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Fractal structure of equipotential curves on a continuum percolation model

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  • Matsutani, Shigeki
  • Shimosako, Yoshiyuki
  • Wang, Yunhong

Abstract

We numerically investigate the electric potential distribution over a two-dimensional continuum percolation model between the electrodes. The model consists of overlapped conductive particles on the background with an infinitesimal conductivity. Using the finite difference method, we solve the generalized Laplace equation and show that in the potential distribution, there appear quasi-equipotential clusters which approximately and locally have the same values as steps and stairs. Since the quasi-equipotential clusters have the fractal structure, we compute the fractal dimension of equipotential curves and its dependence on the volume fraction over [0,1]. The fractal dimension in [1.00, 1.246] has a peak at the percolation threshold pc.

Suggested Citation

  • Matsutani, Shigeki & Shimosako, Yoshiyuki & Wang, Yunhong, 2012. "Fractal structure of equipotential curves on a continuum percolation model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5802-5809.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:23:p:5802-5809
    DOI: 10.1016/j.physa.2012.06.056
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    Keywords

    Continuum percolation; Fractal structure;

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