Effective nonlinear response of random resistor networks with anomalous distributions of conductances

We present numerical simulations of effective nonlinear response for a random nonlinear resistor network consisting of two different kinds of resistors. One kind of resistor with the fraction p has the nonlinear current (i) voltage (v) relation of the form i=g1v+χ1v3, where g1 and χ1 are the linear conductance and nonlinear response. The other kind of resistor with the fraction of 1−p is assumed to be linear, whose conductance g2 obeys an anomalous distribution h(g)∼gα with 0<g<1. An effective medium approximation (EMA) is proposed for the effective nonlinear response, which is valid for the anomalous distribution. Numerical results show that the enhancement of the effective nonlinear response can be achieved when α is negative, and the EMA is found to yield a good description of the simulation data in the whole fraction range. In the dilute limit, the Maxwell–Garnett approximation for the effective nonlinear response is also derived, and it describes the simulation data better than EMA.