title: Mesoscopic description of random walks on combs.
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.
authors.affiliation: Grup de Física Estadística, Departament de Física, Facultat de Ciències, Edifici Cc, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.
authors.forename: Vicenç
authors.initials: V
authors.lastname: Méndez
authors.affiliation: Department of Physics, Technion, Haifa 32000, Israel.
authors.forename: Alexander
authors.initials: A
authors.lastname: Iomin
authors.affiliation: Grup de Física Estadística, Departament de Física, Facultat de Ciències, Edifici Cc, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.
authors.forename: Daniel
authors.initials: D
authors.lastname: Campos
authors.affiliation: Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, USA.
authors.forename: Werner
authors.initials: W
authors.lastname: Horsthemke