DIMENSIONAL CROSSOVER IN THE EFFECTIVE NONLINEAR RESPONSE IN RANDOM NONLINEAR RESISTOR NETWORKS

The effective response of random resistor networks consisting of two d ifferent kinds of resistors is studied numerically on lattices with di fferent thicknesses. One kind of resistor is assumed to be ohmic, whil e the other is assumed to have a nonlinear I-V response of the form i= g nu+chi nu(3). Detailed numerical simulations are performed to extrac t the effective linear and nonlinear responses of the networks as func tions of the concentration of the constituents and thickness of the sy stem. A simple effective-medium approximation incorporating the effect of finite thickness is proposed and results are compared with simulat ion data. It is found that results from the effective-medium approxima tion provide a good description of the simulation results.