a non isothermal ginzburg landau model in superconductivity existence uniqueness and asymptotic behaviour abstract in this paper we study a ginzburg landau model which describes the behaviour of a superconducting material including thermal effects we extend the traditional formulation of the problem by introducing the temperature as an additional state variable accordingly together with the gor kov eliashberg system we introduce an evolution equation for the absolute temperature we examine in detail the case which allows only variations of the concentration of superconducting electrons and of the temperature neglecting the electromagnetic field for this problem existence and uniqueness of the solution are shown finally we analyze the asymptotic behaviour of the solutions proving that the system possesses a global attractor

on the relation between the standard phase field model and a thermodynamically consistent phase field model abstract a further comparison is made between the standard phase field equations t 2 1 2 g u u t 2 u 1 2 l t and the relevant thermodynamically consistent model of phase transitions proposed by the authors physica d 43 1990 44 62 here we concentrate on the usual case where g 3 and for comparison purposes retain this expression for the analogous nonlinear functions in the latter model it is brought out among other things that the standard model is thermodynamically consistent in the sense of being derivable from a free energy functional however this free energy functional is of a somewhat unusual kind it implies that at constant temperature the energy density varies linearly with the order parameter and the entropy density is a non concave function of the example of a hard sphere system indicates that such behaviour is not impossible but in most other models the energy density and the entropy are both strictly concave in

coercive inequalities for gibbs measures abstract we prove the generalized nash and logarithmic nash inequalities for gibbs measures with dirichlet form associated to the kawasaki dynamics

asymptotic behavior of the solution to the non isothermal phase separation abstract we consider the non isothermal phase separation models of the penrose fife type which were proposed in o penrose p c fife thermodynamically consistent models of phase field type for the kinetics of phase transitions physica d 43 1990 44 62 with homogeneous neumann boundary conditions on the nonlinear heat flux q u i e q n 0 on the boundary of a region which the material occupies here u represents the absolute temperature for this model we first show that there exists a unique solution globally in time moreover the limit set associated with the trajectory of the unique global solution is non empty connected and compact in some suitable space as well as being composed of solutions to the steady state problem for the stability of stationary solutions we show that the dynamically stable solutions to the steady state problem are characterized by linearized stable solutions to the elliptic problem with a non local term which is equivalent to our steady state problem

analysis of generalized synchronization in directionally coupled chaotic phase coherent oscillators by local minimal fluctuations the method of local minimum fluctuation is proposed to analyze generalized synchronization in directionally coupled chaotic phase coherent oscillators it is shown that the emergence of generalized synchronization is manifested by the qualitative changes in the statistic of local minimum fluctuations of the receiver oscillator

global solution to a singular integro differential system related to the entropy balance this paper is devoted to the mathematical analysis of a thermodynamic model describing phase transitions with thermal memory in terms of an entropy equation and a momentum balance for the microforces the initial and boundary value problem is addressed for the related integro differential system of partial differential equations pdes existence and uniqueness continuous dependence on the data and regularity results are proved for the global solution in a finite time interval

well posedness for solid liquid phase transitions with a fourth order nonlinearity abstract a phase field system which describes the evolution of both the absolute temperature and the phase variable f during first order transitions in thermal insulators is considered a thermodynamic approach is developed by regarding the order parameter as a phase field and its evolution equation as a balance law by virtue of the special form of the internal energy a third order nonlinearity g 2 f appears in the energy balance in place of the customarily constant latent heat as a consequence the bounds 0 f 1 hold whenever is positive valued in addition a nonlinear fourier law with conductivity proportional to temperature is assumed well posedness for the resulting initial and boundary value problem are then established in a suitable setting

global existence for a phase separation system deduced from the entropy balance abstract this paper is concerned with a thermomechanical model describing phase separation phenomena in terms of the entropy balance and equilibrium equations for the microforces the related system is highly nonlinear and admits singular potentials in the phase equation both the viscous and the non viscous cases are considered in the cahn hilliard relations characterizing the phase dynamics the entropy balance is written in terms of the absolute temperature and of its logarithm appearing under time derivative the initial and boundary value problem is considered for the system of partial differential equations the existence of a global solution is proved via some approximations involving yosida regularizations and a suitable time discretization

