Mathematics > Classical Analysis and ODEs
[Submitted on 10 May 2016 (v1), last revised 11 Oct 2016 (this version, v2)]
Title:Generating Point Configurations via Hypersingular Riesz Energy With an External Field
View PDFAbstract: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.
Submission history
From: Oleksandr Vlasiuk [view email][v1] Tue, 10 May 2016 18:32:17 UTC (853 KB)
[v2] Tue, 11 Oct 2016 22:52:08 UTC (853 KB)
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