has been expanding rapidly during recent years , as techniques to electrically contact and control single molecules in a transport junction have improved @xcite . by studying the electric current through the molecule as function of the applied voltage - bias , spectroscopic information can be extracted @xcite . in setups with a gate - electrode , which can be used to control the electrostatic potential on the molecule , a detailed spectroscopy can be performed @xcite . by applying a temperature - bias and measuring the induced electric current or voltage , additional information can be extracted , such as the type of carriers ( holes / electrons ) dominating transport @xcite . this emerging field of molecular thermoelectrics @xcite is also interesting for applications . molecules have been predicted to be particularly efficient for conversion of heat into electric energy @xcite ( or analogously for cooling , using electric energy to pump heat ) , the reason being their very sharp electronic resonances when weakly coupled to electrodes @xcite . this is similar to the large thermoelectric efficiency of e.g. , semi - conducting nanowires with highly peaked densities of states @xcite . most theoretical works on meso- and nano - scale thermoelectrics have focused on the _ linear , equilibrium _ regime , where one operates close to the small voltage @xmath0 which exactly cancels the current induced by the small thermal bias @xmath1 . here the thermopower ( or seebeck coefficient ) @xmath2 is the decisive quantity , where ( @xmath3 ) @xmath4 is the ( thermal ) conductance . a large efficiency @xmath5 of the device operated as a heat to electric energy converter is then related to a large dimensionless thermoelectric figure of merit @xmath6 , where @xmath7 is the operating temperature and @xmath8 the thermal conductance . in bulk systems , @xmath9 is normally limited by the wiedemann - franz law , stating that @xmath10 is a system independent constant . however , the wiedemann - franz law is a result of fermi - liquid theory and breaks down in mesoscopic and nanoscopic systems , e.g. , due to large coulomb interaction , as has been demonstrated for quantum dots @xcite and metallic islands @xcite , allowing much larger values of @xmath9 to be reached . as @xmath11 , the efficiency approaches the ideal carnot value @xmath12 @xcite . however , in the linear regime , @xmath13 , the efficiency stays low even if @xmath9 can be made very large : @xmath14 . the _ non - linear _ thermoelectric properties of molecular junctions are therefore of great interest . recent experiments @xcite probing the thermopower of thiol end - capped organic molecules showed non - linearities in the measured @xmath15 already at @xmath16 . earlier measurements of thermopower in metallic island single - electron transistors even displayed a change of the sign of the thermopower for very large @xmath1 @xcite . in the interesting regime of sharp electronic resonances , the electron tunnel coupling @xmath17 is small and the main factor limiting the efficiency of molecular energy converters is expected to be the heat current from phonon exchange with rate @xmath18 @xcite . nonetheless , to our knowledge , its effect has this far not been systematically investigated . only by making the tunnel coupling larger , @xmath19 , the phonon contribution to the heat current becomes negligible . in this case , however , the efficiency becomes instead limited by the large electronic life - time broadening of the molecular resonances . the thermoelectric efficiency in this limit of coherent transport was studied very recently in the non - linear regime @xcite using both a many - body transport approach and a ( non - interacting ) approach based on hckel theory . except for the latter work and a few others @xcite , most theoretical studies of molecular thermoelectrics have focused on non - interacting models , using a landauer type approach . however , in the regime of weak tunnel coupling between molecule and electrodes , intra - molecular interactions typically constitute the largest energy scales of the problem . in this paper , we calculate the thermoelectric efficiency and converted electric power of a molecular device , including a single dominant molecular orbital , strong coulomb interaction and coupling to a discrete vibrational mode , as well as coupling to lead phonons and lead electrons . importantly , we include on equal footing the phonon and electron contributions to the heat current , both of which contribute in establishing the stationary occupation of the molecular vibrational mode . the coulomb repulsion and electron - vibration coupling on the molecule are treated non - perturbatively in the limit of weak electron and phonon exchange in which thermoelectric efficiency is high . a central finding is that optimal thermoelectric operation typically is achieved in the _ non - linear , non - equilibrium _ regime . here concepts of figure of merit and thermopower are no longer meaningful and the molecular occupancies , efficiency and output power must be explicitly calculated . the paper is organized as follows : sect . [ sec : model ] introduces the dissipative anderson - holstein model and the thermoelectric transport equations . in sect . [ sec : transport ] we present results for the efficiency and output power as function of the applied bias voltage and energy of the molecular orbital dominating transport . the heating of the molecule is analyzed in sect . [ sec : heat ] and the optimal choice of molecule and junction parameters is discussed in sect . [ sec : optimal ] . section [ sec : conclusions ] summarizes and provides an outlook . throughout the paper we set @xmath20 , where @xmath21 is planck s constant , @xmath22 the boltzmann constant and @xmath23 the electron charge .

we present a detailed study of the _ non - linear _ thermoelectric properties of a molecular junction , represented by a dissipative anderson - holstein model . a single orbital level with strong coulomb interaction is coupled to a localized vibrational mode and we account for both electron and phonon exchange with both electrodes , investigating how these contribute to the heat and charge transport . we calculate the efficiency and power output of the device operated as a heat to electric power converter and identify the optimal operating conditions , which are found to be qualitatively changed by the presence of the vibrational mode . based on this study of a generic model system

we present a detailed study of the _ non - linear _ thermoelectric properties of a molecular junction , represented by a dissipative anderson - holstein model . a single orbital level with strong coulomb interaction is coupled to a localized vibrational mode and we account for both electron and phonon exchange with both electrodes , investigating how these contribute to the heat and charge transport . we calculate the efficiency and power output of the device operated as a heat to electric power converter and identify the optimal operating conditions , which are found to be qualitatively changed by the presence of the vibrational mode . based on this study of a generic model system , we discuss the desirable properties of molecular junctions for thermoelectric applications .

physics0512150

i

optical lattices are periodic arrays of shallow microscopic traps in which ultra - cold atoms can be trapped @xcite . the trapping potential is a consequence of a second - order interaction between the atomic dipole moment and an applied light field @xcite : the associated energy , which is proportional to the irradiance , is generally referred to as the light shift . the periodicity emerges when the total light field is built up by two or more interfering laser beams . optical lattices are widely used as a tool for a range of different scientific studies . in particular , they have lately been extensively utilised in experiments involving bose - einstein condensates @xcite and quantum - state manipulation @xcite . in the latter context , cold atoms in optical lattices have been suggested as a promising candidate for a platform for quantum computing . the attractiveness of optical lattices in attempts to realise rudimentary quantum gates , and in subsequent more ambitious steps towards a quantum computer , comes mainly from the very efficient isolation from ambient effects . early suggestions for quantum information processing with optical lattices @xcite do , however , impose strict , and sometimes conflicting technical demands on the optical lattice . in this paper , we present a solution for obtaining power balanced laser beams to create phase - stable double optical lattices , which is essential in order to realise a quantum gate and to enable other classes of highly controlled quantum - state manipulation in dissipative optical lattices . we have previously presented a way to realise a double set of independent 3d optical lattices that are phase stable @xcite . many of the details behind the phase control and the acquired stability can be found in @xcite . when generating a 3d optical lattice with four ( minimum ) or more laser beams , it can be paramount to have equal power in all beams , especially when dealing with dissipative , near - resonant optical lattices . one example of this is when the depth and the oscillation frequency of the potential wells have to be precisely known ( and reproducible ) for controlled preparation of q - bits or for general investigations of the properties of optical lattices . another example is when using the optical lattices in order to controllably induce small directed drifts in the atomic population @xcite . in the latter case , a spurious drift due to radiation pressure caused by a power imbalance is likely to wash out the desired effect . equal power in all beams can therefore be of more importance than overall power stability in time , since small fluctuations in the total power do not affect the relative power in the individual beams . as long as the optical lattice is of a standard type , involving only one wavelength , obtaining equal power in all beams is trivial e.g. by adjusting the polarisation of each individual beam before passing through a polarising beam - splitter cube , the transmitted power can be equalised for all beams . however , in many suggestions for how to realise quantum computing with optical lattices , more than one wavelength is needed . in our set - up for double optical lattices , we use two laser colours , albeit close in wavelength , and in order to keep the spatial phases of the optical lattices stable , we have to use an elaborate scheme where light from two different lasers are overlapped with crossed polarisation @xcite . eventually , the double optical lattice is formed by eight laser beams arranged in four pairs . each pair contains two laser fields of different wavelengths but with an identical spatial mode . in this case , it is not possible to control the power of all beams individually as is done with a single wavelength , since the beams have orthogonal polarisations and are physically overlapped . adjusting the polarisation of the beams to control the power for one frequency will therefore also change the power in the other frequency , which means that power balance for both frequencies can not be controlled independently . in a recent experiment , where a 3d controllable brownian motor was demonstrated @xcite , the rudimentary power balance in the first experiments with double optical lattices was not enough . therefore , an optical system for controlling the power , without compromising the phase control had to be devised .

we present a method to obtain power - balanced laser beams for doing quantum - state manipulation experiments with phase - stable double optical lattices . double optical lattices are constructed using four pairs of overlapped laser beams with different frequencies . our optical scheme provides a phase stability between the optical lattices of 5 mrad / s , and laser beams with a very clean polarisation state resulting in a power imbalance in the individual laser beams of less than 1% . _ keywords _ : optical system design , optical lattices , cold atoms , quantum - state manipulation

we present a method to obtain power - balanced laser beams for doing quantum - state manipulation experiments with phase - stable double optical lattices . double optical lattices are constructed using four pairs of overlapped laser beams with different frequencies . our optical scheme provides a phase stability between the optical lattices of 5 mrad / s , and laser beams with a very clean polarisation state resulting in a power imbalance in the individual laser beams of less than 1% . _ keywords _ : optical system design , optical lattices , cold atoms , quantum - state manipulation

