Anomalous diffusion in view of Einstein's 1905 theory of Brownian motion
Anomalous diffusion in view of Einstein's 1905 theory of Brownian motion
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DOI：
10.1016/j.physa.2005.03.035
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发表时间：
2005-10-15
影响因子：
3.3
通讯作者：
Thurner, S
中科院分区：
文献类型：
--
作者：
Abe, S;Thurner, S
爱因斯坦的布朗运动理论是重新制定一个广义动力学理论的反常扩散。结果表明，如果放松解析性和位移分布的二阶矩的存在性的假设，分数阶导数自然出现在扩散方程。这是第一次演示的物理起源的分数导数，在显着对比通常的现象学介绍it.It也检查爱因斯坦的方法是否可以推广到非线性动力学理论，推导出一个推广的多孔介质型方程的适当使用的护送分布。(c)版权所有Elsevier B.V.保留所有权利。
Einstein's theory of Brownian motion is revisited in order to formulate a generalized kinetic theory of anomalous diffusion. It is shown that if the assumptions of analyticity and the existence of the second moment of the displacement distribution are relaxed, the fractional derivative naturally appears in the diffusion equation. This is the first demonstration of the physical origin of the fractional derivative, in marked contrast to the usual phenomenological introduction of it. It is also examined if Einstein's approach can be generalized to nonlinear kinetic theory to derive a generalization of the porous-medium-type equation by the appropriate use of the escort distribution. (c) Copyright Elsevier B.V. All rights reserved.