a new system of generalized nonlinear quasi variational like inclusions with a monotone operators in banach spaces in this paper we study some properties of a monotone operator in banach space give the notion of proximal mapping associated with the a monotone operator and show its lipschitz continuity we also consider a new system of generalized nonlinear quasi variational like inclusions with a monotone operators in banach spaces and constructed a new iterative algorithm for solving the system of generalized nonlinear quasi variational like inclusions in banach spaces under suitable assumptions we prove the convergence of the iterative sequences generated by the algorithm

experimental study of the fluctuation theorem in a nonequilibrium steady state the fluctuation theorem ft quantifies the probability of second law violations in small systems over short time scales while this theorem has been experimentally demonstrated for systems that are perturbed from an initial equilibrium state there are a number of studies suggesting that the theorem applies asymptotically in the long time limit to systems in a nonequilibrium steady state the asymptotic application of the ft to such nonequilibrium steady states has been referred to in the literature as the steady state fluctuation theorem or ssft in this paper we demonstrate experimentally the application of the ft to nonequilibrium steady states using a colloidal particle localized in a translating optical trap furthermore we show for this colloidal system that the ft holds under nonequilibrium steady states for all time and not just in the long time limit as in the ssft

variational inclusions with a general h monotone operator in banach spaces in this paper we introduce a new class of operator general h monotone operators in banach space we define a proximal mapping associated with the general h monotone operator and show its lipschitz continuity we also consider a new class of variational inclusions involving these general h monotone operators and constructed a new iterative algorithm for solving the variational inclusion in banach spaces under some suitable conditions we prove the convergence of the iterative sequence generated by the algorithm

chaotic principle an experimental test abstract the chaotic hypothesis discussed in gallavotti and cohen 1995 is tested experimentally in a simple conduction model besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which as the forcing strength grows the attractor ceases to be an anosov system and becomes an axiom a attractor a first text of new predictions is also attempted

steady states invariant measures and response theory using the method of computer simulation we test the predictions of nonlinear response theory for classical systems subject to dissipative external fields we provide convincing numerical evidence that kawasaki methods agree with both the transient time correlation function predictions and with a direct measurement of the nonlinear response furthermore this numerical agreement is observed over a time scale which is sufficiently long for the response to have relaxed to within ensuremath sim 1 of its nonequilibrium steady state value this is in spite of the fact that in the steady state the n particle distribution function ultimately becomes fractal we discuss the normalization of the kawasaki distribution and derive a lagrangian form of the kawasaki response function and show that it is consistent with predictions that are obtained using a natural invariant measure for nonequilibrium steady states c 1995 the american physical society

a new class of completely generalized quasi variational inclusions in banach spaces in this paper a new notion of j proximal mapping for a nonconvex lower semicontinuous subdifferentiable proper functional on banach space is introduced the existence and lipschitz continuity of j proximal mapping of a lower semicontinuous subdifferentiable proper functional are proved by applying the concept we introduce and study a new class of completely generalized quasi variational inclusions in reflexive banach spaces a novel and innovative iterative algorithm for finding the approximate solutions is suggested and analyzed the convergence criteria of the iterative sequences generated by the new iterative algorithm is also given these algorithm and existence result generalize many known results under hilbert space setting in recent literature to reflexive banach spaces

nonlinear 0 1 programming i linearization techniques any real valued nonlinear function in 0 1 variables can be rewritten as a multilinear function we discuss classes of lower and upper bounding linear expressions for multilinear functions in 0 1 variables for any multilinear inequality in 0 1 variables we define an equivalent family of linear inequalities this family contains the well known system of generalized covering inequalities as well as other linear equivalents of the multilinear inequality that are more compact i e of smaller cardinality in a companion paper 7 we discuss dominance relations between various linear equivalents of a multilinear inequality and describe a class of algorithms for multilinear 0 1 programming based on these results

