Neutral coated inclusions of finite conductivity

被引:22
作者
Jarczyk, Pawel [1 ]
Mityushev, Vladimir [1 ]
机构
[1] Pedag Univ, Dept Comp Sci & Comp Methods, PL-30084 Krakow, Poland
来源
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2012年 / 468卷 / 2140期
关键词
coated neutral inclusion; conformal mapping; boundary value problem;
D O I
10.1098/rspa.2011.0230
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
We discuss the conductivity of two-dimensional media with coated neutral inclusions of finite conductivity. Such an inclusion, when inserted in a matrix, does not disturb the uniform external field. We are looking for shapes of the core and coating in terms of the conformal mapping omega(z) of the unit disc onto coated inclusions. The considered inverse problem is reduced to an eigenvalue problem for an integral equation containing singular integrals over a closed curve L-1 on the transformed complex plane. The conformal mapping omega(z) is constructed via eigenfunctions of the integral equation. For each fixed curve L-1, the boundary of the core is given by the curve omega(L-1). The boundary of the coating is obtained by the mapping of the unit circle. It is justified that any shaped inclusion with a smooth boundary can be made neutral by surrounding it with an appropriate coating. Shapes of the neutral inclusions are obtained in analytical form when L-1 is an ellipse.
引用
收藏
页码:954 / 970
页数:17
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