Properties of Screw Dislocation Dynamics: Time Estimates on Boundary and Interior Collisions

In this paper, the dynamics of a system of a nite number of screw dislocations is studied. Under the assumption of antiplane linear elasticity, the two-dimensional dynamics is determined by the renormalized energy. The interaction of one dislocation with the boundary and of two dislocations of opposite Burgers moduli are analyzed in detail, and estimates on the collision times are obtained. Additionally, we obtain sucient conditions that can be used to guarantee that the first collision to occur will be between a specic dislocation and the boundary, or between a specific pair of dislocations. Some exactly solvable cases and numerical simulations show agreement with the estimates obtained.