Non-Linear Langevin and Fractional Fokker-Planck Equations for Anomalous Diffusion by Levy Stable Processes
Abstract
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 L\'{e}vy 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 L\'{e}vy 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.
Keywords
Cite
@article{arxiv.1810.02606,
title = {Non-Linear Langevin and Fractional Fokker-Planck Equations for Anomalous Diffusion by Levy Stable Processes},
author = {Johan Anderson and Sara Moradi and Tariq Rafiq},
journal= {arXiv preprint arXiv:1810.02606},
year = {2018}
}
Comments
20 pages 7 figures