Macroscopic current in fractional anomalous diffusion

Damián H. Zanette

Physica A: Statistical Mechanics and its Applications, 1998, vol. 252, issue 1, 159-164

Abstract: Fick’s law – which relates the macroscopic current with the density in ordinary diffusion – is generalized to fractional diffusion, where either the waiting time distribution or the displacement probability density exhibit power-law decays. These long-tailed distributions give rise to (respectively, temporal or spatial) nonlocality in connection between current and density. In the case of power-law displacement distributions, the current is shown to also display such decays in the spatial coordinate. An illustrative example is explicitly worked out in a one-dimensional system.

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:252:y:1998:i:1:p:159-164

DOI: 10.1016/S0378-4371(97)00613-4

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