Generalized model for dynamic percolation

The dynamics of a carrier performing a biased motion due to an external field in a 3D environment, modeled by dynamic percolation and created by hard-core particles, were analyzed. Based on the decomposition of the third-order correlation functions, an approximate closure scheme was used to derive a system of coupled discrete-space equations that describe the evolution of the density profiles of the environment as observed from the moving carrier and its velocity Vc. The V_c was found to depend on the density of the environment particles in front of and past the carrier. The equation which defines the force-velocity relation for the dynamic percolation under study simplifies considerably in the limit of small applied electric field.