Equivalence of Boltzmann and moment equations

The closure problem for the stellar hydrodynamic equations is studied by describing the family of phase space density functions, for which the collisionless Boltzmann equation is strictly equivalent to a finite subset of moment equations. It is proven that the redundancy of the higher-order moment e...

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Detalles Bibliográficos
Autor: Cubarsí Morera, Rafael|||0000-0001-7748-1322
Tipo de recurso: artículo
Fecha de publicación:2010
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:2117/11956
Acceso en línea:https://hdl.handle.net/2117/11956
https://dx.doi.org/10.1051/0004-6361/201014766
Access Level:acceso abierto
Palabra clave:Kinematics
Hydrodynamics
Galaxies
Statistics
Cinemàtica
Hidrodinàmica
Galàxies
Estadística
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
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oai_identifier_str oai:upcommons.upc.edu:2117/11956
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repository_id_str
spelling Equivalence of Boltzmann and moment equationsCubarsí Morera, Rafael|||0000-0001-7748-1322KinematicsHydrodynamicsGalaxiesStatisticsCinemàticaHidrodinàmicaGalàxiesEstadísticaÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciènciesThe closure problem for the stellar hydrodynamic equations is studied by describing the family of phase space density functions, for which the collisionless Boltzmann equation is strictly equivalent to a finite subset of moment equations. It is proven that the redundancy of the higher-order moment equations and the recurrence of the velocity moments are of similar nature. The method is based on the use of maximum entropy distributions, which are afterwards generalised to phase space density functions depending on any isolating integral of motion in terms of a polynomial function of degree n in the velocities. The equivalence between the moment equations up to an order n + 1 and the collisionless Boltzmann equation is proven. It is then possible to associate the complexity of a stellar system, i.e., the minimum set of velocity moments needed to describe its main kinematic features, with the number of moment equations required to model it.20102010-10-2820112011-03-18journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/11956https://dx.doi.org/10.1051/0004-6361/201014766reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/119562026-05-27T15:37:01Z
dc.title.none.fl_str_mv Equivalence of Boltzmann and moment equations
title Equivalence of Boltzmann and moment equations
spellingShingle Equivalence of Boltzmann and moment equations
Cubarsí Morera, Rafael|||0000-0001-7748-1322
Kinematics
Hydrodynamics
Galaxies
Statistics
Cinemàtica
Hidrodinàmica
Galàxies
Estadística
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
title_short Equivalence of Boltzmann and moment equations
title_full Equivalence of Boltzmann and moment equations
title_fullStr Equivalence of Boltzmann and moment equations
title_full_unstemmed Equivalence of Boltzmann and moment equations
title_sort Equivalence of Boltzmann and moment equations
dc.creator.none.fl_str_mv Cubarsí Morera, Rafael|||0000-0001-7748-1322
author Cubarsí Morera, Rafael|||0000-0001-7748-1322
author_facet Cubarsí Morera, Rafael|||0000-0001-7748-1322
author_role author
dc.subject.none.fl_str_mv Kinematics
Hydrodynamics
Galaxies
Statistics
Cinemàtica
Hidrodinàmica
Galàxies
Estadística
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
topic Kinematics
Hydrodynamics
Galaxies
Statistics
Cinemàtica
Hidrodinàmica
Galàxies
Estadística
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
description The closure problem for the stellar hydrodynamic equations is studied by describing the family of phase space density functions, for which the collisionless Boltzmann equation is strictly equivalent to a finite subset of moment equations. It is proven that the redundancy of the higher-order moment equations and the recurrence of the velocity moments are of similar nature. The method is based on the use of maximum entropy distributions, which are afterwards generalised to phase space density functions depending on any isolating integral of motion in terms of a polynomial function of degree n in the velocities. The equivalence between the moment equations up to an order n + 1 and the collisionless Boltzmann equation is proven. It is then possible to associate the complexity of a stellar system, i.e., the minimum set of velocity moments needed to describe its main kinematic features, with the number of moment equations required to model it.
publishDate 2010
dc.date.none.fl_str_mv 2010
2010-10-28
2011
2011-03-18
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://hdl.handle.net/2117/11956
https://dx.doi.org/10.1051/0004-6361/201014766
url https://hdl.handle.net/2117/11956
https://dx.doi.org/10.1051/0004-6361/201014766
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
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
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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