Upscaling a model for the thermally-driven motion of screw dislocations (Q522190)

The physical system under consideration is defined by mathematical models referred to as kinetic Monte Carlo (KMC) models which are useful when exploited via numerical techniques. The motion is described as a Markov jump process in which the waiting time for transition from state to state are exponentially distributed with rates expressed in terms of the potential energy barrier between the states. The author proves the uniqueness of equilibria containing dislocation configurations, derives an asymptotic characterization of the energy barriers between dislocation configurations, and builds up the rigorous framework for the two-dimensional discrete dislocation dynamics framework.