direct evaluation of large deviation functions we introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities such as current or density that are local in time the large deviation functions are given in terms of the typical properties of a modified dynamics and since they no longer involve rare events can be evaluated efficiently and over a wider ranges of values we illustrate the method with the current fluctuations of the totally asymmetric exclusion process and with the work distribution of a driven lorentz gas

exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra we study the partially asymmetric exclusion process with open boundaries we generalize the matrix approach previously used to solve the special case of total asymmetry and derive exact expressions for the partition sum and currents valid for all values of the asymmetry parameter q due to the relationship between the matrix algebra and the q deformed quantum harmonic oscillator algebra we find that q hermite polynomials along with their orthogonality properties and generating functions are of great utility we employ two distinct sets of q hermite polynomials one for q 1 it turns out that these correspond to two distinct regimes the previously studied case of forward bias q 1 where the boundaries support a current opposite in direction to the bulk bias for the forward bias case we confirm the previously proposed phase diagram whereas the case of reverse bias produces a new phase in which the current decreases exponentially with system size

sampling rare fluctuations of discrete time markov chains we describe a simple method that can be used to sample the rare fluctuations of discrete time markov chains we focus on the case of markov chains with well defined steady state measures and derive expressions for the large deviation rate functions and upper bounds on such functions for dynamical quantities extensive in the length of the markov chain we illustrate the method using a series of simple examples and use it to study the fluctuations of a lattice based model of active matter that can undergo motility induced phase separation

an algorithm for shakedown analysis with nonlinear yield functions abstract this paper is devoted to propose an algorithm to solve the discrete form of the shakedown analysis problem with a nonlinear yield function firstly variational formulations for shakedown analysis of structures under variable loads are considered secondly the corresponding discrete forms are briefly recalled then the algorithm is derived by combining a newton formula based on the discrete equality conditions with a return mapping procedure focusing plastic admissibility the proposed numerical procedure can be applied to finite element models with large number of degrees of freedom because the algorithm is specially designed to take advantage of the structure of such models the numerical procedure is applied to a square plate with a circular hole under variable traction in two directions and the obtained approximations are compared with available results finally a rectangular plate with two small holes is considered in both plane strain and plane stress conditions all application use the mises condition without linearization

computation of collapse states with von mises type yield condition a new computational approach to the problem of limit analysis with quadratic yield condition is developed and tested the problem is solved with the exact convex yield condition and the general case of unbounded yield set corresponding to unrestricted hydrostatic pressure is treated the solution method simultaneously approximates the collapse fields for stresses and flow the approach consists of two separate steps first the continuous problem is discretized by the finite element method into a finite dimensional optimization problem which turns out to be of a very specific form then this problem is solved by a suitable optimization method this way it is not necessary to be an expert in optimization in order to solve collapse problems and we can take advantage of the rapid development in optimization methods for large sparse problems without changing the discretization program the efficiency and accuracy of the method for large problems is demonstrated by solving a classical problem in the plane strain model approximately 90000 finite element nodes with 3 stress components and 2 velocity components at each node in two space dimensions this may be overkill but it shows that we are able to solve problems in three space dimensions

negative specific heat in the canonical statistical ensemble according to thermodynamics the specific heat of boltzmannian short range interacting systems is a positive quantity less intuitive properties are instead displayed by systems characterized by long range interactions in that case the sign of specific heat depends on the considered statistical ensemble negative specific heat can be found in isolated systems which are studied in the framework of the microcanonical ensemble on the other hand it is generally recognized that a positive specific heat should always be measured in systems in contact with a thermal bath for which the canonical ensemble is the appropriate one we demonstrate that the latter assumption is not generally true one can in principle measure negative specific heat also in the canonical ensemble if the system under scrutiny is non boltzmannian and or out of equilibrium

importance sampling for stochastic simulations importance sampling is one of the classical variance reduction techniques for increasing the efficiency of monte carlo algorithms for estimating integrals the basic idea is to replace the original random mechanism in the simulation by a new one and at the same time modify the function being integrated in this paper the idea is extended to problems arising in the simulation of stochastic systems discrete time markov chains continuous time markov chains and generalized semi markov processes are covered applications are given to a gi g 1 queueing problem and response surface estimation computation of the theoretical moments arising in importance sampling is discussed and some numerical examples given

