Asymptotic Analysis of Boundary Layers in a Repulsive Particle System

作者：Hall Cameron L.; Hudson Thomas; van Meurs Patrick^*

来源：Acta Applicandae Mathematicae, 2018, 153(1): 1-54.

DOI：10.1007/s10440-017-0119-0

• Particle system
• Boundary layer
• Discrete-to-continuum asymptotics
• Matched asymptotic expansions
• Gamma-convergence

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. This setting covers, for instance, pile-ups of dislocations, dislocation dipoles and dislocation walls. The main challenge in characterising the boundary behaviour 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 -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.

• 出版日期2018-2