ANNEALED MODEL FOR BREAKDOWN PROCESSES

We consider a stochastic model of breakdown processes, similar to the dielectric breakdown model, but where the connectivity of the crack is not required. Starting with a homogeneous medium, at each time step a bond is broken at random with a probability proportional to the current it carries raised to a power q, For n<2, the breakdown is qualitatively much closer to a percolation process than to DLA-type growth: on a square lattice the final breakdown point occurs after the breaking of a finite concentration of bonds (0.30(1) for q = 1). On the other hand, for n >2, one large cluster of broken bonds generated in the breakdown process is much bigger than the other clusters and it has the scaling properties of the clusters of the dielectric breakdown model of Niemeyer et al. © 1990 IOP Publishing Ltd.