on timoshenko type systems with type iii thermoelasticity asymptotic behavior abstract in this study we consider a thermoelastic beam system where the oscillations are defined by the timoshenko model and heat conduction is given by the green and naghdi theories we provide an explicit characterization of the decay rate which can be exponential or polynomial depending on the relationship between the coefficients of the wave propagation speed

conservative interacting particles system with anomalous rate of ergodicity we analyse certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures furthermore we show that convergence rate to equilibrium is exponential this result is of interest because it presents counterexample to the standard assumption of physicists that conservative system implies polynomial rate of convergence the system in question is stochastic rather than deterministic

stabilisation of a thermo elastic system under nonuniformly bounded disturbances in the boundary input abstractwe consider the exponential stabilisation for a thermo elastic system of type ii with nonuniformly bounded external disturbances in the boundary control we begin with finding feedback controls for the system without disturbances by lyapunov function approach then based on the resulting feedback control we give new dynamic feedback control laws that make the system exponentially stable by tracking disturbances exponentially through a time varying high gain observer we apply the linear operator semi group theory to prove the well posedness of the resulting closed system finally we prove that the solution of the closed loop system can approach zero polynomially or exponentially by the lyapunov function approach

existence and boundedness of solutions for a singular phase field system abstract this paper is devoted to the mathematical analysis of a thermo mechanical model describing phase transitions in terms of the entropy and order structure balance law we consider a macroscopic description of the phenomenon and make a presentation of the model then the initial and boundary value problem is addressed for the related pde system which contains some nonlinear and singular terms with respect to the temperature variable existence of the solution is shown along with the boundedness of both phase variable and absolute temperature finally uniqueness is proved in the framework of a source term depending lipschitz continuously on

hydrodynamic scaling limits with deterministic initial configurations we discuss the hydrodynamic scaling limits starting with deterministic configurations for different models certain estimates on the entropy of the system are derived

a unified procedure for construction of theories of deformable media i classical continuum physics a new unified procedure for constructing continuum theories of deformable media is presented and used in this and a companion paper the procedure starts with a balance of energy and derives from it all the relevant balance laws that may also include those that are associated with thermal electrical and magnetic effects the basic energetic ingredients that are included in the balance of energy depend of course on the nature of the particular theory of material behaviour desired the advantage of the new procedure becomes especially apparent when one considers formulation of a new theory of material behaviour for which additional balance laws involving new kinetic quantities are required to accompany any additional basic kinematic and thermal variables additional to those in the classical formulation indeed in the formulation of such new theories usually little or no previous information is available concerning properties of the new kinetic quantities in the additional balance laws and in this connection the unified procedure of this paper provides a simple attractive setting for deriving the basic equations that are automatically consistent with the energy balance in this paper first the basic features of the new procedure are illustrated in the context of classical thermomechanics generalizations of this thermomechanical theory are then discussed in two cases 1 in the presence of an additional kinematic variable and 2 in the presence of full electromagnetic effects both of these generalizations bring out some interesting novel features when new theories are being constructed

slow decay of gibbs measures with heavy tails we consider glauber dynamics reversible with respect to gibbs measures with heavy tails in the case when spins are unbounded the interactions are bounded and of finite range the self potential enters into two classes of measures concave probability measures and sub exponential laws for which it is known that no exponential decay can occur using coercive inequalities we prove that for concave probability measures the associated infinite volume semi group decays to equilibrium polynomially and stretched exponentially for sub exponential laws this improves and extends previous results by bobkov and zegarlinski

thermodynamically consistent models of phase field type for the kinetics of phase transitions abstract a general framework is given for the phenomenological kinetics of phase transitions in which not only the order parameter but also the temperature may vary in time and space instead of a ginzburg landau free energy functional as used in formulating the cahn hilliard equation we use the analogous entropy functional model entropy functionals and the kinetic equations resulting from them are constructed for various cases phase transitions with and without a critical point and in the former case with or without a latent heat the class considered is general enough to include the entropy functionals for the ising model in mean field approximation the van der waals fluid and a simplified version of the density functional theory of freezing a case without critical point for which the energy is conserved but the order parameter is not provides a thermodynamically consistent derivation of the phase field equations studied by caginalp fix and others and also leads in a natural way to the lyapunov functional given by langer for these equations but the treatment also suggests that a modified version of the phase field equations might provide a more realistic model of freezing

