Approach to asymptotically diffusive behavior for Brownian particles in media with periodic diffusivitiesReport as inadecuate




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1 LOMA - Laboratoire Ondes et Matière d-Aquitaine

Abstract : We analyze the mean squared displacement of a Brownian particle in a medium with a spatially varying local diffusivity which is assumed to be periodic. When the system is asymptotically diffusive the mean squared displacement, characterizing the dispersion in the system, is, at late times, a linear function of time. A Kubo type formula is given for the mean squared displacement which allows the recovery of some known results for the effective diffusion constant $D e$ in a direct way, but also allows an understanding of the asymptotic approach to the diffusive limit. In particular, as well as as computing the slope of a linear fit to the late time mean squared displacement, we find a formula for the constant where the fit intersects the y axis.

Keywords : Stochastic processes Stochastic analysis methods





Author: David S. Dean - Thomas Guérin -

Source: https://hal.archives-ouvertes.fr/



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