Plateau's rotating drops and rotational figures of equilibrium

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Elms, Jeffrey¹  Hynd, Ryan²  Lopez, Roberto³  McCuan, John³ 

[1] Google, 1600 Amphitheatre Pkwy, Mountain View, CA 94043 USA

[2] Univ Penn, Dept Math, 209 South 33rd St, Philadelphia, PA 19104 USA

[3] Georgia Tech, Sch Math, 686 Cherry St, Atlanta, GA 30332 USA

关键词: Rotating drops;    Mean curvature;    Plateau;    Delaunay;   

DOI  :  10.1016/j.jmaa.2016.08.014

来源: Elsevier

【 摘 要 】

We give a detailed classification of all rotationally symmetric figures of equilibrium corresponding to rotating liquid masses subject to surface tension. When the rotation rate is zero, these shapes were studied by Delaunay who found six different qualitative types of complete connected interfaces (spheres, cylinders, unduloids, nodoids, catenoids, and planes). We find twenty-six qualitatively different interfaces providing a complete picture of symmetric equilibrium shapes, some of which have been studied by other authors. In particular, combining our work with that of Beer, Chandrasekhar, Gulliver, Smith, and Ross, we conclude that every compact equilibrium is in either a smooth connected one parameter family of spheroids or a smooth connected one parameter family of tori (possibly immersed in either case). (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free