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The effective conductivity of an infinitely interchangeable mixture

Bruno, Oscar P. (1990) The effective conductivity of an infinitely interchangeable mixture. Communications on Pure and Applied Mathematics, 43 (6). pp. 769-807. ISSN 0010-3640. https://resolver.caltech.edu/CaltechAUTHORS:20181105-131823303

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Abstract

We are concerned with the estimation of the effective electrical conductivity of random heterogenous materials. The purpose of this paper is to discuss a property of “statistical symmetry” verified by the symmetric cell materials of Miller. This property will be referred to as infinite interchangeability. The usual way to approach cell materials is through n‐point correlation functions. The property of infinite interchangebility permits us to approach cell materials from a completely different point of view. Our main result is a simple algorithm, based on this symmetry property, for computing any coefficient of the perturbation expansion in terms of information from the dilute limit. Specifically, knowledge of the coefficients of the expansion in powers of the volume fraction up to order r allows for computation of the perturbation expansion coefficients up to order (2r + 1). This result, which was previously known for r = 2 in the isotropic case and for r = 1 in the anisotropic case, can also be obtained from the standard correlation function approach, as pointed out by Milton.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1002/cpa.3160430604DOIArticle
ORCID:
AuthorORCID
Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 1990 Wiley Periodicals, Inc. Manuscript received: 01 July 1989.
Issue or Number:6
Record Number:CaltechAUTHORS:20181105-131823303
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181105-131823303
Official Citation:Bruno, O. P. (1990), The effective conductivity of an infinitely interchangeable mixture. Comm. Pure Appl. Math., 43: 769-807. doi:10.1002/cpa.3160430604
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90647
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Nov 2018 18:42
Last Modified:03 Oct 2019 20:27

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