0806.2302

c

the nearby dwarf irregular galaxy ic 4662 harbors two sites of recent massive star formation that have thermal radio spectra , bright dust and h@xmath13 emission , and rich mid - ir spectra that feature nebular fine - structure lines , a hint of pahs at 11.3 @xmath14 m , and broad hu@xmath13 emission . our emission - line analysis indicates that this starburst has high excitation and low abundances like many ucd galaxies and in agreement with literature values . however , we find much higher extinctions ( a@xmath3 mag ) than previous shorter - wavelength studies , which can only be reconciled with the optical observations by a mixed geometry for the gas and dust in these regions . sed fitting of the radio - to - near - ir seds of the udhiis in regions a1 and a2 suggests that they are more evolved toward the ssc stage than similar embedded objects ( e.g. in he @xmath29 and ngc 5253 ) : a1 and a2 have lower gas masses in their hiirs and dust masses surrounding them , and this is consistent with their older ages of about 4 ma , inferred from radio and optical / near - ir data . the clusters that power the udhiis have masses of about @xmath23 m@xmath2 ( assuming a full kroupa imf ) , but they may not be massive , compact , monolithic sscs like those found in many starbursts , but rather clusters of @xmath76 m@xmath2 clusters that fill a larger volume of @xmath77 pc diameter . this work was performed in part under the auspices of the u.s . department of energy , national nuclear security administration by the university of california , lawrence livermore national laboratory under contract no . w-7405-eng-48 , and it was also supported by the aerospace corporation s independent research and development program .

we present a multiwavelength study of the formation of massive stellar clusters , their emergence from cocoons of gas and dust , and their feedback on surrounding matter . using data that span from radio to optical wavelengths , including spitzer and hubble acs observations , we examine the population of young star clusters in the central starburst region of the irregular wolf - rayet galaxy ic 4662 . we model the radio - to - ir spectral energy distributions of embedded clusters to determine the properties of their hii regions and dust cocoons ( sizes , masses , densities , temperatures ) , and use near - ir and optical data with mid - ir spectroscopy to constrain the properties of the embedded clusters themselves ( mass , age , extinction , excitation , abundance ) .

we present a multiwavelength study of the formation of massive stellar clusters , their emergence from cocoons of gas and dust , and their feedback on surrounding matter . using data that span from radio to optical wavelengths , including spitzer and hubble acs observations , we examine the population of young star clusters in the central starburst region of the irregular wolf - rayet galaxy ic 4662 . we model the radio - to - ir spectral energy distributions of embedded clusters to determine the properties of their hii regions and dust cocoons ( sizes , masses , densities , temperatures ) , and use near - ir and optical data with mid - ir spectroscopy to constrain the properties of the embedded clusters themselves ( mass , age , extinction , excitation , abundance ) . the two massive star - formation regions in ic 4662 are excited by stellar populations with ages of @xmath0 ma and masses of @xmath1 m@xmath2 ( assuming a kroupa imf ) . they have high excitation and sub - solar abundances , and they may actually be comprised of several massive clusters rather than the single monolithic massive compact objects known as super star clusters ( sscs ) . mid - ir spectra reveal that these clusters have very high extinctions , a@xmath3 mag , and that the dust in ic 4662 is well - mixed with the emitting gas , not in a foreground screen .

0803.0056

c

a 5-dimensional spherically symmetric particle - like solution is found in the einstein - yang - mills gauss - bonnet model . as in other studies in higher dimensional cosmological models , a negative cosmological constant seems to favor for stability and results in most cases in asymptotically anti de sitter space time . in our 5-dimensional eym - gb model , we also find a profound influence of a negative cosmological constant on the behaviour of horizons . the appearance of horizons in e - gb models is not surprising . these gb black holes are found by many authors . however , the lacking of horizons in the eym - gb model for suitable negative cosmological constant is quite new . the explanation for this behaviour must come from the ym term on the right hand side of eq.(9 ) . the zero s of @xmath41 will depend on the behaviour @xmath48 . there could be a connection of the solution presented here with the ads / cft correspondence . as mentioned before , no analytic expression for @xmath41 available . moreover , to obtain the ( n-1)-dimensional entropy on the brane , one needs the junction conditions at the brane ( @xcite ) , which becomes very complicated in the eym - gb model . the junction condition also introduces a brane tension . this tension must cancel the cosmological constant , in order to obtain the desired cft correspondence . the contribution of ym field on the junction could have profound impact on the tension of the brane and the role of a cosmological constant could be different . so the strong influence of a small cosmological constant on the eventually formed gb black hole in our model is quite clear from the consideration mentioned above .

we present a numerical solution on a 5-dimensional spherically symmetric space time , in einstein - yang - mills - gauss - bonnet theory using a two point boundary value routine . it turns out that the gauss - bonnet contribution has a profound influence on the behaviour of the particle - like solution : it increases the number of nodes of the ym field . when a negative cosmological constant in incorporated in the model , it turns out that there is no horizon and no singular behaviour of the model . for positive cosmological constant

we present a numerical solution on a 5-dimensional spherically symmetric space time , in einstein - yang - mills - gauss - bonnet theory using a two point boundary value routine . it turns out that the gauss - bonnet contribution has a profound influence on the behaviour of the particle - like solution : it increases the number of nodes of the ym field . when a negative cosmological constant in incorporated in the model , it turns out that there is no horizon and no singular behaviour of the model . for positive cosmological constant the model has singular behaviour .

1004.1344

c

in summary , we present a theory of quantum circuits based on coded qubits encoded in chirality of electron spin complexes in lateral gated semiconductor triple quantum dot molecules with one electron spin in each dot . using microscopic hamiltonian and exact diagonalization techniques we show how to initialize , coherently control and measure the quantum state of a chirality based coded qubit using static in - plane magnetic field and voltage tuning of individual qds . the microscopic model of two interacting coded qubits is established and mapped to an ising hamiltonian . hence both conditional two - qubit phase gate and voltage controlled single qubit operations are demonstrated .

we present a theory of quantum circuits based on logical qubits encoded in chirality of electron spin complexes in lateral gated semiconductor triple quantum dot molecules with one electron spin in each dot . using microscopic hamiltonian we show how to initialize , coherently control and measure the quantum state of a chirality based coded qubit using static in - plane magnetic field and voltage tuning of individual dots . the microscopic model of two interacting coded qubits is established and mapped to an ising hamiltonian , resulting in conditional two - qubit phase gate .

we present a theory of quantum circuits based on logical qubits encoded in chirality of electron spin complexes in lateral gated semiconductor triple quantum dot molecules with one electron spin in each dot . using microscopic hamiltonian we show how to initialize , coherently control and measure the quantum state of a chirality based coded qubit using static in - plane magnetic field and voltage tuning of individual dots . the microscopic model of two interacting coded qubits is established and mapped to an ising hamiltonian , resulting in conditional two - qubit phase gate .

astro-ph0309705

i

a new era of x - ray astronomy has begun with the launch of the @xmath0 @xmath21-@xmath22 @xmath23 on 1999 july 23 , thanks to its very high sensitivity , broad energy range and high angular resolution ( weisskopf et al . 2002 ) . the two deepest x - ray surveys ever conducted , 2 ms @xmath0 deep field north ( brandt et al . 2003 , alexander et al . 2003 ) and 1 ms @xmath0 deep field south ( giacconi et al . 2002 ; rosati et al . 2001 ) , were obtained using the advanced ccd imaging spectrometer detector ( acis ; garmire et al . 2003 ) on @xmath0 @xmath21-@xmath22 @xmath23 . these two surveys are @xmath14 50 times more sensitive than the deepest pre-@xmath0 observations in the soft x - ray band ( 0.5 2.0 kev , e.g. , hasinger et al . 1998 ) and greater than 100 times more sensitive than those deepest pre-@xmath0 observations in the hard x - ray band ( 2.0 10.0 kev , e.g. , ueda et al . 1999 ; fiore et al . 1999 ) . with these surveys , the `` diffuse '' x - ray background discovered four decades ago ( giacconi et al . 1962 ) has been almost entirely resolved into discrete sources ( i.e. @xmath20 90% in the soft band , and @xmath14 80% in the hard band ) . many other deep x - ray blank - sky surveys from @xmath0 ( stern et al . 2002a ; yang et al . 2003 ; mushotzky et al . 2000 ; manners et al . 2003 ) and xmm ( hasinger et al . 2001 ) were also performed in the past few years . along with multi - band observations of the detected x - ray sources , these deep surveys have brought us many interesting results and more important science issues to be addressed . these include the large scale structures from 2d ( yang et al . 2003 ) and 3d ( gilli et al . 2003 ; barger et al . 2002 ) analyses , type 2 qsos ( norman et al . 2002 ; stern et al . 2002b ) , very high redshift x - ray selected active galactic nuclei ( agn , e.g. , barger et al . 2003 ) , and much more . here we present a new deep ( 172 ks ) @xmath0 acis exposure , obtained originally for the follow - up of ly@xmath24 sources from the large area lyman alpha ( lala ) survey s botes field . the large area lyman alpha ( lala ) survey ( rhoads et al . 2000 , 2003 ; rhoads & malhotra 2001 , malhotra & rhoads 2002 ) was designed to search for lyman @xmath24 emitters at high redshifts through narrowband imaging . the survey comprises two primary fields , 36@xmath136 in size each , located in botes ( at 14:25:57 + 35:32 j2000.0 ) and in cetus ( at 02:05:20 -04:55 j2000.0 ) . both fields were chosen to be inside the large areas of the noao deep wide - field survey ( ndwfs ) , which is a deep optical and ir ( @xmath25 ) imaging survey of 18 @xmath26 of the sky with the primary goal of studying the evolution of large - scale structure from @xmath27 ( jannuzi and dey 1999 ; brown et al . 2003 ; jannuzi et al . 2004 , in preparation ) . five broadband optical images ( @xmath9 , @xmath7 , @xmath11 from ndwfs , and @xmath10 , @xmath12 as part of lala ) and eight narrowband images are used to search for lyman-@xmath24 emitters at z @xmath14 4.5 , 5.7 , and 6.5 respectively . the x - ray image presented here was originally obtained to investigate the x - ray properties of the detected high redshift ly@xmath24 emitters . this study was presented by malhotra et al . ( 2003 ) , where we placed stringent upper limits on the typical x - ray flux of ly@xmath24 sources and conclude that agn ( obscured or otherwise ) can not constitute a dominant portion of the ly@xmath24 source population . this @xmath0 exposure ( 172 ks ) is among the deepest yet obtained by @xmath0 of the extragalactic sky ; only the cdf - n and cdf - s are substantially deeper . in this paper we present a full catalog of the detected x - ray sources , along with an analysis of the x - ray source counts , and the @xmath7-band magnitudes ( or 3@xmath8 upper limits ) for their optical counterparts . to study the nature of these sources , spectroscopic follow - up observations for these sources are under way . the present paper is structured as follows : we present the x - ray observations and data reduction in section 2 , source detection and catalog in section 3 , logn - logs in section 4 , and optical identifications in section 5 . our conclusions and summary are presented in section 6 .

