Cette thèse étudie des méthodes d'assimilation de données par filtrage particulaire à l'estimation d'écoulements fluides observés au travers de séquences d'images. Nous nous appuyons sur un filtre particulaire spécifique dont la distribution de proposition est donnée par un filtre de Kalman d'ensemble, nommé filtre de Kalman d'ensemble pondéré. Deux variations à celui-ci sont introduites et étudiées. La première consiste à utiliser un bruit dynamique (permettant de modéliser l'incertitude du modèle et de séparer les particules entre elles) dont la forme spatiale suit une loi de puissance, cohérente avec la théorie phénoménologique de la turbulence. La deuxième variation repose sur un schéma d'assimilation multi-échelles introduisant un mécanisme de raffinements successifs à partir d'observations à des échelles de plus en plus petites. Ces deux méthodes ont été testées sur des séquences synthétiques et expérimentales d'écoulements 2D incompressibles. Ces résultats montrent un gain important sur l'erreur quadratique moyenne. Elles ont ensuite été testées sur des séquences d'images satellite réelles. Sur les images réelles, une bonne cohérence temporelle est observée, ainsi qu'un bon suivi des structures de vortex. L'assimilation multi-échelles montre un gain visible sur le nombre d'échelles reconstruites. Quelques variations additionnelles sont aussi présentées et testées afin de s'affranchir de problèmes importants rencontrés dans un contexte satellitaire réel. Il s'agit notamment de la prise en compte de données manquantes sur les images de température de surface de l'océan. En dernier lieu, une expérience d'un filtre de Kalman d'ensemble pondéré avec un modèle océanique complet est présentée pour une assimilation de champs de courants de surface en mer d'Iroise, à l'embouchure de la Manche. Quelques autres pistes d'amélioration sont également esquissées et testées. / This thesis studies fluid flows estimation with particle filtering-based assimilation methods imaged using digital cameras. We rely on a specific particle filter, of which the proposal distribution is given by an Ensemble Kalman Filter, namely the Weighted Ensemble Kalman Filter. Two variations of this method are introduced and tested. The first consists in using a dynamical noise (which modelizes the model uncertainty and separates the particles from each others); its spatial form obeys to a power law stemming from the phenomenological theory of the turbulence. The second variation relies on a multiscale assimilation scheme introduicing successive refinements from observations at smaller and smaller scales. These two methods are tested on synthetic and experimental sequences of 2D incompressible flows. Results show an important gain on the Root Mean Square Error. They are then tested on real satellite images. A good temporal coherence and a good tracking of vortex structures are observed on the real images. The multiscale assimilation shows a visible gain on the number of reconstructed scales. Some additional variations are also presented and tested in order to take into account important problems in a real satellite context. The main contribution is the management of missing data areas in the Sea Surface Temperature sequence. Lastly an experiment involving a Weighted Ensemble Kalman Filter with a complete oceanic model is presented for a surface currents fields assimilation in Iroise Sea near the English Channel mouth. Some other improvements are also drawn and tested.

