Exact result for the effective conductivity of a continuum percolation model

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Publication Type Journal Article
School or College College of Science
Department Mathematics
Creator Golden, Kenneth M.
Other Author Berlyand, L.
Title Exact result for the effective conductivity of a continuum percolation model
Date 1994
Description A random two-dimensional checkerboard of squares of conductivities 1 and 8 in proportions p and 1 - p is considered. Classical duality implies that the effective conductivity obeys o* = V8 at p = 1/2. It is rigorously found here that to leading order as 8--0, this exact result holds for all p in the interval (1- pc,pc), where pc=0.59 is the site percolation probability, not just at p = 1/2. In particular, o*(p,8)=78+O (8), as 8 -- 0. which is argued to hold for complex 8 as well. The analysis is based on the identification of a "symmetric" backbone, which is statistically invariant under interchange of the components for any pE(1--pc,pc), like the entire checkerboard at p =1/2. This backbone is defined in terms of "choke points" for the current, which have been observed in an experiment.
Type Text
Publisher American Physical Society
Volume 50
Issue 4
First Page 2114
Last Page 2117
Subject Particles; Matrix; Checkerboard
Language eng
Bibliographic Citation Berlyand, L., & Golden, K. M. (1994). Exact result for the effective conductivity of a continuum percolation model. Physical Review B, 50(4), 2114-7.
Rights Management (c) American Physical Society
Format Medium application/pdf
Format Extent 461,544 bytes
Identifier ir-main,5730
ARK ark:/87278/s6n01r0w
Setname ir_uspace
Date Created 2012-06-13
Date Modified 2012-06-13
ID 705655
Reference URL https://collections.lib.utah.edu/ark:/87278/s6n01r0w
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