Diffusion in Lorentz lattice gas cellular automata: The honeycomb and quasi-lattices compared with the square and triangular lattices

Journal Article · Sun Oct 01 04:00:00 EDT 1995 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/BF02179989· OSTI ID:468309

Wang, F ^[1]; Cohen, E G.D. ^[2]

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1. Univ. of Missouri, Columbia, MO (United States)
2. Rockerfellar Univ., NY (United States)

We study numerically the nature of the diffusion process on a honeycomb and a quasi-lattice, where a point particle, moving along the bonds of the lattice, scatters from randomly places scatterers on the lattice sites according to strictly deterministic rules. For the honeycomb lattice fully occupied by fixed rotators two (symmetric) isolated critical points appear to be present, with the same hyperscaling relation as for the square and the triangular lattices. No such points appear to exist for the quasi-lattice. A comprehensive comparison is made with the behavior on the previously studied square and triangular lattices. A great variety of diffusive behavior is found, ranging from propagation, super-diffusion, normal, quasi-normal, and anomalous, to absence of diffusion. The influence of the scattering rules as well as of the lattice structure on the diffusive behavior of a point particle moving on the all lattices studied so far is summarized.

• Sponsoring Organization: USDOE
• DOE Contract Number: FG02-88ER13847
• OSTI ID: 468309
• Journal Information: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 1-2 Vol. 81; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOLTZMANN STATISTICS
DIAGRAMS
DIFFUSION
EQUATIONS OF MOTION
LORENTZ GAS
MATHEMATICAL MODELS
NUMERICAL DATA