Este trabalho propõe uma técnica de modelagem multiescala concorrente do concreto considerando duas escalas distintas: a mesoescala, onde o concreto é modelado como um material heterogêneo, e a macroescala, na qual o concreto é tratado como um material homogêneo. A heterogeneidade da estrutura mesoscópica do concreto é idealizada considerando três fases distintas, compostas pelos agregados graúdos e argamassa (matriz), estes considerados materiais homogêneos, e zona de transição interfacial (ZTI), tratada como a parte mais fraca entre as três fases. O agregado graúdo é gerado a partir de uma curva granulométrica e posicionado na matriz de forma aleatória. Seu comportamento mecânico é descrito por um modelo constitutivo elástico-linear, devido a sua maior resistência quando comparado com as outras duas fases do concreto. Elementos finitos contínuos com alta relação de aspecto em conjunto com um modelo constitutivo de dano são usados para representar o comportamento não linear do concreto, decorrente da iniciação de fissuras na ZTI e posterior propagação para a matriz, dando lugar à formação de macrofissuras. Os elementos finitos de interface com alta relação de aspecto são inseridos entre todos os elementos regulares da matriz e entre os da matriz e agregados, representando a ZTI, tornando-se potenciais caminhos de propagação de fissuras. No estado limite, quando a espessura do elemento de interface tende a zero (h ?0) e, consequentemente, a relação de aspecto tende a infinito, estes elementos apresentam a mesma cinemática da aproximação contínua de descontinuidades fortes (ACDF), sendo apropriados para representar a formação de descontinuidades associados a fissuras, similar aos modelos coesivos. Um modelo de dano à tração é proposto para representar o comportamento mecânico não linear das interfaces, associado à formação de fissuras, ou até mesmo ao eventual fechamento destas. A fim de contornar os problemas causados pela malha de elementos finitos de transição entre as malhas da macro e da mesoescala, que, em geral, apresentam diferenças expressivas 5 de refinamento, utiliza-se uma técnica recente de acoplamento de malhas não conformes. Esta técnica é baseada na definição de elementos finitos de acoplamento (EFAs), os quais são capazes de estabelecer a continuidade de deslocamento entre malhas geradas de forma completamente independentes, sem aumentar a quantidade total de graus de liberdade do problema, podendo ser utilizados tanto para acoplar malhas não sobrepostas quanto sobrepostas. Para tornar possível a análise em multiescala em casos nos quais a região de localização de deformações não pode ser definida a priori, propõe-se uma técnica multiescala adaptativa. Nesta abordagem, usa-se a distribuição de tensões da escala macroscópica como um indicador para alterar a modelagem das regiões críticas, substituindo-se a macroescala pela mesoescala durante a análise. Consequentemente, a malha macroscópica é automaticamente substituída por uma malha mesoscópica, onde o comportamento não linear está na iminência de ocorrer. Testes numéricos são desenvolvidos para mostrar a capacidade do modelo proposto de representar o processo de iniciação e propagação de fissuras na região tracionada do concreto. Os resultados numéricos são comparados com os resultados experimentais ou com aqueles obtidos através da simulação direta em mesoescala (SDM). / A concurrent multiscale analysis of concrete is presented, in which two distinct scales are considered: the mesoscale, where the concrete is modeled as a heterogeneous material and the macroscale that treats the concrete as a homogeneous material. The mesostructure heterogeneities are idealized as three phase materials composed of the coarse aggregates, mortar matrix and the interfacial transition zone (ITZ). The coarse aggregates are generated from a grading curve and placed into the mortar matrix randomly. Their behavior is described using an elastic-linear constitutive model due to their significant higher strength when compared with the other two phases of the concrete. Special continuum finite elements with a high aspect ratio and a damage constitutive model are used to describe the nonlinear behavior associated to the propagation of cracks, which initiates in the ITZ and then propagates to the mortar matrix given place to a macro-crack formation. These interface elements with a high aspect ratio are inserted in between all regular finite elements of the mortar matrix and in between the mortar matrix and aggregate elements, representing the ITZ. In the limit case, when the thickness of interface elements tends to zero (h ?0) and consequently the aspect ratio tends to infinite, these elements present the same kinematics as the continuous strong discontinuity approach (CSDA), so that they are suitable to represent the formation of discontinuities associated to cracks, similar to cohesive models. A tensile damage model is proposed to model the nonlinear mechanical behavior of the interfaces, associated to the crack formation and also to the possible crack closure. To avoid transition meshes between the macro and the mesoscale meshes, a new technique for coupling non-matching meshes is used. This technique is based on the definition of coupling finite elements (CFEs), which can ensure the continuity of displacement between independent meshes, without increasing the total number of degrees of freedom of the problem. This technique can be used to couple non-overlapping and overlapping meshes.To make possible the concurrent multiscale analysis, where the strain localization region cannot be defined a priori, an adaptive multiscale model is proposed. In this approach the macroscale stress distribution is used as an indicator to properly change from the macroscale to the mesoscale modeling in the critical regions during the analysis. Consequently, the macroscopic mesh is automatically replaced by a mesoscopic mesh where the nonlinear behavior is imminent. A variety of tests are performed to show the ability of the proposed methodology in predicting the behavior of initiation and propagation of cracks in the tensile region of the concrete. The numerical results are compared with the experimental ones or with those obtained by the direct simulation in mesoscale (DSM).

