论文标题
II型和III型O（3） - subgroups的剪辑操作，并应用于Piezoelectricity
Clips operation between type II and type III O(3)-subgroups with application to piezoelectricity
论文作者
论文摘要
剪辑是紧凑型组的封闭亚组的共轭类别之间的二进制操作，如果每个因子E1，e2已知，则引入了直接表示E1 $ \ oplus $ e2的直接表示总和E1 $ \ oplus $ e2的各向同性类别。这尤其允许计算任何可简化表示的各向同性类别，一旦知道了不可减少因素的分解和对不可约因素的对称类别。在三维正交组O（3）的特定情况下，已经计算了某些类型的O（3）亚组之间的剪辑。但是，到目前为止，缺少II型和III型亚组之间的剪辑。这些是在3D耦合的本构法中遇到的。在本文中，我们通过计算丢失的剪辑来完成剪辑表。作为一种应用，我们在完整的3D压电定律上获得了25个各向同性类别，用于标准O（3）表示，其中涉及三种弹性，压电性和介电性本构张量。
Clips is a binary operation between conjugacy classes of closed subgroups of a compact group, which has been introduced to obtain the isotropy classes of a direct sum of representations E1 $\oplus$ E2, if the isotropy classes are known for each factor E1, E2. This allows, in particular, to compute the isotropy classes of any reducible representation, once one knows the decomposition into irreducible factors and the symmetry classes for the irreducible factors. In the specific case of the three dimensional orthogonal group O(3), clips between some types of subgroups of O(3) have already been calculated. However, until now, clips between type II and type III subgroups were missing. Those are encountered in 3D coupled constitutive laws. In this paper, we complete the clips tables by computing the missing clips. As an application, we obtain 25 isotropy classes for the standard O(3) representation on the full 3D Piezoelectric law, which involves the three Elasticity, Piezoelectricity and Permittivity constitutive tensors.
