Steady State of Random Resistor Networks Under Biased Percolation
Cecilia Pennetta
Abstract
It will be presented a recent statistical approach which allows the study of the electrical 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 a disordered material are determined by the competition of two biased processes taking place in a random resistor network. At low bias a scaling relation has been found between the relative variance of resistance fluctuations and the average network resistance. The properties of the nonlinear regime, occurring when the bias overcomes a threshold value, are studied for different values of the model parameters and for different bias conditions. Scaling relations are found for the average resistance and the resistance noise as functions of the external bias. In particular, a strong nonlinearity of these quantities 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.
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