The dynamical thermal fuse model

A dynamical version of the random fuse model is presented in which the temperature T of a fuse resistance r carrying the current i obeys the equation dT/dt=rib-aT, where rib accounts for a generalized Joule heating and -aT describes the coupling to a thermal bath. For random fuse model is recovered in the limit b↦+∞, 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