2006/02/11 by Sergiy Borodachov, S. V. Borodachov, Douglas P. Hardin +6
Mathematics · Physics and Astronomy · #11K41 #28A78 #70F10 #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration #Mathematical Physics (math-ph) #advanced mathematical theories #math-ph #math.MP #msc:11K41 #msc:28A78 #msc:70F10
paper · pdf · doi:10.48550/arxiv.math-ph/0602025
arxiv created 2006/02/11 · openalex publication_date 2006/02/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a compact d-rectifiable set A embedded in Euclidean space and a distribution ρ(x) with respect to d-dimensional Hausdorff measure on A, we address the following question: how can one generate optimal configurations of N points on A that are "well-separated" and have asymptotic distribution ρ(x) as N→ ∞? For this purpose we investigate minimal weighted Riesz energy points, that is, points interacting via the weighted power law potential V=w(x,y)|x-y|-s, where s>0 is a fixed parameter and w is suitably chosen. In the unweighted case (w≡ 1) such points for N fixed tend to the solution of the best-packing problem on A as the parameter s→ ∞.