Crystal dislocations with different orientations and collisions

Abstract

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).

References in corpus (1)

• Slow motion of particle systems as a limit of a reaction-diffusion equation with half-Laplacian in dimension one

Cited by in corpus (10)

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• Metastable Speeds in the Fractional Allen-Cahn Equation
• The Effect of Forest Dislocations on the Evolution of a Phase-Field Model for Plastic Slip
• Hölder regularity for the trajectories of generalized charged particles in 1D
• Uniform distribution of dislocations in Peierls-Nabarro models for semi-coherent interfaces