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Numerical Computations Of Conductivity In Continuum Percolation For Overlapping Spheroids

Author

Listed:
  • SHIGEKI MATSUTANI

    (Analysis Technology Center, Canon Inc., 3-3-20, Shimomaruko, Ota-ku, Tokyo 146-8501, Japan)

  • YOSHIYUKI SHIMOSAKO

    (Analysis Technology Center, Canon Inc., 3-3-20, Shimomaruko, Ota-ku, Tokyo 146-8501, Japan)

  • YUNHONG WANG

    (Analysis Technology Center, Canon Inc., 3-3-20, Shimomaruko, Ota-ku, Tokyo 146-8501, Japan)

Abstract

By numerically solving the generalized Laplace equations by means of the finite difference method, we investigated isotropic electric conductivity of a three-dimensional continuum percolation model consisting of overlapped spheroids of revolution in continuum. Since the computational results strongly depend upon parameters in the discretization methods of the finite difference method, we explored the dependences in details to construct the computational scheme which can represent the continuum percolation model well. Using the discrete scheme, we obtained the conductivity curves,σ =c (p -pc)t, depending upon aspect ratio of the conductive spheroids for the volume fractionp. We found the fact that the critical exponenttis not universal, which depends upon the shape of spheroids with a range varying from1.58 ± 0.08to1.94 ± 0.18whereas 1.85 is reported as the standard one of cubic lattice case [A. B. Harris,Phys. Rev. B28, 2614 (1983)]. We also discussed its relation to the nonuniversality in the broad distribution continuum percolation models.

Suggested Citation

  • Shigeki Matsutani & Yoshiyuki Shimosako & Yunhong Wang, 2010. "Numerical Computations Of Conductivity In Continuum Percolation For Overlapping Spheroids," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 709-729.
    • Handle: RePEc:wsi:ijmpcx:v:21:y:2010:i:06:n:s0129183110015348
    DOI: 10.1142/S0129183110015348
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    Cited by:

    1. 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.

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