Real-space renormalization and effective-medium approximation to the percolation conduction problem

Muhammad Sahimi, Barry D. Hughes, L. E. Scriven, and H. Ted Davis
Phys. Rev. B 28, 307 – Published 1 July 1983
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Abstract

We present a new approach, the renormalized effective-medium approximation (REMA), for the percolation conductivity problem in disordered conductance networks. This approach combines real-space renormalization and effective-medium approximation techniques. We use it to investigate two-, three-, and four-dimensional bond-disordered conductance networks. REMA provides excellent predictions for the network conductivity g(p) over the entire range of fraction p of conducting bonds in two and three dimensions. REMA reproduces the exact bond percolation threshold of the square lattice and predicts bond percolation thresholds for the simple cubic lattices in three and four dimensions which differ only by about 6% and 1%, respectively, from the best available estimates. It also provides good estimates of the conductivity critical exponents t and s in both two and three dimensions.

  • Received 14 March 1983

DOI:https://doi.org/10.1103/PhysRevB.28.307

©1983 American Physical Society

Authors & Affiliations

Muhammad Sahimi, Barry D. Hughes, L. E. Scriven, and H. Ted Davis

  • Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455

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Issue

Vol. 28, Iss. 1 — 1 July 1983

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