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Mixing and fluid dynamics under location uncertainty

Author: Valentin ResseguierÉtienne MéminUniversité de Rennes 1.École doctorale Mathématiques, télécommunications, informatique, signal, systèmes, électronique (Rennes).Université Bretagne Loire.All authors
Publisher: 2017.
Dissertation: Thèse de doctorat : Mathématiques et applications : Rennes 1 : 2017.
Edition/Format:   Computer file : Document : Thesis/dissertation : English
Summary:
Cette thèse concerne le développement, l'extension et l'application d'une formulation stochastique des équations de la mécanique des fluides introduite par Mémin (2014). La vitesse petite échelle, non-résolue, est modélisée au moyen d'un champ aléatoire décorrélé en temps. Cela modifie l'expression de la dérivée particulaire et donc les équations de la mécanique des fluides. Les modèles qui en
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Genre/Form: Thèses et écrits académiques
Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Valentin Resseguier; Étienne Mémin; Université de Rennes 1.; École doctorale Mathématiques, télécommunications, informatique, signal, systèmes, électronique (Rennes).; Université Bretagne Loire.; Institut national de recherche en informatique et en automatique (France). Unité de recherche (Rennes, Bretagne-Atlantique).
OCLC Number: 984720209
Notes: Titre provenant de l'écran-titre.
Description: 1 online resource
Responsibility: Valentin Resseguier ; sous la direction de Étienne Mémin.

Abstract:

Cette thèse concerne le développement, l'extension et l'application d'une formulation stochastique des équations de la mécanique des fluides introduite par Mémin (2014). La vitesse petite échelle, non-résolue, est modélisée au moyen d'un champ aléatoire décorrélé en temps. Cela modifie l'expression de la dérivée particulaire et donc les équations de la mécanique des fluides. Les modèles qui en découlent sont dénommés modèles sous incertitude de position. La thèse s'articulent autour de l'étude successive de modèles réduits, de versions stochastiques du transport et de l'advection à temps long d'un champ de traceur par une vitesse mal résolue. La POD est une méthode de réduction de dimension, pour EDP, rendue possible par l'utilisation d'observations. L'EDP régissant l'évolution de la vitesse du fluide est remplacée par un nombre fini d'EDOs couplées. Grâce à la modélisation sous incertitude de position et à de nouveaux estimateurs statistiques, nous avons dérivé et simulé des versions réduites, déterministe et aléatoire, de l'équation de Navier-Stokes. Après avoir obtenu des versions aléatoires de plusieurs modèles océaniques, nous avons montré numériquement que ces modèles permettaient de mieux prendre en compte les petites échelles des écoulements, tout en donnant accès à des estimés de bonne qualité des erreurs du modèle. Ils permettent par ailleurs de mieux rendre compte des évènements extrêmes, des bifurcations ainsi que des phénomènes physiques réalistes absents de certains modèles déterministes équivalents. Nous avons expliqué, démontré et quantifié mathématiquement l'apparition de petites échelles de traceur, lors de l'advection par une vitesse mal résolu. Cette quantification permet de fixer proprement des paramètres de la méthode d'advection Lagrangienne, de mieux le comprendre le phénomène de mélange et d'aider au paramétrage des simulations grande échelle en mécanique des fluides.

This thesis develops, analyzes and demonstrates several valuable applications of randomized fluid dynamics models referred to as under location uncertainty. The velocity is decomposed between large-scale components and random time-uncorrelated small-scale components. This assumption leads to a modification of the material derivative and hence of every fluid dynamics models. Through the thesis, the mixing induced by deterministic low-resolution flows is also investigated. We first applied that decomposition to reduced order models (ROM). The fluid velocity is expressed on a finite-dimensional basis and its evolution law is projected onto each of these modes. We derive two types of ROMs of Navier-Stokes equations. A deterministic LES-like model is able to stabilize ROMs and to better analyze the influence of the residual velocity on the resolved component. The random one additionally maintains the variability of stable modes and quantifies the model errors. We derive random versions of several geophysical models. We numerically study the transport under location uncertainty through a simplified one. A single realization of our model better retrieves the small-scale tracer structures than a deterministic simulation. Furthermore, a small ensemble of simulations accurately predicts and describes the extreme events, the bifurcations as well as the amplitude and the position of the ensemble errors. Another of our derived simplified model quantifies the frontolysis and the frontogenesis in the upper ocean. This thesis also studied the mixing of tracers generated by smooth fluid flows, after a finite time. We propose a simple model to describe the stretching as well as the spatial and spectral structures of advected tracers. With a toy flow but also with satellite images, we apply our model to locally and globally describe the mixing, specify the advection time and the filter width of the Lagrangian advection method, as well as the turbulent diffusivity in numerical simulations.

