Calculus of Variations and Geometric Measure Theory
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C. Hall - T. Hudson - P. van Meurs

Asymptotic analysis of boundary layers in a repulsive particle system

created by vanmeurs on 08 Sep 2018

[BibTeX]

preprint

Inserted: 8 sep 2018

Year: 2016

ArXiv: 1609.03236 PDF

Abstract:

This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. Our setting covers pile-ups of dislocations, dislocation dipoles and dislocation walls. The main challenge is to control the nonlocal nature of the pairwise particle interactions. Using matched asymptotic expansions for the particle positions and rigorous development of an appropriate energy via Gamma-convergence, we obtain the equilibrium equation solved by the boundary layer correction, associate an energy with an appropriate scaling to this correction, and provide decay rates into the bulk.

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