Inclusions of General Shapes Having Constant Field Inside the Core and NonElliptical Neutral Coated Inclusions With Anisotropic Conductivity
Inclusions of General Shapes Having Constant Field Inside the Core and NonElliptical Neutral Coated Inclusions With Anisotropic Conductivity
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DOI：
10.1137/19m1246225
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发表时间：
2018-09
期刊：
影响因子：
--
通讯作者：
Mikyoung Lim;G. Milton
中科院分区：
文献类型：
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作者：
Mikyoung Lim;G. Milton
对于一定形状的夹杂物，夹杂物内部的场在一定的边界条件下是均匀的。我们提供了一个建设计划的一般形状的夹杂物具有这样的均匀性在两个维度上的基础上的保角映射技术的潜在问题。利用这种复分析方法，我们还设计了具有各向异性电导率的非椭圆中性涂层夹杂。中性涂层夹杂物插入均匀基体时，不会扰动背景均匀场。虽然各种形状的涂层包裹体对单个场是中性的，但只有同心椭圆或共焦椭圆体对所有均匀场都是中性的。本文介绍了我们的工作有关建设的非椭圆形涂层夹杂物的各向异性电导率在两个维度是中性的所有均匀的领域，其中分配的通量条件的核心的边界取决于所施加的背景场。利用这些中性夹杂物，我们得到了圆柱形的中性夹杂物在三维空间中，没有通量施加到边界的核心和各向异性的电导率函数的外壳根据背景均匀场。
For certain shapes of inclusions embedded in a body, the field inside the inclusion is uniform for some boundary condition. We provide a construction scheme for inclusions of general shapes having such a uniformity property in two dimensions based on the conformal mapping technique for the potential problem. Using this complex analysis method, we also design non-elliptical neutral coated inclusions with anisotropic conductivity. Neutral coated inclusions do not perturb a background uniform field when they are inserted into a homogeneous matrix. Although coated inclusions of various shapes are neutral to a single field, only concentric ellipses or confocal ellipsoids can be neutral to all uniform fields. This paper presents our work relating to the construction of non-elliptical coated inclusions with anisotropic conductivity in two dimensions that are neutral to all uniform fields, where the assignment of the flux condition on the boundary of the core depends on the applied background field. Using these neutral inclusions, we obtain cylindrical neutral inclusions in three dimensions, with no flux applied to the boundary of the core and with the anisotropic conductivity function of the shell given in accordance with the background uniform field.