КФУ. Карточка публикации. Minimal surfaces on mirror-symmetric frames: A fluid dynamics analogy

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MINIMAL SURFACES ON MIRROR-SYMMETRIC FRAMES: A FLUID DYNAMICS ANALOGY

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2020

Язык

английский

Авторы, сотрудники КФУ

Алимов Марс Мясумович, автор

Библиографическое описание на языке оригинала

Alimov M.M, Bazilevsky A.V, Kornev K.G., Minimal surfaces on mirror-symmetric frames: A fluid dynamics analogy//Journal of Fluid Mechanics. - 2020. - Vol. 897. - Art. № A36.

Аннотация

Chaplygin's hodograph method of classical fluid mechanics is applied to explicitly solve the Plateau problem of finding minimal surfaces. The minimal surfaces are formed between two mirror-symmetric polygonal frames having a common axis of symmetry. Two classes of minimal surfaces are found: the class of regular surfaces continuously connecting the supporting frames forming a tube with complex shape; and the class of singular surfaces which have a partitioning film closing the tube in between. As an illustration of the general solution, minimal surfaces supported by triangular frames are fully described. The theory is experimentally validated using soap films. The general solution is compared with the known particular solutions obtained by the Weierstrass inverse method.

Ключевые слова

minimal surfaces, complex-valued functions, hodograph method

Название журнала

Journal of Fluid Mechanics

URL

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85087613683&doi=10.1017%2fjfm.2020.391&partnerID=40&md5=5fba8ec397b2e1e6ba29bb79afbe63f5

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https://repository.kpfu.ru/?p_id=237564

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Алимов Марс Мясумович	ru_RU
dc.date.accessioned	2020-01-01T00:00:00Z	ru_RU
dc.date.available	2020-01-01T00:00:00Z	ru_RU
dc.date.issued	2020	ru_RU
dc.identifier.citation	Alimov M.M, Bazilevsky A.V, Kornev K.G., Minimal surfaces on mirror-symmetric frames: A fluid dynamics analogy//Journal of Fluid Mechanics. - 2020. - Vol. 897. - Art. № A36.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/?p_id=237564	ru_RU
dc.description.abstract	Journal of Fluid Mechanics	ru_RU
dc.description.abstract	Chaplygin's hodograph method of classical fluid mechanics is applied to explicitly solve the Plateau problem of finding minimal surfaces. The minimal surfaces are formed between two mirror-symmetric polygonal frames having a common axis of symmetry. Two classes of minimal surfaces are found: the class of regular surfaces continuously connecting the supporting frames forming a tube with complex shape; and the class of singular surfaces which have a partitioning film closing the tube in between. As an illustration of the general solution, minimal surfaces supported by triangular frames are fully described. The theory is experimentally validated using soap films. The general solution is compared with the known particular solutions obtained by the Weierstrass inverse method.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	minimal surfaces	ru_RU
dc.subject	complex-valued functions	ru_RU
dc.subject	hodograph method	ru_RU
dc.title	Minimal surfaces on mirror-symmetric frames: A fluid dynamics analogy	ru_RU
dc.type	Статьи в зарубежных журналах и сборниках	ru_RU