等角立方球的对称群

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Jean-Baptiste Bellet
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引用次数: 4

摘要

等角立方体球体是一种球形网格,广泛应用于计算物理学中。本文讨论了这种网格的数学性质。我们确定了对称群,即保持立方体球体不变的正交变换群。主要结果是它与立方体的对称群重合。所提出的证明强调了立方体球体的度量性质。我们研究了网格上的测地线距离,发现最短的测地线弧与立方体八面体的顶点相匹配。本文的结果为基于立方体旋转不变性的未来数值格式奠定了基础。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Symmetry group of the equiangular cubed sphere
The equiangular cubed sphere is a spherical grid, widely used in computational physics. This paper deals with mathematical properties of this grid. We identify the symmetry group, i.e. the group of the orthogonal transformations that leave the cubed sphere invariant. The main result is that it coincides with the symmetry group of a cube. The proposed proof emphasizes metric properties of the cubed sphere. We study the geodesic distance on the grid, which reveals that the shortest geodesic arcs match with the vertices of a cuboctahedron. The results of this paper lay the foundation for future numerical schemes, based on rotational invariance of the cubed sphere.
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来源期刊
Quarterly of Applied Mathematics
Quarterly of Applied Mathematics 数学-应用数学
CiteScore
1.90
自引率
12.50%
发文量
31
审稿时长
>12 weeks
期刊介绍: The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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