Dimensional crossover in the effective nonlinear response in random nonlinear resistor networks

The effective response of random resistor networks consisting of two different kinds of resistors is studied numerically on lattices with different thicknesses. One kind of resistor is assumed to be ohmic, while 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 extract the effective linear and nonlinear responses of the networks as functions of the concentration of the constituents and thickness of the system. A simple effective-medium approximation incorporating the effect of finite thickness is proposed and results are compared with simulation data. It is found that results from the effective-medium approximation provide a good description of the simulation results.