O propósito deste estudo foi verificar a contribuição dos Distúrbios Ondulatórios de Leste (DOLs) na precipitação observada no período chuvoso (AMJJ) e avaliar previsões sazonais de chuva obtidas do RegCM3 (Regional Climate Model version 3) no Leste do Nordeste do Brasil (LNB). Para a identificação subjetiva dos DOLs foram utilizadas imagens de satélite no infravermelho e os campos de linhas de corrente e vorticidade relativa em 700 e 850 hPa da reanálise ERA-Interim, nos períodos chuvosos de 2006 a 2010. Cerca de 90% dos cavados observados em 700 hPa estiveram associados aos 116 DOLs que atingiram o LNB. Isto fornece média de 23 DOLs por ano com pequena variabilidade interanual. Foram construídas composições de variáveis meteorológicas desde 2 dias antes (-2) até 2 dias depois (+2) dos DOLs atingirem o LNB. A circulação apresentou anomalia ciclônica e confluente, vorticidade relativa ciclônica e convergência entre os dias -2 e 0 em baixos níveis, principalmente em 1000 hPa. Encontraram-se anomalias negativas de radiação de onda longa emergente (ROLE) e de omega e positivas de umidade relativa. A composição de precipitação indicou que são responsáveis por: 70% ou mais da chuva do período chuvoso do litoral norte de Alagoas (AL) ao leste do Rio Grande do Norte (RN), 60% entre a Zona da Mata de AL e o Agreste do RN, e 50% entre Sergipe e demais áreas do RN. Em média, os DOLs apresentaram período de 5,3 dias, comprimento de onda de 4307 km e velocidade de fase de 9,5 m s-1. O RegCM3 simulou a observada propagação para oeste dos cavados em 850-700 hPa, bem como a precipitação associada, para dois eventos de DOLs ocorridos entre 21-25 de maio de 2006. Em termos sazonais, o RegCM3 com a parametrização de Grell previu o padrão espacial da chuva similar à observada, mas superestimou-a. A detecção de DOLs utilizando diagramas do tipo Hovmöller identificou ~68% dos eventos obtidos subjetivamente. Aplicação de algoritmo de tracking utilizando ROLE ou vorticidade mostrou-se insatisfatória no rastreamento de DOLs, identificando, através de ROLE, ~55% dos eventos obtidos subjetivamente. / This study purpose was to verify the contribution of Easterly Wave Disturbances (EWDs) in the observed precipitation over the eastern part of Northeast Brazil (ENEB) during rainy season (AMJJ) and evaluate seasonal rainfall forecasts from RegCM3 (Regional Climate Model version 3). For the EWDs subjective identification it was used infrared satellite images and ERA-Interim reanalysis streamlines and relative vorticity fields at 700 and 850 hPa, at the rainy periods from 2006 to 2010. About 90% of the observed troughs at 700 hPa were associated with 116 EWDs that reached the ENEB. This provides a 23 EWDs average per year with small interannual variability. Meteorological variables compositions were constructed from 2 days before (-2) until 2 days after (+2) EWDs reached the ENEB. The circulation showed cyclonic and confluent anomaly, cyclonic relative vorticity and convergence between days -2 and 0 in low levels, mainly in 1000 hPa. Negative anomalies were found for outgoing longwave radiation (OLR) and omega whereas relative humidity presented positive anomaly. The precipitation composition indicated that the EWDs account for: 70% or more of rainy seasons precipitation from northern coast of Alagoas (AL) to the eastern Rio Grande do Nortes (RN), 60% from ALs Zona da Mata to the RNs Agreste, and 50% between Sergipe and the other RN areas. On average, the EWDs presented a 5.3 days period, a wavelength of 4307 km and phase velocity of 9.5 m s-1. The RegCM3 simulated the observed westward troughs propagation at the 850-700 hPa levels, and their associated precipitation as well, for two EWDs occurred between 21 and 25 May 2006. For seasonal simulations, the RegCM3 with Grell parameterization predicted the spatial pattern similar to the observed rain, but overestimated it. Approximately 68% of the events subjectively obtained EWDs were also identified using Hovmöller diagrams. The tracking algorithm using OLR or vorticity was unsatisfactory in the detection of EWDs, identifying with OLR ~55% of the events subjectively obtained.

