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Probabilistic Cellular Automaton for Random Walkers

Kazume Nishidate
Organization: Iwate University
Department: Department of Electrical and Electronic Engineering
David Fowler
Organization: University of Nebraska-Lincoln
H. Chiba
Takashi Ito
Organization: Japan Information Processing Service Co., Ltd.
K. Kodama
Kiyoshi Nishikawa
Organization: Kanazawa University
Department: Department of Computational Science
Journal / Anthology

Journal of the Physical Society of Japan
Year: 2000
Volume: 69
Issue: 5
Page range: 1352-1355

A cellular-automaton of multiple random walkers is proposed to simulate d-dimensional many-body interacting lattice gas system. The fully parallel dynamics of the random walkers in d-dimensional hyper cubic lattice system is defined by introducing a simple probabilistic local rule set which prohibits the multiple occupancy of the walkers on a lattice site and keeps the conservation of the total number at any time. An equation which essentially governs the dynamics is derived by constructing a Boltzmann transport equation. An expression for the diffusion constant is obtained analytically and compared with the simulation results.

*Mathematics > Discrete Mathematics > Cellular Automata
*Mathematics > Probability and Statistics
*Science > Physics > Thermodynamics and Statistical Mechanics