Le thème central de la thèse est l'interférométrie atomique et la réduction du bruit de phase lié aux vibrations de l'environnement. Les interféromètres atomiques sont des instruments pouvant permettre des mesures fondamentales de grande précision et cette précision est fortement liée à la vitesse des atomes. L'interféromètre qui était utilisé à Toulouse travaillait alors avec des atomes de lithium aux énergies thermiques et le projet était de pouvoir utiliser des atomes fortement ralentis. Les vibrations du sol (bruit sismique) deviennent alors un inconvénient majeur et il est indispensable de s'en affranchir le plus possible. La première partie du travail fut de prévoir une isolation vis à vis du bruit sismique. Un premier filtre est réalisé en plaçant l'ensemble de la manipulation sur un pendule suspendu par 3 fils. Celui ci atténue les vibrations de fréquence supérieure à sa fréquence propre mais amplifie celles de fréquences voisines de celle-ci. Il faut donc un pendule asservi et cela implique un sismomètre sensible pouvant fonctionner sous ultravide. Nous avons développé une stabilisation des mouvements horizontaux en nous appuyant tout d'abord sur des sismomètres simples mais peu sensibles, puis nous avons cherché à améliorer les performances en réalisant un capteur de déplacement basé sur un interféromètre de Michelson à coins de cube. Nous avons suivi en cela les travaux de l'équipe de M.Zumberge qui utilise une détection de deux signaux en quadrature ce qui permet une mesure de déplacement avec une sensibilité meilleure que 4.10-13 m/vHz à 1 Hz et entrepris d'adapter cette technologie à un fonctionnement sous ultravide. Mais les difficultés rencontrées et l'abandon de l'interféromètre tel qu'il était pour en developper un nouveau ne nous ont pas permis d'atteindre complètement notre but et de pouvoir tester le sismomètre in-situ.Cependant, la mise au point et l'optimisation du sismomètre nous a amené à nous pencher sur la théorie des pendules à lame élastique, lesquels sont largement utilisés dans ce genre de capteurs. Il nous est apparu que cette théorie était très incomplète et nous avons entrepris une étude plus systématique de tels pendules ce qui a donné lieu à une publication et fait l'objet de la seconde partie de la thèse. [...] / The main theme of my thesis is atomic interferometry and in particular the reduction of the phase noise induced by vibrations. Atomic interferometers are good devices to achieve accurate and fundamental measuring. The sensibility of these devices is related to the flying time of the atoms inside the apparatus. At Toulouse, our interferometer worked with atoms at thermal velocity and to increase the sensibility we wanted slower atoms. However, this will at the same time increase the effect of vibrations, witch result in a larger phase noise and a jamming of the fringes. In order to reduce this effect, I've put the core of the interferometer on a 3 wires pendulum. A pendulum attenuates the vibrations of frequencies much higher than its resonant frequencies but amplifies those with frequencies close to its resonances. To avoid this phenomenom, we have to enslave the pendulum on the signal given by seismometers. With a first realisation, I was able to stabilize 2 horizontal movements with 2 low sensibility seismometers. To increase the performances, I needed high sensibility seismometer and the possibility to operate under ultra vacuum. I've made a deplacement sensor based on the Michelson interferometer with cube corners, following the works of Zumberge's team. By choosing cleverly the polarisation of the laser beam, we can detect 2 signals in quadrature and the sensibility achieved is better than 4x10-13 m/vHz at 1 Hz. The next step was to migrate this seismometer in ultra vacuum but the retirement of the interferometer using slow down lithium atoms at the benefit of an atomic fountain of rubidium stopped this project. However, this work on the seismometer led me to think about elastic blade pendulums, widely used in such sensors. I've complete the theory, showing the presence of 2 resonance frequencies and, as a test, I've build a such pendulum, for witch I've measured the caracteristics with some position and velocity sensors I've developped for this purpose. I was able to measure precisely the damping of the oscillations of the pendulum and study more precisely the different origins of the damping. Two of them have given some additionnal work : a)the coupling with the resonances of the frame witch support the pendulum may have an effect on the quality factor of the pendulum. [...]