In this thesis we investigated two major issues in astrophysical flows: the transport of magnetic fields in highly conducting fluids in the presence of turbulence, and the turbulence evolution and turbulent dynamo amplification of magnetic fields in collisionless plasmas. The first topic was explored in the context of star-formation, where two intriguing problems are highly debated: the requirement of magnetic flux diffusion during the gravitational collapse of molecular clouds in order to explain the observed magnetic field intensities in protostars (the so called \"magnetic flux problem\") and the formation of rotationally sustained protostellar discs in the presence of the magnetic fields which tend to remove all the angular momentum (the so called \"magnetic braking catastrophe\"). Both problems challenge the ideal MHD description, usually expected to be a good approximation in these environments. The ambipolar diffusion, which is the mechanism commonly invoked to solve these problems, has been lately questioned both by observations and numerical simulation results. We have here investigated a new paradigm, an alternative diffusive mechanism based on fast magnetic reconnection induced by turbulence, termed turbulent reconnection diffusion (TRD). We tested the TRD through fully 3D MHD numerical simulations, injecting turbulence into molecular clouds with initial cylindrical geometry, uniform longitudinal magnetic field and periodic boundary conditions. We have demonstrated the efficiency of the TRD in decorrelating the magnetic flux from the gas, allowing the infall of gas into the gravitational well while the field lines migrate to the outer regions of the cloud. This mechanism works for clouds starting either in magnetohydrostatic equilibrium or initially out-of-equilibrium in free-fall. We estimated the rates at which the TRD operate and found that they are faster when the central gravitational potential is higher. Also we found that the larger the initial value of the thermal to magnetic pressure ratio (beta) the larger the diffusion process. Besides, we have found that these rates are consistent with the predictions of the theory, particularly when turbulence is trans- or super-Alfvénic. We have also explored by means of 3D MHD simulations the role of the TRD in protostellar disks formation. Under ideal MHD conditions, the removal of angular momentum from the disk progenitor by the typically embedded magnetic field may prevent the formation of a rotationally supported disk during the main protostellar accretion phase of low mass stars. Previous studies showed that an enhanced microscopic diffusivity of about three orders of magnitude larger than the Ohmic diffusivity would be necessary to enable the formation of a rotationally supported disk. However, the nature of this enhanced diffusivity was not explained. Our numerical simulations of disk formation in the presence of turbulence demonstrated the efficiency of the TRD in providing the diffusion of the magnetic flux to the envelope of the protostar during the gravitational collapse, thus enabling the formation of rotationally supported disks of radius ~ 100 AU, in agreement with the observations. The second topic of this thesis has been investigated in the framework of the plasmas of the intracluster medium (ICM). The amplification and maintenance of the observed magnetic fields in the ICM are usually attributed to the turbulent dynamo action which is known to amplify the magnetic energy until close equipartition with the kinetic energy. This is generally derived employing a collisional MHD model. However, this is poorly justified a priori since in the ICM the ion mean free path between collisions is of the order of the dynamical scales, thus requiring a collisionless-MHD description. We have studied here the turbulence statistics and the turbulent dynamo amplification of seed magnetic fields in the ICM using a single-fluid collisionless-MHD model. This introduces an anisotropic thermal pressure with respect to the direction of the local magnetic field and this anisotropy modifies the MHD linear waves and creates kinetic instabilities. Our collisionless-MHD model includes a relaxation term of the pressure anisotropy due to the feedback of the mirror and firehose instabilities. We performed 3D numerical simulations of forced transonic turbulence in a periodic box mimicking the turbulent ICM, assuming different initial values of the magnetic field intensity and different relaxation rates of the pressure anisotropy. We showed that in the high beta plasma regime of the ICM where these kinetic instabilities are stronger, a fast anisotropy relaxation rate gives results which are similar to the collisional-MHD model in the description of the statistical properties of the turbulence. Also, the amplification of the magnetic energy due to the turbulent dynamo action when considering an initial seed magnetic field is similar to the collisional-MHD model, particularly when considering an instantaneous anisotropy relaxation. The models without any pressure anisotropy relaxation deviate significantly from the collisional-MHD results, showing more power in small-scale fluctuations of the density and velocity field, in agreement with a significant presence of the kinetic instabilities; however, the fluctuations in the magnetic field are mostly suppressed. In this case, the turbulent dynamo fails in amplifying seed magnetic fields and the magnetic energy saturates at values several orders of magnitude below the kinetic energy. It was suggested by previous studies of the collisionless plasma of the solar wind that the pressure anisotropy relaxation rate is of the order of a few percent of the ion gyrofrequency. The present study has shown that if this is also the case for the ICM, then the models which best represent the ICM are those with instantaneous anisotropy relaxation rate, i.e., the models which revealed a behavior very similar to the collisional-MHD description. / Nesta tese, investigamos dois problemas chave relacionados a fluidos astrofísicos: o transporte de campos