Large lattice fractional Fokker-Planck equation

被引：22

作者：

Tarasov, Vasily E. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Skobeltsyn Inst Nucl Phys, Moscow 119991, Russia

来源：

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT | 2014年

关键词：

diffusion; NONINTEGER DIMENSIONAL SPACE; LONG-RANGE INTERACTION; ANOMALOUS DIFFUSION; RANDOM-WALKS; MODEL; SYSTEMS; EQUILIBRIUM; CALCULUS; DYNAMICS; MEDIA;

D O I：

10.1088/1742-5468/2014/09/P09036

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

An equation of long-range particle drift and diffusion on a 3D physical lattice is suggested. This equation can be considered as a lattice analog of the space-fractional Fokker-Planck equation for continuum. The lattice approach gives a possible microstructural basis for anomalous diffusion in media that are characterized by the non-locality of power law type. In continuum limit the suggested 3D lattice Fokker-Planck equations give fractional Fokker-Planck equations for continuous media with power law non-locality that is described by derivatives of non-integer orders. The consistent derivation of the fractional Fokker-Planck equation is proposed as a new basis to describe space-fractional diffusion processes.

引用

页数：23