Experimental study of energy-minimizing point configurations on spheres

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.

41 pages, 12 figures, to appear in Experimental Mathematics

References in corpus (8)

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• The D_4 root system is not universally optimal
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• Minimal Riesz Energy Point Configurations for Rectifiable d-Dimensional Manifolds
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Cited by in corpus (25)

• Distance-regular graphs
• Distributing many points on spheres: minimal energy and designs
• Quasi-Monte Carlo rules for numerical integration over the unit sphere ${\mathbb{S}}^2$
• Sticky-sphere clusters
• Self Assembled Clusters of Spheres Related to Spherical Codes
• Free energy of singular sticky-sphere clusters
• Three-point bounds for energy minimization
• Optimality and uniqueness of the (4,10,1/6) spherical code
• Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets
• Quantum spherical codes
• The contact polytope of the Leech lattice (complete version)
• Lecture notes: Semidefinite programs and harmonic analysis
• Newton Algorithm on Constraint Manifolds and the 5-electron Thomson problem
• Point configurations that are asymmetric yet balanced
• Theoretical bounds on data requirements for the ray-based classification
• Locally and Globally Optimal Configurations of $N$ Particles on the Sphere with Applications in the Narrow Escape and Narrow Capture Problems
• Universal bounds for spherical codes: the Levenshtein framework lifted
• Moments of isotropic measures and optimal projective codes
• The Triangular Bi-Pyramid Minimizes a Range of Power Law Potentials
• Upper bounds for energies of spherical codes of given cardinality and separation
• Finding and investigating exact spherical codes
• Uniquely optimal codes of low complexity are symmetric
• Characterization of Logarithmic Fekete Critical Configurations of at Most Six Points in All Dimensions
• Some spherical codes in S2 and their algebraic numbers
• Association schemes related to Delsarte-Goethals codes