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Title: A fractional Fokker-Planck model for anomalous diffusion

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.
Authors:
 [1] ;  [2] ;  [3]
  1. Department of Earth and Space Sciences, Chalmers University of Technology, SE-412 96 Göteborg (Sweden)
  2. Department of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH (United Kingdom)
  3. Ecole Polytechnique, CNRS UMR7648, LPP, F-91128 Palaiseau (France)
Publication Date:
OSTI Identifier:
22403323
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 21; Journal Issue: 12; Other Information: (c) 2014 EURATOM; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; DIFFUSION; DISTRIBUTION; DISTRIBUTION FUNCTIONS; ENTROPY; FOKKER-PLANCK EQUATION; STATISTICAL MECHANICS