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arXiv · 1605.03840

Generating Point Configurations via Hypersingular Riesz Energy With an External Field

D. P. Hardin·E. B. Saff·O. V. Vlasiuk
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Abstract

For a compact $ d $-dimensional rectifiable subset of $ \mathbb{R}^{p} $ we study asymptotic properties as $ N\to\infty $ of $N$-point configurations minimizing the energy arising from a Riesz $ s $-potential $ 1/r^s $ and an external field in the hypersingular case $ s\geq d$. Formulas for the weak$ ^* $ limit of normalized counting measures of such optimal point sets and the first-order asymptotic values of minimal energy are obtained. As an application, we derive a method for generating configurations whose normalized counting measures converge to a given absolutely continuous measure supported on a rectifiable subset of $ \mathbb{R}^{p} $. Results on separation and covering properties of discrete minimizers are given. Our theorems are illustrated with several numerical examples.

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BibTeXRIS

D. P. Hardin, E. B. Saff, O. V. Vlasiuk. 2016-10-11. Generating Point Configurations via Hypersingular Riesz Energy With an External Field. https://arxiv.org/abs/1605.03840

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