Generalized diffusion equation

Details Generalized diffusion equation Generalized diffusion equation

2005-08-09

arxiv.org/abs/cond-mat/0508231v1

Physics

Condensed Matter

Statistical Mechanics

5 pages with 3 figures

Scientific paper

10.1016/j.physa.2005.11.054

Modern analyses of diffusion processes have proposed nonlinear versions of the Fokker-Planck equation to account for non-classical diffusion. These nonlinear equations are usually constructed on a phenomenological basis. Here we introduce a nonlinear transformation by defining the $q$-generating function which, when applied to the intermediate scattering function of classical statistical mechanics, yields, in a mathematically systematic derivation, a generalized form of the advection-diffusion equation in Fourier space. Its solutions are discussed and suggest that the $q$-generating function approach should be a useful tool to generalize classical diffusive transport formulations.

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