| Abstract: |
| We consider dynamics of a phase-field model for crystal dislocations in the large body/small Burgers vector limit. In the one-dimensional Peierls-Nabarro setting without a forest dislocation background, the limit of the gradient flows of the energies is the gradient flow of the $\Gamma$-limit, similar to related problems in ferromagnetic materials. Forest dislocations introduce an extra strange term into the $\Gamma$-limit. Although this term may speed up the evolution of the $\Gamma$-limit, we show that it does not represent an additional driving force: instead, the presence of forest dislocations introduces a wiggliness into the system that actually slows down the observed evolution. |
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