Mesoscopic description of random walks on combs

Vicenç Méndez, Alexander Iomin, Daniel Campos, and Werner Horsthemke
Phys. Rev. E 92, 062112 – Published 7 December 2015

Abstract

Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study continuous time random walks on combs and present a generic method to obtain their transport properties. The random walk along the branches may be biased, and we account for the effect of the branches by renormalizing the waiting time probability distribution function for the motion along the backbone. We analyze the overall diffusion properties along the backbone and find normal diffusion, anomalous diffusion, and stochastic localization (diffusion failure), respectively, depending on the characteristics of the continuous time random walk along the branches, and compare our analytical results with stochastic simulations.

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  • Received 9 September 2015
  • Revised 29 October 2015

DOI:https://doi.org/10.1103/PhysRevE.92.062112

©2015 American Physical Society

Authors & Affiliations

Vicenç Méndez1, Alexander Iomin2, Daniel Campos1, and Werner Horsthemke3

  • 1Grup de Física Estadística, Departament de Física, Facultat de Ciències, Edifici Cc, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
  • 2Department of Physics, Technion, Haifa 32000, Israel
  • 3Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, USA

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Vol. 92, Iss. 6 — December 2015

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