Depinning with Dynamic Stress Overshoots: Mean Field Theory

An infinite-range model of an elastic manifold pulled through a random potential by a force F is analyzed focusing on inertial effects. When the inertial parameter M is small, there is a continuous depinning transition from a small-F static phase to a large-F moving phase. When M is increased to Mc , a novel tricritical point occurs. For M>Mc , the depinning transition becomes discontinuous with hysteresis. Yet, the distribution of discrete ''avalanche''-like events as the force is increased in the static phase for M>Mc has an unusual mixture of first-order-like and critical features. The results may be relevant for the onset of crack propagation and for dynamics of geological faults