Resistor networks with distributed breakdown voltages

As a primitive model for structural breakdown in elastic media, we analyze the failure of random resistor-fuse networks with various distributions of properties. We show that variations in breakdown voltage have a more significant effect than variations in resistance values. This is analogous to the fluid-displacement problem [D.Y.C. Chan, B. D. Hughes, L. Paterson, and C. Sirakoff, Phys. Rev. A 38, 4106 (1988)], in which variations in fluid capacity have a greater effect on displacement efficiencies than variations in permeability. An exponential distribution of breakdown voltages creates much more disorder than any uniform distribution, but power-law distributions that emphasize weak bonds can create even greater disorder, up to the percolation limit, in which bonds are broken independently at random.