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Primary Entity<\/h3>\n
<http:\/\/www.worldcat.org\/oclc\/984720209<\/a>> # Mixing and fluid dynamics under location uncertainty<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nbgn:Thesis<\/a>, schema:MediaObject<\/a>, bgn:ComputerFile<\/a>, schema:CreativeWork<\/a> ;\u00A0\u00A0\u00A0\nbgn:inSupportOf<\/a> \"Th\u00E8se de doctorat : Math\u00E9matiques et applications : Rennes 1 : 2017.<\/span>\" ;\u00A0\u00A0\u00A0\nlibrary:oclcnum<\/a> \"984720209<\/span>\" ;\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/id.loc.gov\/vocabulary\/countries\/fr<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/advection_lagrangienne<\/a>> ; # Advection Lagrangienne<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Topic\/fluides_mecanique_des<\/a>> ; # Fluides, M\u00E9canique des<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/dynamique_de_surface_dans_l_ocean<\/a>> ; # Dynamique de surface dans l\'oc\u00E9an<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/proper_orthogonal_decomposition<\/a>> ; # Proper orthogonal decomposition<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/mecanique_des_fluides<\/a>> ; # M\u00E9canique des fluides<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Topic\/processus_stochastiques<\/a>> ; # Processus stochastiques<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/qantification_d_incertitude<\/a>> ; # Qantification d\'incertitude<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/statistique_des_processus<\/a>> ; # Statistique des processus<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/repliement<\/a>> ; # Repliement<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/modele_d_ordre_reduit<\/a>> ; # Mod\u00E8le d\'ordre r\u00E9duit<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/melange<\/a>> ; # M\u00E9lange<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/bifurcation<\/a>> ; # Bifurcation<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/geophysique<\/a>> ; # G\u00E9ophysique<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/prevision_d_ensemble<\/a>> ; # Pr\u00E9vision d\'ensemble<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/calcul_stochastique<\/a>> ; # Calcul stochastique<\/span>\n\u00A0\u00A0\u00A0\nschema:author<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Person\/resseguier_valentin_1990<\/a>> ; # Valentin Resseguier<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Organization\/institut_national_de_recherche_en_informatique_et_en_automatique_france_unite_de_recherche_rennes_bretagne_atlantique<\/a>> ; # Institut national de recherche en informatique et en automatique (France). Unit\u00E9 de recherche (Rennes, Bretagne-Atlantique).<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Organization\/universite_de_rennes_1<\/a>> ; # Universit\u00E9 de Rennes 1.<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Organization\/ecole_doctorale_mathematiques_telecommunications_informatique_signal_systemes_electronique_rennes<\/a>> ; # \u00C9cole doctorale Math\u00E9matiques, t\u00E9l\u00E9communications, informatique, signal, syst\u00E8mes, \u00E9lectronique (Rennes).<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Person\/memin_etienne_1965<\/a>> ; # \u00C9tienne M\u00E9min<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Organization\/universite_bretagne_loire<\/a>> ; # Universit\u00E9 Bretagne Loire.<\/span>\n\u00A0\u00A0\u00A0\nschema:datePublished<\/a> \"2017<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"This thesis develops, analyzes and demonstrates several valuable applications of randomized fluid dynamics models referred to as under location uncertainty. The velocity is decomposed between large-scale components and random time-uncorrelated small-scale components. This assumption leads to a modification of the material derivative and hence of every fluid dynamics models. Through the thesis, the mixing induced by deterministic low-resolution flows is also investigated. We first applied that decomposition to reduced order models (ROM). The fluid velocity is expressed on a finite-dimensional basis and its evolution law is projected onto each of these modes. We derive two types of ROMs of Navier-Stokes equations. A deterministic LES-like model is able to stabilize ROMs and to better analyze the influence of the residual velocity on the resolved component. The random one additionally maintains the variability of stable modes and quantifies the model errors. We derive random versions of several geophysical models. We numerically study the transport under location uncertainty through a simplified one. A single realization of our model better retrieves the small-scale tracer structures than a deterministic simulation. Furthermore, a small ensemble of simulations accurately predicts and describes the extreme events, the bifurcations as well as the amplitude and the position of the ensemble errors. Another of our derived simplified model quantifies the frontolysis and the frontogenesis in the upper ocean. This thesis also studied the mixing of tracers generated by smooth fluid flows, after a finite time. We propose a simple model to describe the stretching as well as the spatial and spectral structures of advected tracers. With a toy flow but also with satellite images, we apply our model to locally and globally describe the mixing, specify the advection time and the filter width of the Lagrangian advection method, as well as the turbulent diffusivity in numerical simulations.