magnéticos em plasmas altamente condutores na presença de turbulência, e a evolução da turbulência e amplificação de campos magnéticos pelo dínamo turbulento em plasmas não-colisionais. O primeiro tópico foi explorado no contexto de formação estelar, onde duas questões intrigantes são intensamente debatidas na literatura: a necessidade da difusão de fluxo magnético durante o colapso gravitacional de nuvens moleculares, a fim de explicar as intensidades dos campos magnéticos observadas em proto-estrelas (o denominado \"problema do fluxo magnético\"), e a formação de discos proto-estelares sustentados pela rotação em presença de campos magnéticos, os quais tendem a remover o seu momento angular (a chamada \"catástrofe do freamento magnético\"). Estes dois problemas desafiam a descrição MHD ideal, normalmente empregada para descrever esses sistemas. A difusão ambipolar, o mecanismo normalmente invocado para resolver estes problemas, vem sendo questionada ultimamente tanto por observações quanto por resultados de simulações numéricas. Investigamos aqui um novo paradigma, um mecanismo de difusão alternativo baseado em reconexão magnética rápida induzida pela turbulência, que denominamos reconexão turbulenta (TRD, do inglês turbulent reconnection diffusion). Nós testamos a TRD através de simulações numéricas tridimensionais MHD, injetando turbulência em nuvens moleculares com geometria inicialmente cilíndrica, permeadas por um campo magnético longitudinal e fronteiras periódicas. Demonstramos a eficiência da TRD em desacoplar o fluxo magnético do gás, permitindo a queda do gás no poço de potencial gravitacional, enquanto as linhas de campo migram para as regiões externas da nuvem. Este mecanismo funciona tanto para nuvens inicialmente em equilíbrio magneto-hidrostático, quanto para aquelas inicialmente fora de equilíbrio, em queda livre. Nós estimamos as taxas em que a TRD opera e descobrimos que são mais rápidas quando o potencial gravitacional é maior. Também verificamos que quanto maior o valor inicial da razão entre a pressão térmica e magnética (beta), mais eficiente é o processo de difusão. Além disto, também verificamos que estas taxas são consistentes com as previsões da teoria, particularmente quando a turbulência é trans- ou super-Alfvénica. Também exploramos por meio de simulações MHD 3D a influência da TRD na formação de discos proto-estelares. Sob condições MHD ideais, a remoção do momento angular do disco progenitor pelo campo magnético da nuvem pode evitar a formação de discos sustentados por rotação durante a fase principal de acreção proto-estelar de estrelas de baixa massa. Estudos anteriores mostraram que uma super difusividade microscópica aproximadamente três ordens de magnitude maior do que a difusividade ôhmica seria necessária para levar à formação de um disco sustentado pela rotação. No entanto, a natureza desta super difusividade não foi explicada. Nossas simulações numéricas da formação do disco em presença de turbulência demonstraram a eficiência da TRD em prover a diffusão do fluxo magnético para o envelope da proto-estrela durante o colapso gravitacional, permitindo assim a formação de discos sutentados pela rotação com raios ~ 100 UA, em concordância com as observações. O segundo tópico desta tese foi abordado no contexto dos plasmas do meio intra-aglomerado de galáxias (MIA). A amplificação e manutenção dos campos magnéticos observados no MIA são normalmente atribuidas à ação do dínamo turbulento, que é conhecidamente capaz de amplificar a energia magnética até valores próximos da equipartição com a energia cinética. Este resultado é geralmente derivado empregando-se um modelo MHD colisional. No entanto, isto é pobremente justificado a priori, pois no MIA o caminho livre médio de colisões íon-íon é da ordem das escalas dinâmicas, requerendo então uma descrição MHD não-colisional. Estudamos aqui a estatística da turbulência e a amplificação por dínamo turbulento de campos magnéticos sementes no MIA, usando um modelo MHD não-colisional de um único fluido. Isto indroduz uma pressão térmica anisotrópica com respeito à direção do campo magnético local. Esta anisotropia modifica as ondas MHD lineares e cria instabilidades cinéticas. Nosso modelo MHD não-colisional inclui um termo de relaxação da anisotropia devido aos efeitos das instabilidades mirror e firehose. Realizamos simulações numéricas 3D de turbulência trans-sônica forçada em um domínio periódico, mimetizando o MIA turbulento e considerando diferentes valores iniciais para a intensidade do campo magnético, bem como diferentes taxas de relaxação da anisotropia na pressão. Mostramos que no regime de plasma com altos valores de beta no MIA, onde estas instabilidades cinéticas são mais fortes, uma rápida taxa de relaxação da anisotropia produz resultados similares ao modelo MHD colisional na descrição das propriedades estatísticas da turbulência. Além disso, a amplificação da energia mangética pela ação do dínamo turbulento quando consideramos um campo magnético semente, é similar ao modelo MHD colisional, particularmente quando consideramos uma relaxação instantânea da anisotropia. Os modelos sem qualquer relaxação da anisotropia de pressão mostraram resultados que se desviam significativamente daqueles do MHD colisional, mostrando mais potências nas flutuações de pequena escala da densidade e velocidade, em concordância com a presença significativa das instabilidades cinéticas nessas escalas; no entanto, as flutuações do campo magnético são, em geral, suprimidas. Neste caso, o dínamo turbulento também falha em amplificar campos magnéticos sementes e a energia magnética satura em valores bem abaixo da energia cinética. Estudos anteriores do plasma não-colisional do vento solar sugeriram que a taxa de relaxação da anisotropia na pressão é da ordem de uma pequena porcentagem da giro-frequência dos íons. O presente estudo mostrou que, se este também é o caso para o MIA, então os modelos que melhor representam o MIA são aqueles com taxas de relaxação instantâneas, ou seja, os modelos que revelaram um comportamento muito similar à descrição MHD colisional.

