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2009 Experimental Study of Energy-Minimizing Point Configurations on Spheres
Brandon Ballinger, Grigoriy Blekherman, Henry Cohn, Noah Giansiracusa, Elizabeth Kelly, Achill Schürmann
Experiment. Math. 18(3): 257-283 (2009).

Abstract

In this paper we report on massive computer experiments aimed at finding spherical point configurations that minimize potential energy. We present experimental evidence for two new universal optima (consisting of 40 points in 10 dimensions and 64 points in 14 dimensions), as well as evidence that there are no others with at most 64 points. We also describe several other new polytopes, and we present new geometrical descriptions of some of the known universal optima.

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Brandon Ballinger. Grigoriy Blekherman. Henry Cohn. Noah Giansiracusa. Elizabeth Kelly. Achill Schürmann. "Experimental Study of Energy-Minimizing Point Configurations on Spheres." Experiment. Math. 18 (3) 257 - 283, 2009.

Information

Published: 2009
First available in Project Euclid: 25 November 2009

zbMATH: 1185.68771
MathSciNet: MR2555698

Subjects:
Primary: 52-04 , 52B11 , 52C17

Keywords: energy minimization , polytopes , universal optimality

Rights: Copyright © 2009 A K Peters, Ltd.

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Vol.18 • No. 3 • 2009
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