Helicoids and vortices

被引:2
|
作者
Chen, Hao [1 ,2 ]
Freese, Daniel [3 ]
机构
[1] Georg August Univ Gottingen, Inst Numer & Angew Math, D-37085 Gottingen, Germany
[2] ShanghaiTech Univ, Inst Math Sci, Shanghai 201210, Peoples R China
[3] Indiana Univ, Dept Math, Bloomington, IN 47405 USA
关键词
minimal surfaces; vortex dynamics; gluing construction; EMBEDDED MINIMAL-SURFACES; GROSS-PITAEVSKII EQUATION; POINT VORTICES; STABILITY; POLYNOMIALS; EXISTENCE; MOTION; RINGS;
D O I
10.1098/rspa.2022.0431
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 point out an interesting connection between fluid dynamics and minimal surface theory: When gluing helicoids into a minimal surface, the limit positions of the helicoids correspond to a 'vortex crystal', an equilibrium of point vortices in two-dimensional fluid that move together as a rigid body. While vortex crystals have been studied for almost 150 years, the gluing construction of minimal surfaces is relatively new. As a consequence of the connection, we obtain many new minimal surfaces and some new vortex crystals by simply comparing notes.
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页数:18
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