A fractional glance to the theory of edge dislocations

2021/10/14 by Dipierro, Serena, Patrizi, Stefania, Valdinoci, Enrico
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.07134

Abstract

We revisit some recents results inspired by the Peierls-Nabarro model on edge dislocations for crystals which rely on the fractional Laplace representation of the corresponding equation. In particular, we discuss results related to heteroclinic, homoclinic and multibump patterns for the atom dislocation function, the large space and time scale of the solutions of the parabolic problem, the dynamics of the dislocation points and the large time asymptotics after possible dislocation collisions.

Related

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• From the Peierls-Nabarro model to the equation of motion of the\n dislocation continuum