Hyperuniformity of quasiperiodic tilings generated by continued fractions

[EN] Hyperuniformity is a property of certain heteroneous media in which density fluctuations in the long wavelength range decay to zero. In reciprocal space this behavior translates into a decay of Fourier intensities in the range near small wavenumbers. In this paper quasiperiodic tilings construc...

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Autores: Lázaro, Mario|||0000-0003-4949-8295, García-Raffi, L. M.|||0000-0003-3985-8453
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/221137
Acceso en línea:https://riunet.upv.es/handle/10251/221137
Access Level:acceso abierto
Palabra clave:Hyperuniformity
Quasiperiodic tilings
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spelling Hyperuniformity of quasiperiodic tilings generated by continued fractionsLázaro, Mario|||0000-0003-4949-8295García-Raffi, L. M.|||0000-0003-3985-8453HyperuniformityQuasiperiodic tilings[EN] Hyperuniformity is a property of certain heteroneous media in which density fluctuations in the long wavelength range decay to zero. In reciprocal space this behavior translates into a decay of Fourier intensities in the range near small wavenumbers. In this paper quasiperiodic tilings constructed by word concatenation are under study. The lattice is generated from a parameter given by its continued fraction so that quasiperiodicity emerges for infinite when irrational generators are into consideration. Numerical simulations show a quite regular quadratic decay of Fourier intensities, regardless of the number considered for the generator parameter, which leads us to formulate the hypothesis that this type of media is strongly hyperuniform of order 3. Theoretical derivations show that the density fluctuations scale in the same proportion as the wavenumbers. Furthermore, it is rigorously proved that the structure factor decays around the origin according to the pattern $S(k) \sim k^4$. This result is validated with several numerical examples with different generating continued fractions.L.M.G.-R. and M.L. are grateful for the partial support under Grant No. PID2020-112759GB-I00 funded by MCIN/AEI/10.13039/501100011033. L.M.G.-R. acknowledge support from Grant No. CIAICO/2023/052 of the "Programa para la promocion de la investigacion cientifica,el desarrollo tecnologico y la innovacion en la Comunitat Valenciana" funded by Generalitat Valenciana. M.L. is grateful for the support of Grant No. CIGE/2021/141 funded by Generalitat Valenciana (Emerging Research Groups).American Physical SocietyDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialDepartamento de Mecánica de los Medios Continuos y Teoría de EstructurasInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería de Caminos, Canales y PuertosGENERALITAT VALENCIANAAGENCIA ESTATAL DE INVESTIGACIONRepositorio Institucional de la Universitat Politècnica de València Riunet20242024-01-03journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/221137reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengGeneralitat Valenciana https://doi.org/10.13039/501100003359 CIGE%2F2021%2F141 ESTUDIO NUMÉRICO Y EXPERIMENTAL DE METAESTRUCTURAS AMORTIGUADASAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 PID2020-112759GB-I00 METAESTRUCTURAS HIPERUNIFORMESGeneralitat Valenciana https://doi.org/10.13039/501100003359 CIAICO%2F2022%2F052 METASUPERFICIES PARA EL CONTROL DE ULTRASONIDOS: FORMACION DE HACES, FOCALIZACION, ABSORCION Y DIFUSIONGeneralitat Valenciana https://doi.org/10.13039/501100003359 CIAICO%2F2023%2F052open accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2211372026-06-13T07:49:27Z
dc.title.none.fl_str_mv Hyperuniformity of quasiperiodic tilings generated by continued fractions
title Hyperuniformity of quasiperiodic tilings generated by continued fractions
spellingShingle Hyperuniformity of quasiperiodic tilings generated by continued fractions
Lázaro, Mario|||0000-0003-4949-8295
Hyperuniformity
Quasiperiodic tilings
title_short Hyperuniformity of quasiperiodic tilings generated by continued fractions
title_full Hyperuniformity of quasiperiodic tilings generated by continued fractions
title_fullStr Hyperuniformity of quasiperiodic tilings generated by continued fractions
title_full_unstemmed Hyperuniformity of quasiperiodic tilings generated by continued fractions
title_sort Hyperuniformity of quasiperiodic tilings generated by continued fractions
dc.creator.none.fl_str_mv Lázaro, Mario|||0000-0003-4949-8295
García-Raffi, L. M.|||0000-0003-3985-8453
author Lázaro, Mario|||0000-0003-4949-8295
author_facet Lázaro, Mario|||0000-0003-4949-8295
García-Raffi, L. M.|||0000-0003-3985-8453
author_role author
author2 García-Raffi, L. M.|||0000-0003-3985-8453
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Departamento de Mecánica de los Medios Continuos y Teoría de Estructuras
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería de Caminos, Canales y Puertos
GENERALITAT VALENCIANA
AGENCIA ESTATAL DE INVESTIGACION
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Hyperuniformity
Quasiperiodic tilings
topic Hyperuniformity
Quasiperiodic tilings
description [EN] Hyperuniformity is a property of certain heteroneous media in which density fluctuations in the long wavelength range decay to zero. In reciprocal space this behavior translates into a decay of Fourier intensities in the range near small wavenumbers. In this paper quasiperiodic tilings constructed by word concatenation are under study. The lattice is generated from a parameter given by its continued fraction so that quasiperiodicity emerges for infinite when irrational generators are into consideration. Numerical simulations show a quite regular quadratic decay of Fourier intensities, regardless of the number considered for the generator parameter, which leads us to formulate the hypothesis that this type of media is strongly hyperuniform of order 3. Theoretical derivations show that the density fluctuations scale in the same proportion as the wavenumbers. Furthermore, it is rigorously proved that the structure factor decays around the origin according to the pattern $S(k) \sim k^4$. This result is validated with several numerical examples with different generating continued fractions.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-01-03
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/221137
url https://riunet.upv.es/handle/10251/221137
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Generalitat Valenciana https://doi.org/10.13039/501100003359 CIGE%2F2021%2F141 ESTUDIO NUMÉRICO Y EXPERIMENTAL DE METAESTRUCTURAS AMORTIGUADAS
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 PID2020-112759GB-I00 METAESTRUCTURAS HIPERUNIFORMES
Generalitat Valenciana https://doi.org/10.13039/501100003359 CIAICO%2F2022%2F052 METASUPERFICIES PARA EL CONTROL DE ULTRASONIDOS: FORMACION DE HACES, FOCALIZACION, ABSORCION Y DIFUSION
Generalitat Valenciana https://doi.org/10.13039/501100003359 CIAICO%2F2023%2F052
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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