Nonlinear electrodynamics of fractal structure

Nonlinear effects in the two-component medium with conductivities σ1 (metal) and σ2 (insulator) near the percolations threshold is studied. For the medium having cubic nonlinearity an effective nonlinear conductivity ae and correlation functions of the electrical field 〈e4〉 and current 〈j4〉 have been studied as functions of parameters h = σ2/σ1. It is shown that the conductivity ae and correlators at the percolation threshold grow as ae≈h−w, 〈e4〉≈h−γ, 〈j4〉≈h−ζ for h⪡1. Dykhne's relations are used to derive important inequalities for the ae and critical exponents. The nonlinear conductivity, correlators and corresponding critical exponents have been determined by numerical calculations.