we present an analysis of a deep , 172 ks @xmath0 observation of the large area lyman alpha survey ( lala ) botes field , obtained with the advanced ccd imaging spectrometer ( acis - i ) on the @xmath0 x - ray observatory . this is one of the deepest @xmath0 images of the extragalactic sky ; only the 2 ms cdf - n and 1 ms cdf - s are substantially deeper . in this paper we present the x - ray source catalog obtained from this image , along with an analysis of source counts , and optical identifications .

we present an analysis of a deep , 172 ks @xmath0 observation of the large area lyman alpha survey ( lala ) botes field , obtained with the advanced ccd imaging spectrometer ( acis - i ) on the @xmath0 x - ray observatory . this is one of the deepest @xmath0 images of the extragalactic sky ; only the 2 ms cdf - n and 1 ms cdf - s are substantially deeper . in this paper we present the x - ray source catalog obtained from this image , along with an analysis of source counts , and optical identifications . the x - ray image is composed of two individual observations obtained in 2002 , and reaches 0.5 2.0 and 2.0 10.0 kev flux limits of 1.5 @xmath1 10@xmath2 and 1.0 @xmath1 10@xmath3 ergs @xmath4 s@xmath5 , respectively , for point sources near the aim point . a total of 168 x - ray sources were detected : 160 in the 0.5 7.0 kev band , 132 in the 0.5 2.0 kev band , and 111 in the 2.0 7.0 kev band . the x - ray source counts were derived and compared with those from other @xmath0 deep surveys ; the hard x - ray source density of the lala botes field is 33% higher than that of cdf - s at the flux level of 2.0 @xmath1 10@xmath3 ergs @xmath4 s@xmath5 , confirming the field - to - field variances of the hard band source counts reported by previous studies . the deep exposure resolves @xmath6 72% of the 2.0 10.0 kev x - ray background . our primary optical data are @xmath7-band imaging from noao deep wide - field survey ( ndwfs ) , with limiting magnitude of @xmath7 = 25.7 ( vega , 3@xmath8 , 4 diameter aperture ) . we have found optical counterparts for 152 of the 168 @xmath0 sources ( 90% ) ; 144 of these are detected on the @xmath7-band image , and 8 have optical counterparts in other bands ( either @xmath9,@xmath10,@xmath11,@xmath12 ) . among the @xmath7-band non - detected sources , not more than 11 of them can possibly be at @xmath13 5 , based on the hardness ratios of their x - ray emission and nondetections in bluer bands ( @xmath9,@xmath10 ) . the majority ( @xmath14 76% ) of the x - ray sources are found to have log(@xmath15/@xmath16 ) within 0.0@xmath171 , which are believed to be agns . most of the x - ray faint / optically bright sources ( log(@xmath15/@xmath16 ) @xmath18 -1.0 ) are optically extended , which are low - z normal galaxies or low luminosity agns . there is also a population of sources which are x - ray @xmath19 for their optical magnitudes ( log(@xmath15/@xmath16 ) @xmath20 1.0 ) , which are harder in x - ray and are probably obscured agns .

1101.1698

i

be stars are rapidly rotating b - type stars that at times host a circumstellar gas disk @xcite . they exhibit various observational attributes such as photospheric non - radial pulsations , hydrogen and iron emission lines that are formed in the disk , infrared , millimeter , and radio continuum excess emission from the disk , intrinsic linear polarization from electron scattering in the disk , and , in an increasing number of cases , the presence of a compact companion @xcite . the circumstellar ionized gas around be stars gives rise to a large infrared excess emission that is seen in their spectral energy distribution . observations conducted by @xcite at 10 @xmath0 m were the first to suggest that the ir excess of be stars is due to free - free and bound - free emission and not due to thermal dust emission . an early study by @xcite confirmed that the large ir emission detected from 33 be stars originates in the free - free emission only and that thermal dust emission fails to reproduce the observations at 20 @xmath0 m . the ir excess from ionized disk gas was subsequently investigated with space - based data from iras @xcite , iso @xcite , and msx @xcite , and with ground - based mid - ir @xcite and near - ir data from the 2mass survey @xcite . the near- and mid - ir excess flux emission is known to increase with wavelength and to dominate over the stellar flux at long wavelengths . observations probing the circumstellar disk structure at many wavelengths and across all be spectral types are necessary to understand the complex physical processes involving disk formation . models of the disk continuum emission have become increasingly comprehensive in recent years . some of the first models that assumed a simple geometry and gas density distribution @xcite were successful in fitting the color excesses in many cases . a significant improvement came with the development of the viscous decretion disk model @xcite in which the gas orbits with nearly - keplerian velocity , but with a small radial outflow motion caused by turbulent viscosity . these models characterize the disk density with a radial power law , @xmath5 , and a vertical extension set by hydrostatic equilibrium . the ir - excesses predicted are similar to those observed , but often require a density exponent with smaller absolute value and/or a non - isothermal temperature distribution in order to match observations @xcite . recent models include radiation processes in the disk and determine fully consistent temperature and density distributions @xcite , and these are remarkably successful in explaining the continuum and line emission in some be stars @xcite . the advent of optical long baseline interferometry has now led to the direct resolution of be star disks in both emission lines @xcite and in the ir - continuum @xcite . these observations offer us the means to explore the geometry of be disks and to measure the disk gas temperature . since the ir - excess flux depends mainly on the projected size of the disk and the gas surface brightness ( from the temperature dependent source function ) , a comparison of the angular size and flux excess provides a way to investigate the disk - to - star temperature ratio and ( in principle ) to study spatial temperature variations in the disk . our goal in this paper is to explore the ir - excess flux predictions for a parametrized version of the isothermal , viscous disk model that we have developed to study chara array @xmath4-band observations of be disks @xcite . we calculate the near - ir color excesses for various representative stellar and disk parameters and compare these with new ir measurements from the akari satellite @xcite . in 2 , we describe the model in detail and discuss how the different physical parameters of the model influence the color excess . in 3 , we discuss the color - color diagrams and compare our results to the akari all - sky survey observations of be stars . finally in 4 , we consider the example of the be star @xmath2 tau , and we show that the predicted variation of circumstellar disk angular size with wavelength is consistent with the available multi - wavelength observations .

we calculate color excess estimates relative to the stellar @xmath1-band flux for a sample of 130 be stars using photometry from 2mass and the akari infrared camera all - sky survey . the color excess relations from our models make a good match of the observed color excesses of be stars .

we present an analysis of the near - infrared continuum emission from the circumstellar gas disks of be stars using a radiative transfer code for a parametrized version of the viscous decretion disk model . this isothermal gas model creates predicted images that we use to estimate the hwhm emission radius along the major axis of the projected disk and the spatially integrated flux excess at wavelengths of 1.7 , 2.1 , 4.8 , 9 , and 18 @xmath0 m . we discuss in detail the effect of the disk base density , inclination angle , stellar effective temperature , and other physical parameters on the derived disk sizes and color excesses . we calculate color excess estimates relative to the stellar @xmath1-band flux for a sample of 130 be stars using photometry from 2mass and the akari infrared camera all - sky survey . the color excess relations from our models make a good match of the observed color excesses of be stars . we also present our results on the projected size of the disk as a function of wavelength for the classical be star @xmath2 tauri , and we show that the model predictions are consistent with interferometric observations in the @xmath3 , @xmath4 , and 12 @xmath0 m bands .