on large deviations theory and asymptotically efficient monte carlo estimation it is shown how large deviations theory can be applied to construct an asymptotically efficient simulation distribution for monte carlo simulation using the importance sampling technique a sufficient and necessary condition is given for the asymptotic efficiency of the candidate simulation distributions this is done in the multidimensional setting that is required by many practical simulation problems the result obtained is applied primarily in two areas first the generalization of previous work dealing with functionals of markov chains is discussed a second area of application is the simulation of nonlinear systems with gaussian inputs as an example of a system with gaussian inputs the simulation of a digital communication channel with nonlinear isi intersymbol interference characteristic of satellite data links is considered in the case of linear isi the asymptotically efficient exponentially twisted distribution turns out to agree with a method previously proposed by d lu and k yao 1988 the large deviations point of view provides some useful insight on how to extent the lu and yao method to nonlinear channels

upper bound limit analysis using discontinuous velocity fields abstract a new method for computing rigorous upper bounds under plane strain conditions is described it is based on a linear three noded triangular element which has six unknown nodal velocities and a fixed number of unknown plastic multiplier rates and uses the kinematic theorem to define a kinematically admissible velocity field as the solution of a linear programming problem unlike existing formulations which permit only a limited number of velocity discontinuities whose directions of shearing must be specified a priori the new formulation permits velocity discontinuities at all edges shared by adjacent triangles and the directions of shearing are found automatically the variation of the velocity jump along each discontinuity is described by an additional set of four unknowns all of the unknowns are subject to the constraints imposed by an associated flow rule and the velocity boundary conditions the objective function corresponds to the dissipated power or some related load parameter of interest and is minimised to yield the desired upper bound since plastic deformation may occur not only in the discontinuities but also throughout the triangular elements as well the method is capable of modelling complex velocity fields accurately and typically produces tight upper bounds on the true limit load the formulation is applicable to materials whose strength is cohesive frictional purely cohesive and uniform or purely cohesive and linearly varying and thus quite general the new procedure is very efficient and always requires fewer elements than existing methods to obtain useful upper bound solutions moreover because of the extra degrees of freedom introduced by the discontinuities the linear elements no longer need to be arranged in a special pattern to model incompressible behaviour accurately

large deviations of the current for driven periodic diffusions we study the large deviations of the time integrated current for a driven diffusion on the circle often used as a model of nonequilibrium systems we obtain the large deviation functions describing the current fluctuations using a fourier bloch decomposition of the so called tilted generator and we also construct from this decomposition the effective biased auxiliary or driven markov process describing the diffusion as current fluctuations are observed in time this effective process provides a clear physical explanation of the various fluctuation regimes observed it is used here to obtain an upper bound on the current large deviation function which we compare to a recently derived entropic bound and to study the low noise limit of large deviations

direct evaluation of dynamical large deviation rate functions using a variational ansatz we describe a simple form of importance sampling designed to bound and compute large deviation rate functions for time extensive dynamical observables in continuous time markov chains we start with a model defined by a set of rates and a time extensive dynamical observable we construct a reference model a variational ansatz for the behavior of the original model conditioned on atypical values of the observable direct simulation of the reference model provides an upper bound on the large deviation rate function associated with the original model an estimate of the tightness of the bound and if the ansatz is chosen well the exact rate function the exact rare behavior of the original model does not need to be known in advance we use this method to calculate rate functions for currents and counting observables in a set of network and lattice models taken from the literature straightforward ansatze yield bounds that are tighter than bounds obtained from level 2 5 of large deviations via approximations that involve uniform scalings of rates we show how to correct these bounds in order to recover the rate functions exactly our approach is complementary to more specialized methods and offers a physically transparent framework for approximating and calculating the likelihood of dynamical large deviations

fluctuations of power injection in randomly driven granular gases we investigate the large deviation function w for the fluctuations of the power w t wt integrated over a time t injected by a homogeneous random driving into a granular gas in the infinite time limit our analytical study starts from a generalized liouville equation and exploits a molecular chaos like assumption we obtain an equation for the generating function of the cumulants which appears as a generalization of the inelastic boltzmann equation and has a clear physical interpretation reasonable assumptions are used to obtain in a closed analytical form a legendre transform is sufficient to get the large deviation function w our main result apart from an estimate of all the cumulants of w t at large times t is that has no negative branch this immediately results in the inapplicability of the gallavotti cohen fluctuation relation gcfr that in previous studies had been suggested to be valid for injected power in driven granular gases we also present numerical results in order to discuss the finite time behavior of the fluctuations of w t we discover that their probability density function converges extremely slowly to its asymptotic scaling form the third cumulant saturates after a characteristic time larger than 50 mean free times and the higher order cumulants evolve even slower the asymptotic value is in good agreement with our theory remarkably a numerical check of the gcfr is feasible only at small times at most 10 since negative events disappear at larger times at such small times this check leads to the misleading conclusion that gcfr is satisfied for w we offer an explanation for this remarkable apparent verification in the inelastic maxwell model where a better statistics can be achieved we are able to numerically observe the failure of gcfr

