NCSU Differential Equations/Nonlinear Analysis Seminars

Location and Time: SAS 4201, Wednesday 15:00 -16:00

Organizers: Lorena Bociu, Patrick Combettes, Ryan Murray, and Khai T. Nguyen

NEXT TALK

Wednesday, Oct 30, 15:00-16:00, Room: SAS 4201

Speaker: Stefania Patrizi, The University of Texas at Austin
Title: The discrete dislocation dynamics of multiple dislocation loops
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 $\epsilon>0$, the rescaled solution solves a fractional Allen–Cahn equation. We show that, as $\epsilon \to 0$, the limiting solution exhibits multiple interfaces evolving independently and according to their mean curvature. 

This is a joint work with Mary Vaughan  (University of Western Australia).

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