cond-mat0011391

i

we present a rigorous mathematical examination of the problem of josephson vortices and of the meissner effect in thin - layer josephson - junction stacks and layered superconductors , with a static external magnetic field @xmath13 applied parallel to the layers ( along the @xmath14 axis , see fig . 1 . ) we consider periodic systems composed of an arbitrary number @xmath0 of identical superconductor / insulator ( s / i ) junctions ( @xmath15 , where @xmath2 is the number of s - layers , with @xmath16 being the layering axis ) . our starting point is the microscopic gibbs free - energy functional derived in ref . . mathematical structure of this functional is analogous to that of the phenomenological lawrence - doniach model . @xcite thus , the treatment of our paper fully applies to the latter model as well . mathematically , both josephson vortices in moderate fields @xmath17 and the inhomogeneous meissner state are described by solutions of a system of nonlinear second - order differential equations for phase differences , @xmath18 , with square - integrable first - order derivatives.@xcite ( for brevity , we call here such solutions localized ) . our approach is substantially based on the observation of a nontrivial property of the differential equations for @xmath18 : we show that the problem of finding localized solutions for @xmath18 can be reduced to solving a standard initial value problem . using this key mathematical result , we establish an exact criterion of the existence of localized solutions . the existence criterion , in turn , allows us to obtain a complete classification of physical localized solutions . we have found three types of such solutions : meissner solutions , topological vortex - plane solutions,@xcite and topological incoherent vortex solutions . meissner solutions are localized near the side boundaries @xmath19 and @xmath20 . in contrast to the well - known single - junction case,@xcite the meissner solutions in stacks with @xmath21 turn out to be characterized by several josephson lengths @xmath3 ( @xmath4 lengths for even @xmath2 , and @xmath22 lengths for odd @xmath2 ) . the meissner solutions persist up to a certain superheating field of the meissner phase , @xmath6 . we derive an exact expression for @xmath6 as an explicit function of @xmath2 . we show that the field @xmath6 simultaneously determines the penetration field for vortex planes . ( see below . ) thermodynamically stable vortex - plane solutions represent a chain of @xmath23 josephson vortices ( one vortex per each i - layer ) , positioned in the symmetry plane @xmath24 . these solutions are uniquely determined by the vortex - penetration conditions at @xmath25 . they are characterized by the same set of @xmath3 as the meissner solutions . such solutions were previously obtained for infinite ( @xmath26 ) layered superconductors.@xcite under the name of the coherent mode or the in - phase mode they are well - known in double - junction stacks.@xcite for @xmath27 , the existence of the coherent mode was predicted in ref . . ( the authors of ref . specially emphasized the importance of this mode for practical applications . ) besides giving a proof of the existence and stability of the vortex planes in the general case @xmath15 , we derive exact analytical expressions for their self - energy @xmath28 and for the lower critical field @xmath10 . incoherent vortex solutions comprise single - vortex solutions , vortex solutions with @xmath29 vortices in the plane @xmath30 as well as different vortex - antivortex configurations . all such solutions satisfy the existence criterion . however , in contrast to the vortex - plane solutions , they prove to be thermodynamically unstable and do not meet the vortex - penetration conditions at any @xmath31 . it should be noted that the single - vortex solutions obtained in this paper have no resemblance to hypothetical abrikosov - type vortices , introduced without proper mathematical justification in some previous publications.@xcite besides being thermodynamically unstable , the actual single - vortex solutions are not uniquely determined by asymptotic boundary conditions . they are accompanied by singular phase - difference distribution in all @xmath0 junctions , and their spatial dependence is characterized , in general , by @xmath0 length scales . section ii of the paper is devoted to exact mathematical formulation of the problem . in section iii , we derive all major physical and mathematical results sketched above . the general consideration of this section is illustrated by several concrete examples in section iv . in particular , we analyze 1 - 4-junction stacks and investigate a transition to the layered - superconductor limit ( @xmath12 ) . the obtained results are discussed in section v. appendices a - c contain some additional mathematics , relevant to the subject of our study .

we present an exact mathematical description of josephson vortices and of the meissner effect in periodic thin - layer superconductor / insulator structures with an arbitrary number of identical junctions @xmath0 ( @xmath1 , where @xmath2 is the number of superconducting layers ) in terms of localized solutions to a system of differential equations for phase differences . we establish a general criterion of the existence of localized solutions . we show that meissner solutions are characterized by several josephson lengths @xmath3 ( @xmath4 lengths for even @xmath2 , and @xmath5 lengths for odd @xmath2 ) . we derive an exact expression for the superheating field of the meissner state , @xmath6 , as an explicit function of @xmath7 . for josephson vortices , we find two basically different types of topological solutions : vortex - plane solutions and incoherent vortex solutions . thermodynamically stable vortex - plane solutions represent a chain of @xmath0 vortices ( one vortex per each insulating layer ) . they are characterized by the same set of @xmath8@xmath9 as the meissner solutions . we obtain exact analytical expressions for their self - energy and for the lower critical field @xmath10 . incoherent vortex solutions comprise solutions with @xmath11 vortices and different vortex - antivortex configurations . in contrast to the vortex - plane solutions , they prove to be thermodynamically unstable , and their spatial dependence is characterized , in general , by @xmath0 length scales . as an illustration , we analyze 1 - 4-josephson - junction stacks and investigate a transition to the layered superconductor limit ( @xmath12 ) .

we present an exact mathematical description of josephson vortices and of the meissner effect in periodic thin - layer superconductor / insulator structures with an arbitrary number of identical junctions @xmath0 ( @xmath1 , where @xmath2 is the number of superconducting layers ) in terms of localized solutions to a system of differential equations for phase differences . we establish a general criterion of the existence of localized solutions . we show that meissner solutions are characterized by several josephson lengths @xmath3 ( @xmath4 lengths for even @xmath2 , and @xmath5 lengths for odd @xmath2 ) . we derive an exact expression for the superheating field of the meissner state , @xmath6 , as an explicit function of @xmath7 . for josephson vortices , we find two basically different types of topological solutions : vortex - plane solutions and incoherent vortex solutions . thermodynamically stable vortex - plane solutions represent a chain of @xmath0 vortices ( one vortex per each insulating layer ) . they are characterized by the same set of @xmath8@xmath9 as the meissner solutions . we obtain exact analytical expressions for their self - energy and for the lower critical field @xmath10 . incoherent vortex solutions comprise solutions with @xmath11 vortices and different vortex - antivortex configurations . in contrast to the vortex - plane solutions , they prove to be thermodynamically unstable , and their spatial dependence is characterized , in general , by @xmath0 length scales . as an illustration , we analyze 1 - 4-josephson - junction stacks and investigate a transition to the layered superconductor limit ( @xmath12 ) .

1512.02818

i

* probabilistic vs. deterministic domain decomposition . * in the solution of large boundary value problems ( bvps ) arising in realistic applications ( such as airfoil simulation or weather forecast ) , the discretization of the bvp on a domain @xmath0 leads to algebraic systems of equations that can only be solved on a parallel computer with @xmath1 processors . not only does parallelization require multiple processors but also parallel algorithms . the classical schwarz alternating method @xcite is the best known of the state - of - the - art algorithms which we will refer to as deterministicand serves to illustrate the difficulty that they all face . the idea is to divide @xmath0 into a set of @xmath2 overlapping subdomains , @xmath3 , and have processor @xmath4 solve the restriction of the partial differential equation ( pde ) to the subdomain @xmath5 . but because the solution is not known in the first place , an initial guess has to be made at start , in order to give processor @xmath4 a well - posed ( yet incorrect ) problem . the boundary conditions ( bcs ) along the fictitious interfaces of @xmath5 are then updated from the solution of the surrounding subdomains in an iterative way , hopefully leading to convergence . however , since the inter - processor communication involved in this updating procedure is intrinsically sequential , it will eventually set an upper limit to the scalability of the algorithm according to amdahl s law . summing up , the matrix algebra arising in the discretization of bvps does not , in general , lend itself optimally to parallellization . + an alternative to deterministic methods which is specifically designed to circumvent the scalability issue is the probabilistic domain decomposition ( pdd ) method , which has been successfully applied to elliptic @xcite , parabolic @xcite and hyperbolic bvps @xcite . pdd consists of two stages . in the first stage , the solution is calculated only on a set of interfacial nodes along the fictitious interfaces , by solving the probabilistic representation of the bvp with the monte carlo method . more precisely , the pointwise solution of the bvp is @xmath6 $ ] , i.e. the expected value of a functional @xmath7 of a given stochastic process @xmath8 conditioned to @xmath9 . it is then possible to reconstruct ( approximately ) the solution on the interfaces , so that the pde restricted to each of the subdomains is now well posed , and can be independently solved the second stage of pdd . note that both stages in pdd are embarrasingly parallel by construction . moreover , pdd is naturally fault - tolerant . subdomains and @xmath10 interfaces with @xmath11 nodes each ( @xmath12 ) . * b ) * fem mesh on subdomain @xmath13 . * c ) * the nodal values interpolated with rbfs along the interface @xmath14 , making up a dirichlet bc for @xmath13 and @xmath15 . ] * nomenclature of pdd . * in this paper , we shall exclusively deal with elliptic bvps . let us introduce some terminology ( see figure [ i : figura1 ] ) . the domain @xmath16 ( not necessarily simply connected ) on which the bvp is being solved is partitioned into @xmath17 _ nonoverlapping _ subdomains @xmath18 . the boundary @xmath19 of a subdomain @xmath20 contains several ( @xmath21 ) _ artificial interfaces_each of which is shared between @xmath20 and another adjacent subdomain which are labeled @xmath22 ( note that this labeling is not unique ) . a subdomain boundary @xmath19 may or not contain some portion of the actual boundary . in sum , @xmath23 . artificial interfaces are discretized into _ interfacial nodes _ ( or simply , nodes ) uniquely labeled @xmath24 . assume @xmath17 functions @xmath25 defined on @xmath17 domains @xmath26 such that @xmath27 if @xmath28 . then , their direct sum is defined as @xmath29 the solution of the bvp on the nodes is calculated by resorting to the probabilistic formulation of the bvp with a monte carlo method , yielding the _ nodal values _ ( or _ nodal solutions _ ) @xmath30 . consider a subdomain @xmath20 . a dirichlet bc can then be provided on every @xmath31 by interpolation of the nodal values @xmath32 . along with the actual bcs which apply on @xmath33 , the bvp on @xmath20 now is well posed and can be solved right away , yielding @xmath34 . once the subdomain solutions @xmath35 are available , they are put together to form a global pdd solution : @xmath36 . ( we reserve @xmath37 for the exact solution of the bvp and denote the global pdd approximations with @xmath38 . ) since adjacent subdomains @xmath39 and @xmath5 share a dirichlet bc on their common interface , the pdd solution is continuous in @xmath0although not necessarily differentiable . * the cost of computing the nodal solutions . * the convenience of pdd depends on whether a suitable stochastic representation for the bvp under consideration is available , and on the cost involved in numerically solving it . due to the poor accuracy of the monte carlo method ( compared with deterministic ones ) , the bulk of the cost of pdd falls on the calculation of the nodal solutions to within a required accuracy . more precisely , given a _ nodal error tolerance _ @xmath40 and a _ confidence interval _ @xmath41 , the cost of solving the bvp on an interfacial node scales as @xmath42 , where @xmath43 is the weak convergence rate of the numerical integration scheme ( also called the _ bias _ ) . this poor rate of convergence is due to the slow convergence of both the statistical error and the bias , which have to be tackled simultaneously . for bvps with dirichlet bcs there quite a few linear integrators ( i.e. with @xmath44 ) . regarding the statistical error , replacing the mean by a multilevel estimator of the expected value of feynman - kac functionals has recently been shown to dramatically reduce the cost to @xmath45 @xcite . when the bias law is sharp , extrapolation la talay - tubaro or regression methods in the spirit of @xcite can further improve the accuracy at virtually no extra cost . * using rougher numerical solutions to reduce the variance . * by construction , pdd offers an additional device to accelerate the monte carlo simulation of the nodal values , namely the possibility of calculating and exploiting rougher estimates of the global solution of the bvp . assuming that a numerical solution @xmath46 with a _ target nodal error tolerance _ @xmath47 is required , it may be worth to calculate before a rougher approximation @xmath48 , with an @xmath49 tolerance ; and then use it to draw the stochastic pathwise nodal control variate @xmath50 alongside the monte carlo realizations of the feynman - kac functional . ( in ( [ f : intro_xi ] ) , the integrals are ito s , @xmath51 is the bvp potential , and @xmath52 and @xmath53 are the diffusion matrix and first - exit time from @xmath0 of the stochastic process ( [ f : sde ] ) driven by a wiener process @xmath54 . ) this allows one to construct afterwards an estimator of the feynman - kac functional involving the control variate ( [ f : intro_xi ] ) , which has the same expected value but a much smaller variance . this notion is what we call iterpdd . in order to fix ideas , let us introduce the following notation : @xmath55 means that @xmath38 is a pdd approximation obtained with tolerance @xmath40 and no variance reduction ; while @xmath56= \textrm{iterpdd$(a_0,a_1)$ , or simply iterpdd$(a_0,a_1)$}\ ] ] means that first @xmath57 is calculated without variance reduction , then differentiated in order to construct @xmath58 according to ( [ f : intro_xi ] ) , which in turn is used as control variate in order to reduce the variance in calculating @xmath59 with a target tolerance @xmath47 , which is the ultimate goal . because the nodal values of @xmath59 can now be calculated with much less variance , statistical errors are smaller , and the time ( or cost ) it takes the computer to hit the tolerance @xmath47 is also less . in fact , @xmath60\big)\times$cost plainpdd$(a_0)$},\end{aligned}\ ] ] where @xmath61 $ ] is pearson s correlation . as ( [ f : cost_of_iterpdd ] ) indicates , there is a tradeoff between the effort invested in calculating @xmath62 , and the reduction of variance yielded by @xmath63 , which depends on the quality of @xmath62 . the most straightforward procedure is to simply guess some @xmath49 . while numerical tests indicate that the iterpdd strategy can be quite successful , a poorly chosen @xmath64 may well result in an overall cost of iterpdd@xmath65 _ larger _ than that of plainpdd@xmath66 . therefore , at the heart of iterpdd lies an optimization problem for @xmath64 . in order to make educated guesses of @xmath64 given @xmath47 , two questions must be tackled : i ) how does the cost of a @xmath67plainpdd@xmath68 simulation depend on @xmath40 ; and ii ) how does @xmath69 $ ] depend on @xmath40 . the former requires that the sde integrator have a predictable and sharp order of weak convergence . deriving a _ sensitivity formula _ for ii ) is one of the main points of this paper . * a multigrid - like pdd algorithm . * with such a sensitivity formula in place which can predict an optimal ( or more realistically , good enough ) initial tolerance @xmath64 for @xmath70=$]iterpdd@xmath65 , it is natural to try and compute @xmath62 faster by finding @xmath71 which minimizes the cost of @xmath72=$]iterpdd@xmath73 . much like in the multigrid method , a number @xmath74 and an _ optimal sequence _ of nested iterpdd simulations can be envisioned with tolerances @xmath75 which fully exploits the potential of control variates for a given bvp . however , in iterpdd , given a target tolerance @xmath47 , the number @xmath74 and the sequence @xmath76 must be determined _ before _ actually running one single pdd simulation . to compound matters , all of @xmath74 , @xmath77 , and in general any result provided by any such _ scheduling algorithm _ will be affected by the randomness introduced by monte carlo , making its performance meaningful only in terms of its expected value and variance . * outline of the paper . * we start by revisiting the probabilistic formulation of elliptic bvps with dirichlet bcs in section [ s : representation ] , and identifying the pathwise control variates . section [ s : theory ] formally poses the problem namely , acceleration of pdd with the iterpdd scheme and presents our own theoretical results concerning the aforesaid sensitivity @xmath69 $ ] . section [ s : globalerror ] links the nodal target error tolerance , @xmath47 , to the global pdd error tolerance @xmath78and discusses the stability of pdd . in section [ s : approximations ] , the formal restrictions in section [ s : theory ] are relaxed leading to practical , but partially heuristic , scheduling algorithm / sensitivity formula ( algorithm [ a : scheduling ] ) and final iterative , multigrid - like pdd loop ( algorithm [ a : iterpdd ] ) . they are numerically tested in section [ s : experiment ] , and section [ s : conclusions ] concludes the paper .