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"Cette th\u00E8se concerne le d\u00E9veloppement, l\'extension et l\'application d\'une formulation stochastique des \u00E9quations de la m\u00E9canique des fluides introduite par M\u00E9min (2014). La vitesse petite \u00E9chelle, non-r\u00E9solue, est mod\u00E9lis\u00E9e au moyen d\'un champ al\u00E9atoire d\u00E9corr\u00E9l\u00E9 en temps. Cela modifie l\'expression de la d\u00E9riv\u00E9e particulaire et donc les \u00E9quations de la m\u00E9canique des fluides. Les mod\u00E8les qui en d\u00E9coulent sont d\u00E9nomm\u00E9s mod\u00E8les sous incertitude de position. La th\u00E8se s\'articulent autour de l\'\u00E9tude successive de mod\u00E8les r\u00E9duits, de versions stochastiques du transport et de l\'advection \u00E0 temps long d\'un champ de traceur par une vitesse mal r\u00E9solue. La POD est une m\u00E9thode de r\u00E9duction de dimension, pour EDP, rendue possible par l\'utilisation d\'observations. L\'EDP r\u00E9gissant l\'\u00E9volution de la vitesse du fluide est remplac\u00E9e par un nombre fini d\'EDOs coupl\u00E9es. Gr\u00E2ce \u00E0 la mod\u00E9lisation sous incertitude de position et \u00E0 de nouveaux estimateurs statistiques, nous avons d\u00E9riv\u00E9 et simul\u00E9 des versions r\u00E9duites, d\u00E9terministe et al\u00E9atoire, de l\'\u00E9quation de Navier-Stokes. Apr\u00E8s avoir obtenu des versions al\u00E9atoires de plusieurs mod\u00E8les oc\u00E9aniques, nous avons montr\u00E9 num\u00E9riquement que ces mod\u00E8les permettaient de mieux prendre en compte les petites \u00E9chelles des \u00E9coulements, tout en donnant acc\u00E8s \u00E0 des estim\u00E9s de bonne qualit\u00E9 des erreurs du mod\u00E8le. Ils permettent par ailleurs de mieux rendre compte des \u00E9v\u00E8nements extr\u00EAmes, des bifurcations ainsi que des ph\u00E9nom\u00E8nes physiques r\u00E9alistes absents de certains mod\u00E8les d\u00E9terministes \u00E9quivalents. Nous avons expliqu\u00E9, d\u00E9montr\u00E9 et quantifi\u00E9 math\u00E9matiquement l\'apparition de petites \u00E9chelles de traceur, lors de l\'advection par une vitesse mal r\u00E9solu. Cette quantification permet de fixer proprement des param\u00E8tres de la m\u00E9thode d\'advection Lagrangienne, de mieux le comprendre le ph\u00E9nom\u00E8ne de m\u00E9lange et d\'aider au param\u00E9trage des simulations grande \u00E9chelle en m\u00E9canique des fluides.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:exampleOfWork<\/a> <http:\/\/worldcat.org\/entity\/work\/id\/4188066548<\/a>> ;\u00A0\u00A0\u00A0\nschema:genre<\/a> \"Th\u00E8ses et \u00E9crits acad\u00E9miques<\/span>\" ;\u00A0\u00A0\u00A0\nschema:inLanguage<\/a> \"en<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Mixing and fluid dynamics under location uncertainty<\/span>\" ;\u00A0\u00A0\u00A0\nschema:productID<\/a> \"984720209<\/span>\" ;\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/tel.archives-ouvertes.fr\/tel-01507292<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/www.theses.fr\/2017REN1S004\/abes<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/ecm.univ-rennes1.fr\/nuxeo\/site\/esupversions\/9aa190a0-9f16-45ba-a1f9-0b7bb4c8219e<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/www.theses.fr\/2017REN1S004\/document<\/a>> ;\u00A0\u00A0\u00A0\nwdrs:describedby<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/984720209<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

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<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Organization\/ecole_doctorale_mathematiques_telecommunications_informatique_signal_systemes_electronique_rennes<\/a>> # \u00C9cole doctorale Math\u00E9matiques, t\u00E9l\u00E9communications, informatique, signal, syst\u00E8mes, \u00E9lectronique (Rennes).<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Organization<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"\u00C9cole doctorale Math\u00E9matiques, t\u00E9l\u00E9communications, informatique, signal, syst\u00E8mes, \u00E9lectronique (Rennes).<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Organization\/institut_national_de_recherche_en_informatique_et_en_automatique_france_unite_de_recherche_rennes_bretagne_atlantique<\/a>> # Institut national de recherche en informatique et en automatique (France). Unit\u00E9 de recherche (Rennes, Bretagne-Atlantique).