Derivation of a kinetic model from a stochastic particle system

Pierre Degond; Simone Goettlich; Axel Klar; Mohammed Seaid; Andreas Unterreiter

doi:10.3934/krm.2008.1.557

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2008, Volume 1, Issue 4: 557-572. Doi: 10.3934/krm.2008.1.557

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Derivation of a kinetic model from a stochastic particle system

1.
3-Université de Toulouse (UPS, INSA, UT1, UTM) & CNRS, Institut de Mathématiques de Toulouse (UMR 5219), 118 Route de Narbonne, F-31062 Toulouse
2.
TU Kaiserslautern, Department of Mathematics, Postfach 3049, 67653 Kaiserslautern
3.
Fraunhofer Institute ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern
4.
University of Durham, School of Engineering, South Road Durham DH1 3LE
5.
TU Berlin, Department of Mathematics, Straße des 17.Juni 136, 10623 Berlin

Received: July 2008

Revised: September 2008

Published: October 2008

Abstract / Introduction Related Papers Cited by

Abstract

We study a stochastic lattice particle system with exclusion principle. A kinetic equation and its diffusion limit are formally derived from the Monte Carlo dynamics. This derivation is investigated analytically and numerically and compared with the classical hydrodynamic limit of the stochastic exclusion process. Numerical results are presented for different values of jump probabilities.

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Mathematics Subject Classification: 65C05, 82C22.

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