WIAS Preprint No. 1988, (2014)

Crystal dislocations with different orientations and collisions


  • Patrizi, Stefania
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 82D25 35R09 74E15 35R11 47G20


  • Peierls-Nabarro model, nonlocal integro-differential equations, dislocation dynamics, attractive/repulsive potentials, collisions




We study a parabolic differential equation whose solution represents the atom dislocation in a crystal for a general type of Peierls-Nabarro model with possibly long range interactions and an external stress. Differently from the previous literature, we treat here the case in which such dislocation is not the superpositions of transitions all occurring with the same orientations (i.e. opposite orientations are allowed as well). We show that, at a long time scale, and at a macroscopic space scale, the dislocations have the tendency to concentrate as pure jumps at points which evolve in time, driven by the external stress and by a singular potential. Due to differences in the dislocation orientations, these points may collide in finite time.

Appeared in

  • Arch. Ration. Mech. Anal., 217 (2015) pp. 231--261.

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