Conductivity exponent in three-dimensional percolation by diffusion based on molecular trajectory algorithm and blind-ant rules

Wei Cen, Dongbing Liu and Bingquan Mao

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 5, 1909-1918

Abstract: Diffusion on random systems above and at their percolation threshold in three dimensions is carried out by a molecular trajectory method and a simple lattice random walk method, respectively. The classical regimes of diffusion on percolation near the threshold are observed in our simulations by both methods. Our Monte Carlo simulations by the simple lattice random walk method give the conductivity exponent μ/ν=2.32±0.02 for diffusion on the incipient infinite clusters and μ/ν=2.21±0.03 for diffusion on a percolating lattice above the threshold. However, while diffusion is performed by the molecular trajectory algorithm either on the incipient infinite clusters or on a percolating lattice above the threshold, the result is found to be μ/ν=2.26±0.02. In addition, it takes less time step for diffusion based on the molecular trajectory algorithm to reach the asymptotic limit comparing with the simple lattice random walk.

Keywords: Conductivity exponent; Diffusion; Molecular trajectory algorithm; Blind-ant rules; Percolation; Convergence (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:5:p:1909-1918

DOI: 10.1016/j.physa.2011.11.008

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