THE DYNAMIC THERMAL FUSE MODEL

A dynamical version of the random fuse model is presented in which the temperature T of a fuse of resistance r carrying the current i obeys the equation dT/dt = ri(b) - aT, where ri(b) accounts for a generalized Joule heating and - aT describes the coupling to a thermal bath. For random resistances with the same temperature threshold T(r) for rupture, the quasi-static random fuse model is recovered in the limit b --> + infinity, whereas the other extreme b --> 0 corresponds to the percolation model. In the intermediate regime, the competition between the two time scales T(r)/ri(b) and a-1 of the temperature field produces a rich phenomenology of rupture patterns which present sensitive dependence upon the input current.