Fractional diffusion equation for an n-dimensional correlated Lévy walk

Research output: Contribution to journalArticle

  • Authors:
  • Jake P. Taylor-King
  • Rainer Klages
  • Sergei Fedotov
  • Robert A. Van Gorder

Abstract

Lévy walks define a fundamental concept in random walk theory that allows one to model diffusive spreading faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a diffusion equation for an n-dimensional correlated Lévy walk remained elusive. Starting from a fractional Klein-Kramers equation here we use a moment method combined with a Cattaneo approximation to derive a fractional diffusion equation for superdiffusive short-range auto-correlated Lévy walks in the large time limit, and we solve it. Our derivation discloses different dynamical mechanisms leading to correlated Lévy walk diffusion in terms of quantities that can be measured experimentally.

Bibliographical metadata

Original languageEnglish
JournalPhysical Review E: covering statistical, nonlinear, biological, and soft matter physics
Volume94
Early online date6 Jul 2016
DOIs
StatePublished - 2016