Random walks with random velocities

Vasily Zaburdaev, Michael Schmiedeberg, and Holger Stark
Phys. Rev. E 78, 011119 – Published 22 July 2008

Abstract

We consider a random walk model that takes into account the velocity distribution of random walkers. Random motion with alternating velocities is inherent to various physical and biological systems. Moreover, the velocity distribution is often the first characteristic that is experimentally accessible. Here, we derive transport equations describing the dispersal process in the model and solve them analytically. The asymptotic properties of solutions are presented in the form of a phase diagram that shows all possible scaling regimes, including superdiffusive, ballistic, and superballistic motion. The theoretical results of this work are in excellent agreement with accompanying numerical simulations.

  • Figure
  • Figure
  • Received 30 October 2007

DOI:https://doi.org/10.1103/PhysRevE.78.011119

©2008 American Physical Society

Authors & Affiliations

Vasily Zaburdaev*, Michael Schmiedeberg, and Holger Stark

  • Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany

  • *Vasily.Zaburdaev@tu-berlin.de
  • Michael.Schmiedeberg@tu-berlin.de
  • Holger.Stark@tu-berlin.de

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Issue

Vol. 78, Iss. 1 — July 2008

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