Use of comb-like models to mimic anomalous diffusion on fractal structures

George H. Weiss, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We discuss some properties of random walks on comb-like structures. These have been used as analogues for the study of anomalous diffusion along a percolation cluster intersected by loopless dead-ends. It is shown that a number of transport properties along a backbone can be found by using an approximation method based on the continuous-time random walk (CTRW). The principal property resulting from this analysis is the asymptotic form of the probability distribution for the location of a random walker at step n. This allows the calculation of such quantities as the mean-squared displacement after n steps, the expected number of distinct sites visited, and changes in properties of the random walk in response to biasing fields. It is shown that when the times between successive visits to the backbone are random, and distributed according to a stable law different critical phenomena can occur in the model.

Original languageEnglish
Pages (from-to)941-947
Number of pages7
JournalPhilosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties
Issue number6
StatePublished - Dec 1987


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