phase field equations with memory the hyperbolic case we present a phenomenological theory for phase transition dynamics with memory which yields a hyperbolic generalization of the classical phase field model when the relaxation kernels are assumed to be exponential thereafter we focus on the implications of our theory in the hyperbolic case and we derive asymptotically an equation of motion in two dimensions for the interface between two different phases this equation can be considered as a hyperbolic generalization of the classical flow by mean curvature equation as well as a generalization of the born infeld equation we use a crystalline algorithm to study the motion of closed curves for the generalized hyperbolic flow by mean curvature equation our hyperbolic generalization of flow by mean curvature and present some numerical results which indicate that a certain type of two dimensional relaxation damped oscillation may occur

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

spectral gap for zero range dynamics we give a lower bound on the spectral gap for symmetric zero range processes under some conditions on the rate function we show that the gap shrinks as n 2 independent of the density for the dynamics localized on a cube of size n d we follow the method outlined by lu and yau where a similar spectral gap is proved for kawasaki dynamics

a first order phase transition with non constant density abstract we introduce a new model for first order phase transitions accounting for non constant densities of the phases during the process the resulting initial and boundary value problem for a pde system is recovered by thermodynamical principles the resulting system presents some singularities and strong nonlinearities accounting for internal constraints ensuring in particular the positivity of the pressure and the temperature physical consistency for the order parameter comes from a maximum principle argument existence of a weak solution is proved by a regularization passage to the limit procedure

a re examination of the basic postulates of thermomechanics this paper is mainly concerned with a re examination of the basic postulates and the consequent procedure for the construction of the constitutive equations of material behaviour in thermomechanics however the implication of the basic postulates and the significance of the related procedure for the development of the constitutive equations is also illustrated in some detail in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed more specifically after briefly examining the nature of the basic equations of motion for a system of particles within the scope of the classical newtonian mechanics the basic postulates of the purely mechanical theory for a continuum including its specialization for a rigid body is re examined this includes some differences from the usual procedure on the subject next thermal variables are introduced and after observing a useful analogy between the thermal and mechanical variables a discussion of a theory of heat or a purely thermal theory is provided which differs from the usual development in the classical thermodynamics a detailed application of the latter development is then made to the problem of heat flow in a stationary rigid solid using several different and well motivated constitutive equations special cases of these include linearized theories of the classical heat flow by conduction and of heat flow transmitted as thermal waves the remainder of the paper is concerned with thermal mechanical theory of deformable media along with discussions of a number of related issues on the subject

l_2 rates of convergence for attractive reversible nearest particle systems the critical case reversible nearest particle systems are certain one dimensional interacting particle systems whose transition rates are determined by a probability density beta n with finite mean on the positive integers the reversible measure for such a system is the distribution nu of the stationary renewal process corresponding to this density in an earlier paper we proved under certain regularity conditions that the system converges exponentially rapidly in l 2 nu if and only if the system is supercritical this in turn is equivalent to beta n having exponential tails in this paper we consider the critical case and give moment conditions on beta n which are separately necessary and sufficient for the convergence of the process in l 2 nu at a specified algebraic rate in order to do so we develop conditions on the generator of a general markov process which correspond to algebraic l 2 convergence of the process the use of these conditions is also illustrated in the context of birth and death chains on the positive integers

transition from intermittency to periodicity in lag synchronization in coupled rossler oscillators the dynamical and statistical behavior of lag synchronization in two coupled self sustained chaotic rossler oscillators is reexamined the lack of uniqueness in the conventional characterization of lag synchronization based on the similarity function has caused much skepticism about the existence of lag synchronization we provide an evidence that the emergence of lag synchronization is associated with the transition from on off intermittency to a periodic structure in the laminar phase distribution

