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arXiv · 2406.14793

The discrete dislocation dynamics of multiple dislocation loops

Stefania Patrizi·Mary Vaughan
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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 $\mathbb{R}^n$, $n \geq 2$. After suitably rescaling the equation with a small phase parameter $\varepsilon>0$, the rescaled solution solves a fractional Allen-Cahn equation. We show that, as $\varepsilon \to 0$, the limiting solution exhibits multiple interfaces evolving independently and according to their mean curvature.

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Stefania Patrizi, Mary Vaughan. 2024-06-20. The discrete dislocation dynamics of multiple dislocation loops. https://arxiv.org/abs/2406.14793

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