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Macroscopic current in fractional anomalous diffusion

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  • Zanette, Damián H.

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.

Suggested Citation

  • Zanette, Damián H., 1998. "Macroscopic current in fractional anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 252(1), pages 159-164.
    • Handle: RePEc:eee:phsmap:v:252:y:1998:i:1:p:159-164
    DOI: 10.1016/S0378-4371(97)00613-4
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    Cited by:

    1. Paradisi, Paolo & Cesari, Rita & Mainardi, Francesco & Tampieri, Francesco, 2001. "The fractional Fick's law for non-local transport processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 130-142.

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