受静电力作用的静态肥皂膜桥：平衡情形
Stationary Soap Film Bridge Subjected to an Electrostatic Force: The Balanced Case
AI总结：
本文解析研究了受静电力的静态肥皂膜桥自由边界问题，构造了局部静态解分支，证明了稳定性转变的参数阈值，并得出膜随静电力增强单调向外偏转的结论。
摘要：
我们解析地研究了一个描述受静电力作用的肥皂膜桥的静态自由边界问题。从一个圆柱体出发，若其表面张力与静电力完美平衡，肥皂膜便形成，我们构造了静态解的一个局部分支。然后，我们证明存在一个特征模型参数的尖锐阈值，在此处该分支的稳定性表现由稳定转变为不稳定。最后，我们表明，若静电力强度增加，肥皂膜会单调向外偏转。除严格结果外，本文还讨论了静电力的一种可能平衡效应。
英文摘要：
We analytically study a stationary free boundary problem describing a soap film bridge subjected to an electrostatic force. Starting from a cylinder that the soap film forms if its surface tension and the electrostatic force are perfectly balanced, we construct a local branch of stationary solutions. Then, we prove that there is a sharp threshold value for a characteristic model parameter at which the stability behaviour of this branch switches from stable to unstable. Finally, we show that the soap film deflects monotonically outwards if the strength of the electrostatic force is increased. Besides rigorous results, we also discuss a possible balancing effect of the electrostatic force.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
