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Title: Dislocation dynamics in crystals: A macroscopic theory in a fractional Laplace setting
Authors: Dipierro, SerenaPalatucci, GiampieroValdinoci, Enrico
Issue Date: 2013
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1847, ISSN 0946 – 8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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.
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
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
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Appears in Collections:Mathematik



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