电介质
极限(数学)
物理
常量(计算机编程)
凝聚态物理
几何学
离子
领域(数学)
材料科学
数学分析
数学
量子力学
计算机科学
程序设计语言
纯数学
出处
期刊:Siam Journal on Applied Mathematics
[Society for Industrial and Applied Mathematics]
日期:1992-10-01
卷期号:52 (5): 1391-1404
被引量:102
摘要
This paper is devoted to the study of the electrostatic potential in a composite dielectric medium. The geometry consists of a membrane-like layer with one dielectric constant, perforated by a hole filled with a material with a different dielectric constant. The field is due to a known, but otherwise arbitrary, distribution $f(z)$ of charges in the hole, where z is the coordinate along the axis of the hole. The induced surface charge at the interface between the two media is found as an asymptotic series in the small aspect ratio $\alpha $ of the hole, for the case in which $f(z)$ vanishes at the endpoints and is $C^1 $. This analysis reveals the existence of a distinguished limit in which the small ratio of the permittivities $\epsilon $ is proportional to $ - \alpha ^2 $ In $\alpha $.
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