convergence of large deviation estimators we study the convergence of statistical estimators used in the estimation of large deviation functions describing the fluctuations of equilibrium nonequilibrium and manmade stochastic systems we give conditions for the convergence of these estimators with sample size based on the boundedness or unboundedness of the quantity sampled and discuss how statistical errors should be defined in different parts of the convergence region our results shed light on previous reports of phase transitions in the statistics of free energy estimators and establish a general framework for reliably estimating large deviation functions from simulation and experimental data and identifying parameter regions where this estimation converges

a unified approach to remeshing strategies for finite element h adaptivity in h adaptivity a remeshing strategy is needed to compute the distribution of required element size using the estimated error distribution several authors have introduced different remeshing strategies yielding very different results in this work these methods are included in a unified framework emphasizing the role of the underlying hypotheses moreover an objective tool to evaluate the accuracy of the resulting finite element solution is presented thus a new remeshing strategy is introduced to optimize the accuracy of the adapted solutions the different remeshing strategies are compared with well known numerical examples

large deviations in fast slow systems the incidence of rare events in fast slow systems is investigated via analysis of the large deviation principle ldp that characterizes the likelihood and pathway of large fluctuations of the slow variables away from their mean behavior such fluctuations are rare on short time scales but become ubiquitous eventually classical results prove that this ldp involves an hamilton jacobi equation whose hamiltonian is related to the leading eigenvalue of the generator of the fast process and is typically non quadratic in the momenta in other words the ldp for the slow variables in fast slow systems is different in general from that of any stochastic differential equation sde one would write for the slow variables alone it is shown here that the eigenvalue problem for the hamiltonian can be reduced to a simpler algebraic equation for this hamiltonian for a specific class of systems in which the fast variables satisfy a linear equation whose coefficients depend nonlinearly on the slow variables and the fast variables enter quadratically the equation for the slow variables these results are illustrated via examples inspired by kinetic theories of turbulent flows and plasma in which the quasipotential characterizing the long time behavior of the system is calculated and shown again to be different from that of an sde

automatic mesh refinement in limit analysis a strategy for automatic mesh refinement in limit analysis is combined with a recently developed computational method in the absence of estimates of the local error the strategy can be based on the deformations and on slack in the yield condition the approach is tested on standard problems in plane strain including the classical punch problem very accurate results are obtained with the use of moderate computational power

universal bounds on current fluctuations for current fluctuations in nonequilibrium steady states of markovian processes we derive four different universal bounds valid beyond the gaussian regime different variants of these bounds apply to either the entropy change or any individual current e g the rate of substrate consumption in a chemical reaction or the electron current in an electronic device the bounds vary with respect to their degree of universality and tightness a universal parabolic bound on the generating function of an arbitrary current depends solely on the average entropy production a second stronger bound requires knowledge both of the thermodynamic forces that drive the system and of the topology of the network of states these two bounds are conjectures based on extensive numerics an exponential bound that depends only on the average entropy production and the average number of transitions per time is rigorously proved this bound has no obvious relation to the parabolic bound but it is typically tighter further away from equilibrium an asymptotic bound that depends on the specific transition rates and becomes tight for large fluctuations is also derived this bound allows for the prediction of the asymptotic growth of the generating function even though our results are restricted to networks with a finite number of states we show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle our bounds provide a general class of constraints for nonequilibrium systems

large deviations of the dynamical activity in the east model analysing structure in biased trajectories we consider large deviations of the dynamical activity in the east model we bias this system to larger than average activity and investigate the structure that emerges to best characterize this structure we exploit the fact that there are effective interactions that would reproduce the same behaviour in an equilibrium system we combine numerical results with linear response theory and variational estimates of these effective interactions giving the first insights into such interactions in a many body system across a wide range of biases the system exhibits a hierarchy of responses to the bias remaining quasi equilibrated on short length scales but deviating far from equilibrium on large length scales we discuss the connection between this hierarchy and the hierarchical ageing behaviour of the system

