Boundary-layer analysis of repelling particles pushed to an impenetrable barrier

Patrick van Meurs

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arXiv · 2105.07163

Boundary-layer analysis of repelling particles pushed to an impenetrable barrier

Patrick van Meurs

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Abstract

This paper considers the equilibrium positions of $n$ particles in one dimension. Two forces act on the particles; a nonlocal repulsive particle-interaction force and an external force which pushes them to an impenetrable barrier. While the continuum limit as $n \to \infty$ is known for a certain class of potentials, numerical simulations show that a discrete boundary layer appears at the impenetrable barrier, i.e. the positions of $o(n)$ particles do not fit to the particle density predicted by the continuum limit. In this paper we establish a first-order $\Gamma$-convergence result which guarantees that these $o(n)$ particles converge to a specific continuum boundary-layer profile.

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Patrick van Meurs. 2021-05-15. Boundary-layer analysis of repelling particles pushed to an impenetrable barrier. https://arxiv.org/abs/2105.07163

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