Crystal dislocations with different orientations and collisions

TL;DR

This paper analyzes a parabolic differential equation modeling crystal dislocations with varying orientations and collisions, incorporating long-range interactions and external stress, extending previous models that assumed uniform dislocation orientations.

Contribution

It introduces a novel approach to modeling dislocations with mixed orientations, broadening the understanding of dislocation dynamics in crystals.

Findings

Dislocation solutions with different orientations are characterized.

Long-range interactions significantly influence dislocation behavior.

External stress impacts the stability of dislocation configurations.

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).