KFU. Card publication. Minimal surfaces on mirror-symmetric frames: A fluid dynamics analogy

KAZAN
FEDERAL UNIVERSITY

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

Form of presentation

Articles in international journals and collections

Year of publication

2020

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., Minimal surfaces on mirror-symmetric frames: A fluid dynamics analogy//Journal of Fluid Mechanics. - 2020. - Vol. 897. - Art. № A36.

Annotation

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.

Keywords

minimal surfaces, complex-valued functions, hodograph method

The name of the journal

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

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

https://repository.kpfu.ru/eng/?p_id=237564&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Alimov Mars Myasumovich	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/eng/?p_id=237564&p_lang=2	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	Articles in international journals and collections	ru_RU