Collapsing and the convex hull property in a soap film capillarity model

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-11-01 DOI:10.1016/j.anihpc.2021.02.005

Darren King, Francesco Maggi, Salvatore Stuvard

引用次数: 8

Abstract

Soap films hanging from a wire frame are studied in the framework of capillarity theory. Minimizers in the corresponding variational problem are known to consist of positive volume regions with boundaries of constant mean curvature/pressure, possibly connected by “collapsed” minimal surfaces. We prove here that collapsing only occurs if the mean curvature/pressure of the bulky regions is negative, and that, when this last property holds, the whole soap film lies in the convex hull of its boundary wire frame.

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肥皂膜毛细模型中的塌缩和凸壳性质

在毛细理论的框架下，研究了悬挂在钢丝架上的肥皂膜。在相应的变分问题中，已知最小值由具有恒定平均曲率/压力边界的正体积区域组成，可能由“塌陷”的最小曲面连接。我们在这里证明，只有当大体积区域的平均曲率/压力为负时，才会发生坍缩，并且，当最后一个性质成立时，整个肥皂膜位于其边界线框架的凸壳中。

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.