Reciprocity relations for the effective electrical conductivity of randomly inhomogeneous media in the fractal regime View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1998-04

AUTHORS

A. A. Snarskii, K. V. Slipchenko, I. V. Bezsudnov

ABSTRACT

An exact relation for the realization-averaged effective conductivities in the fractal region is found for two-dimensional randomly inhomogeneous media. It has the form {σe(τ,L)~× {1/σe(−τ,L)~−1=σe2(τ=0, L≫ξ), where ξ is the correlation length (the self-averaging scale), L is the size of the system, τ=(p-pc)/pc, and pc is the percolation threshold. For L≫ ξ, the system is self-averaged, and the relation transforms into the Dykhne reciprocity relation, A. M. Dykhne, Zh. Éksp. Teor. Fiz. 59, 110 (1970) [Sov. Phys. JETP 32, 63 (1971)] σe(τ)σe(−τ])=σe2(τ=0)= σ1σ2. A similar relation is obtained for media with an exponentially broad distribution of local conductivities, as well as for individual realizations of some deterministic structures. More... »

PAGES

811-814

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Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/1.558543

DOI

http://dx.doi.org/10.1134/1.558543

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1031200700


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