Field distributions and effective-medium approximation for weakly nonlinear media
- 1 April 2000
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 61 (14), 9365-9372
- https://doi.org/10.1103/physrevb.61.9365
Abstract
An effective-medium theory is proposed for random weakly nonlinear dielectric media. It is based on a Gaussian approximation for the probability distributions of the electric field in each component of a multiphase 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 and In a high contrast situation, the noise exponents are near the percolation threshold. Numerical results are provided for different weak nonlinearities. The use of the Bruggeman formula as a starting point for nonlinear homogeneization theories in dimensions is questioned on the basis of known exact bounds on the noise exponents.
Keywords
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