Some Applications of Spherical Designs(<Special Topic>A Mathematical Challenge to a New Phase of Materials Science)

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  • 球デザインの材料科学への応用(<特集>離散幾何学から提案する新物質創成・物性発現の解明)
  • 球デザインの材料科学への応用
  • タマ デザイン ノ ザイリョウ カガク エ ノ オウヨウ

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Abstract

In this paper, we introduce some applications of spherical designs to materials science. A spherical design, which is a notion of pure mathematics, has been mainly studied well in algebraic combinatorics. Spherical design is defined as what giving a good configuration of finite points on sphere from the viewpoint of the surface integral. On the other hand, it is closely related to minimizing potential energy of finite points on sphere. We extend the theory of potential energy minimization to Euclidean designs, which is a natural generalization of spherical designs to Euclidean space, and apply Euclidean design to structural analysis of metal clusters, in particular, to rhodium clusters. Some other applications of spherical design are stated.

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