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 M(c), a novel tricritical point occurs. For M>M(c), 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>M(c) 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.