application of importance sampling to the computation of large deviations in nonequilibrium processes we present an algorithm for finding the probabilities of rare events in nonequilibrium processes the algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently by keeping track of the relative weight of phase space trajectories generated by the modified and the original dynamics one can obtain the required probabilities the algorithm is tested on two model systems of steady state particle and heat transport where we find a huge improvement from direct simulation methods

large deviations for exchangeable random vectors satisfies a large deviation principle with rate function a x inf a6 x o e s u 1 where s 4 is the support of the mixing measure 4 if x1 x2 is a sequence of i i d random vectors xn the corresponding sequence of sample means and pown po x1 then pon is exponentially continuous if the classical rate function ar v is jointly lower semicontinuous and a uniform integrability condition introduced by de acosta is satisfied these results are applied in section 4 to derive a large deviation theory for exchangeable random variables the resulting rate functions are typically nonconvex if the parameter space e is not compact then examples can be constructed where a full large deviation principle is not satisfied because the upper bound fails for a noncompact set

an adaptive approach to limit analysis abstract the main objective of this paper is to propose an adaptive mesh refinement procedure for finite element models in limit analysis we use an a posteriori indicator based on the local directional interpolation error and a recovering scheme to compute second derivatives of the finite element solution the proposed mesh adaptation process gives improved results in localizing regions of rapid or abrupt variations of the variables whose location is not known a priori limit analysis of bodies in plane strain and plane stress is considered in the applications

statistical theory of quasistationary states beyond the single water bag case study an analytical solution for the out of equilibrium quasi stationary states of the paradigmatic hamiltonian mean field hmf model can be obtained from a maximum entropy principle the theory has been so far tested with reference to a specific class of initial condition the so called single level water bag type in this paper a step forward is taken by considering an arbitrary number of overlapping water bags the theory is benchmarked to direct microcanonical simulations performed for the case of a two levels water bag the comparison is shown to return an excellent agreement

rare behavior of growth processes via umbrella sampling of trajectories we compute probability distributions of trajectory observables for reversible and irreversible growth processes these results reveal a correspondence between reversible and irreversible processes at particular points in parameter space in terms of their typical and atypical trajectories thus key features of growth processes can be insensitive to the precise form of the rate constants used to generate them recalling the insensitivity to microscopic details of certain equilibrium behavior we obtained these results using a sampling method inspired by the s ensemble large deviation formalism that amounts to umbrella sampling in trajectory space the method is a simple variant of existing approaches and applies to ensembles of trajectories controlled by the total number of events it can be used to determine large deviation rate functions for trajectory observables in or out of equilibrium

coarse grained distributions and superstatistics abstract we show an interesting connection between non standard non boltzmannian distribution functions arising in the theory of violent relaxation for collisionless stellar systems d lynden bell mon not r astron soc 136 1967 101 and the notion of superstatistics recently introduced by beck and cohen physica a 322 2003 267 the common link between these two theories is the emergence of coarse grained distributions arising out of fine grained distributions the coarse grained distribution functions are written as a superposition of boltzmann factors weighted by a non universal function even more general distributions can arise in case of incomplete violent relaxation non ergodicity they are stable stationary solutions of the vlasov equation we also discuss analogies and differences between the statistical equilibrium state of a multi components self gravitating system and the metaequilibrium or quasi equilibrium states of a collisionless stellar system finally we stress the important distinction between entropies generalized entropies relative entropies and h functions we discuss applications of these ideas in two dimensional turbulence and for other systems with long range interactions

dynamic phase transitions in simple driven kinetic networks we analyze the probability distribution for entropy production rates of trajectories evolving on a class of out of equilibrium kinetic networks these networks can serve as simple models for driven dynamical systems where energy fluxes typically result in nonequilibrium dynamics by analyzing the fluctuations in the entropy production we demonstrate the emergence in a large system size limit of a dynamic phase transition between two distinct dynamical regimes

