Boundary-Layer Analysis of Repelling Particles Pushed to an Impenetrable Barrier

نویسندگان

چکیده

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

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ژورنال

عنوان ژورنال: Siam Journal on Mathematical Analysis

سال: 2022

ISSN: ['0036-1410', '1095-7154']

DOI: https://doi.org/10.1137/21m1420198