Higher order nonlinear response in random resistor networks: numerical studies for arbitrary nonlinearity

Abstract

The higher order effective response of random resistor networks (RRNs) consisting of two different kinds resistor is studied numerically. One kind of resistor is assumed to be Ohmic, while the other is assumed to have a nonlinear I–V response of the formi=συ + χυβ, β=5 or β=7. The effective response of the network is assumed to take the form ofi=σeυ + χeυβ + ηeυ2β. We generalized the algorithm of Yang and Hui to calculate both χe and ηe. Numerical results of χe and ηe are compared to theoretical predictions of a recently derived Clausius-Mossotti (CM) approximation. The Clausius-Mossotti approximation results are found to provide a good description of the results of the simulations in cases of low contrast between the two components in the networks.