WIAS Preprint No. 1847, (2013)

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


  • Dipierro, Serena
  • Palatucci, Giampiero
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35Q99 35B40 35J25 35D30 35G25 70F99


  • nonlinear problems, nonlocal Allen-Cahn equation, reaction-diffusion, Peierls--Nabarro model, dislocation dynamics, particle systems, fractional Laplacian, fractional Sobolev spaces


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

Appeared in

  • Comm. Math. Phys., 333 (2015) pp. 1061--1105.

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