NUMERICAL COMPUTATIONS OF CONDUCTIVITY IN CONTINUUM PERCOLATION FOR OVERLAPPING SPHEROIDS

Shigeki Matsutani (), Yoshiyuki Shimosako () and Yunhong Wang
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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

International Journal of Modern Physics C (IJMPC), 2010, vol. 21, issue 06, 709-729

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.

Keywords: Continuum percolation; conductivity; critical exponents; nonuniversality; 05.10.-a; 05.10.Ln; 05.60.Cd; 64.60.ah; 72.80.Ng; 73.22.-f (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0129183110015348

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