coexistence of chaotic and non chaotic states in the two dimensional gauss navier stokes dynamics recently gallavotti proposed an equivalence conjecture in hydrodynamics which states that forced damped fluids can be equally well represented by means of the navier stokes equations ns and by means of time reversible modifications of ns called gauss navier stokes equations gns this equivalence conjecture received numerical support in several recent papers concerning two dimensional fluid mechanics the corresponding results rely on the fact that the ns and gns systems only have one attracting set performing similar two dimensional simulations we find that there are conditions to be met by the gns system for this to be the case in particular increasing the reynolds number while keeping fixed the number of fourier modes leads to the coexistence of different attractors this makes difficult a test of the equivalence conjecture but constitutes a spurious effect due to the insufficient spectral resolution with sufficiently fine spectral resolution the steady states are unique and the equivalence conjecture can be conveniently established

finding multiple solutions to general integer linear programs integer linear programming ilp problems occur frequently in many applications in practice alternative optima are useful since they allow the decision maker to choose from multiple solutions without experiencing any deterioration in the objective function this study proposes a general integer cut to exclude the previous solution and presents an algorithm to identify all alternative optimal solutions of an ilp problem numerical examples in real applications are presented to demonstrate the usefulness of the proposed method

a dynamical systems interpretation of the dissipation function t mixing and their relation to thermodynamic relaxation we review the notions of the dissipation function and t mixing for non invariant measures recently introduced for nonequilibrium molecular dynamics models we provide a dynamical systems interpretation for the dissipation function and related results providing new perspectives into results such as the second law inequality we then consider the problem of relaxation within this framework the convergence of time averages along single phase space trajectories as opposed to the convergence of ensemble averages as a first step in this direction we observe that t mixing implies convergence to a unique asymptotic ensemble independent on the initial ensemble in particular the initial ensemble can be concentrated arbitrarily closely to any point in phase space

on the fluctuation relation for nose hoover boundary thermostated systems we discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats at different temperatures the system is a modified lorentz gas in which the fixed scatterers exchange energy with the gas of particles and the thermostats are modelled by two nose hoover thermostats applied at the boundaries of the system the transient fluctuation relation which holds only for a precise choice of the initial ensemble is verified at all times as expected times longer than the mesoscopic scale needed for local equilibrium to be settled are required if a different initial ensemble is considered this shows how the transient fluctuation relation asymptotically leads to the steady state relation when as explicitly checked in our systems the condition found in d j searles et al j stat phys 128 1337 2007 for the validity of the steady state fluctuation relation is verified for the steady state fluctuations of the phase space contraction rate and of the dissipation function a similar relaxation regime at shorter averaging times is found the quantity satisfies with good accuracy the fluctuation relation for times larger than the mesoscopic time scale the quantity appears to begin a monotonic convergence after such times this is consistent with the fact that and differ by a total time derivative and that the tails of the probability distribution function of are gaussian

note on two theorems in nonequilibrium statistical mechanics an attempt is made to clarify the difference between a theorem derived by evans and searles in 1994 on the statistics of trajectories in phase space and a theorem proved by the authors in 1995 on the statistics of fluctuations on phase space trajectory segments in a nonequilibrium stationary state

smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics this paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics we adopt a new point of view which has emerged progressively in recent years and which takes seriously into account the chaotic character of the microscopic time evolution the emphasis is on nonequilibrium steady states rather than the traditional approach to equilibrium point of view of boltzmann the nonequilibrium steady states in presence of a gaussian thermostat are described by srb measures in terms of these one can prove the gallavotti cohen fluctuation theorem one can also prove a general linear response formula and study its consequences which are not restricted to near equilibrium situations at equilibrium one recovers in particular the onsager reciprocity relations under suitable conditions the nonequilibrium steady states satisfy the pairing theorem of dettmann and morriss the results just mentioned hold so far only for classical systems they do not involve large size i e they hold without a thermodynamic limit

a branch and bound algorithm for designing reliable systems at a minimum cost a nonlinear integer programming model for the optimal design of a series parallel reliability system is presented together with an enumeration algorithm for its solution and an example the algorithm is based on an efficient procedure for solving the continuous relaxation of the mathematical model

surrogate dual multiplier search procedures in integer programming search procedures for optimal lagrange multipliers are highly developed and provide good bounds in branch and bound procedures that have led to the successful application of lagrangean duality in integer programming although the surrogate dual generally provides a better objective bound there has been little development of surrogate multiplier search procedures this paper develops and empirically analyzes several surrogate multiplier search procedures results indicate that the procedures can produce possibly superior bounds in an amount of time comparable to other techniques our discussion also highlights the similarity of the procedures to some well known lagrangean search techniques

