Error of the Network Approximation for Densely Packed Composites with Irregular Geometry

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Abstract
We introduce a discrete network,approximation,to the problem,of the effective conductivity of the high contrast, highly packed composites in which inclusions are irregularly (ran- domly) distributed in a hosting medium,so that a significant fraction of them may not participate in the conducting spanning cluster. For this class of spacial arrays of inclusions we derive a discrete network approximation,and obtain its a priori error estimate. We obtained an explicit dependence of the network approximation,and its error on the irregular geometry of the inclusions’ array. We use variational techniques to provide rigorous mathematical,justification for the approximation and its error estimate. Key words. effective conductivity, discrete network, error estimate, variational bounds AMS subject classifications. 74Q05, 35Q72, 94C05 PII. S0036141001397144