Self-consistent effective-medium approximation for strongly nonlinear media
Résumé
A self-consistent effective-medium theory is proposed for random dielectric composites of arbitrary non-linear constitutive law. It is based on a Gaussian approximation for the probability distributions of the electric field in each component, and on second-order Taylor expansions with an integral remainder of the local energies. The effective energy is exact to second order in contrast. With power-law media with constitutive relation D=chi E^{gamma-1}, the critical exponents are s=t=(gamma+1)/2. The theory reduces to Bruggeman's in the linear case gamma=1, and its percolation threshold is independent of the nonlinearity.