Homogenization of random elliptic systems with an application to Maxwell's equations

TL;DR

This paper develops a homogenization framework for elliptic systems with random coefficients, applying it to Maxwell's equations in complex media, advancing understanding of wave propagation in random environments.

Contribution

It introduces a novel homogenization approach for elliptic systems with random, composition-based coefficients, extending scalar stochastic homogenization techniques to vector systems.

Findings

Established homogenization results for elliptic systems with random coefficients

Applied the theory to Maxwell's equations in random media

Provided insights into wave behavior in complex, dissipative materials

Abstract

We study the homogenization of elliptic systems of equations in divergence form where the coefficients are compositions of periodic functions with a random diffeomorphism with stationary gradient. This is done in the spirit of scalar stochastic homogenization by Blanc, Le Bris and P.-L. Lions. An application of the abstract result is given for Maxwell's equations in random dissipative bianisotropic media.