L'objectif de ces travaux de thèse est de proposer des approches de modélisation et d'expérimentation de l'impact de structures déformables et indéformables sur différents milieux. Différents modèles analytiques et des simulations numériques sont développés en comparaison aux résultats expérimentaux. Une première partie se consacre à la caractérisation de la similitude entre la réponse à l'impact à l'eau d'un solide et la réponse d'un solide impactant une structure déformable. Des simulations éléments finis (EF) et SPH sont réalisées pour l'impact à l'eau d'un tube cylindrique (sans rupture). Un modèle analytique d'impact à l'eau est proposé pour prédire l'évolution de l'effort (pic, durée). L'analyse des résultats permet de dimensionner un programmateur d'impact solide reproduisant le pic d'effort. Des simulations EF de l'impact sur un tube cylindrique, à géométrie adapté, dans la direction longitudinale, sont réalisées et comparées à quelques expériences tests. Le «flambage dynamique» (dû au comportement inélastique du matériau et aux ondes de déformations) des tubes est alors observé. Une seconde partie traite du cas de la perforation sous impact d'une tôle mince à faibles vitesses d'impact (< 10 m/s, vitesse de déformation < 1000 s-1). Des essais sur puits de chute instrumenté (force, déplacement, déformée de tôle, avancée de fissure) sont analysés. Des simulations EF en éléments coques avec un critère de rupture ductile par endommagement sont réalisées. Les paramètres de rupture dynamique sont identifiés par méthode inverse à l'aide d'essais de résilience Charpy sur l'alliage d'aluminium de désignation 2024 T3. Une analyse des pics de force lors de l'impact permet une meilleure compréhension des mécanismes de perforation. En parallèle, un nouveau modèle analytique, basé sur les énergies impliquées lors de l'impact, est proposé et comparé aux simulations EF. L'étude numérique de la perforation est étendue aux grandes vitesses d'impact et de déformation (100 - 1000 m/s, vitesse de déformation <100 000 s-1) pour identifier les transitions des différents mécanismes de perforation connus (pétalisation, fragmentation des pétales, fragmentation complète). / The objective of this work is to propose approaches to model and to assess experimentally the structural impact on different media. A variety of analytic models and numerical simulations are developed comparing to experimental results. The first part of this work presents a discussion on the similitude between a water impact and an impact on a deformable solid structure. Water impact simulations of a deformable cylinder (without rupture) are performed by finite elements (FE, Coupled Eulerian Lagrangian) and SPH analysis. An analytical model of water impact is proposed for the prediction of peak force evolution. The analysis of results permits to design an impact programmer reproducing this peak force. FE longitudinal impact simulations on cylindrical tubes, with an adapted geometry, are performed and compared with some experiments. The “dynamic buckling” of tubes under impact (due to the material inelastic behavior and to strain waves) is observed. The second part deals with the low velocity perforation (< 10 m/s, strain rate < 1000 s-1) of thin plates. Some experiments on an instrumented drop test (force, displacement, plate shape, crack propagation) are analyzed. Shell FE simulations, with a damage rupture criteria implemented are performed. Parameters are identified by inverse method with the help of Charpy tests made on 2024 T3 aluminum alloy. An analysis of the peak force, during impact, leads to a good understanding of the perforation mechanism. In parallel, a new analytical model, based on an energetic approach of the perforation, is proposed and compared with FE simulations. The numerical perforation study is extended to high velocities and high strain rates (100 - 1000m/s, strain rate < 100 000 s-1) in order to identify different well-known transitions of perforation (Petalisation, petals' fragmentation, total plate's fragmentation).

