Fractal bodies invisible in 2 and 3 directions

Bibliographic Details
Main Author: Plakhov, Alexander
Publication Date: 2013
Other Authors: Roshchina, Vera
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/15146
Summary: We study the problem of invisibility for bodies with a mirror surface in the framework of geometrical optics. We show that for any two given directions it is possible to construct a two-dimensional fractal body invisible in these directions. Moreover, there exists a three-dimensional fractal body invisible in three orthogonal directions. The work continues the previous study in [1, 12], where two-dimensional bodies invisible in one direction and three dimensional bodies invisible in one and two orthogonal directions were constructed.
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spelling Fractal bodies invisible in 2 and 3 directionsInvisibility in geometrical opticsProblems of minimal resistanceBilliardsWe study the problem of invisibility for bodies with a mirror surface in the framework of geometrical optics. We show that for any two given directions it is possible to construct a two-dimensional fractal body invisible in these directions. Moreover, there exists a three-dimensional fractal body invisible in three orthogonal directions. The work continues the previous study in [1, 12], where two-dimensional bodies invisible in one direction and three dimensional bodies invisible in one and two orthogonal directions were constructed.American Institute of Mathematical Sciences (AIMS)2016-02-04T18:18:04Z2013-04-01T00:00:00Z2013-04info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/15146eng1078-094710.3934/dcds.2013.33.1615Plakhov, AlexanderRoshchina, Verainfo: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:10773/15146Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T13:51:28.705179Repositórios 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 Fractal bodies invisible in 2 and 3 directions
title Fractal bodies invisible in 2 and 3 directions
spellingShingle Fractal bodies invisible in 2 and 3 directions
Plakhov, Alexander
Invisibility in geometrical optics
Problems of minimal resistance
Billiards
title_short Fractal bodies invisible in 2 and 3 directions
title_full Fractal bodies invisible in 2 and 3 directions
title_fullStr Fractal bodies invisible in 2 and 3 directions
title_full_unstemmed Fractal bodies invisible in 2 and 3 directions
title_sort Fractal bodies invisible in 2 and 3 directions
author Plakhov, Alexander
author_facet Plakhov, Alexander
Roshchina, Vera
author_role author
author2 Roshchina, Vera
author2_role author
dc.contributor.author.fl_str_mv Plakhov, Alexander
Roshchina, Vera
dc.subject.por.fl_str_mv Invisibility in geometrical optics
Problems of minimal resistance
Billiards
topic Invisibility in geometrical optics
Problems of minimal resistance
Billiards
description We study the problem of invisibility for bodies with a mirror surface in the framework of geometrical optics. We show that for any two given directions it is possible to construct a two-dimensional fractal body invisible in these directions. Moreover, there exists a three-dimensional fractal body invisible in three orthogonal directions. The work continues the previous study in [1, 12], where two-dimensional bodies invisible in one direction and three dimensional bodies invisible in one and two orthogonal directions were constructed.
publishDate 2013
dc.date.none.fl_str_mv 2013-04-01T00:00:00Z
2013-04
2016-02-04T18:18:04Z
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/10773/15146
url http://hdl.handle.net/10773/15146
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1078-0947
10.3934/dcds.2013.33.1615
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 American Institute of Mathematical Sciences (AIMS)
publisher.none.fl_str_mv American Institute of Mathematical Sciences (AIMS)
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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repository.mail.fl_str_mv info@rcaap.pt
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