Journal ArticleDOI
Stochastic dynamics of a subsystem interacting with a solid body with application to diffusive processes in solids
Roumen Tsekov,Eli Ruckenstein +1 more
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In this paper, the dynamics of a mechanical subsystem interacting with a solid body is studied, where the Newton equations are transformed to a set of stochastic generalized Langevin equations describing the evolution of the coordinates of the subsystem particles.Abstract:
In this paper the dynamics of a mechanical subsystem interacting with a solid body is studied. The Newton equations are transformed to a set of stochastic generalized Langevin equations describing the evolution of the coordinates of the subsystem particles. The solid is modeled as a bath of interacting harmonic oscillators, and the effect of their spatial correlations on the statistical properties of the Langevin forces is accounted for. The most important result is the relation established between the static interaction of the subsystem with the solid body and the dissipative and fluctuation forces. In the particular case of a subsystem consisting of a single particle, an expression is derived for the friction tensor in terms of the static interaction potential and Debye cutoff frequency of the solid. The analysis is applied in the latter case to some simple processes occurring in solids, such as adsorption, desorption, and diffusion.read more
Citations
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Multiple hops in multidimensional activated surface diffusion
TL;DR: In this article, Kramers' theory is used to derive simple expressions for the hopping distribution in multidimensional activated surface diVusion, provided that the average energy loss of the particle as it goes from one barrier to the next is of the order of k B T or more.
Journal ArticleDOI
Diffusion of inert gases in silica sodalite: Importance of lattice flexibility
TL;DR: In this paper, the authors quantify this explanation by incorporating lattice flexibility into transition state theory to compute transport rates of inert gas molecules (Ne, Ar and Kr) through narrow windows of silica sodalite cages.
Journal ArticleDOI
Does lattice vibration drive diffusion in zeolites
TL;DR: In this paper, the effect of lattice vibration as a driving force for sorbate diffusion in zeolites has been investigated and a generalized Langevin equation has been derived with the magnitude of the lattice vibrations captured by two parameters.
Journal ArticleDOI
Temperature control in molecular dynamic simulations of non-equilibrium processes.
Dawid Toton,Dawid Toton,Christian D. Lorenz,Nikolaos Rompotis,Nikolaos Rompotis,Natalia Martsinovich,Natalia Martsinovich,Lev Kantorovich +7 more
TL;DR: It is stressed that a meaningful compromise between computational efficiency and a physically appropriate implementation of the NVT thermostat can be achieved, at least for solid state and surface problems, if the so-called stochastic boundary conditions (SBC), recently derived from the GLE, are used.
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Activated surface diffusion: Are correlated hops the rule or the exception?
TL;DR: In this article, the authors show that if the damping is associated with acoustic phonons and the coupling of the adatom with the surface is not too strong, then the friction coefficient is Ohmic.
References
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Journal ArticleDOI
Nonlinear generalized Langevin equations
TL;DR: In this article, exact generalized Langevin equations are derived for arbitrarily nonlinear systems interacting with specially chosen heat baths, and an example is presented in which the Langevin equation is nonlinear but approximately Markovian.
Journal ArticleDOI
Statistical Mechanics of Assemblies of Coupled Oscillators
G. W. Ford,Mark Kac,P. Mazur +2 more
TL;DR: In this article, it was shown that a system of coupled harmonic oscillators can be made a model of a heat bath and that a particle coupled harmonically to the bath and by an arbitrary force to a fixed center will exhibit Brownian motion.
Journal ArticleDOI
Generalized Langevin equation approach for atom/solid-surface scattering: General formulation for classical scattering off harmonic solids
Steven A. Adelman,J. D. Doll +1 more
TL;DR: In this paper, a general theoretical framework for introducing manybody or lattice effects into gas/solid scattering is presented, which is restricted to classical scattering off harmonic lattices but is otherwise completely general.
Book
The Nonequilibrium Statistical Mechanics of Open and Closed Systems
K. Lindenberg,Katja Lindenberg +1 more
TL;DR: In this paper, the evolution of complex systems langevin equations some problems, evolution of probability, stochastic rate equations single degree of freedom delta-correlated gaussian fluctuation many degrees of freedom fluctuations with a finite correlation time (colored noise) statistical measures.
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