an enumerative algorithm framework for a class of nonlinear integer programming problems this paper presents a framework for a branch and search algorithm for solving a class of general integer restricted linearly constrained quadratic integer programming problems where the objective function is a nonseparable quadratic concave function

equilibrium fluctuation relations and transport for irreversible deterministic dynamics abstract in a recent paper m colangeli et al j stat mech p04021 2011 it was argued that the fluctuation relation for the phase space contraction rate could suitably be extended to non reversible dissipative systems we strengthen here those arguments providing analytical and numerical evidence based on the properties of a simple irreversible nonequilibrium baker model we also consider the problem of response showing that the transport coefficients are not affected by the irreversibility of the microscopic dynamics in addition we prove that a form of detailed balance hence of equilibrium holds in the space of relevant variables despite the irreversibility of the phase space dynamics this corroborates the idea that the same stochastic description which arises from a projection onto a subspace of relevant coordinates is compatible with quite different underlying deterministic dynamics in other words the details of the microscopic dynamics are largely irrelevant for what concerns properties such as those concerning the fluctuation relations the equilibrium behavior and the response to perturbations

dynamical ensembles equivalence in fluid mechanics abstract an attempt to put together various theoretical mathematical or experimental results recently developed in apparently unrelated subjects namely ruelle s 1980 approach to turbulence the body of nose hoover type of molecular dynamics experiments evans and morriss 1990 evans et al 1993 bonetto et al 1996 mathematical results on lyapunov exponents the pairing rule dressler 1988 and dettman and morriss 1995 and experimental results on them sarman et al 1992 bohr et al 1996 theoretical as well as mathematical results on fluctuations frisch and parisi 1984 multifractality and gallavoti and cohen 1995 chaotic hypothesis the key idea that we try to clarify is that of dynamical ensembles as a generalization of the classical equilibrium ensembles arguing that they should be identified with the srb distributions and that they share several properties with the classical ensembles most of the results invoked here did not deal directly with the navier stokes equations and yet they seem to have a lot to do with them as we shall argue here the discussion will focus on the navier stokes and dissipative euler equations with the aim of proposing several experiments apt to test the equivalence of dynamical ensembles and the chaotic hypothesis the ideas developed to a great extent from the efforts put in interpreting the experimental results in bonetto et al 1996

fluctuation relation beyond linear response theory the fluctuation relation fr is an asymptotic result onthe distribution of certain observables averaged over timeintervals as and it is a generalization of thefluctuation dissipation theorem to far from equilibrium systemsin a steady state which reduces to the usual green kubo gk relation in the limit of small external non conservative forces fr is a theorem for smooth uniformly hyperbolic systems and it isassumed to be true in all dissipative chaotic enough systemsin a steady state in this paper we develop a theory of finitetime corrections to fr needed to compare the asymptoticprediction of fr with numerical observations which necessarilyinvolve fluctuations of observables averaged over finite timeintervals we perform a numerical test of fr in two cases inwhich non gaussian fluctuations are observable while gk does notapply and we get a non trivial verification of fr that is independent of and different from linear response theory our results are compatible with the theory of finite timecorrections to fr while fr would be observably violated well within the precision of our experiments if such correctionswere neglected

a local fluctuation theorem abstract a mechanism for the validity of a local version of the fluctuation theorem uniform in the system size is discussed for a reversible chain of weakly coupled anosov systems

on typicality in nonequilibrium steady states from the statistical mechanical viewpoint relaxation of macroscopic systems and response theory rest on a notion of typicality according to which the behavior of single macroscopic objects is given by appropriate ensembles ensemble averages of observable quantities represent the measurements performed on single objects because almost all objects share the same fate in the case of non dissipative dynamics and relaxation toward equilibrium states almost all is referred to invariant probability distributions that are absolutely continuous with respect to the lebesgue measure in other words the collection of initial micro states single systems that do not follow the ensemble is supposed to constitute a set of vanishing phase space volume this approach is problematic in the case of dissipative dynamics and relaxation to nonequilibrium steady states because the relevant invariant distributions attribute probability 1 to sets of zero volume while evolution commonly begins in equilibrium states i e in sets of full phase space volume we consider the relaxation of classical thermostatted particle systems to nonequilibrium steady states we show that the dynamical condition known as omega t mixing is necessary and sufficient for relaxation of ensemble averages to steady state values moreover we find that the condition known as weak t mixing applied to smooth observables is sufficient for ensemble relaxation to be independent of the initial ensemble lastly we show that weak t mixing provides a notion of typicality for dissipative dynamics that is based on the non invariant lebesgue measure and that we call physical ergodicity