Les travaux de thèse sont consacrés à l’étude numérique de l’application de macro-déformations successives alternées a la paroi d’un tube. La modification de l’écoulement du fait des déformations permet de modifier ses propriétés en termes de transfert thermique et de mélange. L’objectif de l’étude d’un tel dispositif est entre autre de l’appliquer pour des configurations d’échangeurs multifonctionnels, qui sont à la fois échangeurs de chaleur et réacteurs chimiques. L’étude s’intéresse principalement aux écoulements laminaires. Les calculs sont réalisés avec le code ANSYS Fluent. L’étude est tout d’abord consacrée à la caractérisation de l’écoulement secondaire créé par les déformations ainsi qu’à l’influence des différents paramètres de déformation. Afin d’améliorer le mélange dans l’écoulement, l’étude d’une configuration coaxiale déformée a été envisagée (cette géométrie correspond de plus à une configuration d’écoulement utilisée dans l’industrie). Deux configurations annulaires ont été considérées. Dans un premier temps, les déformations pariétales ont été appliquées aux tubes interne et externe : différents déphasages longitudinaux et angulaires entre ces deux déformations ont été étudiés pour optimiser les performances thermo-hydrauliques. La seconde configuration combine des déformations sur la paroi externe et un swirl sur la paroi interne de la géométrie. Cette configuration particulière permet en régime laminaire d’augmenter significativement le mélange du fait de l’apparition d’advection chaotique dans l’écoulement. Cette dernière géométrie est appliquée dans le cas d’un échangeur solaire à concentration et permet d’améliorer les performances par rapport à un tube lisse dans des conditions similaires. La dernière partie de l’étude est consacrée à une validation expérimentale des résultats numériques lorsque les déformations sont appliquées à une plaque. Des mesures par PIV et LDA ont été réalisées pour mesurer la vitesse locale de l’écoulement. / The work presented here is focused on the numerical study of specific successive wall deformations in alternate directions, applied to a tubular geometry. Those deformations help modifying the flow structure and thus its heat transfer and mixing properties. One of the main aims of the study is to apply those deformations to multifunctional exchangers which are heat exchangers and chemical reactors at the same time. The study is mainly focused on laminar flows and all the numerical calculations were performed using the CFD code ANSYS Fluent. The first step of the study is to assess the secondary flow created by the wall deformations. The influence of several deformation geometrical parameters has also been studied. In order to enhance the mixing in the deformed tube, the wall deformations have been applied to coaxial configurations (often used in the industry). Two kinds of annular configurations have been evaluated. At first, the wall deformations are applied to the external and internal walls of the coaxial tube. The effect on the heat transfer enhancement of the longitudinal and angular phase-shifting between the two deformations has been specifically assessed. The second configuration considered combines the alternate deformations on its external walls and a swirled internal wall. This particular annular configuration creates chaotic advection in laminar flows, therefore helping increasing the mixing. This geometry is used as a solar captor and helps increasing the global performances when compared with a smooth tube usually used. The last part of the presented work is focused on the experimental validation of the numerical results. Techniques such as PIV and LDA are used to measure local velocity fields in a plane duct with alternate deformations applied to its lower wall.

L'objectif principal de cette thèse est de proposer de nouveaux mécanismes de transport de solides dans les disques protoplanétaires afin de résoudre le problème de la dérive radiale des solides causée par la friction du gaz. En effet, malgré d'importants efforts théoriques et expérimentaux, il reste difficile à expliquer comment de petites particules de poussière submillimétriques forment des blocs kilométriques dans les conditions qui règnent au sein des disques protoplanétaires. Je montre que les mécanismes de transport proposés dans cette thèse sont en mesure de résoudre ce problème de dérive et j'étudie leurs effets sur la formation des premiers solides. Dans un premier temps, je considère les effets de la photophorèse et des jets magnétiques sur le mouvement radial des grains dans les disques protoplanétaires. Le premier est dû aux effets thermiques du rayonnement stellaire sur la surface des grains, tandis que le deuxième est provoqué par les lignes de champ magnétique stellaire qui traversent le disque. Les résultats sont obtenus en résolvant les équations du mouvement des particules de façon numérique. Le transport induit par ces mécanismes a d'importantes conséquences pour la composition des météorites qui sont discutées dans le contexte de la nébuleuse solaire. Dans un deuxième temps, j'étudie la formation de pièges à particules causés par la présence de plusieurs planètes dans le disque grâce à des simulations hydrodynamiques. Ces résultats incluent la croissance des grains et sont