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)

DOI Web Site
  • 田上 真
    九州工業大学システム創成情報工学研究系

書誌事項

タイトル別名
  • Some Applications of Spherical Designs(<Special Topic>A Mathematical Challenge to a New Phase of Materials Science)
  • 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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抄録

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.

収録刊行物

  • 応用数理

    応用数理 23 (4), 166-170, 2013

    一般社団法人 日本応用数理学会

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