KFU. Card publication. Soap film on two noncircular frames

KAZAN
FEDERAL UNIVERSITY

- RUS
- 中文
- ES

SOAP FILM ON TWO NONCIRCULAR FRAMES

Form of presentation

Articles in international journals and collections

Year of publication

2021

Язык

английский

Authors, employees of KFU

Alimov Mars Myasumovich, author

Bibliographic description in the original language

Alimov M.M, Bazilevsky A.V, Kornev K.G., Soap film on two noncircular frames//Physics of Fluids. - 2021. - Vol.33, Is.5. - Art. № 052104.

Annotation

The classical Plateau problem of finding minimal surfaces supported by two noncircular coaxial rings is studied theoretically and experimentally. Using a fluid dynamics analogy, we generalize the classical catenoid solution for a film on circular rings to the general cases of noncircular rings. Some examples of analytical solutions for elliptical, polygonal, and ovoidal rings are presented. The shapes of a tubular film and a film separated by a lamella at the wrist are obtained in an analytical form. The stability of these films is analyzed and compared with the classical catenoid. The data on critical parameters of all minimal surfaces are collected in the tables that can be used in practical applications. The theory is experimentally validated using soap films on elliptical identical frames. Moreover, the shapes of soap films on two different elliptical frames demonstrate a new feature: a flat separating lamella lying parallel to the rings was never observed in experiments. All lamellae appeared deformed suggesting the existence of a new family of minimal surfaces which does not exist in the case of frames of the same sizes.

Keywords

Plateau problem, minimal surface, complex variable

The name of the journal

Physics of Fluids

URL

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85105443653&doi=10.1063%2f5.0047461&partnerID=40&md5=df092c7a74f99dab9139befbace2cee5

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=253305&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Alimov Mars Myasumovich	ru_RU
dc.date.accessioned	2021-01-01T00:00:00Z	ru_RU
dc.date.available	2021-01-01T00:00:00Z	ru_RU
dc.date.issued	2021	ru_RU
dc.identifier.citation	Alimov M.M, Bazilevsky A.V, Kornev K.G., Soap film on two noncircular frames//Physics of Fluids. - 2021. - Vol.33, Is.5. - Art. № 052104.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=253305&p_lang=2	ru_RU
dc.description.abstract	Physics of Fluids	ru_RU
dc.description.abstract	The classical Plateau problem of finding minimal surfaces supported by two noncircular coaxial rings is studied theoretically and experimentally. Using a fluid dynamics analogy, we generalize the classical catenoid solution for a film on circular rings to the general cases of noncircular rings. Some examples of analytical solutions for elliptical, polygonal, and ovoidal rings are presented. The shapes of a tubular film and a film separated by a lamella at the wrist are obtained in an analytical form. The stability of these films is analyzed and compared with the classical catenoid. The data on critical parameters of all minimal surfaces are collected in the tables that can be used in practical applications. The theory is experimentally validated using soap films on elliptical identical frames. Moreover, the shapes of soap films on two different elliptical frames demonstrate a new feature: a flat separating lamella lying parallel to the rings was never observed in experiments. All lamellae appeared deformed suggesting the existence of a new family of minimal surfaces which does not exist in the case of frames of the same sizes.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Plateau problem	ru_RU
dc.subject	minimal surface	ru_RU
dc.subject	complex variable	ru_RU
dc.title	Soap film on two noncircular frames	ru_RU
dc.type	Articles in international journals and collections	ru_RU