convergence to equilibrium of conservative particle systems on mathbb z bm d we consider the ginzburg landau process on the lattice zd whose potential is a bounded perturbation of the gaussian potential we prove that the decay rate to equilibrium in the variance sense is t d 2 up to a logarithmic correction for any function u with finite triple norm that is u x zd xu

generalized synchronization of chaos in directionally coupled chaotic systems synchronization of chaotic systems is frequently taken to mean actual equality of the variables of the coupled systems as they evolve in time we explore a generalization of this condition which equates dynamical variables from one subsystem with a function of the variables of another subsystem this means that synchronization implies a collapse of the overall evolution onto a subspace of the system attractor in full space we explore this idea in systems where a response system bold y ital t is driven with the output of a driving system bold x ital t but there is no feedback to the driver we lose generality but gain tractability with this restriction to investigate the existence of the synchronization condition bold y ital t phi bold x ital t we introduce the idea of mutual false nearest neighbors to determine when closeness in response space implies closeness in driving space the synchronization condition also implies that the response dynamics is determined by the drive alone and we provide tests for this as well examples are drawn from computer simulations on various known cases of synchronization and on data from nonlinear electrical circuits determining the presence of generalized synchronization will be quite important when one has only scalarmore observations from the drive and from the response systems since the use of time delay or other embedding methods will produce imperfect coordinates in which strict equality of the synchronized variables is unlikely to transpire less

a skew symmetry preserving computational technique for obtaining the positive and the bounded solutions of a time delayed advection diffusion reaction equation abstract in this work we consider a one dimensional time delayed advective version of the well known fisher kolmogorov petrovsky piscounov equation from population dynamics which extends several models from mathematical physics including the classical wave equation the nonlinear klein gordon equation a fitzhugh nagumo equation from electrodynamics and the burgers huxley equation and the newell whitehead segel equation from fluid mechanics we propose a skew symmetry preserving finite difference scheme for approximating the solutions of the model under investigation and establish conditions on the model coefficients and the numerical parameters under which the method provides positive or bounded approximations for initial data which are likewise positive or bounded respectively the derivation of the conditions under which the positivity and the boundedness of the approximations is guaranteed is based on the properties of the inverses of m matrices in fact the conditions obtained here assure that the iterative method is described in vector form through the multiplication by a matrix of this type we provide simulations in order to show that the technique is indeed conditionally positivity preserving and boundedness preserving

logarithmic sobolev inequality for lattice gases with mixing conditions let mu lambda l lambda gc denote the grand canonical gibbs measure of a lattice gas in a cube of sizel with the chemical potential and a fixed boundary condition let mu lambda l n c be the corresponding canonical measure defined by conditioning mu lambda l lambda gc on sigma x in lambda eta x n consider the lattice gas dynamics for which each particle performs random walk with rates depending on near by particles the rates are chosen such that for everyn andl fixed mu lambda l n c is a reversible measure suppose that the dobrushin shlosman mixing conditions holds for mu l lambda gc forall chemical potentials we prove that smallint f log fd mu lambda l n c leqq const l 2 d sqrt f for any probability densityf with respect to mu lambda l n c here the constant is independent ofn orl andd denotes the dirichlet form of the dynamics the dependence onl is optimal

on the spectral gap of kawasaki dynamics under a mixing condition revisited we consider a conservative stochastic spin exchange dynamics which is reversible with respect to the canonical gibbs measure of a lattice gas model we assume that the corresponding grand canonical measure satisfies a suitable strong mixing condition we give an alternative and quite natural from the physical point of view proof of the famous lu yau result which states that the relaxation time in a box of side l scales like l2 we then show how to use such an estimate to prove a decay to equilibrium for local functions of the form 1 t e where e is positive and arbitrarily small and 12 for d 1 1 for d 2

time discretization and global solution for a doubly nonlinear volterra equation this note addresses the analysis of an abstract doubly nonlinear volterra equation with a nonsmooth kernel and possibly unbounded and degenerate operators by exploiting a suitable implicit time discretization technique we obtain the existence of a global strong solution as a by product the discrete scheme is proved to be conditionally stable and convergent

