Abstract
We study the motion of a point particle along the bonds of a two-dimensional random lattice, whose sites are randomly occupied with right and left rotators, which scatter the particle according to deterministic scattering rules. We consider both a Poisson (PRL) and a vectorized random lattice (VRL) and fixed as well as flipping scatterers. On both lattices, for fixed scatterers and equal concentrations of right and left rotators the same anomalous diffusion of the particle is obtained as before for the triangular lattice, where the mean square displacement is ∼t, the diffusion process non-Gaussian, and the particle trajectories exhibit scaling behavior as at a percolation threshold. For unequal concentrations the particle is trapped exponentially rapidly. This system can be considered as an extreme case of the Lorentz lattice gases on regular lattices discussed before or as an example of the motion of a particle along cracks or (grain or cellular) boundaries on a two-dimensional surface.
Similar content being viewed by others
References
N. H. Christ, R. Friedberg, and T. D. Lee,Nucl. Phys., B 202:89 (1982); R. Friedberg and H.-C. Ren,Nucl. Phys. B 235[FS11]:310 (1984).
D. Weaire and N. Rivier,Contempt. Phys. 25:59 (1984); N. Rivier, Phil. Mag. B52:795 (1985).
C. Moukarzel,Physica A 199:19 (1993).
E. G. D. Cohen and F. Wang, New results for diffusion in Lorentz lattice gas cellular automata,J. Stat. Phys. 81:445 (1995).
E. G. D. Cohen and F. Wang, Novel phenomena in Lorentz lattice gases,Physica A 219:56 (1995).
F. Wang, Motion in Lorentz lattice gases, Ph.D. Thesis, Rockefeller University (1995).
F. Wang and E. G. D. Cohen, Diffusion in Lorentz lattice gas cellular automata: The honebcomb and quasi-lattices compared with the square and triangular lattices,J. Stat. Phys. 81:467 (1995).
P. J. Grenn and R. Sibson,Computer J. 21:168 (1977).
C. Moukarzel and H. J. Herrmann,J. Stat. Phys. 68:911 (1992); C. Moukarzel,Physica A 190:13 (1992).
M. Magnasco,Phil. Mag. B 69:397 (1994).
G. A. van Velzen, Lorentz lattice gases, Ph.D. Thesis, University of Utrecht (1990).
X. P. Kong and E. G. D. Cohen,J. Stat. Phys. 63:737 (1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wang, F., Cohen, E.G.D. Diffusion on random lattices. J Stat Phys 84, 233–261 (1996). https://doi.org/10.1007/BF02179584
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02179584