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.
抄録全体を表示