Exact solutions for the insulated and perfect conductivity problems with concentric balls

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-07-12 DOI:10.3934/mine.2023060

Zhiwen Zhao

引用次数: 1

Abstract

The insulated and perfect conductivity problems arising from high-contrast composite materials are considered in all dimensions. The solution and its gradient, respectively, represent the electric potential and field. The novelty of this paper lies in finding exact solutions for the insulated and perfect conductivity problems with concentric balls. Our results show that there appears no electric field concentration for the insulated conductivity problem, while the electric field for the perfect conductivity problem exhibits sharp singularity with respect to the small distance between interfacial boundaries of the interior and exterior balls. This discrepancy reveals that concentric balls is the optimal structure of insulated composites, but not for superconducting composites.

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同心球绝缘和完全导电性问题的精确解

高对比复合材料的绝缘和完美导电性问题在各个维度上都得到了考虑。溶液及其梯度分别表示电势和场。本文的新颖之处在于找到了同心球的绝缘和完全电导率问题的精确解。结果表明，绝缘电导率问题不存在电场集中，而完美电导率问题的电场在内外球界面边界距离较小的情况下表现出明显的奇异性。这一差异表明同心球是绝缘复合材料的最佳结构，但不适用于超导复合材料。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.