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We study the nonequilibrium spatial correlations of the density fluctuations for a selected reagent as well as the spatial correlations of its energetic states in a stationary state of a model chemical system. In the considered chemical model the reagent of interest appears as a product of a binary process and vanishes as the result of a fast unimolecular decay. Assuming that the lifetime of the reagent is short enough to treat its motion as a ballistic rather than diffusive one we derive analytical formulae for all correlation functions. The results obtained from these formulae agree well with correlations directly measured in molecular dynamics simulations.

In this paper we consider a chemical process, for which the reagent of interest decays shortly after it is created. For such a system the standard theory of nonequilibrium spatial correlations in the density fluctuations, which leads to Ornstein–Zernike type of expression, does not work. We compare results of molecular simulations with another theoretical description based on the assumption that the lifetime of the reagent is short enough to treat its motion as a ballistic rather than diffusive one.

A kinetic model of a reaction–diffusion system by which fluctuation around a nonequilibrium steady state can be analyzed without resorting to a local equilibrium assumption is discussed. The spatial correlation function of concentration fluctuations is analytically calculated, and it is shown that (i) the result is consistent with the previous studies for sufficiently slow chemical reactions, and (ii) how the correlation function is modified when chemical reactions are fast.

The k-dependent hydrodynamic fluctuations for binary classical fluids are discussed. The aim of this paper is to give the microscopic basis for the phenomenological formulation of hydrodynamics of binary fluids which was explored by the present author. The generalized Langevin equation formalism is used to derive closed equations for the fluctuations of temperature, mass, relative velocity, etc. Explicit expressions for the k-dependent thermodynamic susceptibilities are also derived. Using these quantities, it is shown that the equations for fluctuations reduce to the macroscopic equations in the long wavelength limit.

The mesoscopic description of a system with chemical reactions predicts that if the detailed balance condition is not satisfied then the nonequilibrium spatial correlations between concentrations of reactants may appear. The present work is concerned with the dynamics of their growth. We assume that the system is homogeneous at the beginning and study how fast the nonequilibrium correlations develop. The theory based on the master equation is compared with molecular dynamics simulations performed for a model system of “reacting” hard spheres. The qualitative characteristics of the growth of the spatial correlations, predicted by the theory based on a master equation, are confirmed in our simulations. However, this theory fails to give the correct quantitative description of this process.

A general formalism of nonequilibrium thermodynamics of multicomponent fluids is given. Reversible parts of balance equations for the extensive variables are constructed in such a way that the growth rate of the extensive variables are related to their conjugate intensive parameters in an antisymmetric manner. This enables us to give the balance equation for the diffusional flow which plays an important role in the study of superfluidity and complex fluids.

The mesoscopic description of a system with chemical reactions predicts that if the detailed balance condition is not satisfied, then nonequilibrium spatial correlations between concentrations of reactants may appear. The present work is concerned with molecular dynamics simulations of such correlations in a model system of “reacting” hard spheres. The simulations have shown that if the detailed balance condition is satisfied, then the nonequilibrium spatial correlations are absent. In a steady state for which the detailed balance condition is not satisfied, the nonequilibrium correlations are present and their spatial exponential decay predicted by the theory based on a master equation, is confirmed in our simulations.

Starting from the Langevin equation a nonlinear evolution equation describing the mean square distance of initially close tagged particles in a turbulent medium is obtained. The equation is the same as that derived for a turbulent plasma by Misguich and Balescu using renormalized kinetic theory. The approach is extended to incorporate stable drift in connection with the diffusion of macro particles in a turbulent fluid. The initial ≈t3 and intermediate exponential growth of the mean square distance subsist even under the presence of stable drift in agreement with many confirmed observations.

A general method to calculate explicitly the stationary probability of nonlinear systems subjected to a special case of coloured noise is presented. For a simple model system the “phase diagram” for the various noise-induced transitions is determined.

