Asymptotics for Discrete Weighted Minimal Riesz Energy Problems on Rectifiable Sets
| dc.creator | Borodachov, S. V. | |
| dc.creator | Hardin, D. P. | |
| dc.creator | Saff, E. B. | |
| dc.date | 2006-02-11 | |
| dc.date.accessioned | 2026-07-07T07:02:57Z | |
| dc.date.available | 2026-07-07T07:02:57Z | |
| dc.description | 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 $N\to \infty$? 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 ($w\equiv 1$) such points for $N$ fixed tend to the solution of the best-packing problem on $A$ as the parameter $s\to \infty$. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0602025 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0602025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108795 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 11K41, 70F10, 28A78 | |
| dc.title | Asymptotics for Discrete Weighted Minimal Riesz Energy Problems on Rectifiable Sets | |
| dc.type | text |