Dislocation dynamics in crystals: A macroscopic theory in a fractional Laplace setting

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Date
2013
Volume
1847
Issue
Journal
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

We consider an evolution equation arising in the PeierlsNabarro model for crystal dislocation. We study the evolution of such dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. these dislocation points evolve according to the external stress and an interior repulsive potential.

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Keywords
Nonlinear problems, nonlocal Allen-Cahn equation, reaction-diffusion, Peierls–Nabarro model, dislocation dynamics, particle systems, fractional Laplacian, fractional Sobolev spaces.Evolutionsgleichung, Gitterbaufehler, Peierls-Instabilität
Citation
Dipierro, S., Palatucci, G., & Valdinoci, E. (2013). Dislocation dynamics in crystals: A macroscopic theory in a fractional Laplace setting (Vol. 1847). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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