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arXiv · 2201.13091

Helicoids and vortices

Hao Chen·Daniel Freese
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Abstract

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 2D 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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BibTeXRIS

Hao Chen, Daniel Freese. 2022-01-31. Helicoids and vortices. https://doi.org/10.1098/rspa.2022.0431

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