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Dislocation Dynamics in Crystals: A Macroscopic Theory in a Fractional Laplace Setting

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Abstract

We consider an evolution equation arising in the Peierls–Nabarro model for crystal dislocation. We study the evolution of such a 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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Authors and Affiliations

  1. School of Mathematics, University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland, UK

    Serena Dipierro

  2. SISSA, Via Bonomea 256, 34136, Trieste, Italy

    Giampiero Palatucci

  3. Weierstrass Institut für Angewandte Analysis und Stochastik, Hausvogteiplatz 11A, 10117, Berlin, Germany

    Enrico Valdinoci

  4. Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Parma, Italy

    Giampiero Palatucci

Authors
  1. Serena Dipierro
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  2. Giampiero Palatucci
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  3. Enrico Valdinoci
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Corresponding author

Correspondence to Giampiero Palatucci.

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Communicated by L. Caffarelli

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Dipierro, S., Palatucci, G. & Valdinoci, E. Dislocation Dynamics in Crystals: A Macroscopic Theory in a Fractional Laplace Setting. Commun. Math. Phys. 333, 1061–1105 (2015). https://doi.org/10.1007/s00220-014-2118-6

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  • DOI: https://doi.org/10.1007/s00220-014-2118-6

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