Non-Linear Langevin and Fractional Fokker–Planck Equations for Anomalous Diffusion by Lévy Stable Processes

Anderson, Johan; Moradi, Sara; Rafiq, Tariq

doi:10.3390/e20100760

Non-Linear Langevin and Fractional Fokker–Planck Equations for Anomalous Diffusion by Lévy Stable Processes

Journal Article · Wed Oct 03 00:00:00 EDT 2018 · Entropy

DOI:https://doi.org/10.3390/e20100760· OSTI ID:1610207

Anderson, Johan ^[1]; Moradi, Sara ^[2]; Rafiq, Tariq ^[3]

Chalmers Univ. of Technolgy, Goteburg (Sweden); DOE/OSTI
Royal Military Academy, Brussels (Belgium)
Lehigh Univ., Bethlehem, PA (United States)

The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable Lévy distribution as solutions to the FFP equation. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data.

Research Organization:: Lehigh Univ., Bethlehem, PA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-92ER54141; SC0013977

OSTI ID:: 1610207

Journal Information:: Entropy, Journal Name: Entropy Journal Issue: 10 Vol. 20; ISSN ENTRFG; ISSN 1099-4300

Publisher:: MDPICopyright Statement

Country of Publication:: United States

Language:: English

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