increasingly accurate approximations to the solution are used as control variates in order to reduce the monte carlo error of the following iterates resulting in an overall acceleration of pdd for a given error tolerance . besides , the theoretical framework allows to explore other aspects of pdd , such as stability . one numerical example is worked out , yielding an improvement of between one and two orders of magnitude over the previous version of pdd .

we present an iterative scheme , reminiscent of the multigrid method , to solve large boundary value problems with probabilistic domain decomposition ( pdd ) . in it , increasingly accurate approximations to the solution are used as control variates in order to reduce the monte carlo error of the following iterates resulting in an overall acceleration of pdd for a given error tolerance . the key ingredient of the proposed algorithm is the ability to approximately predict the speedup with little computational overhead and in parallel . besides , the theoretical framework allows to explore other aspects of pdd , such as stability . one numerical example is worked out , yielding an improvement of between one and two orders of magnitude over the previous version of pdd . * keywords : * pdd , domain decomposition , scalability , high - performance supercomputing , variance reduction , feynman - kac formula .

1301.6571

i

the development of sustainable energy solutions based on scalable processes and non - toxic materials constitutes a key priority in the current scientific research agenda , and in this area nanostructured energy - harvesting solar and thermoelectric devices are playing a lead role . recently there has been a surge of interest in devices using semiconducting metal chalcogenides of the stibnite family . for example recent studies have demonstrated the potential of these semiconductors both in photovoltaics applications,@xcite and in thermoelectric generators.@xcite in the area of nanostructured photovoltaics semiconducting metal chalcogenides have successfully been used to replace the inorganic dye in dye - sensitized solar cells,@xcite leading to the development of solid - state semiconductor - sensitized solar cells.@xcite in these devices thin layers or nanoparticles of the semiconducting chalcogenides act as light absorbers , and upon photoexcitation they transfer an electron to the acceptor ( typically tio@xmath0 ) and a hole to the hole - transporter ( for example a conducting polymer ) . the record efficiency within this class of devices is 5.1% and was obtained using stibnite ( sb@xmath0s@xmath1 ) as semiconductor sensitizer.@xcite a recent atomistic computational study of photovoltaic interfaces for semicondictor - sensitized solar cells pointed out that , in addition to stibnite , the other members of the stibnite mineral family , namely antimonselite ( sb@xmath0se@xmath1 ) , bismuthinite ( bi@xmath0s@xmath1 ) , and guanajuatite ( bi@xmath0se@xmath1 ) , exhibit optical properties similar to stibnite and should be considered as potential candidates for novel semiconductor sensitizers.@xcite using density - functional calculations and empirical scissor corrections of the band gaps , in ref . it was found that stibnite and antimonselite should form type - ii heterojunctions with tio@xmath0 , while bismuthinite should form a type - i heterojunction and hence would not be able to transfer electrons to tio@xmath0 . these theoretical predictions have recently been confirmed by the experimental investigations of refs . , thereby providing a motivation for further studies and for the more sophisticated analysis presented in this work . the four minerals of the stibnite family crystallize in an orthorhombic structure consisting of parallel one - dimensional ( a@xmath4b@xmath5)@xmath6 ribbons , with a = sb , bi and b = s , se . a ball - and - stick model of this structure is shown in fig . [ fig : cryst ] . besides its natural occurrence in mineral form , stibnite can be synthesised using a variety of low - cost fabrication techniques.@xcite using these techniques it is possible to obtain a good degree of crystallinity,@xcite to control dimensionality,@xcite and to tune the optical properties.@xcite b@xmath1 semiconducting metal chalcogenides of the stibnite family , with a standing for sb or bi ( brown ) , and b for s or se ( yellow ) . the two inequivalent ( a@xmath4b@xmath5)@xmath6 ribbons in the unit cell are highlighted in red , and the perspective view is along the direction of the ribbons . ] semiconductors of the stibnite family have also been synthesized in various nanostructured forms . for example refs . and refs . reported nanowires and nanotubes , respectively , of stibnite , antimonselite and bismuthinite . nanowires of stibnite were found to exhibit enhanced ferroelectric and piezoelectric properties as compared to their bulk counterpart.@xcite nanowires and nanotubes of antimonselite were found to exhibit conductivities much higher than their bulk counterpart,@xcite and are being considered for thermoelectric applications . in the case of bismuthinite , ref . reported nanowires with diameters as small as 1.6 nm , corresponding to a transverse size of only two ribbons . the rhombohedral phase of bi@xmath0se@xmath1 has been investigated extensively since this compound is a prototypical topological insulator.@xcite however to the best of our knowledge little is known about orthorhombic bi@xmath0se@xmath1 , i.e. guanajuatite , which is stable only at high temperature and pressure.@xcite the band gaps of stibnite , antimonselite and bismuthinite have been measured extensively via optical absorption experiments . the band gap of stibnite ranges between 1.42 - 1.78 ev.@xcite for antimonselite ref . reported a direct gap of 1.55 ev , while ref . gave an indirect gap between 1 - 1.2 ev . the measured band gap of bismuthinite is 1.38 - 1.58 ev.@xcite the spread in the measured gaps can be attributed to the different preparation conditions used , yielding different degrees of polycrystallinity and even amorphous samples in some cases , and also different stoichiometries . in addition all these compounds exhibit closely lying direct and indirect transitions ( cf . [ fig : bandstruct ] below ) , thereby complicating the assignment of the nature of the optical gap . all four minerals of the stibnite family have been investigated in detail using density - functional theory ( dft ) calculations . the electronic properties of these compounds have been studied in refs . , and the elastic and optical properties have been calculated in ref . . a comparison of the theoretical studies published so far shows some inconsistencies in the calculated band gaps , for example the values reported for stibnite are in the range 1.18 - 1.55 ev.@xcite as expected all the calculated dft gaps underestimate the measured band gaps . to the best of our knowledge only one work@xcite reported a calculation of the quasiparticle band gap of stibnite and antimonselite within the gw approximation.@xcite the electronic structure of the rhombohedral bi@xmath0se@xmath1 has also been explored within the gw approach @xcite . within this context there exists a need for detailed and reproducible calculations of the electronic structure of stibnite and related compounds based on state - of - the - art quasiparticle techniques . in line with this need the goal of the present work is to report a systematic and reproducible study of the quasiparticle band structures of all four a@xmath0b@xmath1 semiconducting metal chalcogenides of the stibnite family . an emphasis is placed on convergence tests and on the sensitivity of the quasiparticle corrections to the structural parameters , the inclusion of semicore @xmath3 states in the calculations , and relativistic effects . our calculated band gaps are 1.5 ev ( sb@xmath0s@xmath1 ) , 1.3 ev ( sb@xmath0se@xmath1 ) , 1.4 ev ( bi@xmath0s@xmath1 ) and 0.9 ev ( bi@xmath0se@xmath1 ) . by inspection of the band structures we infer that all four compounds have direct band gaps , although in most cases an indirect transition just below the direct gap ( within 0.1 ev ) is also possible . the inclusion of semicore electrons in the calculations is found to modify the band gaps by 0.1 - 0.2 ev . in addition we find that the gaps are rather sensitive to the lattice parameters , as they change by up to 0.3 ev when the lattice parameters are taken from experiment or fully optimized within dft . relativistic corrections are found to be essentially negligible for sb@xmath0s@xmath1 and sb@xmath0se@xmath1 , while in the case of bi@xmath0s@xmath1 and bi@xmath0se@xmath1 the band gaps decrease by 0.3 - 0.4 ev upon inclusion of spin - orbit coupling . the manuscript is organized as follows . in sec . [ sec : methodology ] we describe the computational methodology and the convergence tests for the gw calculations . in sec . [ sec : results ] we present our main results , including quasiparticle band structures and band gaps . in sec . [ sec : discussion ] we discuss our findings in relation to the photovoltaics applications of the materials considered in this work . in sec . [ sec : conclusions ] we summarize our results and present our conclusions .

