基于连续时间无规行走模型研究反常扩散

Approach of continuous time random walk modelto anomalous diffusion

基于连续时间无规行走(CTRW)理论,数值研究了布朗粒子的欠扩散、正常扩散和超扩散三种扩散行为.解决了CTRW模型的跳跃步长和等待时间分布函数的可实现化问题,对Metropolis抽样方法进行了改进以适用于周期势.探讨了布朗马达依靠闪烁棘轮和摇摆棘轮整流反常扩散所获得的定向速度,结果显示,闪烁布朗马达定向流极大值出现在超扩散条件下;摇摆布朗马达定向流最大值出现在弹道扩散条件下.

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 superdiffusion in a flashing ratchet and in the case of ballistic diffusion in a rocking ratchet.