directement comparés aux travaux similaires considérant une seule planète dans le disque. Le cas de l'étoile HD 100546, pour lequel les observations récentes suggèrent la présence de deux planètes dans le disque, est examiné en détail. L'évolution du disque en considérant différentes tailles de grain est étudiée au moyen de simulations hydrodynamiques SPH. Les distributions de la poussière et du gaz dans le disque sont particulièrement révélatrices car elles permettent de mettre à l'épreuve les différents scenarios proposés par les observations. L'étude de ces mécanismes montre que, selon leur taille et leur composition, les grains s'accumulent à différentes distances radiales dans le disque. Ces processus empêchent donc l'accrétion des solides par l'étoile et résolvent ainsi le problème de la barrière de dérive radiale. Les futures observations avec des instruments tels que ALMA, SPHERE et MATISSE permettront de mieux contraindre l'efficacité de ces mécanismes dans les disques protoplanétaires / The main goal of this work is to study new transport mechanisms of solids in protoplanetary disks and its implications for the composition of the first solids. The motion of solids inside the disk leads to the so-called radial-drift barrier caused by the gas aerodynamic drag, which is a severe problem for planet formation theory. In this context, it is hard to explain how sub-mm grains reach planetesimal sizes during the disk lifespan. First of all, I study the effects of photophoresis on the dust grains illuminated by the stellar radiation and quantify the efficiency of radial transport as a function of the particle properties. Then, I study the ejection of particles from the inner regions of the disk via the so-called stellar fountain model. Due to the stellar magnetic field which threads the disk, solid particles enter a jet that sends them outwards up to a few astronomical units. Both processes, photophoresis and jets, have important implications for the composition of meteorites which are discussed within the Solar Nebula scenario. In the last chapter, I study dust dynamics in multi-planetary systems through SPH simulations. The formation of particle traps in a disk with two planets is treated in detail and compared to previous work considering a single planet. Then I consider the case of HD 100546, a star with a disk which might harbor two planets according to recent observations, and study the disk evolution in different scenarios. By considering different grains sizes it is then possible to establish a link with interferometric observations of the system. We consider models with different planetary masses and radial distances in order to better constrain these quantities. The study of these mechanisms reveals that, according to particle size and composition, grains can pile up at different radial distances in the disk. This prevents the accretion by the central star by stopping the radial drift of solids, which shows that these mechanisms are good candidates to solve the radial-drift barrier. Future observations using ALMA, SPHERE and MATISSE will provide insights into the efficiency of these transport processes in protoplanetary disks

Cette thèse est consacrée à l’étude des systèmes d’équations différentielles ordinaires, et ceux aux dérivées partielles paraboliques issus de modèles de dynamique des populations et de la biologie. L’objectif principal est de faire l’analyse mathématique, la simulation numérique ainsi que l’identification des diffusions croisées dans les modèles construits. Nous présentons d’abord un système de réaction-diffusion modélisant la croissance de plantes en compétition spatiale dans un milieu saturé. Nous effectuons par la suite l’étude théorique et numérique de tels systèmes, ainsi que l’étude des problèmes d’identification des termes de diffusions croisées. Ensuite, nous proposons un modèle proie-prédateur de type Leslie-Gower modifié avec une fonction de réponse de type Crowley-Martin. Nous étudions dans un premier temps la dynamique temporelle globale du modèle considéré, et nous présentons des simulations numériques pour illustrer les résultats théoriques. En outre, nous introduisons la dimension spatiale dans le modèle dynamique considéré, et nous effectuons une analyse théorique complète de la dynamique spatio-temporelle du modèle. / This thesis is devoted to the study of ordinary differential systems, and systems of non linear parabolic PDEs resulting from models of population dynamics and biology. The main objective is to perform mathematical analysis, numerical simulations, and identification of cross-diffusion in built models. We first present a reaction-diffusion system that models the spatial competition of plants in a saturated environment. We then perform a theoretical and a numerical study of such systems, and handle the identification of cross-diffusion problem. Secondly, we propose a modified Leslie-Gower-type predator-prey model with a Crowley-Martin type functional response. Within this context, we study the global temporal dynamics of the considered model, and present numerical simulations as illustration of the theoretical results. Finally, we introduce the spatial dimension in the previous dynamical model, and perform a comprehensive theoretical analysis of the spatio-temporal model.