we perform extensive convergence tests and identify a sensitivity of the quasiparticle corrections to the structural parameters and to the semicore @xmath3 electrons . our calculated band gaps are 1.5 ev ( sb@xmath0s@xmath1 ) , 1.3 ev ( sb@xmath0se@xmath1 ) , 1.4 ev ( bi@xmath0s@xmath1 ) and 0.9 ev ( bi@xmath0se@xmath1 ) . by comparing our calculated gaps with the ideal shockley - queisser value

we present first - principles calculations of the quasiparticle band structures of four isostructural semiconducting metal chalcogenides a@xmath0b@xmath1 ( with a = sb , bi and b = s , se ) of the stibnite family within the g@xmath2w@xmath2 approach . we perform extensive convergence tests and identify a sensitivity of the quasiparticle corrections to the structural parameters and to the semicore @xmath3 electrons . our calculations indicate that all four chalcogenides exhibit direct band gaps , if we exclude some indirect transitions marginally below the direct gap . relativistic spin - orbit effects are evaluated for the kohn - sham band structures , and included as scissor corrections in the quasiparticle band gaps . our calculated band gaps are 1.5 ev ( sb@xmath0s@xmath1 ) , 1.3 ev ( sb@xmath0se@xmath1 ) , 1.4 ev ( bi@xmath0s@xmath1 ) and 0.9 ev ( bi@xmath0se@xmath1 ) . by comparing our calculated gaps with the ideal shockley - queisser value we find that all four chalcogenides are promising as light sensitizers for nanostructured photovoltaics .

1301.6571

c

in this work we report a systematic study of the quasiparticle band structures of the four isostructural metal chalcogenides stibnite ( sb@xmath0s@xmath1 ) , antimonselite ( sb@xmath0se@xmath1 ) , bismuthinite ( bi@xmath0s@xmath1 ) , and guanajuatite ( bi@xmath0se@xmath1 ) , within the gw approximation . in order to ensure reproducibility of our results we have placed an emphasis on convergence tests and explored the effects of various calculation parameters , such as for instance the role of semicore @xmath3 electrons and lattice parameters . the inclusion of semicore electrons in the calculations is found to modify the band gaps by up to 0.2 ev , and the choice of experimental vs. optimized lattice parameters can lead to differences of up to 0.3 ev in the calculated gaps . these findings indicate that some caution should be used in discussing the theoretical band gaps of these materials and in comparing with experiment . relativistic effects are found to lower the conduction bands of all four materials . spin - orbit coupling effects are important in bi@xmath0s@xmath1 and bi@xmath0se@xmath1 , where they reduce the band gaps by 0.3 - 0.4 ev , while they are essentially negligible for sb@xmath0s@xmath1 and sb@xmath0se@xmath1 . our calculations indicate that all four compounds have direct band gaps , barring indirect transitions marginally below the direct gap . the calculated band gaps are 1.54 ev ( stibnite ) , 1.27 ev ( antimonselite ) , 1.42 ev ( bismuthinite ) and 0.91 ev ( guanajuatite ) . these values fall within the range of measured optical gaps , although it must be observed that there is a considerable scatter in the experimental data , possibly due to different preparation conditions . using a modified shockley - queisser analysis,@xcite we estimate the ultimate performance of solar cells based on these compounds as light sensitizers . this analysis indicates that all four materials have potential for high - efficiency nanostructured solar cells . the highest theoretical efficiencies are obtained for antimonselite and bismuthinite , followed closely by stibnite and guanajuatite , the high temperature polymorph of the topological insulator bi@xmath0se@xmath1 . future calculations should address the optical absorption spectra of these compounds within the bethe - salpeter approach , in order to establish whether excitonic effects are small as our data appear to suggest . it will be also interesting to extend the present study to the case of individual nanoribbons of these metal chalcogenides , since liquid - phase exfoliation techniques for van der waals bonded materials are becoming increasingly popular.@xcite we hope that the present study will contribute to the ongoing research on new materials for energy applications , and stimulate further efforts to understand and exploit these fascinating and relatively unexplored compounds .

we present first - principles calculations of the quasiparticle band structures of four isostructural semiconducting metal chalcogenides a@xmath0b@xmath1 ( with a = sb , bi and b = s , se ) of the stibnite family within the g@xmath2w@xmath2 approach . our calculations indicate that all four chalcogenides exhibit direct band gaps , if we exclude some indirect transitions marginally below the direct gap .

we present first - principles calculations of the quasiparticle band structures of four isostructural semiconducting metal chalcogenides a@xmath0b@xmath1 ( with a = sb , bi and b = s , se ) of the stibnite family within the g@xmath2w@xmath2 approach . we perform extensive convergence tests and identify a sensitivity of the quasiparticle corrections to the structural parameters and to the semicore @xmath3 electrons . our calculations indicate that all four chalcogenides exhibit direct band gaps , if we exclude some indirect transitions marginally below the direct gap . relativistic spin - orbit effects are evaluated for the kohn - sham band structures , and included as scissor corrections in the quasiparticle band gaps . our calculated band gaps are 1.5 ev ( sb@xmath0s@xmath1 ) , 1.3 ev ( sb@xmath0se@xmath1 ) , 1.4 ev ( bi@xmath0s@xmath1 ) and 0.9 ev ( bi@xmath0se@xmath1 ) . by comparing our calculated gaps with the ideal shockley - queisser value we find that all four chalcogenides are promising as light sensitizers for nanostructured photovoltaics .

