Linear and nonlinear regime of a Random Resistor Network under biased   percolation
  We investigate the steady state of a two-dimensional random resistor network subjected to two competing biased percolations as a function of the bias strength. The properties of the linear and nonlinear regimes are studied by means of Monte Carlo simulations. In constant current conditions, a scaling relation is found between $<R>/<R>_0$ and $I/I_0$, where $<R>$ is the average network resistance, $<R>_0$ the Ohmic resistance and $I_0$ an appropriate threshold value for the onset of nonlinearity. A similar scaling relation is found also for the relative variance of resistance fluctuations. These results are in good agreement with electrical breakdown measurements performed in composite materials. 
C. Pennetta, E. Alfinito and L. Reggiani