The fractional Fick's law for non-local transport processes

Paolo Paradisi, Rita Cesari, Francesco Mainardi and Francesco Tampieri

Physica A: Statistical Mechanics and its Applications, 2001, vol. 293, issue 1, 130-142

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 Lévy–Feller statistics. This means that the fundamental solutions can be interpreted as Lévy stable probability densities (in the Feller parameterization) with index α (1<α⩽2) and skewness θ (|θ|⩽2−α). 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 (θ≠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.

Keywords: Diffusion; Stable probability distributions; Fractional derivatives (search for similar items in EconPapers)
Date: 2001
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037843710000491X
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:293:y:2001:i:1:p:130-142

DOI: 10.1016/S0378-4371(00)00491-X

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().