Diffusion with stochastic resetting

We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We also show that the mean time to find a stationary target by a diffusive searcher is finite and has a minimum value at an optimal resetting rate r*. Resetting also alters fundamentally the late time decay of the survival probability of a stationary target when there are multiple searchers: while the typical survival probability decays exponentially with time, the average decays as a power law with an exponent depending continuously on the density of searchers.     

A concept of multi-scale modeling for radiative heat transfer in particle polydispersions

To take the local thermal nonequilibrium between particles and the nonuniformity of temperature within a single particle into account, a concept of multi-scale modeling of radiative transfer is presented. Particles are considered to interact with thermal radiation on both micro-scale of a single particle and meso-scale of a particle cell to produce radiative source term at the local or meso-scale level of a particle cell for the modeling of radiative transfer at macro-scale of overall particle system. The accurate modeling of radiative transfer in particle polydispersions are related to the modeling of radiative transfer in following three different scales: macro-scale of the overall particle system, meso-scale of particle cell, and micro-scale of single particle. Two examples are taken to show the necessity of multi-scale modeling for radiative transfer in particle polydispersions. The results show that omitting local thermal nonequilibrium and nonuniformity will result in errors for the solution of radiative heat transfer to some extent, and the multi-scale modeling is necessary for the radiative transfer in particle system with large local thermal nonequilibrium and nonuniformity.     

The nonequilibrium Lorentz gas

We study the conductivity of a Lorentz gas system, composed of a regular array of fixed scatterers and a point-like moving particle, as a function of the strength of an applied external field. In order to obtain a nonequilibrium stationary state, the speed of the point particle is fixed by the action of a Gaussian thermostat. For small fields the system is ergodic and the diffusion coefficient is well defined. We show that in this range the Periodic Orbit Expansion can be successfully applied to compute the values of the thermodynamic variables. At larger values of the field we observe a variety of possible dynamics, including the breakdown of ergodic behavior, and later the existence of a single stable trajectory for the largest fields. We also study the behavior of the system as a function of the orientation of the array of scatterers with respect to the external field. Finally, we present a detailed dynamical study of the transitions in the bifurcation sequence in both the elementary cell and the fundamental domain. The consequences of this behavior for the ergodicity of the system are explored. (c) 1995 American Institute of Physics.     

Nonlinear diffusion and Nelson-Brown movement

The nonlinear diffusion process, which can be described as the Nelson-Brown motion, is considered. The obtained equation becomes the classical linear diffusion equation for small relaxation times, and for long relaxation times it is transferred into the Schrödinger-like equation. The possible nonequilibrium stationary states are discussed.     

Dissipative processes during the nonequilibrium phase transformations in martensitic thermoelastic alloys

Martensitic thermoelastic transformations are considered under nonequilibrium conditions, where a system nonmonotonically tends toward a stationary process. The specific features of a phase transformation are experimentally studied on molecular models under these nonequilibrium conditions. A resonance mode of the phase transformation, which can increase the process rate by an order of magnitude without increasing the heat source temperature, is found. The dissipative processes that occur under the monotonic and resonance conditions of martensitic thermoelastic transformations are estimated. The resonance mode is shown to be accompanied by negative entropy production and to demonstrate the self-organization of the system. These results can be used to design materials and techniques for the processing of low-potential heat sources.     

Spatial correlations in nonequilibrium systems: The effect of diffusion

We show how the ideas of the fluctuation-dissipation theory can be used to calculate spatial correlations in interacting systems away from equilibrium. The only spatially dependent dissipative process considered is diffusion, and spatial correlations are generated by the nonlocal spatial dependence of the chemical potential. The results are the lowest order in a hierarchy of generalized hydrodynamic type calculations applicable to nonequilibrium systems. We derive equations for the density correlation functions at stationary state supported by diffusive fluxes and show that they have the local equilibrium form. The static correlation function is obtained from the fluctuation-dissipation theorem, which we show to be equivalent to the Ornstein-Zernike integral equation. At equilibrium we demonstrate that the dynamical structure factor obtained by these methods includes the expected wave-vector dependent diffusion constant. Finally we derive a necessary and sufficient condition for local equilibrium to obtain at a stationary state and show by explicit calculation that chemical processes can give rise to significant nonequilibrium correlations.     

A remark on the hydrodynamics of the zero-range processes

The nonequilibrium stationary hydrodynamical properties of the symmetric nearest neighbor zero-range processes are studied: local equilibrium and Fourier's law are proven to hold, and the bulk diffusion coefficient and the equal time covariance of the limiting nonequilibrium stationary density fluctuations field are computed. The result fits with those already known and confirms some conjectures derived from a time-dependent macroscopic analysis. The very simple proof is based on a result already published but may be not so well known in this context.Partially supported by NATO Grant No. 040.82.Partially supported by FAPESP: Fundacão de Amparo à Pesquisa do Estado de São Paulo, Grant No. 82/1719-9.     

Brownian motion in a fluid in elongational flow

Brownian motion of a spherical particle in stationary elongational flow is studied. We derive the Langevin equation together with the fluctuation-dissipation theorem for the particle from nonequilibrium fluctuating hydrodynamics to linear order in the elongation-rate-dependent inverse penetration depths. We then analyze how the velocity autocorrelation function as well as the mean square displacement are modified by the elongational flow. We find that for times small compared to the inverse elongation rate the behavior is similar to that found in the absence of the elongational flow. Upon approaching times comparable to the inverse elongation rate the behavior changes and one passes into a time domain where it becomes fundamentally different. In particular, we discuss the modification of thet ^–3/2 long-time tail of the velocity autocorrelation function and comment on the resulting contribution to the mean square displacement. The possibility of defining a diffusion coefficient in both time domains is discussed.     