<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Organization<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Institut national de recherche en informatique et en automatique (France). Unit\u00E9 de recherche (Rennes, Bretagne-Atlantique).<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Organization\/universite_bretagne_loire<\/a>> # Universit\u00E9 Bretagne Loire.<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Organization<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Universit\u00E9 Bretagne Loire.<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Organization\/universite_de_rennes_1<\/a>> # Universit\u00E9 de Rennes 1.<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Organization<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Universit\u00E9 de Rennes 1.<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Person\/memin_etienne_1965<\/a>> # \u00C9tienne M\u00E9min<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"1965<\/span>\" ;\u00A0\u00A0\u00A0\nschema:deathDate<\/a> \"\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"M\u00E9min<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"\u00C9tienne<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"\u00C9tienne M\u00E9min<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Person\/resseguier_valentin_1990<\/a>> # Valentin Resseguier<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"1990<\/span>\" ;\u00A0\u00A0\u00A0\nschema:deathDate<\/a> \"\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Resseguier<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Valentin<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Valentin Resseguier<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/advection_lagrangienne<\/a>> # Advection Lagrangienne<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Advection Lagrangienne<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/bifurcation<\/a>> # Bifurcation<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Bifurcation<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/calcul_stochastique<\/a>> # Calcul stochastique<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Calcul stochastique<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/dynamique_de_surface_dans_l_ocean<\/a>> # Dynamique de surface dans l\'oc\u00E9an<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Dynamique de surface dans l\'oc\u00E9an<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/geophysique<\/a>> # G\u00E9ophysique<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"G\u00E9ophysique<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/mecanique_des_fluides<\/a>> # M\u00E9canique des fluides<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"M\u00E9canique des fluides<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/melange<\/a>> # M\u00E9lange<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"M\u00E9lange<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/modele_d_ordre_reduit<\/a>> # Mod\u00E8le d\'ordre r\u00E9duit<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Mod\u00E8le d\'ordre r\u00E9duit<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/prevision_d_ensemble<\/a>> # Pr\u00E9vision d\'ensemble<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Pr\u00E9vision d\'ensemble<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/proper_orthogonal_decomposition<\/a>> # Proper orthogonal decomposition<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Proper orthogonal decomposition<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/qantification_d_incertitude<\/a>> # Qantification d\'incertitude<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Qantification d\'incertitude<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/repliement<\/a>> # Repliement<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Repliement<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Thing\/statistique_des_processus<\/a>> # Statistique des processus<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Statistique des processus<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Topic\/fluides_mecanique_des<\/a>> # Fluides, M\u00E9canique des<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Fluides, M\u00E9canique des<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4188066548#Topic\/processus_stochastiques<\/a>> # Processus stochastiques<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Processus stochastiques<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.loc.gov\/vocabulary\/countries\/fr<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\ndcterms:identifier<\/a> \"fr<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.theses.fr\/2017REN1S004\/document<\/a>>\u00A0\u00A0\u00A0\nrdfs:comment<\/a> \"Acc\u00E8s au texte int\u00E9gral<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n