An inverse problem of Newtonian aerodynamics
Autor(a) principal: | |
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Data de Publicação: | 2010 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/15149 |
Resumo: | We consider a rarefied medium in Rd, d ≥ 2 consisting of non-interacting point masses moving at unit velocity in all directions. Given the density of velocity distribution, one easily calculates the pressure created by the medium in any direction. We then consider the inverse problem: given the pressure distribution f : Sd−1 →R+, determine the density ρ : Sd−1 →R+. Assuming that the reflection of medium particles by obstacles is elastic, we show that the solution for the inverse problem is generally non-unique, derive exact inversion formulas, and state necessary and sufficient conditions for existence of a solution. We also present arguments indicating that the inversion is typically unique in the case of non-elastic reflection, and derive exact inversion formulas in a special case of such reflection. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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An inverse problem of Newtonian aerodynamicsInverse problemRarefied flowFourier seriesSpherical convolution operatorsFourier-Laplace multipliersSpherical harmonicsWe consider a rarefied medium in Rd, d ≥ 2 consisting of non-interacting point masses moving at unit velocity in all directions. Given the density of velocity distribution, one easily calculates the pressure created by the medium in any direction. We then consider the inverse problem: given the pressure distribution f : Sd−1 →R+, determine the density ρ : Sd−1 →R+. Assuming that the reflection of medium particles by obstacles is elastic, we show that the solution for the inverse problem is generally non-unique, derive exact inversion formulas, and state necessary and sufficient conditions for existence of a solution. We also present arguments indicating that the inversion is typically unique in the case of non-elastic reflection, and derive exact inversion formulas in a special case of such reflection.2016-02-05T11:14:20Z2010-01-01T00:00:00Z2010info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/15149eng2041-3165Plakhov, AlexanderSamko, Stefaninfo: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:RCAAP2024-02-22T11:27:56Zoai:ria.ua.pt:10773/15149Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:34.177752Repositório 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 |
An inverse problem of Newtonian aerodynamics |
title |
An inverse problem of Newtonian aerodynamics |
spellingShingle |
An inverse problem of Newtonian aerodynamics Plakhov, Alexander Inverse problem Rarefied flow Fourier series Spherical convolution operators Fourier-Laplace multipliers Spherical harmonics |
title_short |
An inverse problem of Newtonian aerodynamics |
title_full |
An inverse problem of Newtonian aerodynamics |
title_fullStr |
An inverse problem of Newtonian aerodynamics |
title_full_unstemmed |
An inverse problem of Newtonian aerodynamics |
title_sort |
An inverse problem of Newtonian aerodynamics |
author |
Plakhov, Alexander |
author_facet |
Plakhov, Alexander Samko, Stefan |
author_role |
author |
author2 |
Samko, Stefan |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Plakhov, Alexander Samko, Stefan |
dc.subject.por.fl_str_mv |
Inverse problem Rarefied flow Fourier series Spherical convolution operators Fourier-Laplace multipliers Spherical harmonics |
topic |
Inverse problem Rarefied flow Fourier series Spherical convolution operators Fourier-Laplace multipliers Spherical harmonics |
description |
We consider a rarefied medium in Rd, d ≥ 2 consisting of non-interacting point masses moving at unit velocity in all directions. Given the density of velocity distribution, one easily calculates the pressure created by the medium in any direction. We then consider the inverse problem: given the pressure distribution f : Sd−1 →R+, determine the density ρ : Sd−1 →R+. Assuming that the reflection of medium particles by obstacles is elastic, we show that the solution for the inverse problem is generally non-unique, derive exact inversion formulas, and state necessary and sufficient conditions for existence of a solution. We also present arguments indicating that the inversion is typically unique in the case of non-elastic reflection, and derive exact inversion formulas in a special case of such reflection. |
publishDate |
2010 |
dc.date.none.fl_str_mv |
2010-01-01T00:00:00Z 2010 2016-02-05T11:14:20Z |
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/10773/15149 |
url |
http://hdl.handle.net/10773/15149 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2041-3165 |
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.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 |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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 |
repository.mail.fl_str_mv |
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1799137555839451136 |