Combinatorial algebraic approach for modified second-generation time-delay interferometry
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1103/PhysRevD.107.024042 http://hdl.handle.net/11449/246767 |
Resumo: | We generalize the combinatorial algebraic approach first proposed by Dhurandhar et al. to construct various classes of modified second-generation time-delay interferometry (TDI) solutions. The main idea behind the original algorithm is to enumerate, in a given order, a specific type of commutator between two monomials defined by the products of particular time-displacement operators. On the one hand, the enumeration process can be implemented using the properties of the commutative ring and the relevant equation for the TDI solution. On the other hand, these commutators are shown to vanish if we only keep up the first-order contributions regarding the rate of change of armlengths. In other words, each commutator furnishes a valid TDI solution pertaining to the given type of modified second-generation combinations. In this work, Dhurandhar's algorithm, which only involved time-delay operators and was primarily applied to Michelson-type solutions, is extended by introducing the time-advance ones and then utilized to seek combinations of the Beacon, Relay, Monitor, Sagnac, and fully symmetric Sagnac types. We discuss the relation between the present scheme's solutions and those obtained by the geometric TDI approach, a well-known method of exhaustion of virtual optical paths. In particular, we report the results on novel Sagnac-inspired solutions that cannot be straightforwardly obtained using the geometric TDI algorithm. The average response functions, floor noise power spectral densities, and sensitivity functions are evaluated for the obtained solutions. |
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Combinatorial algebraic approach for modified second-generation time-delay interferometryWe generalize the combinatorial algebraic approach first proposed by Dhurandhar et al. to construct various classes of modified second-generation time-delay interferometry (TDI) solutions. The main idea behind the original algorithm is to enumerate, in a given order, a specific type of commutator between two monomials defined by the products of particular time-displacement operators. On the one hand, the enumeration process can be implemented using the properties of the commutative ring and the relevant equation for the TDI solution. On the other hand, these commutators are shown to vanish if we only keep up the first-order contributions regarding the rate of change of armlengths. In other words, each commutator furnishes a valid TDI solution pertaining to the given type of modified second-generation combinations. In this work, Dhurandhar's algorithm, which only involved time-delay operators and was primarily applied to Michelson-type solutions, is extended by introducing the time-advance ones and then utilized to seek combinations of the Beacon, Relay, Monitor, Sagnac, and fully symmetric Sagnac types. We discuss the relation between the present scheme's solutions and those obtained by the geometric TDI approach, a well-known method of exhaustion of virtual optical paths. In particular, we report the results on novel Sagnac-inspired solutions that cannot be straightforwardly obtained using the geometric TDI algorithm. The average response functions, floor noise power spectral densities, and sensitivity functions are evaluated for the obtained solutions.MOE Key Laboratory of Fundamental Physical Quantities Measurement Hubei Key Laboratory of Gravitation and Quantum Physics PGMF School of Physics Huazhong University of Science and TechnologyEscola de Engenharia de Lorena Universidade de São Paulo, SPFaculdade de Engenharia de Guaratinguetá Universidade Estadual Paulista, SPCenter for Gravitation and Cosmology College of Physical Science and Technology Yangzhou UniversityFaculdade de Engenharia de Guaratinguetá Universidade Estadual Paulista, SPHuazhong University of Science and TechnologyUniversidade de São Paulo (USP)Universidade Estadual Paulista (UNESP)Yangzhou UniversityWu, Zhang-QiWang, Pan-PanQian, Wei-Liang [UNESP]Shao, Cheng-Gang2023-07-29T12:49:55Z2023-07-29T12:49:55Z2023-01-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevD.107.024042Physical Review D, v. 107, n. 2, 2023.2470-00292470-0010http://hdl.handle.net/11449/24676710.1103/PhysRevD.107.0240422-s2.0-85147433349Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review Dinfo:eu-repo/semantics/openAccess2023-07-29T12:49:56Zoai:repositorio.unesp.br:11449/246767Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:33:50.323186Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Combinatorial algebraic approach for modified second-generation time-delay interferometry |
title |
Combinatorial algebraic approach for modified second-generation time-delay interferometry |
spellingShingle |
Combinatorial algebraic approach for modified second-generation time-delay interferometry Wu, Zhang-Qi |
title_short |
Combinatorial algebraic approach for modified second-generation time-delay interferometry |
title_full |
Combinatorial algebraic approach for modified second-generation time-delay interferometry |
title_fullStr |
Combinatorial algebraic approach for modified second-generation time-delay interferometry |
title_full_unstemmed |
Combinatorial algebraic approach for modified second-generation time-delay interferometry |
title_sort |
Combinatorial algebraic approach for modified second-generation time-delay interferometry |
author |
Wu, Zhang-Qi |
author_facet |
Wu, Zhang-Qi Wang, Pan-Pan Qian, Wei-Liang [UNESP] Shao, Cheng-Gang |
author_role |
author |
author2 |
Wang, Pan-Pan Qian, Wei-Liang [UNESP] Shao, Cheng-Gang |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Huazhong University of Science and Technology Universidade de São Paulo (USP) Universidade Estadual Paulista (UNESP) Yangzhou University |
dc.contributor.author.fl_str_mv |
Wu, Zhang-Qi Wang, Pan-Pan Qian, Wei-Liang [UNESP] Shao, Cheng-Gang |
description |
We generalize the combinatorial algebraic approach first proposed by Dhurandhar et al. to construct various classes of modified second-generation time-delay interferometry (TDI) solutions. The main idea behind the original algorithm is to enumerate, in a given order, a specific type of commutator between two monomials defined by the products of particular time-displacement operators. On the one hand, the enumeration process can be implemented using the properties of the commutative ring and the relevant equation for the TDI solution. On the other hand, these commutators are shown to vanish if we only keep up the first-order contributions regarding the rate of change of armlengths. In other words, each commutator furnishes a valid TDI solution pertaining to the given type of modified second-generation combinations. In this work, Dhurandhar's algorithm, which only involved time-delay operators and was primarily applied to Michelson-type solutions, is extended by introducing the time-advance ones and then utilized to seek combinations of the Beacon, Relay, Monitor, Sagnac, and fully symmetric Sagnac types. We discuss the relation between the present scheme's solutions and those obtained by the geometric TDI approach, a well-known method of exhaustion of virtual optical paths. In particular, we report the results on novel Sagnac-inspired solutions that cannot be straightforwardly obtained using the geometric TDI algorithm. The average response functions, floor noise power spectral densities, and sensitivity functions are evaluated for the obtained solutions. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-07-29T12:49:55Z 2023-07-29T12:49:55Z 2023-01-15 |
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://dx.doi.org/10.1103/PhysRevD.107.024042 Physical Review D, v. 107, n. 2, 2023. 2470-0029 2470-0010 http://hdl.handle.net/11449/246767 10.1103/PhysRevD.107.024042 2-s2.0-85147433349 |
url |
http://dx.doi.org/10.1103/PhysRevD.107.024042 http://hdl.handle.net/11449/246767 |
identifier_str_mv |
Physical Review D, v. 107, n. 2, 2023. 2470-0029 2470-0010 10.1103/PhysRevD.107.024042 2-s2.0-85147433349 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Physical Review D |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128533020540928 |