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.

References in corpus (3)

• Paradoxes of Subdiffusive Infiltration in Disordered Systems
• Hitting and Trapping Times on Branched Structures
• Biased random walks on combs

Cited by in corpus (7)

• The two-particle problem in comb-like structures
• Lévy processes on a generalized fractal comb
• Quenched and Annealed Disorder Mechanisms in Comb-Models with Fractional Operators
• Langevin dynamics for ramified structures
• Anomalous diffusion and FRAP dynamics in the random comb model
• Propagators of random walks on comb lattices of arbitrary dimension
• Random walks on uniform and non-uniform combs and brushes