Field distributions and effective-medium approximation for weakly nonlinear media
Abstract
An effective-medium theory is proposed for random weakly nonlinear dielectric media. It is based on a new gaussian approximation for the probability distributions of the electric field in each component of a multi-phase composite. These distributions are computed to linear order from a Bruggeman-like self-consistent formula. The resulting effective-medium formula for the nonlinear medium reduces to Bruggeman's in the linear case. It is exact up to second order in a weak-disorder expansion, and close to the exact result in the dilute limit (in particular, it is exact for d=1 and d=infinity. In a high contrast situation, the noise exponents are kappa=kappa'=0 near the percolation threshold. Numerical results are provided for different weak nonlinearities.
Cite
@article{arxiv.cond-mat/0001228,
title = {Field distributions and effective-medium approximation for weakly nonlinear media},
author = {Yves-Patrick Pellegrini},
journal= {arXiv preprint arXiv:cond-mat/0001228},
year = {2008}
}
Comments
12 pages, 6 eps figures