• Rapid Communication

Governing equations and solutions of anomalous random walk limits

Mark M. Meerschaert, David A. Benson, Hans-Peter Scheffler, and Peter Becker-Kern
Phys. Rev. E 66, 060102(R) – Published 30 December 2002
PDFExport Citation

Abstract

Continuous time random walks model anomalous diffusion. Coupling allows the magnitude of particle jumps to depend on the waiting time between jumps. Governing equations for the long-time scaling limits of these models are found to have fractional powers of coupled space and time differential operators. Explicit solutions and scaling properties are presented for these equations, which can be used to model flow in porous media and other physical systems.

  • Received 5 June 2002

DOI:https://doi.org/10.1103/PhysRevE.66.060102

©2002 American Physical Society

Authors & Affiliations

Mark M. Meerschaert*

  • Department of Mathematics, University of Nevada, Reno, Nevada 89557-0084

David A. Benson

  • Desert Research Institute, 2215 Raggio Parkway, Reno, Nevada 89512

Hans-Peter Scheffler and Peter Becker-Kern

  • Fachbereich Mathematik, University of Dortmund, 44221 Dortmund, Germany

  • *Electronic address: mcubed@unr.edu

References (Subscription Required)

Click to Expand
Issue

Vol. 66, Iss. 6 — December 2002

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×