<p>The present thesis is devoted to the homogenization of certain elliptic and parabolic partial differential equations by means of appropriate generalizations of the notion of two-scale convergence. Since homogenization is defined in terms of H-convergence, we desire to find the H-limits of sequences of periodic monotone parabolic operators with two spatial scales and an arbitrary number of temporal scales and the H-limits of sequences of two-dimensional possibly non-periodic linear elliptic operators by utilizing the theories for evolution-multiscale convergence and λ-scale convergence, respectively, which are generalizations of the classical two-scale convergence mode and custom-made to treat homogenization problems of the prescribed kinds. Concerning the multiscaled parabolic problems, we find that the result of the homogenization depends on the behavior of the temporal scale functions. The temporal scale functions considered in the thesis may, in the sense explained in the text, be slow or rapid and in resonance or not in resonance with respect to the spatial scale function. The homogenization for the possibly non-periodic elliptic problems gives the same result as for the corresponding periodic problems but with the exception that the local gradient operator is everywhere substituted by a differential operator consisting of a product of the local gradient operator and matrix describing the geometry and which depends, effectively, parametrically on the global variable.</p>

The present thesis is devoted to the homogenization of certain elliptic and parabolic partial differential equations by means of appropriate generalizations of the notion of two-scale convergence. Since homogenization is defined in terms of H-convergence, we desire to find the H-limits of sequences of periodic monotone parabolic operators with two spatial scales and an arbitrary number of temporal scales and the H-limits of sequences of two-dimensional possibly non-periodic linear elliptic operators by utilizing the theories for evolution-multiscale convergence and λ-scale convergence, respectively, which are generalizations of the classical two-scale convergence mode and custom-made to treat homogenization problems of the prescribed kinds. Concerning the multiscaled parabolic problems, we find that the result of the homogenization depends on the behavior of the temporal scale functions. The temporal scale functions considered in the thesis may, in the sense explained in the text, be slow or rapid and in resonance or not in resonance with respect to the spatial scale function. The homogenization for the possibly non-periodic elliptic problems gives the same result as for the corresponding periodic problems but with the exception that the local gradient operator is everywhere substituted by a differential operator consisting of a product of the local gradient operator and matrix describing the geometry and which depends, effectively, parametrically on the global variable.

La Corrosion Haute Température (HTC), en environnements divers et sévères, d'alliages métalliques toujours plus élaborés en termes de composition et micro-structure, est un sujet industriel et scientifique très complexe. La PhotoElectroChimie (PEC) est une technique de choix pour caractériser les propriétés physico-chimiques et électroniques des couches d'oxydation très hétérogènes formées en HTC. Sur des exemples d'alliages modèles mais représentatifs de la réalité industrielle (aciers duplex, base-Nickel 690), ce travail présente le développement et la validation d'un dispositif expérimental permettant d'appliquer pour la première fois tout l'arsenal des techniques PEC à l'échelle mésoscopique (typiquement 30 µm), ainsi que la validation d'une modélisation originale développée au SIMaP des spectres de photocourants en énergie, qui permet de les décrire et ajuster finement et d'en extraire notamment avec précision les gaps des oxydes semiconducteurs présents dans la couche thermique. / High Temperature Corrosion (HTC), in various and severe atmospheres, of continually more elaborated (composition, micro–structure) metallic alloys, is a rather complex industrial and scientific topic. PhotoElectroChemistry (PEC) acquired a special place in the characterization of physico–chemical and electronic properties of the highly heterogeneous oxidation layers formed in HTC. Through studies of model but industrially representative samples (duplex stainless steel, Ni–base alloy 690), this work presents the development and validation of an experimental set–up allowing for the first time to use the whole set of PEC techniques at the mesoscopic level (typically 30 µm), as well as the validation of an original model of photocurrent energy spectra, developed at SIMaP, allowing to well describe, and accurately fit the latter spectra, and thus yielding, notably, precise bandgap values for the semiconducting components of the thermal scale.

