CTRW pathways to the fractional diffusion equation

被引:100
作者
Barkai, E [1 ]
机构
[1] MIT, Dept Chem, Cambridge, MA 02139 USA
基金
美国国家科学基金会;
关键词
D O I
10.1016/S0301-0104(02)00533-5
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
The foundations of the fractional diffusion equation are investigated based on coupled and decoupled continuous time random walks (CTRW). For this aim we find an exact solution of the decoupled CTRW, in terms of an infinite sum of stable probability densities. This exact solution is then used to understand the meaning and domain of validity of the fractional diffusion equation. An interesting behavior is discussed for coupled memories (i.e., Levy walks). The moments of the random walk exhibit strong anomalous diffusion, indicating (in a naive way) the breakdown of simple scaling behavior and hence of the fractional approximation. Still the Green function P(x, t) is described well by the fractional diffusion equation, in the long time limit. (C) 2002 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:13 / 27
页数:15
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