Singular cotangent models 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...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/532557 |
| Acceso en línea: | http://hdl.handle.net/2072/532557 |
| Access Level: | acceso abierto |
| Palabra clave: | b-symplectic geometry Cotangent models Escape orbits Fluids with dissipation Manifold with boundary Twisted cotangent models |
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Singular cotangent models in fluids with dissipationCoquinot, B.Mir, P.Miranda, E.b-symplectic geometryCotangent modelsEscape orbitsFluids with dissipationManifold with boundaryTwisted cotangent modelsIn 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 canonical one models systems on manifolds with boundary and the twisted one represents Hamiltonian systems with a singularity on the fiber. The twisted cotangent model includes (for linear potentials) the case of fluids with dissipation. We prove (non)-existence of cotangent lift dynamics and show the existence of an infinite number of escape orbits in this model. We also discuss more general physical interpretations of the twisted and non-twisted b-symplectic models. Twisted b-symplectic models yield in a natural way escape orbits that go to the critical set. Under compactness assumptions those escape orbits are continued as singular periodic orbits in the sense of Miranda and Oms (2021) and Miranda (2020). 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. © 2023 The Author(s)Cystic Fibrosis Foundation, CFF: 100010434 LCF/BQ/DR21/11880025, MCIN/AEI/10.13039/501100011033, PID2019-103849GB-I00; Institució Catalana de Recerca i Estudis Avançats, ICREA; Agencia Estatal de Investigación, AEI: CEX2020-001084-MElsevier B.V.2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion11 p.application/pdfhttp://hdl.handle.net/2072/532557RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésPhysica D: Nonlinear PhenomenaL'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2072/5325572026-05-29T05:05:01Z |
| dc.title.none.fl_str_mv |
Singular cotangent models in fluids with dissipation |
| title |
Singular cotangent models in fluids with dissipation |
| spellingShingle |
Singular cotangent models in fluids with dissipation Coquinot, B. b-symplectic geometry Cotangent models Escape orbits Fluids with dissipation Manifold with boundary Twisted cotangent models |
| title_short |
Singular cotangent models in fluids with dissipation |
| title_full |
Singular cotangent models in fluids with dissipation |
| title_fullStr |
Singular cotangent models in fluids with dissipation |
| title_full_unstemmed |
Singular cotangent models in fluids with dissipation |
| title_sort |
Singular cotangent models in fluids with dissipation |
| dc.creator.none.fl_str_mv |
Coquinot, B. Mir, P. Miranda, E. |
| author |
Coquinot, B. |
| author_facet |
Coquinot, B. Mir, P. Miranda, E. |
| author_role |
author |
| author2 |
Mir, P. Miranda, E. |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
b-symplectic geometry Cotangent models Escape orbits Fluids with dissipation Manifold with boundary Twisted cotangent models |
| topic |
b-symplectic geometry Cotangent models Escape orbits Fluids with dissipation Manifold with boundary Twisted cotangent models |
| 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 canonical one models systems on manifolds with boundary and the twisted one represents Hamiltonian systems with a singularity on the fiber. The twisted cotangent model includes (for linear potentials) the case of fluids with dissipation. We prove (non)-existence of cotangent lift dynamics and show the existence of an infinite number of escape orbits in this model. We also discuss more general physical interpretations of the twisted and non-twisted b-symplectic models. Twisted b-symplectic models yield in a natural way escape orbits that go to the critical set. Under compactness assumptions those escape orbits are continued as singular periodic orbits in the sense of Miranda and Oms (2021) and Miranda (2020). 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. © 2023 The Author(s) |
| publishDate |
2023 |
| dc.date.none.fl_str_mv |
2023 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/2072/532557 |
| url |
http://hdl.handle.net/2072/532557 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Physica D: Nonlinear Phenomena |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
11 p. application/pdf |
| dc.publisher.none.fl_str_mv |
Elsevier B.V. |
| publisher.none.fl_str_mv |
Elsevier B.V. |
| dc.source.none.fl_str_mv |
RECERCAT (Dipòsit de la Recerca de Catalunya) reponame:Recercat. Dipósit de la Recerca de Catalunya instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
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Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| reponame_str |
Recercat. Dipósit de la Recerca de Catalunya |
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Recercat. Dipósit de la Recerca de Catalunya |
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1869405473280622592 |
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15.811543 |