The authors study diffusion in percolation systems at criticality in the presence of a constant bias field E. Using the exact enumeration method they show that the mean displacement of a random walker varies as (r(t)) approximately log t/A(E) where A/(E)=In((1+E)/(1-E)) for small E. More generally, diffusion on a given configuration is characterised by the probability P(r,t) that the random walker is on site r at time t. They find that the corresponding configurational average shows simple scaling behaviour and is described by a single exponent. In contrast their numerical results indicate that the averaged moments (Pq(t))= Sigma rP q(r,t)) are described by an infinite hierarchy of exponents. For zero bias field, however, all moments are determined by a single gap exponent.

Bunde, A., Harder, H., Havlin, S., Eduardo Roman, H. (1987). Biased diffusion in percolation systems: Indication of multifractal behaviour. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 20(13), L865-L871 [10.1088/0305-4470/20/13/010].

Biased diffusion in percolation systems: Indication of multifractal behaviour

Eduardo Roman H.
1987

Abstract

The authors study diffusion in percolation systems at criticality in the presence of a constant bias field E. Using the exact enumeration method they show that the mean displacement of a random walker varies as (r(t)) approximately log t/A(E) where A/(E)=In((1+E)/(1-E)) for small E. More generally, diffusion on a given configuration is characterised by the probability P(r,t) that the random walker is on site r at time t. They find that the corresponding configurational average shows simple scaling behaviour and is described by a single exponent. In contrast their numerical results indicate that the averaged moments (Pq(t))= Sigma rP q(r,t)) are described by an infinite hierarchy of exponents. For zero bias field, however, all moments are determined by a single gap exponent.
Articolo in rivista - Articolo scientifico
biased diffusion on percolation clusters, criticality, exact enumeration, mutlifractality
English
1987
20
13
L865
L871
010
none
Bunde, A., Harder, H., Havlin, S., Eduardo Roman, H. (1987). Biased diffusion in percolation systems: Indication of multifractal behaviour. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 20(13), L865-L871 [10.1088/0305-4470/20/13/010].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/326824
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