Upscaling a model for the thermally-driven motion of screw dislocations
Résumé
We formulate and study a Markovian model for the thermally-driven motion of screw dislocations. Waiting times for transitions from state to state are assumed to be exponentially distributed with rates expressed in terms of the energy barrier between the states. By using a form of duality, asymptotic descriptions of the energy barriers are computed, and two dimensionless parameters are identified. In a certain parameter regime, the process satisfies a large deviations principle. This gives a description of the most probable path as a gradient flow with non-quadratic dissipation: by then considering a further parameter regime, we recover the usual quadratic dissipation used in discrete dislocation dynamics simulations.
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