TY - JOUR

T1 - Use of comb-like models to mimic anomalous diffusion on fractal structures

AU - Weiss, George H.

AU - Havlin, Shlomo

PY - 1987/12

Y1 - 1987/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0023558502&partnerID=8YFLogxK

U2 - 10.1080/13642818708215329

DO - 10.1080/13642818708215329

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AN - SCOPUS:0023558502

SN - 1364-2812

VL - 56

SP - 941

EP - 947

JO - Philosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties

JF - Philosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties

IS - 6

ER -