The Clausius-Mossotti formula

Mitia Duerinckx (1, 2) , Antoine Gloria (3, 1)

1 ULB - Département de Mathématique [Bruxelles]
2 LMO - Laboratoire de Mathématiques d'Orsay
3 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

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 can be applied to dilute systems in many other contexts.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Mitia Duerinckx, Antoine Gloria. The Clausius-Mossotti formula. 2022. ⟨hal-03876866⟩