The Clausius–Mossotti formula

Article type: Research Article

Authors: Duerinckx, Mitia^a | Gloria, Antoine^{b; c; a; *}

Affiliations: [a] Université Libre de Bruxelles, Département de Mathématique, 1050 Brussels, Belgium | [b] Sorbonne Université, CNRS, Université de Paris, Laboratoire Jacques-Louis Lions, 75005 Paris, France | [c] Institut Universitaire de France, France

Correspondence: [*] Corresponding author. E-mail: antoine.gloria@sorbonne-universite.fr.

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.

Keywords: Dilute expansion, homogenization, effective coefficients

DOI: 10.3233/ASY-231840

Journal: Asymptotic Analysis, vol. 134, no. 3-4, pp. 437-453, 2023