New results for diffusion in Lorentz lattice gas cellular automata

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

DOI:https://doi.org/10.1007/BF02179988· OSTI ID:468308

Cohen, E G.D. ^[1]; Wang, F ^[2]

---

1. Rockefellar Univ., New York, NY (United States)
2. Univ. of Missouri, Columbia, MO (United States)

New calculations to over ten million time steps have revealed a more complex diffusive behavior than previously reported of a point particle on a square and triangular lattice randomly occupied by mirror or rotator scatterers. For the square lattice fully occupied by mirrors where extended closed particle orbits occur, anomalous diffusion was still found. However, for a not fully occupied lattice the superdiffusion, first noticed by Owczarek and Prellberg for a particular concentration, obtains for all concentrations. For the square lattice occupied by rotators and the triangular lattice occupied by mirrors or rotators, an absence of diffusion (trapping) was found for all concentrations, except on critical lines, where anomalous diffusion (extended closed orbits) occurs and hyperscaling holds for all closed orbits with universal exponents d{sub f}=7/4 and {tau}=15/7. Only one point on these critical lines can be related to a corresponding percolation problem. The questions arise therefore whether the other critical points can be mapped onto a new percolation-like problem and of the dynamical significance of hyperscaling.

• Sponsoring Organization: USDOE
• DOE Contract Number: FG02-88ER13847
• OSTI ID: 468308
• 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
DIAGRAMS
DIFFUSION
LORENTZ GAS
MATHEMATICAL MODELS
NUMERICAL DATA