Interaction of 3-level atom with radiation

The stochastic limit of quantum theory suggests a new, constructive, approach to nonequilibrium phenomena. We illustrate this approach when considering the interaction of 3-level system with a quantum field in a nonequilibrium state. We describe a class of states of the quantum field for which a stationary state drives the system to an inversely populated state. We find that the quotient of the population of the energy levels in the simplest case is described by the double Einstein formula which involves products of two Einstein emission/absorption factors. Emission and absorption of radiation by 3-level atom in nonequilibrium stationary state is described.     

Grain boundary diffusion patterns under nonequilibrium and migration of grain boundaries in nanoctructure materials

In this work, the model of grain boundary diffusion from a permanent source along nonequilibrium migratory grain boundaries is considered. Grain boundary nonequilibrium is characterized by a value of boundary excess energy up to which relaxation goes. It is shown increasing excess energy and migration velocity of nonequilibrium boundaries lead to increasing diffusant volume penetrating into a sample during annealing time.     

Nonequilibrium Linear Response for Markov Dynamics,II: Inertial Dynamics

We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be expressed as a sum of two temporal correlations in the unperturbed system, one entropic, the other frenetic. The decomposition arises from the (anti)symmetry under time-reversal on the level of the nonequilibrium action. The response formula involves a statistical averaging over explicitly known observables but, in contrast with the equilibrium situation, they depend on the model dynamics in terms of an excess in dynamical activity. As an example, the Einstein relation between mobility and diffusion constant is modified by a correlation term between the position and the momentum of the particle.     

Interdiffusion in condensed solutions

Expressions for the coefficient of interdiffusion of components in a binary condensed vacancy-free alloy and a diffusion coefficient matrix for the same alloy with equilibrium and nonequilibrium vacancies are studied. In the first alloy, metastable states may appear if the mixing energy is positive. In the case of the second alloy, closed spinodals may arise under certain conditions. In binary systems with a constant concentration of particles having close atomic volumes, a vacancy stationary nonequilibrium distribution is observed, which may generate vacancy “channels” through which atoms diffuse much more rapidly than in the regular lattice.     

Traveling waves and nonequilibrium stationary patterns in two-component reactive langmuir monolayers

A simple kinetic model of a two-component phase-separating Langmuir monolayer with a chemical reaction is proposed. Its analysis and numerical simulations show that nonequilibrium periodic stationary structures and patterns of traveling stripes can spontaneously develop. The nonequilibrium phase diagram of this system is constructed and the properties of the patterns are discussed.     

Fourier's law from closure equations

We sketch a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is proportional to the temperature gradient with a temperature dependent heat conductivity and the stationary temperature exhibits a nonlinear profile.     

Approach to field-induced stationary state in a gas of hard rods

The Boltzmann equation describing one-dimensional motion of a charged hard rod in a neutral hard rod gas at temperatureT = 0 is solved. Under the action of a constant and uniform field the charged particle attains a stationary state. In the long time limit the velocity autocorrelation function decays via damped oscillations. In the reference system moving with the mean particle velocity the decay of fluctuations in the position space is governed (in the hydrodynamic limit) by the diffusion equation. Both the stationary current and the diffusion coefficient are proportional to the square root of the field. It is conjectured that this result also holds forT > 0 in a strong field limit.On leave from the Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-081 Warsaw, Poland.     

Expression for the stationary distribution in nonequilibrium steady states

We study the nonequilibrium steady state realized in a general stochastic system attached to multiple heat baths. Starting from the detailed fluctuation theorem, we derive concise and suggestive expressions for the corresponding stationary distribution which are correct up to the second order in thermodynamic forces. The probability of a microstate eta is proportional to exp[Phi(eta)] where Phi(eta)=-[under summation operator]kbeta_{k}E_{k}(eta) is the excess entropy change. Here, E_{k}(eta) is the difference between two kinds of conditioned path ensemble averages of excess heat transfer from the kth heat bath whose inverse temperature is beta_{k}. This result can be easily extended to steady states maintained with other sources, e.g., particle current driven by an external force. Our expression may be verified experimentally in nonequilibrium states realized, for example, in mesoscopic systems.     

On the asymptotic behaviour of Spitzer's model for evolution of one-dimensional point systems

A nearest-neighbor gradient dynamics of one-dimensional infinite particle systems is considered; the model admits a two-parameter family of stationary configurations. Some domains of attraction of stationary configurations are described, and the continuum (hydrodynamical) limit of the system is investigated. It is shown that the mean density of points satisfies a nonlinear diffusion equation in the hydrodynamical limit.Research supported by I.H.E.S., Bures-sur-Yvette, France.     

Relaxation rates of the nonequilibrium concentration and flow of a substance in a medium with sink and arbitrary space-varying diffusion coefficient

We determine the relaxation rates of the stationary nonequilibrium concentration and flow of a substance in a medium with sink and arbitrary space-varying diffusion coefficient. We used the method proposed previously by the author to find the temporal characteristics of nonstationary diffusion in a one-dimensional medium. It is shown that the flow inside the medium relaxes to the steady state faster than the concentration. Some specific examples are analyzed. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol.42, No.6, pp. 581–589, June 1999.