Retroreflecting curves in nonstandard analysis

Detalhes bibliográficos
Autor(a) principal: Almeida, R
Data de Publicação: 2009
Outros Autores: Neves, V, Plakhov, A
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/4153
Resumo: We present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class C(1), except for a hyper-finite set of values, such that the probability of a particle being reflected from the curve with the velocity opposite to the velocity of incidence, is infinitely close to 1. The constructed curves are of two kinds: a curve infinitely close to a straight line and a curve infinitely close to the boundary of a bounded convex set. We shall see that the latter curve is a solution of the problem: find the curve of maximum resistance infinitely close to a given curve.
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spelling Retroreflecting curves in nonstandard analysisNonstandard AnalysisRetroreflectorsMaximum resistance problemsReflectionBilliardsWe present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class C(1), except for a hyper-finite set of values, such that the probability of a particle being reflected from the curve with the velocity opposite to the velocity of incidence, is infinitely close to 1. The constructed curves are of two kinds: a curve infinitely close to a straight line and a curve infinitely close to the boundary of a bounded convex set. We shall see that the latter curve is a solution of the problem: find the curve of maximum resistance infinitely close to a given curve.National Academy of Sciences of Ukraine2011-10-13T12:07:59Z2009-01-01T00:00:00Z2009info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/4153eng1812-9471Almeida, RNeves, VPlakhov, Ainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:04:28Zoai:ria.ua.pt:10773/4153Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:42:12.157795Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Retroreflecting curves in nonstandard analysis
title Retroreflecting curves in nonstandard analysis
spellingShingle Retroreflecting curves in nonstandard analysis
Almeida, R
Nonstandard Analysis
Retroreflectors
Maximum resistance problems
Reflection
Billiards
title_short Retroreflecting curves in nonstandard analysis
title_full Retroreflecting curves in nonstandard analysis
title_fullStr Retroreflecting curves in nonstandard analysis
title_full_unstemmed Retroreflecting curves in nonstandard analysis
title_sort Retroreflecting curves in nonstandard analysis
author Almeida, R
author_facet Almeida, R
Neves, V
Plakhov, A
author_role author
author2 Neves, V
Plakhov, A
author2_role author
author
dc.contributor.author.fl_str_mv Almeida, R
Neves, V
Plakhov, A
dc.subject.por.fl_str_mv Nonstandard Analysis
Retroreflectors
Maximum resistance problems
Reflection
Billiards
topic Nonstandard Analysis
Retroreflectors
Maximum resistance problems
Reflection
Billiards
description We present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class C(1), except for a hyper-finite set of values, such that the probability of a particle being reflected from the curve with the velocity opposite to the velocity of incidence, is infinitely close to 1. The constructed curves are of two kinds: a curve infinitely close to a straight line and a curve infinitely close to the boundary of a bounded convex set. We shall see that the latter curve is a solution of the problem: find the curve of maximum resistance infinitely close to a given curve.
publishDate 2009
dc.date.none.fl_str_mv 2009-01-01T00:00:00Z
2009
2011-10-13T12:07:59Z
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/10773/4153
url http://hdl.handle.net/10773/4153
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1812-9471
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 National Academy of Sciences of Ukraine
publisher.none.fl_str_mv National Academy of Sciences of Ukraine
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
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collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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