J. Phys. I France
Volume 2, Numéro 8, August 1992
Page(s) 1621 - 1644
DOI: 10.1051/jp1:1992231
J. Phys. I France 2 (1992) 1621-1644

The dynamical thermal fuse model

Christian Vanneste and Didier Sornette

Laboratoire de Physique de la Matière Condensée Université de Nice-Sophia Antipolis, Faculté des Sciences, B.P. n$^{\circ}$ 71, 06108 Nice Cedex 2, France

(Received 3 April 1992, accepted 14 April 1992)

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 ${\rm d}T/{\rm d}t=ri^b-aT$, 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 $b\to +\infty$, whereas the other extreme $b\to 0$ 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.

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