Discrete Minimal Energy on Flat Tori and Four-Point Maximal Polarization on S^2

Discrete Minimal Energy on Flat Tori and Four-Point Maximal Polarization on S^2

Let $Lambda$ be a lattice in $R^d$ with positive co-volume. Among $Lambda$-periodic $N$-point configurations, we consider the minimal renormalized Riesz $s$-energy $mathcal{E}_{s,Lambda}(N)$. While the dominant term in the asymptotic expansion of $mathcal{E}_{s,Lambda}(N)$ as $N$ goes to infinity in...

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Bibliographische Detailangaben
1. Verfasser: Su, Yujian
Format: Dissertation
Sprache:eng
Schlagworte:
Epstein Hurwitz Zeta function
Ewald summation
max-min problems
periodic energy
polarization
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Zusammenfassung:Let $Lambda$ be a lattice in $R^d$ with positive co-volume. Among $Lambda$-periodic $N$-point configurations, we consider the minimal renormalized Riesz $s$-energy $mathcal{E}_{s,Lambda}(N)$. While the dominant term in the asymptotic expansion of $mathcal{E}_{s,Lambda}(N)$ as $N$ goes to infinity in the long range case that $0