时间分形条件下的无规行走理论及其在色散输运过程中的应用

FRACTAL TIME RANDOM WALKS AND DISPERSION TRANSPORT

本文研究了跳跃等待时间分布函数Q(t)～t^(-α)(t→∞,0<α<1)情形下的连续时间无规行走。系统、严格地描述了(0,t)时间中的粒子跳动次数作为时间轴上点集的分形特征(时间分形)。从一个关于粒子跳跃的微观动力学模型出发,从物理上导出了时间分形,明确将α用有关动力学参量表示。本文理论很好地解释了非晶态材料中输运过程的色散现象。

We study continuous time random walk with the waiting time distribution having long-time tailτ-1, 0 <α < 1. The fractal time behavior of the hopping event set is treated in a systematic and rigorous way. We construct a dynamic model which shows the fractal time behavior. The expertmenu of dispersion diffution in amorphous systems are well explained by our theory.