In this paper, we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.
Bibliographical noteThis article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Anderson, J, Kim, EJ & Moradi, S 2014, 'A fractional Fokker-Planck model for anomalous diffusion' Physics of Plasmas, vol. 21, no. 12, 122109 and may be found at https://dx.doi.org/10.1063/1.4904201URL/link for published article abstract.
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- Anomalous Diffusion
- Fractional Fokker-Planck Equation
ASJC Scopus subject areas
- Condensed Matter Physics