Generalized diffusion equation
arXiv:cond-mat/0508231 · doi:10.1016/j.physa.2005.11.054
Abstract
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 -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 -generating function approach should be a useful tool to generalize classical diffusive transport formulations.
5 pages with 3 figures