1205.6932

i

disentangling the stellar populations of galaxies is important to understanding their evolution and the enhancement of star formation in the universe , since the integrated spectrum of galaxies is sensitive to the mass , age , metallicity , dust and star formation history of their dominant stellar populations . despite this complexity , the observed optical spectra of galaxies can be accurately reproduced ( e.g. , worthey 1994 ) . high - quality observational data is paramount to test and improve spectrophotometric models , which are used , in turn , to derive the main properties of high redshift galaxies . optical lick spectral indices have usually been used in stellar population studies of local galaxies ( worthey & ottaviani 1997 ) , but they have problems due to blended features and various population of galaxies . near - infrared ( nir , hereafter ) spectroscopy has advantages compared to optical , because red giant branch ( rgb ) stars dominate at @xmath7 m and the wavelength region contains many diagnostic stellar absorption lines ( e.g. , mgi 1.575@xmath3 m , si @xmath8 m , co(6 - 3 ) 1.619@xmath3 m , mgi 1.711@xmath3 m , nai @xmath9 m , cai 2.263@xmath3 m and co(2 - 0 ) bandhead @xmath102.29@xmath3 m ) which can be used as indicators of stellar population in terms of their temperature and/or luminosity . the contributions of dwarf , giant and supergiant stars can be characterized by different depths of their absorption lines and by different shapes of their nir continuum ( e.g. lanon et al . 1999 ) . much of the work at nir wavelengths has focused on unusual objects with either active galactic nuclei ( agn ) or very strong star formation activity . these surveys include those of luminous and ultraluminous infrared galaxies ( goldader et al . 1997 ; burston , ward , & davies 2001 ; dannerbauer et al . 2005 ) , various types of starbursts ( engelbracht et al . 1998 ; vanzi & rieke 1997 ; coziol , doyon , & demers 2001 ; reunanen , tacconi - garman & ivanov 2007 ) , seyfert galaxies ( ivanov et al . 2000 ; reunanen , kotilainen , & prieto 2002,2003 ; riffel et al . 2009 ) liners ( larkin et al . 1998 ; alonso - herrero et al . 2000 ) , and ellipticals ( silva et al . 2008 ; cesetti et al . however , relatively little nir spectroscopy exists for inactive nearby spiral galaxies . such surveys are necessary , though , for understanding their star formation histories , and for setting a baseline for the nir emission from inactive spiral galaxies . without such a baseline , the contribution of quiescent stellar populations to nir emission in more exotic systems like ultraluminous infrared galaxies and starbursts will remain unknown . the two largest previous nir spectroscopic studies of inactive spirals were performed by mannucci et al . ( 2001 ) and bendo & joseph ( 2004 ) . mannucci et al . ( 2001 ) studied 28 galaxies with a 7 x 53 arcsec aperture and r = 400 - 500 . generally , they found a high degree of uniformity for the spectra of spirals ( earlier types being more homogeneous ) but their study was hampered by the low spectral resolution which prevented them from detecting faint and/or blended lines . more recently , bendo & joseph ( 2004 ) studied 41 galaxies in the k - band and 20 galaxies in the h - band , with slightly higher spectral resolution r = 8001200 . they extracted spectra from 30@xmath1115arcsec apertures , and found that in almost all cases evolved red stars completely dominate the nuclear stellar populations , while young stars were virtually non - existent . we stress , however , that both these studies suffer from poor spatial resolution , leading to a possible mix of bulge and disk stellar populations . to improve this situation , we present in this work nir spectroscopy of nearby inactive spiral galaxies along the hubble sequence , to study their stellar population content and sf histories . stellar emission and absorption features can probe with great detail the age and sf properties of the stellar population in the nucleus and as a function of radius . comparison of these properties along the hubble sequence of spirals will assess any relationship of sf with hubble stage . we present nir spectroscopy for a sample of 29 nearby ( @xmath2 ) spirals with reasonable spatial resolution ( @xmath121 kpc / arcsec ) and medium spectral resolution ( @xmath13600 ) to study the nir properties and ages of their stellar populations . except for a few individual sources , these are the first medium resolution nir spectra of a sizable sample of low redshift spirals . long - slit spectra of the spirals are extracted across the nucleus to detect all the important diagnostic absorption lines , and emission from the galaxies can usually be studied to large distance from the nucleus . our aim is to study the stellar population of spirals based on the nir stellar absorption indices , and to inter - compare these indices within the different morphology types . this paper is organized as follows : in section[sec : sample ] we describe the sample selection , observations , data reduction and methods of analysis . in section[sec : results ] , we present the results and discussion concerning the properties of the galaxies , and the composite quiescent spectra , and in section[sec : conclusions ] we summarize our conclusions based on the full sample of 29 spiral galaxies . throughout this paper , we adopt a concordance cosmology with @xmath14 = 70 mpc@xmath15 , @xmath16 = 0.3 and @xmath17 = 0.7 .

we present high spatial resolution , medium spectral resolution near - infrared ( nir ) @xmath0- and @xmath1-band long - slit spectroscopy for a sample of 29 nearby ( @xmath2 ) inactive spiral galaxies , to study the composition of their nir stellar populations . these spectra contain a wealth of diagnostic stellar absorption lines , e.g. mgi 1.575@xmath3 m , sii 1.588@xmath3 m , co ( 6 - 3 ) 1.619@xmath3 m , mgi 1.711@xmath3 m , nai 2.207@xmath3 m , cai 2.263@xmath3 m and the @xmath4co and @xmath5co bandheads longward of 2.29@xmath3 m . the strength of the absorption lines depends on the luminosity and/or temperature of stars and , therefore , spectral indices can be used to trace the stellar population of galaxies . [ firstpage ] galaxies : elliptical and lenticular , cd galaxies : spiral galaxies : stellar content infrared : galaxies

we present high spatial resolution , medium spectral resolution near - infrared ( nir ) @xmath0- and @xmath1-band long - slit spectroscopy for a sample of 29 nearby ( @xmath2 ) inactive spiral galaxies , to study the composition of their nir stellar populations . these spectra contain a wealth of diagnostic stellar absorption lines , e.g. mgi 1.575@xmath3 m , sii 1.588@xmath3 m , co ( 6 - 3 ) 1.619@xmath3 m , mgi 1.711@xmath3 m , nai 2.207@xmath3 m , cai 2.263@xmath3 m and the @xmath4co and @xmath5co bandheads longward of 2.29@xmath3 m . we use nir absorption features to study the stellar population and star formation properties of the spiral galaxies along the hubble sequence , and we produce the first high spatial resolution nir @xmath6-band template spectra for low redshift spiral galaxies along the hubble sequence . these templates will find applications in a variety of galaxy studies . the strength of the absorption lines depends on the luminosity and/or temperature of stars and , therefore , spectral indices can be used to trace the stellar population of galaxies . the entire sample testifies that the evolved red stars completely dominate the nir spectra , and that the hot young star contribution is virtually nonexistent . [ firstpage ] galaxies : elliptical and lenticular , cd galaxies : spiral galaxies : stellar content infrared : galaxies

1205.6932

c

we have presented medium resolution nir @xmath6-band spectra of a sizable sample of low redshift inactive spiral galaxies , to study their stellar populations along the hubble sequence , based on the diagnostic stellar absorption lines . our main results are : ( i ) the ews of the sii , co(1.62 ) nai , cai and co(2.29 ) features in the spirals are most consistent with those of giant stars , whereas ellipticals ( from literature ) show a contribution from main sequence dwarf stars , and on average , ew(co2.29 ) of spirals is somewhat greater than that of ellipticals . most likely , the ews are not significantly affected by non - stellar dilution . ( ii ) overall , evolved red stars completely dominate the nir spectra , while contribution from hot young stars is virtually nonexistent . ( iii ) we produce high spatial resolution nir @xmath6-band template spectra for spirals along the hubble sequence , that will form a baseline for comparison to galaxies with more exotic star formation or agn activity .

we use nir absorption features to study the stellar population and star formation properties of the spiral galaxies along the hubble sequence , and we produce the first high spatial resolution nir @xmath6-band template spectra for low redshift spiral galaxies along the hubble sequence . the entire sample testifies that the evolved red stars completely dominate the nir spectra , and that the hot young star contribution is virtually nonexistent .

we present high spatial resolution , medium spectral resolution near - infrared ( nir ) @xmath0- and @xmath1-band long - slit spectroscopy for a sample of 29 nearby ( @xmath2 ) inactive spiral galaxies , to study the composition of their nir stellar populations . these spectra contain a wealth of diagnostic stellar absorption lines , e.g. mgi 1.575@xmath3 m , sii 1.588@xmath3 m , co ( 6 - 3 ) 1.619@xmath3 m , mgi 1.711@xmath3 m , nai 2.207@xmath3 m , cai 2.263@xmath3 m and the @xmath4co and @xmath5co bandheads longward of 2.29@xmath3 m . we use nir absorption features to study the stellar population and star formation properties of the spiral galaxies along the hubble sequence , and we produce the first high spatial resolution nir @xmath6-band template spectra for low redshift spiral galaxies along the hubble sequence . these templates will find applications in a variety of galaxy studies . the strength of the absorption lines depends on the luminosity and/or temperature of stars and , therefore , spectral indices can be used to trace the stellar population of galaxies . the entire sample testifies that the evolved red stars completely dominate the nir spectra , and that the hot young star contribution is virtually nonexistent . [ firstpage ] galaxies : elliptical and lenticular , cd galaxies : spiral galaxies : stellar content infrared : galaxies

astro-ph0405141

c

cygnus x-1 was already known to have a ` very flat ' ( @xmath16 @xmath17 ) spectrum from the radio ( 2 ghz ) through mm ( 350 ghz ) bands while in the low / hard x - ray state ( fender et al . this was naturally interpreted as a high - frequency extension of the self - absorbed synchrotron spectrum from a steady jet of the kind envisaged by blandford & konigl ( 1979 ) , hjellming & johnston ( 1988 ) , falcke & biermann ( 1996 ) , and others . direct evidence for the extension of the synchrotron spectrum to the near - infrared has also been found in the low / hard state black hole binary gx 339 - 4 ( corbel & fender 2002 ) . however , these conclusions are heavily based upon interpretations of broad - band spectra . in this paper we have reported the quenching of this mm emission when cygnus x-1 changed to a softer ( high / soft or intermediate ) x - ray state , precisely as has been seen for this and other black hole x - ray binaries in the radio band ( fender et al . 1999 ; corbel et al . 2001 ; gallo , fender & pooley 2003 ) . it was already known in the case of the black hole transient xte j1118 + 480 that the mm emission dropped significantly as the source faded ( fender et al . 2001 ) . in fig 2 we present the x - ray and mm data for cyg x-1 and xte j1118 + 480 , superimposed upon the x - ray : radio diagram for all low / hard state galactic black hole binaries from gallo et al . the points for cyg x-1 lie exactly in the same ` cloud ' of points as the radio emission , due to the very flat radio mm spectrum . the points for xte j1118 + 480 are significantly above the relation , due to the strongly inverted ( @xmath9 ) radio mm spectrum observed from this source , as a result of which the flux density at 350 ghz is @xmath18 times that at 5 ghz . this indicates that , while the @xmath19 relation seems to hold without serious consideration of the source spectrum , spectral effects will be important in investigating the correlation in other bands . the combination of the data for cyg x-1 and that of xte j1118 + 480 clearly indicates that * in the low / hard state , the mm emission correlates with the x - ray flux * in softer states , the mm emission is quenched this behaviour is exactly as observed for the relation between radio and x - ray emission . note that while it is clearly easier to demonstrate trends in the disc - jet coupling by means of radio and x - ray monitoring ( e.g. gallo , fender & pooley 2003 ) , it is of utmost importance to establish as convincingly as possible the full spectral extent of the jet component . only by firmly establishing the contribution of jets to the broadband spectrum of x - ray binaries can we accurately estimate their contribution to the overall energetics of the system ( e.g. fender 2001 ) . in this respect , our mm observations are important as they lie much closer to the spectral regime in which other processes may contribute . bremsstrahlung emission from stellar winds ( e.g. wright & barlow 1975 ; panagia & felli 1975 ) and self - absorbed ( cyclo-)synchrotron emission from advection - dominated accretion flows ( e.g. mahadevan 1997 ; narayan , mahadevan & quataert 1998 ) are associated with spectral indices @xmath20 and may therefore be invoked to explain the mm emission much more readily than the radio . the coupling revealed here argues however that in black hole x - ray binaries in the low / hard state the jet dominates the emission in the mm band . we therefore conclude that the mm emission arises from the same physical component as the radio emission , most likely to be a jet - like outflow . at such high frequencies we are probing @xmath0 times closer to the base of the jet than in the radio band . the next step will be to see if infrared emission , probing another 100 - 1000 times closer , shows the same coupling to x - ray states . in this direction we suggest that the 10@xmath21 m band , where new detectors are now available , and the thermal emission from companion stars and accretion discs should generally be weak .

