The discrete dislocation dynamics of multiple dislocation loops

2024/06/20 by Patrizi, Stefania, Vaughan, Mary
#35R09 #35R11 #47G20 #74E15 #82D25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.14793

Abstract

We consider a nonlocal reaction-diffusion equation that physically arises from the classical Peierls-Nabarro model for dislocations in crystalline structures. Our initial configuration corresponds to multiple slip loop dislocations in ℝⁿ, n ≥ 2. After suitably rescaling the equation with a small phase parameter ε>0, the rescaled solution solves a fractional Allen-Cahn equation. We show that, as ε → 0, the limiting solution exhibits multiple interfaces evolving independently and according to their mean curvature.

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