The Clausius-Mossotti formula for dilute random media of perfectly conducting inclusions

Yaniv Almog

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arXiv · 1606.07765

The Clausius-Mossotti formula for dilute random media of perfectly conducting inclusions

Yaniv Almog

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Abstract

We consider a large number of randomly dispersed spherical, identical, perfectly conducting inclusions (of infinite conductivity) in a bounded domain. The host medium's conductivity is finite and can be inhomogeneous. In the dilute limit, with some boundedness assumption on a large number (proportional to the global volume fraction raised to the power of -1/2) of marginal probability densities, we prove convergence in H^1 norm of the expectation of the solution of the steady state heat equation, to the solution of an effective medium problem, where the conductivity is given by the Clausius-Mossotti formula. Error estimates are provided as well.

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Yaniv Almog. 2016-06-24. The Clausius-Mossotti formula for dilute random media of perfectly conducting inclusions. https://arxiv.org/abs/1606.07765

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