Generalized model for dynamic percolation
We study the dynamics of a carrier, which performs a biased motion under the influence of an external field E-->, in an environment which is modeled by dynamic percolation and created by hard-core particles. The particles move randomly on a simple cubic lattice, constrained by hard-core exclusion, and they spontaneously annihilate and reappear at some prescribed rates. We determine the density profiles of the "environment" particles, as seen from the stationary moving carrier, and calculate its terminal velocity V(c) as the function of the applied field and other system parameters. For sufficiently small driving forces the force exerted on the carrier by the "environment" particles shows a viscouslike behavior. An analog Stokes formula for such dynamic percolative environments and the corresponding friction coefficient are derived. We show that the density profile of the environment particles is strongly inhomogeneous: In front of the stationary moving carrier the density is higher than the average density rho(s), while past the carrier the local density is lower than rho(s).
Benichou
O
Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris-Sud, 91405 Orsay Cedex, France and Laboratoire de Physique Theorique des Liquides, Universite Paris 6, 4, Place Jussieu, 75252 Paris, France.
Klafter
J
Moreau
M
Oshanin
G