Este trabalho propõe uma técnica de modelagem multiescala concorrente do concreto considerando duas escalas distintas: a mesoescala, onde o concreto é modelado como um material heterogêneo, e a macroescala, na qual o concreto é tratado como um material homogêneo. A heterogeneidade da estrutura mesoscópica do concreto é idealizada considerando três fases distintas, compostas pelos agregados graúdos e argamassa (matriz), estes considerados materiais homogêneos, e zona de transição interfacial (ZTI), tratada como a parte mais fraca entre as três fases. O agregado graúdo é gerado a partir de uma curva granulométrica e posicionado na matriz de forma aleatória. Seu comportamento mecânico é descrito por um modelo constitutivo elástico-linear, devido a sua maior resistência quando comparado com as outras duas fases do concreto. Elementos finitos contínuos com alta relação de aspecto em conjunto com um modelo constitutivo de dano são usados para representar o comportamento não linear do concreto, decorrente da iniciação de fissuras na ZTI e posterior propagação para a matriz, dando lugar à formação de macrofissuras. Os elementos finitos de interface com alta relação de aspecto são inseridos entre todos os elementos regulares da matriz e entre os da matriz e agregados, representando a ZTI, tornando-se potenciais caminhos de propagação de fissuras. No estado limite, quando a espessura do elemento de interface tende a zero (h ?0) e, consequentemente, a relação de aspecto tende a infinito, estes elementos apresentam a mesma cinemática da aproximação contínua de descontinuidades fortes (ACDF), sendo apropriados para representar a formação de descontinuidades associados a fissuras, similar aos modelos coesivos. Um modelo de dano à tração é proposto para representar o comportamento mecânico não linear das interfaces, associado à formação de fissuras, ou até mesmo ao eventual fechamento destas. A fim de contornar os problemas causados pela malha de elementos finitos de transição entre as malhas da macro e da mesoescala, que, em geral, apresentam diferenças expressivas 5 de refinamento, utiliza-se uma técnica recente de acoplamento de malhas não conformes. Esta técnica é baseada na definição de elementos finitos de acoplamento (EFAs), os quais são capazes de estabelecer a continuidade de deslocamento entre malhas geradas de forma completamente independentes, sem aumentar a quantidade total de graus de liberdade do problema, podendo ser utilizados tanto para acoplar malhas não sobrepostas quanto sobrepostas. Para tornar possível a análise em multiescala em casos nos quais a região de localização de deformações não pode ser definida a priori, propõe-se uma técnica multiescala adaptativa. Nesta abordagem, usa-se a distribuição de tensões da escala macroscópica como um indicador para alterar a modelagem das regiões críticas, substituindo-se a macroescala pela mesoescala durante a análise. Consequentemente, a malha macroscópica é automaticamente substituída por uma malha mesoscópica, onde o comportamento não linear está na iminência de ocorrer. Testes numéricos são desenvolvidos para mostrar a capacidade do modelo proposto de representar o processo de iniciação e propagação de fissuras na região tracionada do concreto. Os resultados numéricos são comparados com os resultados experimentais ou com aqueles obtidos através da simulação direta em mesoescala (SDM). / A concurrent multiscale analysis of concrete is presented, in which two distinct scales are considered: the mesoscale, where the concrete is modeled as a heterogeneous material and the macroscale that treats the concrete as a homogeneous material. The mesostructure heterogeneities are idealized as three phase materials composed of the coarse aggregates, mortar matrix and the interfacial transition zone (ITZ). The coarse aggregates are generated from a grading curve and placed into the mortar matrix randomly. Their behavior is described using an elastic-linear constitutive model due to their significant higher strength when compared with the other two phases of the concrete. Special continuum finite elements with a high aspect ratio and a damage constitutive model are used to describe the nonlinear behavior associated to the propagation of cracks, which initiates in the ITZ and then propagates to the mortar matrix given place to a macro-crack