Abstract:
Many complex systems respond to a continuous input of energy by an accumulation of stress over time, interrupted by sudden energy releases called avalanches. Recently, it has been pointed out that several basic features of avalanche dynamics are induced at the microscopic level by relaxation processes, which are neglected by most models. We have studied a minimal modification of a well-known model of avalanche dynamics, in which we take into account the presence of "relaxation processes". Precisely, we study a viscoelastic interface driven in a disordered medium. 

In mean-field, we prove that our model interface has a periodic behavior (with a new, emerging time scale), with avalanche events that span the whole system. We compute semi-analytically the friction force acting on this surface, and find that it is compatible with classical friction experiments. 

In finite dimensions (2D), the mean-field system-sized events become local, and numerical simulations give qualitative and quantitative results in good agreement with several important features of real earthquakes.