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The fractional Fick's law for non-local transport processes (Articolo in rivista)

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The fractional Fick's law for non-local transport processes (Articolo in rivista) (literal)

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P. Paradisi, R. Cesari, F. Mainardi, F. Tampieri (2001)
The fractional Fick's law for non-local transport processes
in Physica. A (Print)
(literal)

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P.Paradisi, R. Cesari, F. Tampieri: ISAC - CNR F. Mainardi: Dipartimento di Fisica, Universitá di Bologna e ISAC-CNR (literal)

Titolo

Abstract

Fick's law is extensively adopted as a model for standard diffusion processes. However, requiring separation of scales, it is not suitable for describing non-local transport processes. We discuss a generalized non-local Fick's law derived from the space-fractional diffusion equation generating the L\'evy-Feller statistics. This means that the fundamental solutions can be interpreted as L\'evy stable probability densities (in the Feller parameterization) with index $\alpha$ (<\alpha \le 2$) and skewness $\theta$ ($|\theta| \le 2-\alpha$). We explore the possibility of defining an equivalent local diffusivity by displaying a few numerical case studies concerning the relevant quantities (flux and gradient). It turns out that the presence of asymmetry ($\theta \ne 0$) plays a fundamental role: it produces shift of the maximum location of the probability density function and gives raise to phenomena of counter-gradient transport. (literal)

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