synchronisation of canonical measures for hyperbolic attractors under suitable conditions it is shown how to change the velocity of ac2 axioma attractor so that the sinai ruelle bowen measure coincides with the measure of maximal entropy these measures are obtained as limits of certain closed orbital measures

the steady state fluctuation relation for the dissipation function we give a proof of transient fluctuation relations for the entropy production dissipation function in nonequilibrium systems which is valid for most time reversible dynamics we then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax producing a unique nonequilibrium steady state although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown if such a steady state exists the generation of the steady state fluctuation relation from the transient relation is shown to be very general it is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation which is needed also for e g the existence of transport coefficients because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities the steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor whose convergence is problematic for systems close to equilibrium we examine some model dynamics that have been considered previously and show how they are described in the context of this work

fluctuation theorem for stochastic systems the fluctuation theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics it has been proved in a number of different ways for thermostatted deterministic nonequilibrium systems in the present paper we show that the fluctuation theorem is also valid for a class of stochastic nonequilibrium systems the theorem is therefore not reliant on the reversibility or the determinism of the underlying dynamics numerical tests verify the theoretical result

application of the gallavotti cohen fluctuation relation to thermostated steady states near equilibrium the fluctuation relation of the gallavotti cohen fluctuation theorem gcft concerns fluctuations in the phase space compression rate of dissipative reversible dynamical systems it has been proven for anosov systems but it is expected to apply more generally this raises the question of which non anosov systems satisfy the fluctuation relation we analyze time dependent fluctuations in the phase space compression rate of a class of n particle systems that are at equilibrium or in near equilibrium steady states this class does not include anosov systems or isoenergetic systems however it includes most steady state systems considered in molecular dynamics simulations of realistic systems we argue that the fluctuations of the phase space compression rate of these systems at or near equilibrium do not satisfy the fluctuation relation of the gcft although the discrepancies become somewhat smaller as the systems move further from equilibrium in contrast similar fluctuation relations for an appropriately defined dissipation function appear to hold both near and far from equilibrium

fluctuation theorems for entropy production in open systems we derive a fluctuation theorem to describe entropy fluctuations in steady states of systems with density gradients due to open boundaries the fluctuations are related to the growth rate of the phase space density instead of the phase space contraction rate explicit derivations are presented for a multibaker map but the arguments are rather general and should hold for a much wider class of dynamical systems a comparison with recent results for stochastic systems is also given

lyapunov spectra and nonequilibrium ensembles equivalence in 2d fluid mechanics we perform numerical experiments to study the lyapunov spectra of dynamical systems associated with the navier stokes ns equation in two spatial dimensions truncated over the fourier basis recently new equations called gns equations have been introduced and conjectured to be equivalent to the ns equations at large reynolds numbers the lyapunov spectra of the ns and of the corresponding gns systems overlap adding evidence in favor of the conjectured equivalence already studied and partially extended in previous papers we make use of the lyapunov spectra to study a fluctuation relation which had been proposed to extend the fluctuation theorem to strongly dissipative systems preliminary results towards the formulation of a local version of the fluctuation formula are also presented

chaotic hypothesis fluctuation theorem and singularities the chaotic hypothesis has several implications which have generated interest in the literature because of their generality and because a few exact predictions are among them however its application to physics problems requires attention and can lead to apparent inconsistencies in particular there are several cases that have been considered in the literature in which singularities are built in the models for instance when among the forces there are lennard jones potentials which are infinite in the origin and the constraints imposed on the system do not forbid arbitrarily close approach to the singularity even though the average kinetic energy is bounded the situation is well understood in certain special cases in which the system is subject to gaussian noise here the treatment of rather general singular systems is considered and the predictions of the chaotic hypothesis for such situations are derived the main conclusion is that the chaotic hypothesis is perfectly adequate to describe the singular physical systems we consider ie deterministic systems with thermostat forces acting according to gauss principle for the constraint of constant total kinetic energy isokinetic gaussian thermostats close and far from equilibrium near equilibrium it even predicts a fluctuation relation which in deterministic cases with more general thermostat forces ie not necessarily of gaussian isokinetic nature extends recent relations obtained in situations in which the thermostatting forces satisfy gauss principle this relation agrees where expected with the fluctuation theorem for perfectly chaotic systems the results are compared with some recent works in the literature

