Effective nonlinear response in random nonlinear resistor networks: Numerical studies

The effective response of random resistor networks consisting of two different kinds of 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 form i=gv+χ${\mathit{v}}^3$. The effective response is calculated by numerically solving Kirchhoff’s law at each node for the voltages. For a given fraction of nonlinear resistors, the effective response is extracted by averaging over different configurations. Numerical results are compared to theoretical predictions based on effective-medium approximation. The effective-medium-approximation results represent a reasonable description of the simulation results.