Mathematical Sciences: Minimal Discrete Energy Problems and Approximation Theory

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Saff DMS-9501130 The PI's will investigate the optimal and near optimal arrangements of N points on the surface of the unit sphere. Potential theoretic methods will be used to analyze the extremal energy when these points on the sphere interact through a power law potential. They will focus on asymptotic results for this extremal energy and aim at producing algorithms or simple formulas for points on the sphere that yield close-to-optimal energy. This research has connections with the structural analysis of large order carbon fullerenes. Approximation is the defining feature of mathematical analysis. Compact expressions of solutions of problems arising in the physical universe rarely occur. More often, the solutions must be approximated by known quantities which have desirable properties and are easily computed. This research contributes to the dual goals of understanding the special functions of analysis and discovering their approximation properties.