reversibility coarse graining and the chaoticity principle we describe a way of interpreting the chaotic principle of gc1 more extensively than it was meant in the original works mathematically the analysis is based on the dynamical notions of axiom a and axiom b and on the notion of axiom c that we introduce arguing that it is suggested by the results of an experiment bgg on chaotic motions physically we interpret a breakdown of the anosov property of a time reversible attractor replaced as a control parameter changes by an axiom a property as a spontaneous breakdown of the time reversal symmetry the relation between time reversal and the symmetry that remains after the breakdown is analogous to the breakdown of t invariance while tcp still holds

a tight linearization and an algorithm for zero one quadratic programming problems this paper is concerned with the solution of linearly constrained zero one quadratic programming problems problems of this kind arise in numerous economic location decision and strategic planning situations including capital budgeting facility location quadratic assignment media selection and dynamic set covering a new linearization technique is presented for this problem which is demonstrated to yield a tighter continuous or linear programming relaxation than is available through other methods an implicit enumeration algorithm which uses lagrangian relaxation benders cutting planes and local explorations is designed to exploit the strength of this linearization computational experience is provided to demonstrate the usefulness of the proposed linearization and algorithm

extended heat fluctuation theorems for a system with deterministic and stochastic forces heat fluctuations over a time tau in a nonequilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components a brownian particle dragged through a fluid by a harmonic potential which is moved with constant velocity using a langevin equation we find the exact fourier transform of the distribution of these fluctuations for all tau by a saddle point method we obtain analytical results for the inverse fourier transform which for not too small tau agree very well with numerical results from a sampling method as well as from the fast fourier transform algorithm due to the interaction of the deterministic part of the motion of the particle in the mechanical potential with the stochastic part of the motion caused by the fluid the conventional heat fluctuation theorem is for infinite and for finite tau replaced by an extended fluctuation theorem that differs noticeably and measurably from it in particular for large fluctuations the ratio of the probability for absorption of heat by the particle from the fluid to the probability to supply heat by the particle to the fluid is much larger here than in the conventional fluctuation theorem

on a new system of generalized mixed quasi variational like inclusions with h η accretive operators in real q uniformly smooth banach spaces abstract in this paper we introduce and study a new system of generalized mixed quasi variational like inclusions with h accretive operators which contains variational inequalities variational inclusions systems of variational inequalities and systems of variational inclusions in the literature as special cases by using the resolvent technique for the h accretive operators we prove the existence of solutions and the convergence of a new p step iterative algorithm for this system of generalized mixed quasi variational like inclusions in real q uniformly smooth banach spaces the results in this paper unify extend and improve some known results from the literature

existence and algorithm of solutions for generalized mixed implicit quasi variational inequalities1this project was supported by the national science foundation of people s republic china 1 in this paper by applying the auxiliary variational principle technique some existence theorems of solutions for a class of generalized mixed implicit quasi variational inequalities are proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria are also given as special cases of these results the open problem put forward by noor is answered positively and some results of existence and algorithm of solutions for generalized implicit quasi complementarity problems are also obtained our results are new and generalize a number of known results of mixed variational inequalities mixed quasi variational inequalities and quasi complementary problems involving single valued and set valued mappings in recent literatures

computer experiments on quadratic programming algorithms abstract this paper compares the computational performance of five quadratic programming algorithms these include wolfe s simplex method lemke s complementary pivot method convex simplex method and quadratic differential algorithm execution time and iteration count are used as the major criteria for comparison since lemke s algorithm out performed all other methods in the study a detailed statistical analysis was performed to determine the relative importance of problem parameters on the efficiency of lemke s algorithm an analysis of variance showed that the number of variables the percent of positive linear terms in the objective the number of constraints and their interactions were the significant factors for both iteration count and execution time finally regression equations for iteration count and execution time are derived as a function of fifteen problem parameters