Singular cotangent models and complexity in fluids with dissipation

In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a b-cotangent model. We provide physical interpretations of the singular symplectic geometry underlying in b-cotangent bundles featuring two models: the canonical (or non-twis...

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Detalles Bibliográficos
Autores: Coquinot, Baptiste, Mir Garcia, Pau|||0000-0002-6761-2445, Miranda Galcerán, Eva|||0000-0001-9518-5279
Tipo de recurso: informe técnico
Fecha de publicación:2022
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/370090
Acceso en línea:https://hdl.handle.net/2117/370090
Access Level:acceso abierto
Palabra clave:Hamilton spaces
Differential topology
Symplectic geometry
Fluid dynamics
Hamilton, Espais de
Topologia diferencial
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
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spelling Singular cotangent models and complexity in fluids with dissipationCoquinot, BaptisteMir Garcia, Pau|||0000-0002-6761-2445Miranda Galcerán, Eva|||0000-0001-9518-5279Hamilton spacesDifferential topologySymplectic geometryFluid dynamicsHamilton, Espais deTopologia diferencialÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencialIn this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a b-cotangent model. We provide physical interpretations of the singular symplectic geometry underlying in b-cotangent bundles featuring two models: the canonical (or non-twisted) model and the twisted one. The first one models systems on manifolds with boundary and the twisted model represents Hamiltonian systems where the singularity of the system is in the fiber of the bundle. The twisted cotangent model includes (for linear potentials) the case of fluids with dissipation. We relate the complexity of the fluids in terms of the Reynolds number and the (non)-existence of cotangent lift dynamics. We also discuss more general physical interpretations of the twisted and non-twisted b-symplectic models. These models offer a Hamiltonian formulation for systems which are dissipative, extending the horizons of Hamiltonian dynamics and opening a new approach to study non-conservative systems.20222022-06-1720222022-07-13reporthttp://purl.org/coar/resource_type/c_93fcAOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/370090reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3700902026-05-27T15:37:01Z
dc.title.none.fl_str_mv Singular cotangent models and complexity in fluids with dissipation
title Singular cotangent models and complexity in fluids with dissipation
spellingShingle Singular cotangent models and complexity in fluids with dissipation
Coquinot, Baptiste
Hamilton spaces
Differential topology
Symplectic geometry
Fluid dynamics
Hamilton, Espais de
Topologia diferencial
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
title_short Singular cotangent models and complexity in fluids with dissipation
title_full Singular cotangent models and complexity in fluids with dissipation
title_fullStr Singular cotangent models and complexity in fluids with dissipation
title_full_unstemmed Singular cotangent models and complexity in fluids with dissipation
title_sort Singular cotangent models and complexity in fluids with dissipation
dc.creator.none.fl_str_mv Coquinot, Baptiste
Mir Garcia, Pau|||0000-0002-6761-2445
Miranda Galcerán, Eva|||0000-0001-9518-5279
author Coquinot, Baptiste
author_facet Coquinot, Baptiste
Mir Garcia, Pau|||0000-0002-6761-2445
Miranda Galcerán, Eva|||0000-0001-9518-5279
author_role author
author2 Mir Garcia, Pau|||0000-0002-6761-2445
Miranda Galcerán, Eva|||0000-0001-9518-5279
author2_role author
author
dc.subject.none.fl_str_mv Hamilton spaces
Differential topology
Symplectic geometry
Fluid dynamics
Hamilton, Espais de
Topologia diferencial
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
topic Hamilton spaces
Differential topology
Symplectic geometry
Fluid dynamics
Hamilton, Espais de
Topologia diferencial
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
description In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a b-cotangent model. We provide physical interpretations of the singular symplectic geometry underlying in b-cotangent bundles featuring two models: the canonical (or non-twisted) model and the twisted one. The first one models systems on manifolds with boundary and the twisted model represents Hamiltonian systems where the singularity of the system is in the fiber of the bundle. The twisted cotangent model includes (for linear potentials) the case of fluids with dissipation. We relate the complexity of the fluids in terms of the Reynolds number and the (non)-existence of cotangent lift dynamics. We also discuss more general physical interpretations of the twisted and non-twisted b-symplectic models. These models offer a Hamiltonian formulation for systems which are dissipative, extending the horizons of Hamiltonian dynamics and opening a new approach to study non-conservative systems.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-06-17
2022
2022-07-13
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/370090
url https://hdl.handle.net/2117/370090
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
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
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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