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Seminario di Equazioni Differenziali e Applicazioni: Dislocation dynamics in crystals: nonlocal effects and a macroscopic theory in a fractional Laplace setting

Giovedì 22 Maggio 2014, ore 12:15 - Aula 1BC45 - Enrico Valdinoci

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SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI

Giovedì 22 Maggio 2014 alle ore 12:15 in aula 1BC45, Enrico Valdinoci (Università di Milano e Weierstrass Institute, Berlino) terrà un seminario dal titolo "Dislocation dynamics in crystals: nonlocal effects and a macroscopic theory in a fractional Laplace setting".

Abstract
We consider an evolution equation arising in the Peierls-Nabarro 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. Though the problem seems of local nature, the leading order of the diffusion turns out to be a nonlocal integrodifferential operator.

Rif. Int. M. Bardi, E. Feleqi, G. Colombo

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