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Conductance fluctuations in random resistor networks

One of the common models of studying percolation is random graphs with random resistance in the edges. Clearly there is no conductance of the network below pc. Since 1970s, a significant amount was effort was given to understand the scaling of conductance near percolation threshold and therefore conductance exponents were introduced that depended on dimension of the system. Near percolation threshold, it was observed that the distribution of current in the network is broad and different moment scale differently; hence they were termed multifractal. In this work, we studied conductance and its fluctuations away from the percolation threshold. We use different class of bond diluted models for comparison.

potential distribution
Fig: Above figure shows the potential at different sites in the network at steady state and we can clearly interesting patterns emerging out.

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