formation. These interface elements with a high aspect ratio are inserted in between all regular finite elements of the mortar matrix and in between the mortar matrix and aggregate elements, representing the ITZ. In the limit case, when the thickness of interface elements tends to zero (h ?0) and consequently the aspect ratio tends to infinite, these elements present the same kinematics as the continuous strong discontinuity approach (CSDA), so that they are suitable to represent the formation of discontinuities associated to cracks, similar to cohesive models. A tensile damage model is proposed to model the nonlinear mechanical behavior of the interfaces, associated to the crack formation and also to the possible crack closure. To avoid transition meshes between the macro and the mesoscale meshes, a new technique for coupling non-matching meshes is used. This technique is based on the definition of coupling finite elements (CFEs), which can ensure the continuity of displacement between independent meshes, without increasing the total number of degrees of freedom of the problem. This technique can be used to couple non-overlapping and overlapping meshes.To make possible the concurrent multiscale analysis, where the strain localization region cannot be defined a priori, an adaptive multiscale model is proposed. In this approach the macroscale stress distribution is used as an indicator to properly change from the macroscale to the mesoscale modeling in the critical regions during the analysis. Consequently, the macroscopic mesh is automatically replaced by a mesoscopic mesh where the nonlinear behavior is imminent. A variety of tests are performed to show the ability of the proposed methodology in predicting the behavior of initiation and propagation of cracks in the tensile region of the concrete. The numerical results are compared with the experimental ones or with those obtained by the direct simulation in mesoscale (DSM).

Variabilité spatiale multiéchelle du zooplancton dans un lagoon récifal côtier - L'identification des changements dans les patrons écologiques selon l'échelle spatiale et la compréhension des processus qui génèrent ces changements sont d'une importance considérable en océanographie. Dans ce contexte, comprendre comment une communauté biologique répond à l'hétérogénéité environnementale requiert la connaissance des processus impliqués et l'échelle spatiale à laquelle ils opèrent. Les relations spatiales entre la variabilité du zooplancton et l'hétérogénéité environnementale sont encore imprécises dans les écosystèmes tropicaux côtiers. L'objectif de ce travail de thèse a donc été de déterminer les échelles de dépendance spatiale des patrons du zooplancton associé à un lagon récifal côtier et des processus environnementaux sous-jacents. Dans ce contexte, les intérêts de cette recherche ont été de quantifier les patrons de la variabilité du zooplancton dans l'espace, de comprendre comment ces patrons changent avec l'échelle spatiale et de déterminer les processus physiques et biologiques responsables de ces patrons spatiaux. L'échantillonnage, effectué le long d'un transect de la côte vers le large dans le lagon du Grand-Cul-de-Sac Marin (Guadeloupe), a concerné deux classes de taille du zooplancton (190–600 µm et > 600 µm) pour lesquelles la biomasse et l'abondance ont été estimées. L'analyse multiéchelle a été utilisée pour caractériser les patrons du zooplancton aux différentes échelles spatiales (de l'échelle de l'habitat à celle du lagon tout entier) et pour identifier les processus responsables de ces structures spatiales. Cette étude a montré que la variabilité du zooplancton est un phénomène multiéchelle dont l'amplitude et la dépendance spatiale dépendent de la taille des organismes, de leur motilité et de la variable-réponse considérée (biomasse ou abondance). La biomasse et l'abondance du zooplancton varient en réponse à la distribution spatiale du phytoplancton, au comportement du zooplancton, à l'hétérogénéité de l'habitat, à l'hydrodynamique et aux évènements météorologiques. La nature et les effets de ces processus sont dépendants de l'échelle spatiale. Ce travail a montré comment le changement d'échelle spatiale met en évidence différents niveaux d'organisation de la communauté zooplanctonique en réponse à l'hétérogénéité environnementale.

