ABSTRACT

A two-dimensional inclusion of core–shell structure is neutral to multiple uniform fields if and only if the core and the shell are concentric disks, provided that the conductivity of the matrix is isotropic. An inclusion is said to be neutral if upon its insertion the uniform field is not perturbed at all. In this paper, we consider inclusions of core–shell structure of general shape which are weakly neutral to multiple uniform fields. An inclusion is said to be weakly neutral if the field perturbation is mild. We show, by an implicit function theorem, that if the core is a small perturbation of a disk, then we can coat it by a shell so that the resulting structure becomes weakly neutral to multiple uniform fields.

摘要

当且仅当核和壳是同心圆盘时，核壳结构的二维包含对多个均匀场是中性的，前提是基体的电导率是各向同性的。如果在插入时均匀场完全不受干扰，则称夹杂物是中性的。在本文中，我们考虑了对多个均匀场呈弱中性的一般形状核壳结构的夹杂物。如果场扰动轻微，则称夹杂物为弱中性。我们通过一个隐函数定理证明，如果核心是一个盘的小扰动，那么我们可以用一个壳覆盖它，这样得到的结构对多个均匀场变得弱中性。