Optimal roughening of convex bodies

Bibliographic Details
Main Author: Plakhov, Alexander
Publication Date: 2012
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/15147
Summary: A body moves in a rarefied medium composed of point particles at rest. The particles make elastic reflections when colliding with the body surface, and do not interact with each other. We consider a generalization of Newton’s minimal resistance problem: given two bounded convex bodies C1 and C2 such that C1 ⊂ C2 ⊂ R3 and ∂C1 ∩ ∂C2 = ∅, minimize the resistance in the class of connected bodies B such that C1 ⊂ B ⊂ C2. We prove that the infimum of resistance is zero; that is, there exist ”almost perfectly streamlined” bodies.
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spelling Optimal roughening of convex bodiesBilliardsShape optimizationProblems of minimal resistanceNewtonian aerodynamicsRough surfaceA body moves in a rarefied medium composed of point particles at rest. The particles make elastic reflections when colliding with the body surface, and do not interact with each other. We consider a generalization of Newton’s minimal resistance problem: given two bounded convex bodies C1 and C2 such that C1 ⊂ C2 ⊂ R3 and ∂C1 ∩ ∂C2 = ∅, minimize the resistance in the class of connected bodies B such that C1 ⊂ B ⊂ C2. We prove that the infimum of resistance is zero; that is, there exist ”almost perfectly streamlined” bodies.University of Toronto Press2016-02-05T10:41:34Z2012-01-01T00:00:00Z2012info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/15147eng0008-414X10.4153/CJM-2011-070-9Plakhov, Alexanderinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T03:56:06Zoai:ria.ua.pt:10773/15147Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T13:51:28.757711Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Optimal roughening of convex bodies
title Optimal roughening of convex bodies
spellingShingle Optimal roughening of convex bodies
Plakhov, Alexander
Billiards
Shape optimization
Problems of minimal resistance
Newtonian aerodynamics
Rough surface
title_short Optimal roughening of convex bodies
title_full Optimal roughening of convex bodies
title_fullStr Optimal roughening of convex bodies
title_full_unstemmed Optimal roughening of convex bodies
title_sort Optimal roughening of convex bodies
author Plakhov, Alexander
author_facet Plakhov, Alexander
author_role author
dc.contributor.author.fl_str_mv Plakhov, Alexander
dc.subject.por.fl_str_mv Billiards
Shape optimization
Problems of minimal resistance
Newtonian aerodynamics
Rough surface
topic Billiards
Shape optimization
Problems of minimal resistance
Newtonian aerodynamics
Rough surface
description A body moves in a rarefied medium composed of point particles at rest. The particles make elastic reflections when colliding with the body surface, and do not interact with each other. We consider a generalization of Newton’s minimal resistance problem: given two bounded convex bodies C1 and C2 such that C1 ⊂ C2 ⊂ R3 and ∂C1 ∩ ∂C2 = ∅, minimize the resistance in the class of connected bodies B such that C1 ⊂ B ⊂ C2. We prove that the infimum of resistance is zero; that is, there exist ”almost perfectly streamlined” bodies.
publishDate 2012
dc.date.none.fl_str_mv 2012-01-01T00:00:00Z
2012
2016-02-05T10:41:34Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/15147
url http://hdl.handle.net/10773/15147
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0008-414X
10.4153/CJM-2011-070-9
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv University of Toronto Press
publisher.none.fl_str_mv University of Toronto Press
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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