From reactive lattice gas automaton rules to its partial differential equations
作者:
A.T. Lawniczak,
期刊:
Transport Theory and Statistical Physics
(Taylor Available online 2000)
卷期:
Volume 29,
issue 3-5
页码: 261-288
ISSN:0041-1450
年代: 2000
DOI:10.1080/00411450008205875
出版商: Taylor & Francis Group
关键词: reactive lattice gas automata;reaction-diffusion dynamics;mesoscopic models;mesoscopic dynamics;Boltzmann equations;pattern formation;fluctuations
数据来源: Taylor
摘要:
We present a general statistical mechanical theory of multispecies lattice gas automata (LGA) for reaction-diffusion systems. We describe how reactive and elastic collisions and free streaming of molecules between collisions are modeled by LGA chemical transformation, mixing and propagation steps. We characterize these steps in terms of microdynamical variables and transition probabilities. From these steps we construct diffusion and reaction-diffusion automaton dynamics. We describe these dynamics in terms of LGA microdynamical equations and discrete lattice Boltzmann equations. From the LGA discrete Boltzmann equations we derive the corresponding LGA macroscopic diffusion and reaction-diffusion PDEs. By comparing these equations with those arising from phelattice gas research J.P. Boon, D. Dab, K. Diemer, D. Gruner, B. Hasslacher, R. Kapral, P. Masiar, S. Ponce-Dawson and J.P. Voroney.
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