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The Clausius–Mossotti formula

Published:2023-09-01 Issue:3-4 Volume:134 Page:437-453
ISSN:1875-8576
Container-title:Asymptotic Analysis
language:
Short-container-title:ASY

Author:

Duerinckx Mitia¹,Gloria Antoine²³¹

Affiliation:

1. Université Libre de Bruxelles, Département de Mathématique, 1050 Brussels, Belgium

2. Sorbonne Université, CNRS, Université de Paris, Laboratoire Jacques-Louis Lions, 75005 Paris, France

3. Institut Universitaire de France, France

Abstract

In this note, we provide a short and robust proof of the Clausius–Mossotti formula for the effective conductivity in the dilute regime, together with an optimal error estimate. The proof makes no assumption on the underlying point process besides stationarity and ergodicity, and it can be applied to dilute systems in many other contexts.

Publisher

IOS Press

Subject

General Mathematics

Reference32 articles.

1. Averaging of dilute random media: A rigorous proof of the Clausius-Mossotti formula;Almog;Arch. Ration. Mech. Anal.,2013

2. The Clausius-Mossotti formula in a dilute random medium with fixed volume fraction;Almog;Multiscale Model. Simul.,2014

3. A numerical approach related to defect-type theories for some weakly random problems in homogenization;Anantharaman;Multiscale Model. Simul.,2011

4. Elements of mathematical foundations for numerical approaches for weakly random homogenization problems;Anantharaman;Commun. Comput. Phys.,2012

5. The determination of the bulk stress in suspension of spherical particles to order c 2;Batchelor;J. Fluid Mech.,1972

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