we present millimetre wavelength observations of the black hole candidate x - ray binary cygnus x-1 which indicate a suppression , or quenching , of the emission as the source switches to a softer x - ray state . combining the data with those for another black hole candidate , xte j1118 + 480 , we demonstrate that the millimetre emission shows the same coupling to x - rays as the radio emission , although with a much stronger sensitivity to spectral shape . we therefore confirm the association of the millimetre emission with the jets in low / hard state black hole candidate x - ray binaries .

we present millimetre wavelength observations of the black hole candidate x - ray binary cygnus x-1 which indicate a suppression , or quenching , of the emission as the source switches to a softer x - ray state . combining the data with those for another black hole candidate , xte j1118 + 480 , we demonstrate that the millimetre emission shows the same coupling to x - rays as the radio emission , although with a much stronger sensitivity to spectral shape . we therefore confirm the association of the millimetre emission with the jets in low / hard state black hole candidate x - ray binaries .

0708.1030

i

ngc 346:kwbbe 200 is a b - type star whose optical spectrum is dominated by fe ii , [ o i ] , [ fe ii ] , and strong p - cygni h i emission lines , and exhibits clear evidence of having a circumstellar envelope characterized by the presence of gas and warm ( t@xmath16 @xmath0800 k ) dust . based on these observational properties , we suggest that ngc 346:kwbbe 200 is a b[e]sg star , representing the fifth such object identified to date in the smc . our crude estimate of the star s luminosity , log ( l / l@xmath8 ) @xmath04.4 , its location on a hr diagram , and its observed line profile morphologies suggests it is most likely to be a b[e ] supergiant . we recommend several observational approaches be pursued to further constrain the evolutionary status of ngc 346:kwbbe 200 . mid- to far - ir photometric observations would allow one to search for the presence of cool dust , which is one of the defining characteristics of haeb[e ] stars @xcite and would not be an expected characteristic of b[e]sgs . moreover , high resolution optical and uv spectroscopic observations would facilitate the derivation of a more reliable estimate of ngc 346:kwbbe 200 s spectral type and luminosity , hence providing more conclusive evidence of the post - main sequence evolutionary status suggested in this paper . optical photometric monitoring , to search for and characterize variability , and measurements of the star s rotational velocity would aid efforts to explore evolutionary links between the b[e]sg and lbv phases of massive star evolution . we thank ted gull and aki roberge for helpful discussions about these results . we also thank our referee , jorick vink , for providing useful feedback which improved the content and presentation of this paper . support for this project was provided by nasa npp and gsrp fellowships to jpw ( nnh06cc03b , ngt5 - 50469 ) , a nasa ltsa grant nag5 - 8054 and a research corporation cottrell scholar award to ksb , and a nsf grant ( ast-0307686 ) to jeb . this work is based in part on observations made with the spitzer space telescope , which is operated by the jet propulsion laboratory , california institute of technology under a contract with nasa . we have also made use of the simbad database operated at cds , strasbourg , france , and the nasa ads system . -267 ) , line - profile morphology ( p - cygni ) , and broad electron scattering wings ( @xmath0 -2100 km s@xmath2 and @xmath0 + 2190 km s@xmath2 ) of the h@xmath1 line in ngc 346:kwbbe 200 is similar to that observed in other b[e]sgs @xcite . [ ha ] ] sgs ( blue circles ) from @xcite , @xcite , and the 2mass catalog are shown on a near - ir 2-color diagram . ngc 346:kwbbe 200 s near - ir color clearly coincides with that of other dusty magellanic cloud ( b[e ] and herbig ae / be ) stars and is inconsistent with the observed near - ir colors of magellanic cloud classical be stars . [ 2cd ] ] @xmath0 800k , dust . the optical photometry are consistent with a kurucz model atmosphere having t@xmath9 = 19,000k and r@xmath10 = 14 r@xmath8 . the extrapolated stellar luminosity , log ( l / l@xmath8 ) @xmath04.4 , and observed line profile morphologies suggest that ngc 346:kwbbe 200 is a b[e]sg . [ sed ] ] sgs ( red , green , and blue triangles respectively ) and galactic haebe stars ( yellow squares ) . temperature and luminosity values were taken from @xcite and references therein for all of these ancillary sources , except for the luminosity of mwc 1080 @xcite and v594 cas @xcite , whose tabulated values within @xcite did not match their quoted literature origin and/or could not be otherwise verified . also overplotted are the canonical evolutionary tracks and zams for 9 and 15 m@xmath8 ( z = 0.001 ) stars ( black lines ) and 3 and 5 m@xmath8 ( z = 0.020 ) stars ( red lines ) , the birthline for the z = 0.020 models ( light blue line ) , and isochrones for the z = 0.001 models ( dashed green , blue , and yellow lines ) . ngc 346:kwbbe 200 is well above the birthline of late - type b stars ( 5 m@xmath8 ) , and appears to be most similar to the lower luminosity magellanic cloud b[e]sgs stars reported by @xcite . furthermore , its observed photometric and spectroscopic properties do not indicate that the star is highly embedded in a natal star formation envelope , as would be expected if it were truly located at the log(t ) = 4.25 isochrone of the 15 m@xmath8 pre - ms evolutionary track of @xcite . [ hrd ] ] lccccc wavelength & line & ew ( ) & comment + + 3970 & h @xmath5 & & p - cygni + 4101 & h @xmath17 & 0.4 & p - cygni + 4233 & fe ii & -1.3 & + 4340 & h @xmath18 & -5.2 & p - cygni + 4417 & fe ii & & + 4491 & fe ii & & blend@xmath19 + 4508 & fe ii & & + 4515 & fe ii & & + 4522 & fe ii & & blend@xmath11 + 4534 & ti ii + fe ii & & blend@xmath20 + 4549 & fe ii + ti ii & & blend@xmath12 + 4555 & fe ii & & + 4584 & fe ii & & + 4629 & fe ii & & + 4861 & h @xmath21 & -29.3 & p - cygni@xmath22 + 4921 & he i & & abs + 4924 & fe ii & -2.3 & + 5015 & he i & & abs + 5018 & fe ii & -3.5 & + 5158 & [ fe ii ] & & + 5169 & fe ii & & p - cygni ? + 5184 & [ fe ii ] & & + 5198 & fe ii & -1.0 & + 5235 & fe ii & -1.2 & + 5276 & fe ii & & + 5317 & fe ii & -2.4 & + 5363 & fe ii & & + 5535 & fe ii & & + 6148 & fe ii & -0.4 & + 6238 & fe ii & & + 6248 & fe ii & -0.7 & + 6300 & [ o i ] & -1.2 & + 6318 & mg i & & + 6363 & [ o i ] + fe ii & & blend@xmath23 + 6385 & fe ii & -0.8 & + 6417 & fe ii & & + 6433 & fe ii & & + 6456 & fe ii & & + 6516 & fe ii & & + 6563 & h @xmath1 & -267 & p - cygni@xmath24 + lc parameter & value + + u & 14.834 @xmath250.048 + b & 15.957 @xmath250.048 + v & 15.606 @xmath250.038 + i & 15.240 @xmath250.148 + j & 14.551 @xmath250.046 + h & 13.855 @xmath250.043 + k & 12.772 @xmath250.032 + 3.6 @xmath3 m & 10.53 @xmath250.05@xmath19 + 4.5 @xmath3 m & 9.76 @xmath250.04@xmath19 + 5.8 @xmath3 m & 8.85 @xmath250.04@xmath19 + 8.0 @xmath3 m & 7.81 @xmath250.03@xmath19 + t@xmath9 & @xmath019000 k + r@xmath10 & @xmath014 r@xmath26 + log ( l@xmath10/l@xmath26 ) & @xmath04.4 + t@xmath16 & @xmath0800 k +

we detect numerous fe ii , [ o i ] , and [ fe ii ] lines , as well as strong p - cygni profile h i emission lines in its optical spectrum . the star s near - ir color and optical to ir sed clearly indicate the presence of an infrared excess , consistent with the presence of gas and warm , t @xmath0800 k , circumstellar dust . based on a crude estimate of the star s luminosity and the observed spectroscopic line profile morphologies , we find that the star is likely to be a b - type supergiant . we suggest that ngc 346:kwbbe 200 is a newly discovered b[e ] supergiant star , and represents the fifth such object to be identified in the smc .

we present new optical spectroscopic and archival spitzer irac photometric observations of a b - type star in the smc cluster ngc 346 , ngc 346:kwbbe 200 . we detect numerous fe ii , [ o i ] , and [ fe ii ] lines , as well as strong p - cygni profile h i emission lines in its optical spectrum . the star s near - ir color and optical to ir sed clearly indicate the presence of an infrared excess , consistent with the presence of gas and warm , t @xmath0800 k , circumstellar dust . based on a crude estimate of the star s luminosity and the observed spectroscopic line profile morphologies , we find that the star is likely to be a b - type supergiant . we suggest that ngc 346:kwbbe 200 is a newly discovered b[e ] supergiant star , and represents the fifth such object to be identified in the smc .