Steady State of Random Resistor Networks under Biased Percolation: a Framework for Noise in Disordered Media ?

Recently we have developed a new statistical approach which allows the study of the electrical noise and conduction of disordered materials over the full range of bias values, from the linear regime up to the electrical breakdown. In this approach, the resistance and the resistance fluctuations of disordered materials are determined by the competition of biased processes taking place in random resistor networks. In particular, the properties of the nonlinear regime are studied for different values of the model parameters and for different bias conditions. A strong nonlinearity of the relative variance of resistance fluctuations emerges in the pre-breakdown region which is also characterized by non-Gaussian noise. These results compare well with measurements of the electrical resistance and resistance noise performed in composites and in other conducting materials. The possibility of defining reliable failure precursors and other suitable quantities characterizing electrical breakdown phenomena in disordered materials is then discussed.