Simulation of dielectric failure by means of resistor-diode random lattices

It is possible to obtain an experimental simulation of electrical failures in studying the onset voltage of the nonlinearity of a two-dimensional random lattice of resistors and diodes. If there are more diodes than resistors, the onset voltage $V_b$ is identical to the breakdown voltage of an insulator made of resistors and insulating elements which can be broken. Near $p_c$, $V_b$ goes to zero with an exponent equal to 1.1 ± 0.3 in agreement with computer simulation. If now there are more resistors than diodes, the onset voltage $V_{\mathrm{NL}}$ is similar to the "fusing" current of a conductor made of conductive parts that behave like fuses and insulating parts (fuse model). Near $p_c$, $V_{\mathrm{NL}}$ goes to zero with an exponent equal to 0.5 ± 0.2 and it is shown to be larger than the exponent of the fuse model equal to $v-1=0.33\mathrm{}$ in two dimensions.