relaxation to equilibrium of conservative dynamics i zero range processes under mild assumptions we prove that for any local function u the decay rate to equilibrium in the variance sense of zero range dynamics on the d dimensional integer lattice is c u t d 2 o t d 2 the constant c u is computed explicitly

general energy decay in a timoshenko type system of thermoelasticity of type iii with a viscoelastic damping in this paper we consider a one dimensional linear thermoelastic system of timoshenko type where the heat conduction is given by green and naghdi theories we prove a general decay result from which the exponential and polynomial decays are only special cases

a note on discontinuity waves in type iii thermoelasticity two recent nonlinear theories of thermoelasticity developed by green and naghdi are examined it is shown that in type ii theory second sound is permissible and both mechanical and temperature waves may propagate in type iii theory we show that the situation is more analogous to that in classical nonlinear thermoelasticity one wave propagates and a homothermal temperature wave is allowed

strain gradient theory of chiral cosserat thermoelasticity without energy dissipation in this paper we use the green naghdi theory of thermomechanics of continua to derive a linear strain gradient theory of cosserat thermoelastic bodies the theory is capable of predicting a finite speed of heat propagation and leads to a symmetric conductivity tensor the constitutive equations for isotropic chiral thermoelastic materials are presented in this case in contrast with the classical cosserat thermoelasticity a thermal field produces a microrotation of the particles the thermal field is influenced by the displacement and microrotation fields even in the equilibrium theory existence and uniqueness results are established the theory is used to study the effects of a concentrated heat source in an unbounded homogeneous and isotropic chiral solid

poincare and logarithmic sobolev inequality for ginzburg landau processes in random environment we consider reversible conservative ginzburg landau processes in a random environment whose potential are bounded perturbations of the gaussian potential evolving on a d dimensional cube of length l we prove in all dimensions that the spectral gap of the generator and the logarithmic sobolev constant are of order l 2 almost surely with respect to the environment

weak solutions to the penrose fife phase field model for a class of admissible heat flux laws abstract this paper is concerned with a thermodynamically consistent model for diffusive phase transitions proposed by penrose and fife the model has recently received a good deal of attention and the related initial boundary value problems have been investigated from the mathematical point of view in the case where the order parameter is not conserved the common working assumption for the heat flow was that such a flux is proportional to the gradient of the inverse absolute temperature this position seems to be helpful for the analysis due to the coupling term in the phase field equation which depends right on the inverse temperature here we prove the existence of weak solutions in a wide setting of constitutive laws for the heat flux different from the previous ones and considerably more significant owing to their behaviour for high temperatures we also discuss the limiting situation of zero interfacial energy for the order parameter

multivalued mappings in generalized chaos synchronization the onset of generalized synchronization of chaos in directionally coupled systems corresponds to the formation of a continuous mapping that enables one to persistently define the state of the response system from the trajectory of the drive system a recently developed theory of generalized synchronization of chaos deals only with the case where this synchronization mapping is a single valued function in this paper we explore generalized synchronization in a regime where the synchronization mapping can become a multivalued function specifically we study the properties of the multivalued mapping that occurs between the drive and response systems when the systems are synchronized with a frequency ratio other than one to one and address the issues of the existence and continuity of such mappings the basic theoretical framework underlying the considered synchronization regimes is then developed

an unconditionally stable algorithm for generalized thermoelasticity based on operator splitting and time discontinuous galerkin finite element methods an efficient time stepping algorithm is proposed based on operator splitting and the space time discontinuous galerkin finite element method for problems in the non classical theory of thermoelasticity the non classical theory incorporates three models the classical theory based on fourier s law of heat conduction resulting in a hyperbolic parabolic coupled system a non classical theory of a fully hyperbolic extension and a combination of the two the general problem is split into two contractive sub problems namely the mechanical phase and the thermal phase each sub problem is discretized using the space time discontinuous galerkin finite element method the sub problems are stable which then leads to unconditional stability of the global product algorithm a number of numerical examples are presented to demonstrate the performance and capability of the method