We present a stochastic theory of the kinetics of phase transitions in univariant, nonuniform systems. We assume a master equation and a relation of the transition probability to the free energy [J. S. Langer, Ann. Phys. (N.Y) 65, 53 (1971)]. The free energy is taken to be of the Cahn–Hilliard form. By means of path integral methods we obtain a formal solution from which we derive a deterministic differential equation for the most probable variation of the density distribution in time. This equation is of the Landau–Ginzburg type. We show the existence of a Liapunoff function for this kinetic equation, which is then used to derive simply the classical result of nucleation theory for the critical radius of a droplet. Next we show from the kinetic equation that if the structure of the free energy is such that a phase transition occurs and metastable states are possible, then the kinetics of the decay to the stable and metastable states is nonlinear, of the cubic type. Finally we derive from the kinetic equa...

We consider a classical stochastic model describing particle transport on a lattice with randomly distributed nearest-neighbor transition rates. Applying an effective medium theory to the model, we determine average properties related to the particle's dynamics ind-dimensions. In particular, we calculate the mean-square displacement, and the fourth moment of the displacement in one-, two- and three dimensions. The results compare favorably with Monte Carlo simulations of the model. We also present preliminary results for the velocity autocorrelation function.

Fluctuations around the steady state in chemical reactions are discussed. The connection between the two approaches in the literature, the Langevin equation approach and the master equation approach, is shown in terms of a path integral.

Phenomenological master equations are useful for discussions of various aspects of the kinetics of phase transitions. The transition rate in such master equations is of a form proposed by Langer; the rate is an exponential of the change of the free energy of the system due to a change in a thermodynamic variable. We present a derivation of this form from a microscopic theory for an Ising model which exhibits first and second order phase transition. Using Zwanzig’s formalism we derive a master equation for a spin system which interacts with a phonon heat bath. Thus, we obtain the transition rate on a time scale of one microscopic event (one spin flip). This form differs from the phenomenological one in that it depends on details of the dynamics of the system, the heat bath, and the interaction between them. These details are removed by a further averaging (coarse‐graining). If a Markoffian master equation is assumed to exist on a phenomenological time scale large compared to the microscopic time scale, yet small compared to the relaxation time of the system, then we show that the transition rate in that master equation has the form proposed by Langer.

The nonlinear master equation previously proposed by Malek-Mansour and Nicolis is applied to the analysis of unstable transitions leading to temporally or spatially organized patterns. Thecorrelation length of the destabilizing fluctuations is determined, and a number of striking analogies with equilibrium phase transitions are pointed out.

Assuming that a macrovariable follows a Markovian process, the extensive property of its probability distribution is proved to propagate. This is a generalization of the Gaussian properties of the equilibrium distribution to nonequilibrium nonstationary processes. It is basically a WKB-like asymptotic evaluation in the inverse of the size of the macrosystem. Evolution of the variable along the most probable path and fluctuation properties around the path are considered from a general point of view with an emphasis on the relation of nonlinearity of evolution and the associated fluctuation. Anomalous behavior of the fluctuation is discussed in connection with unstable, critical, or marginal states. A general treatment is given for the asymptotic properties of relaxation eigenmodes.

On obtient des resultats exacts et explicites pour la relaxation d'une classe de systemes non lineaires sous l'effet d'un bruit blanc gaussien

By using the formula for the steady state probability distribution of fluctuations in a non-linear system under the influence of two-level Markovian noise, the existence of phase transitions of such a system with the variation of intensity and correlation time of the noise is shown. Explicit results for the Verhulst model and a model for population genetics are given and compared with the previous results for the white noise case., info:eu-repo/semantics/published

A critical cluster in homogeneous nucleation can be defined in two ways. Thermodynamically, the size of the critical cluster corresponds to a maximum of the free energy of the system; kinetically the critical cluster is defined such that all supercritical clusters grow and all others decay. We describe the evolution of a cluster by a postulated stochastic master equation in which the transition probabilities are given by a formula proposed by Langer. We derive from these assumptions, by a path integral method, an equation for the most probable evolution of the size of the cluster and show thereby that under these circumstances the two definitions are equivalent.