Publication: Asymptotic properties of discrete minimal s, log<sup>t</sup>-energy constants and configurations
Issued Date
2021-06-01
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20738994
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2-s2.0-85107463502
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Mahidol University
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SCOPUS
Bibliographic Citation
Symmetry. Vol.13, No.6 (2021)
Suggested Citation
Nichakan Loesatapornpipit, Nattapong Bosuwan Asymptotic properties of discrete minimal s, log<sup>t</sup>-energy constants and configurations. Symmetry. Vol.13, No.6 (2021). doi:10.3390/sym13060932 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/76608
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Title
Asymptotic properties of discrete minimal s, log<sup>t</sup>-energy constants and configurations
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Abstract
We investigated the energy of N points on an infinite compact metric space (A, d) of a diameter less than 1 that interact through the potential (1/ds )(log 1/d)t, where s, t ≥ 0 and d is the metric distance. With Eslogt (A, N) denoting the minimal energy for such N-point configurations, we studied certain continuity and differentiability properties of Eslogt (A, N) in the variable s. Then, we showed that in the limits, as s → ∞ and as s → s0 > 0, N-point configurations that minimize the s, logt-energy tends to an N-point best-packing configuration and an N-point configuration that minimizes the s0, logt-energy, respectively. Furthermore, we considered when A are circles in the Euclidean space R2 . In particular, we proved the minimality of N distinct equally spaced points on circles in R2 for some certain s and t. The study on circles shows a possibility for the utilization of N points generated through such new potential to uniformly discretize on objects with very high symmetry.