Open AccessHomogenization of stiff inclusions through network approximation
Author(s) -
David Gérard-Varet,
Alexandre Girodroux-Lavigne
Publication year - 2022
Publication title -
networks and heterogeneous media
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.732
H-Index - 34
eISSN - 1556-181X
pISSN - 1556-1801
DOI - 10.3934/nhm.2022002
Subject(s) - homogenization (climate) , homogeneous , logarithm , conductivity , upper and lower bounds , mathematics , mathematical analysis , physics , combinatorics , biodiversity , ecology , quantum mechanics , biology
We investigate the homogenization of inclusions of infinite conductivity, randomly stationary distributed inside a homogeneous conducting medium. A now classical result by Zhikov shows that, under a logarithmic moment bound on the minimal distance between the inclusions, an effective model with finite homogeneous conductivity exists. Relying on ideas from network approximation, we provide a relaxed criterion ensuring homogenization. Several examples not covered by the previous theory are discussed.