Les systèmes d’assistance à la réverbération sont des dispositifs électroacoustiques installés dans les salles de spectacle pour moduler leur acoustique en fonction du type de représentation qui s’y déroule. Afin de pouvoir dimensionner ces systèmes en amont de leur installation, ce travail s’intéresse au développement, à la mise en œuvre et à la mise à l’épreuve de modèles prévisionnels de l’effet de ses systèmes sur les caractéristiques acoustiques d’une salle, en se concentrant sur les systèmes dits régénératifs diagonaux. Le premier modèle présenté est basé sur une approche systémique exacte et sur l’utilisation de simulations numériques. Il s’agit d’un modèle dont le principe est déjà décrit dans la littérature spécialisée, mais auquel est intégré ici un algorithme de détermination automatique des paramètres de réglage d’un système d’assistance à la réverbération reproduisant la méthode manuelle. Parce que l’utilisation de simulations numériques impose une modélisation détaillée de la salle et un important temps de calcul, ce modèle n’est pas compatible avec la réactivité demandée lors d’une phase d’avant-projet. Dans cette optique, deux autres modèles bases sur les hypothèses de champ diffus et, par là même, plus rapides d’exécution, sont développés. L’un repose aussi sur une approche systémique exacte, mais utilise la théorie stochastique de l’acoustique géométrique des salles plutôt que des simulations numériques. L’autre repose sur une approche énergétique simple. Les confrontations de ces deux modèles avec celui reposant sur des simulations numériques sont exposées pour cinq salles, en considérant la prévision d’évolution de six indices acoustiques courants due à l’introduction d’un système d’assistance à la réverbération. Il en ressort que ces deux modèles aboutissent à des erreurs prévisionnelles comparables et que celles-ci sont équivalentes à celles des formules de Sabine ou d’Eyring ou de la théorie révisée des champs diffus de Barron et Lee appliquées dans une salle sans système. Parallèlement, l’étude et la prévision de l’effet d’un système d’assistance à la réverbération régénératif en augmentation du couplage de deux espaces mal couples au sein d’une même salle sont présentées. Il est montré que ce type d’utilisation permet effectivement une augmentation du couplage et que celle-ci peut être correctement abordée à partir d’un modèle énergétique développé ici. Il est aussi montré à partir de simulations numériques, que cette utilisation permet d’homogénéiser les caractéristiques acoustiques entre les deux espaces couplés. / Reverberation enhancement systems (RES) are electro-acoustic devices installed in auditoria to adapt the listening conditions according to the performances. In order to design these systems before their installation, this work deals with the development, the implementation and the testing of prediction tools of the effect of these systems on the acoustic characteristics of a room, by focusing on diagonal regenerative RES. The first proposed tool is based on a systemic approach and numerical simulations. This tool, whose principle is already described in the literature, is here enhanced by the use of an algorithm that automatically fine-tunes the system parameters. As numerical simulations require detailed 3D models of rooms and high computation times, this tool is not compatible with the responsiveness needed for a preliminary design stage. With this in mind, two other models based on the diffuse field assumptions are also developed to predict the action of a RES. One of them is also based on a systemic approach but it uses the stochastic geometric theory of room acoustics instead of numerical simulations. The other model is based on a simple energetic approach. The confrontation of the results given by these two models with the results given by the model based on numerical simulations has been carried out in five rooms considering the effect of a RES on six common room acoustic criteria. It appeared that these two models lead to prediction errors similar to those obtained with the Sabine or Eyring’s formula, or the Barron and Lee’s revised theory applied in a room without RES. In the same time, the study of the effect of a RES used to enhance the coupling between two poor coupled room is presented. It is shown that this particular use of a RES actually increases the coupling effect, and that this effect can be correctly described and predicted by an energetic model developed here. It is also shown by numerical simulations that this system can balance the listening conditions between two coupled rooms.

In our everyday life, turbulence is an omnipresent phenomenon and yet remains poorly understood. Its random and chaotic nature makes it a subject almost impossible to treat from the mathematical point of view and, at present, there<p>is no real prospect of a simple analytic theory. Scientists have therefore regarded the numerical simulation as an alternative to compute the relevant properties of turbulent flows. In this context, our thesis aims at developing and using accurate computational methods, namely pseudo-spectral methods, for studying hydrodynamic (1st part) and magnetohydrodynamic (2nd part) turbulence.<p><p>In the hydrodynamic part, Chapter I introduces the governing equations of fluid mechanics as well as the main issues related to the numerical study of turbulent flows. In particular, the Direct Numerical Simulations (DNS) of turbulence, in which accurate numerical solutions of the Navier-Stokes equations are obtained, are shown to be limited to moderately turbulent flows.<p>Chapter II introduces the Large Eddy Simulation (LES) technique which aims at simulating highly turbulent flows and which is based on a separation of scales.<p>In practice, it consists of simulating the large - resolved - scales of the flow explicitly while modelling the small - unresolved - scales. Two different approaches for modelling the kinetic energy of the unresolved scales are proposed and their respective advantages and drawbacks are discussed.<p>Chapter III is devoted the study of the mixing-layer using both DNS and LES. It consists of an inhomogeneous turbulent flow which has been studied experimentally and for which well-documented measurements are available. A highly accurate DNS mimicking the same experiment has been produced. It allows to study the inhomogeneity and anisotropy properties of this flow. Also, LES of the same flow, using different models, have been evaluated. In Chapter IV, we explore a pseudo-spectral method to investigate turbulence in a pipe. In this case, the method has to take into account two additional difficulties: i) the presence of the boundary and ii) the axis singularity. We detail how to circumvent these issues.