A computer-simulation study of anomalous diffusion on percolating clusters near to the critical point

Štefan Barta and Peter Dieška

Physica A: Statistical Mechanics and its Applications, 1995, vol. 215, issue 3, 251-260

Abstract: We have verified the scaling hypothesis for the following quantities via a computer simulation: the average probability density P(r,t,Δp) ∼ 〈r2(t)〉−df2F(√z), the diffusion coefficient D(r,t,Δp) ∼ t2dw−1h(t/τ)D0(z) and the mean-square displacement (MSD) 〈r2(t)〉 ∼ t2dwf2(t/τ), where z = r2/〈r2(t)〉. It was found that there exists a cross-over value zc, which divides interval z in two regions, where the diffusion coefficient exhibits a power-law dependence on variable z with the different exponents. In the region z < zc this exponent depends on Δp contrary to region z > zc. On the basis of the analogy of the average probability in the asymptotic form and the mean-square displacement in the case of the self-avoiding and ordinary random walk models the relation γ = dw/(dw − 1) was derived.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:215:y:1995:i:3:p:251-260

DOI: 10.1016/0378-4371(95)00040-E

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