Bruno, O. and Golden, K. (1990) Interchangeability and bounds on the effective conductivity of the square lattice. Journal of Statistical Physics, 61 (1-2). pp. 365-386. ISSN 0022-4715. doi:10.1007/BF01013970. https://resolver.caltech.edu/CaltechAUTHORS:20181107-080002180
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Abstract
The effective conductivity σ* of an infinitely interchangeable two-component random medium is considered. This class of media includes cell materials in the continuum and the bond lattice on ℤ^d, where the cells or bonds are randomly assigned the conductivities σ_1 and σ_2 (σ_1, σ_2 ne0) with probabilities p_1 and p_2 = 1−p_1. A rigorous basis for the very old and widely used low volume fraction expansion of σ* is established, by proving that σ* is an analytic function of p_2 in a suitable domain containing [0, 1]. In the case of the bond lattice in d = 2, rigorous fourth-order upper and lower bounds on σ* valid for all p_2, σ_1, and σ_2 are derived. The four perturbation coefficients entering into the bounds are obtained from the first-order volume fraction coefficient using the method of infinite interchangeability.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1990 Plenum Publishing Corporation. Received July 13, 1989; final May 11, 1990. The work of O.B. was supported in part by ARO through grant DAAL 03-88-F-0110, and the work of K.G. by AFOSR through grant AFOSR-90-0203. | |||||||||
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| Subject Keywords: | Effective conductivity; random resistor network; composites; cell materials; perturbation expansions; bounds | |||||||||
| Issue or Number: | 1-2 | |||||||||
| DOI: | 10.1007/BF01013970 | |||||||||
| Record Number: | CaltechAUTHORS:20181107-080002180 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20181107-080002180 | |||||||||
| Official Citation: | Bruno, O. & Golden, K. J Stat Phys (1990) 61: 365. https://doi.org/10.1007/BF01013970 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 90686 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 07 Nov 2018 17:52 | |||||||||
| Last Modified: | 16 Nov 2021 03:34 |
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