Le procédé de coextrusion permet de combiner à l’état fondu plusieurs couches de polymères dans une même structure. La compatibilisation des différentes couches est généralement réalisée à l’aide de liants qui réagissent in-situ. Bien que la compatibilisation puisse permettre de réduire ou même supprimer les instabilités macroscopiques d’écoulement, un nouveau défaut qualifié de « granité » peut apparaitre. Très peu de travaux de la littérature traitent les mécanismes gouvernant ce type de défaut. Les phénomènes mis en jeu sont particulièrement complexes puisqu’ils impliquent de façon couplée des phénomènes hydrodynamiques via l’écoulement, la rhéologie des différentes couches et des phénomènes physico-chimiques via la diffusion et la réaction chimique aux interfaces polymère/polymère. Ce mémoire s’articule autour d’une étude multi-échelle du rôle des copolymères aux interfaces sur la stabilité des écoulements stratifiés. L’étude a été réalisée à la fois sur des systèmes non-réactifs et réactifs constitués d’une couche barrière, le polyamide 6 (PA6) ou le poly(éthylène-co-alcool vinylique) (EVOH), avec un polypropylène (PP) ou un polypropylène greffé anhydride maléique (PP-g-AM). Le défaut de « granité » a été mis en évidence en coextrusion. Les paramètres procédé et matériaux influençant son apparition ont été identifiés. Il a pu être différencié des défauts et des instabilités interfaciales généralement rencontrées en coextrusion. Le phénomène de compatibilisation a également été étudié via les caractérisations morphologiques (MET, MEB, AFM) et physico-chimiques (XPS) aux interfaces. Le comportement rhéologique en cisaillement et élongation en viscoélasticité linéaire et non linéaire s’est révélé très sensible à l’effet la présence de copolymères aux interfaces et à leur architecture moléculaire. Cette étude a permis de déterminer les propriétés intrinsèques de l’interface/interphase en fonction du copolymère formé entre le liant et le PA6 ou l’EVOH. Elles ont pu être corrélées aux défauts macroscopiques observés dans les films multicouches coextrudés. La stabilité de ces écoulements stratifiés résulte d’un couplage de phénomènes qui se produisent à différentes échelles : nano (réaction de copolymérisation), micro (interphase) et macro (écoulement dans le procédé). / Several polymers can be combined in one multilayer structure by reactive coextrusion. Tie-layers are often used to compatibilize the adjacent layers and may reduce or suppress the interfacial instabilities and the defects in the multilayer coextrusion flow. However, an additional defect defined as the “grainy” defect can be observed. In the best of our knowledge, no study in literature has been devoted to understand its origin. The phenomena are quite complex due to the coupling of the effects of flow and the physico-chemical mechanisms at the interface. The aim of this work is to understand the relations between the instabilities and the defects encountered in multilayer coextruded films and the role of the copolymer formed in-situ between tie and barrier layers. Polyamide 6 (PA6) and ethylene-vinyl alcohol copolymer (EVOH) were used as the barrier layers sandwiched in a polypropylene (PP) with or without a polypropylene grafted maleic anhydride (PP-g-MA) as a tie-layer. The effect of the process parameters and the structure of the polymers on the generation of the “grainy” defect was assessed in correlation with the rheological and the physicochemical properties of the layers. These experiments have shown that this defect appeared mainly in the compatibilized EVOH system and could be distinguished from the usual coextrusion instabilities. The interfacial properties between tie and barrier layers were investigated. The characterization of the interfacial morphology by TEM and AFM highlighted an irregular and rough interface between PP-g-MA and EVOH while a flat interface was observed with PA6 and PP-g-MA. Step shear and startup elongation rheology was shown to be sensitive to the copolymer at the polymer/polymer interface. The study of the interfacial properties highlighted that the copolymer architecture significantly impacts the interfacial roughness and the rheology of the multilayer stuctures. Hence, relations between the relaxation process, the interfacial morphology and the copolymer architecture were established in correlation with the generation of the macroscopic grainy defect in coextrusion.