<p><p>The second part of the thesis is devoted to magnetohydrodynamic (MHD) turbulence. It concerns phenomena where electrically conducting flows interact with electromagnetism and for which governing equations are derived in Chapter V. In Chapter VI, a detailed analysis of the energy transfers between the magnetic and velocity fields is performed thanks to a high resolution database of homogeneous MHD turbulence. It provides some insights to understand the physics of the nonlinear interactions and is also a valuable diagnostic in the framework of LES modelling. Finally, the inhomogeneous configuration studied in Chapter III has been extended to MHD. Several statistics related to the kinetic and magnetic energies are measured and LES of this flow are performed and presented in Chapter VII. / Doctorat en sciences, Spécialisation physique / info:eu-repo/semantics/nonPublished

L'époque de la Réionisation est la transition d'un Univers rempli d'hydrogène neutre et relativement froid à un Univers rempli de gaz chaud et ionisé. Cette transition intervient à peine un milliard d'années après le Big Bang. Le processus de réionisation est dû à l'émission de photons ionisants par les premières étoiles et premières galaxies à se former. Le travail de cette thèse consiste en l'étude de la formation des galaxies pendant et après la Réionisation, et en particulier de l'impact de cette dernière sur la formation stellaire. En utilisant des modèles et des simulations numériques, il est possible d'étudier le processus de Réionisation de l'Univers en détail, avec comme contraintes les observations du milieu inter-galactique et des galaxies à haut redshift. Dans cette thèse, je me suis concentré dans un premier temps sur les effets de coupure de la formation stellaire pendant et après la Réionisation de manière globale. J'ai eu accès à des simulations d'un nouveau type, qui modélisent la propagation du rayonnement ionisant couplé avec la dynamique et avec l'évolution des propriétés de la matière dans un volume cosmologique. J’ai aussi étudié en détail l'impact de la Réionisation sur les plus petites galaxies, en particulier, le cas de leur distribution spatiale dans l'Univers local, dans le but de reproduire et comprendre certaines observations. / The Epoch of Reionization is the transition from a Universe full of cold and neutral hydrogen to a hot and ionized Universe: it occurs one billion years after the Big Bang. The Reionization is driven by the ionizing photons emitted by the first stars and galaxies. This thesis analyses the galaxy formation during and after the Reionization. Focusing on the feedback of the Reionization on the stellar formation. Using models and numerical simulations, we can study in details the Reionization process. Observations of galaxies and intergalactic medium at high redshift constrain those models, as well as observations of the local Universe, which is the only place where low luminosity galaxies can be observed. In this thesis, I focus on the radiative suppression of stellar formation caused by the Reionization. For this purpose, I used a new generation of simulations, able to take into account the radiative transfer as well as the hydrodynamics in a cosmological volume. I also studied in details the Reionization of the smallest galaxies, focusing on their spatial distribution in the local Universe to understand and reproduce the observations. I looked in particular at the distribution of satellites around M31-like galaxies and find that the observed vast plane of satellites can be reproduced in our models.

La technique de la microscopie à grille de balayage (SGM) consiste à mesurer la conductance d'un gaz bidimensionnel d'électrons (2DEG) sous l'influence d'une pointe balayant la surface de l'échantillon. Dans ce travail, une approche analytique complétée par des simulations numériques est développée pour étudier la relation entre les mesures SGM et les propriétés électroniques locales dans des systèmes mésoscopiques. La correspondance entre la réponse SGM et la densité locale partielle (PLDOS) est étudiée pour un contact quantique entouré d’un 2DEG en présence ou en absence de désordre, pour une pointe perturbative ou non perturbative. Une correspondance SGM-PLDOS parfaite est trouvée pour des transmissions entières et des pointes locales. La dégradation de la correspondance en dehors de cette situation est étudiée. D’autre part, la liaison entre la réponse SGM et la transformée de Hilbert de la densité locale est discutée. Pour étudier le rôle de la force de la pointe sur la conductance SGM, une formule analytique donnant la conductance totale est obtenue. Dans le cas d'une pointe à taille finie nous proposons une méthode basée sur les fonctions de Green permettant de calculer la conductance en connaissant les propriétés non-perturbées. En plus, nous avons étudié la dépendance des branches de la PLDOS en fonction de l’énergie de Fermi. / The scanning gate microscopy (SGM) technique consists in measuring the conductance of a two dimensional electron gas (2DEG) under the influence of a scanning tip. In this work, an analytical approach complemented by numerical simulations is developed to study the connection between SGM measurements and local electronic properties in mesoscopic devices. The connection between the SGM response and the partial local density of states (PLDOS) is studied for the case of a quantum point contact surrounded by clean or disordered 2DEG for perturbative or non-perturbative, local or extended tips. An SGM-PLDOS correspondence is found for integer transmissions and local tips. The degradation of this correspondence out of these conditions is studied. Moreover, a presumed link between the SGM response and the Hilbert transform of the LDOS is discussed. To study the role of the tip strength, an analytical formula giving the full conductance in the case of local tips is obtained. Furthermore, a Green function method enabling to calculate the quantum conductance in the presence of a finite size tip in terms of the unperturbed properties is proposed. Finally the dependence of the PLDOS branches on the Fermi energy is studied.