Approach of continuous time random walk model to anomalous diffusion

Abstract

A numerical method based on the continuous time random walk (CTRW) theory is developed to study the normal diffusion and anomalous diffusion including both sub-diffusion and super-diffusion. The probability density functions for both the jump distance and the residence time in the CTRW model are determined as well as the Metropolis sampling method in the periodic potential has been improved. The directional transport of a Brownian motor in both a flashing ratchet potential and a rocking ratchet potential is investigated. Our results have shown that the maximum of directional current occurs in the case of super-diffusion in a flashing ratchet and in the case of ballistic diffusion in a rocking ratchet.