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The Random Walk s Guide to Anomalous Diffusion: A Fractional Dynamics Approach

book
Language:
Author: by Ralf Metzler and Joseph Klafter
Url: http://www.tau.ac.il/~klafter1/258.pdf
Format: Pdf
Year: 2000
Category: Mathematical Physics
Pages: 77
Clicks: 1220

Description
Fractional kinetic equations of the di!usion, di!usion}advection, and Fokker}Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous di!usion and non-exponential relaxation patterns. These fractional equations are derived asymptotically from basic random walk models, and from a generalised master equation. Several physical consequences are discussed which are relevant to dynamical processes in complex systems. Methods of solution are introduced and for some special cases exact solutions are calculated. This report demonstrates that fractional equations have come of age as a complementary tool in the description of anomalous transport processes. 2000 Elsevier Science B.V. All rights reserved.

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