simple bounds on fluctuations and uncertainty relations for first passage times of counting observables recent large deviation results have provided general lower bounds for the fluctuations of time integrated currents in the steady state of stochastic systems a corollary are so called thermodynamic uncertainty relations connecting precision of estimation to average dissipation here we consider this problem but for counting observables i e trajectory observables which in contrast to currents are non negative and nondecreasing in time and possibly symmetric under time reversal in the steady state their fluctuations to all orders are bound from below by a conway maxwell poisson distribution dependent only on the averages of the observable and of the dynamical activity we show how to obtain the corresponding bounds for first passage times times when a certain value of the counting variable is first reached and their uncertainty relations just like entropy production does for currents dynamical activity controls the bounds on fluctuations of counting observables

lower bound limit analysis of cohesive frictional materials using second order cone programming the formulation of limit analysis by means of the finite element method leads to an optimization problem with a large number of variables and constraints here we present a method for obtaining strict lower bound solutions using second order cone programming socp for which efficient primaldual interior point algorithms have recently been developed following a review of previous work we provide a brief introduction to socp and describe how lower bound limit analysis can be formulated in this way some methods for exploiting the data structure of the problem are also described including an efficient strategy for detecting and removing linearly dependent constraints at the assembly stage the benefits of employing socp are then illustrated with numerical examples through the use of an effective algorithm software very large optimization problems with up to 700 000 variables are solved in minutes on a desktop machine the numerical examples concern plane strain conditions and the mohr coulomb criterion however we show that socp can also be applied to any other problem of lower bound limit analysis involving a yield function with a conic quadratic form notable examples being the drucker prager criterion in 2d or 3d and nielsen s criterion for plates

a new discontinuous upper bound limit analysis formulation summary a new upper bound formulation of limit analysis of two and three dimensional solids is presented in contrast to most discrete upper bound methods the present one is formulated in terms of stresses rather than velocities and plastic multipliers however by means of duality theory it is shown that the formulation does indeed result in rigorous upper bound solutions also kinematically admissible discontinuities which have previously been shown to be very efficient are given an interpretation in terms of stresses this allows for a much simpler implementation and in contrast to existing formulations extension to arbitrary yield criteria in two and three dimensions is straightforward finally the capabilities of the new method are demonstrated through a number of examples copyright 2005 john wiley sons ltd

large deviation of the density profile in the steady state of the open symmetric simple exclusion process we consider an open one dimensional lattice gas on sites i 1 n with particles jumping independently with rate 1 to neighboring interior empty sites the simple symmetric exclusion process the particle fluxes at the left and right boundaries corresponding to exchanges with reservoirs at different chemical potentials create a stationary nonequilibrium state sns with a steady flux of particles through the system the mean density profile in this state which is linear describes the typical behavior of a macroscopic system i e this profile occurs with probability 1 when n the probability of microscopic configurations corresponding to some other profile x x i n has the asymptotic form exp n f f is the large deviation functional in contrast to equilibrium systems for which f eq is just the integral of the appropriately normalized local free energy density the f we find here for the nonequilibrium system is a nonlocal function of this gives rise to the long range correlations in the sns predicted by fluctuating hydrodynamics and suggests similar non local behavior of f in general sns where the long range correlations have been observed experimentally

upper and lower bounds in limit analysis adaptive meshing strategies and discontinuous loading summary upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimisation problems the membership constraints for von mises and mohrcoulomb plasticity criteria are written as a set of quadratic constraints which permits to solve the optimisation problem using specific algorithms for second order conic program socp from the stress field at the lower bound and the velocities at the upper bound we construct a novel error estimate based on elemental and edge contributions to the bound gap these contributions are employed in an adaptive remeshing strategy that is able to reproduce fan type mesh patterns around points with discontinuous surface loading the solution of this type of problems is analysed in detail and from this study some additional meshing strategies are also described we particularise the resulting formulation and strategies to two dimensional problems in plane strain and we demonstrate the effectiveness of the method with a set of numerical examples extracted from the literature copyright c 2007 john wiley sons ltd

scaling of the dynamics of homogeneous states of one dimensional long range interacting systems quasistationary states of long range interacting systems have been studied at length over the last 15 years it is known that the collisional terms of the balescu lenard and landau equations vanish for one dimensional systems in homogeneous states thus requiring a new kinetic equation with a proper dependence on the number of particles here we show that the scalings discussed in the literature are mainly due either to small size effects or the use of unsuitable variables to describe the dynamics the scaling obtained from both simulations and theoretical considerations is proportional to the square of the number of particles and a general form for the kinetic equation valid for the homogeneous regime is obtained numerical evidence is given for the hamiltonian mean field and ring models and a kinetic equation valid for the homogeneous state is obtained for the former system