Fluid motion has always been of great importance for humanity since much of our progress has been related to our understanding of fluid dynamics and to our control over the fluids surrounding us. In particular, the experimental techniques and the methods for numerical simulation developed during the last century allowed for great progresses both in creating new technologies and in improving old ones. Despite the great importance of experimental techniques, measuring all properties of a fluid throughout the whole domain, without intefering with the flow to be studied, is impossible. Also, building models even in scale is usually expansive. Both of these reasons have driven the development of numerical methods to the point they became an invaluable tool for fluid dynamic studies and the main tool for developing engineering solutions. If numerical methods are to be of any use, though, they have to correctly describe the problem geometry as well as capture the rich dynamics in a variety of flow situations, such as turbulence, boundary-layers and shock-waves. This thesis addresses two of these problems. In particular, I show modified versions of two immersed-interface methods to describe the geometry, simplifying their implementations with no impact to their applicability. I also introduce two methods for handling shock-waves: first aiming to minimize computational costs, then improving shock-wave resolution without increasing the number of grid points. / O movimento dos fluidos sempre foi de grande importância para a humanidade, dado que muito de nosso progresso esteve intimamente relacionado a um entendimento mais profundo de fluidodinâmica e de como controlar os flúidos ao nosso redor. Em particular, os métodos experimentais e de simulação computacional, desenvolvidos no último século, nos permitiram grandes avanços na criação de novas tecnologias e na otimização das já existentes. Apesar de sua grande importância, as dificuldades de se mensurar todas as propriedades de um flúido em todo o espaço, sem interferir com o comportamento do fluxo, além dos custos de se elaborar experimentos em tamanho real ou em escala, fez com que cada vez mais os métodos numéricos se tornassem uma importante ferramenta no estudo da fluido dinâmica e a principal ferramenta para o desenvolvimento de soluções de engenharia. Porém, para efetivamente substituir experimentos, os métodos numéricos tem que ser capazes de corretamente descrever a geometria do problema, além de capturarem todo tipo de comportamento apresentado pelos flúidos, como turbulência, camada limite e ondas de choque. Esta tese busca contribuir com dois destes desafios. Em particular, mostro versões modificadas de métodos de interface imersa para a descrição da geometria, simplificando as implementações originais sem prejudicar sua aplicabilidade. Também abordo métodos para tratar ondas de choque: primeiro buscando minimizar o esforço computacional e depois buscando aumentar a resolução do choque sem precisar refinar a malha computacional.

Le but de cette thèse est la construction d'une méthode de calcul effectif des multiplicateurs de Stokes avec évaluation de l'erreur. Cette méthode s'applique à tous les systèmes de niveau unique et au premier niveau des systèmes de niveaux multiples. Dans une partie théorique, nous commençons par établir la résurgence des solutions formelles en suivant la méthode d'Ecalle par perturbation régulière et séries majorantes. Nous déduisons de celle-ci une description précise des singularités dans le plan de Borel en déterminant les coefficients de résurgence et les multiplicateurs de Stokes. Dans la partie numérique, nous supposons que les systèmes sont à coefficients rationnels et nous choisissons de travailler dans le plan de Borel en calculant les coefficients de résurgence par prolongements analytiques successifs. En particulier, nous construisons des algorithmes permettant d'évaluer l'erreur. Nous illustrons également cette méthode de calcul par plusieurs exemples numériques.

This thesis is on the existence and uniqueness of weak solutions to the Navier-Stokes equations in R3 which govern the velocity of incompressible fluid with viscosity ν. The solution is obtained in the space of tempered distributions on R3 given an initial condition and forcing data which are dominated by majorizing kernels. The solution takes the form of an expectation of functionals on a Markov process indexed by a binary branching tree. / Graduation date: 2012

Recent increases in computing power and memory have created renewed interest in alternative grid schemes such as unstructured grids, which facilitate rapid grid generation by relaxing restrictions on grid structure. Three rotor models have been incorporated into a popular fixed-wing unstructured computational fluid dynamics (CFD) solver to increase its capability and facilitate availability to the rotorcraft community. The benefit of unstructured grid methods is demonstrated through rapid generation of high fidelity configuration models. The simplest rotor model is the steady state actuator disk approximation. By transforming the unsteady rotor problem into a steady state one, the actuator disk can provide rapid predictions of performance parameters such as lift and drag. The actuator blade and overset blade models provide a depiction of the unsteady rotor wake, but incur a larger computational cost than the actuator disk. The actuator blade model is convenient when the unsteady aerodynamic behavior needs to be investigated, but the computational cost of the overset approach is too large. The overset or chimera method allows the blades loads to be computed from first-principles and therefore provides the most accurate prediction of the rotor wake for the models investigated. The physics of the flow fields of these models for rotor/fuselage interaction are explored, along with efficiencies and limitations of each methodology.

Thèse (D.Eng.)--Université du Québec à Chicoutimi, 2001. / Document électronique également accessible en format PDF. CaQCU

Zugl.: Stuttgart, Univ., Diss., 2009

anglicky In the presented work, we study the existence and uniqueness of solutions to the generalized Stokes problem. We, further, focus on the higher differentiability and the Hölder continuity of solutions to the generalized Stokes and generalized Navier-Stokes system. We reach the full regularity in an arbitrary dimension for a linear case, while in a nonlinear case we work only in dimensions d = 2, 3. In dimension d = 2 we are able to proof the full regularity of solution, in dimension d = 3 we obtain only a partial regularity. All main results are introduced in the first section. 1

Some climate models are still lacking features such as dynamical modelling of ice sheets due to their computational cost which results in poor accuracy and estimates of e.g. sea level rise. The need for low-cost high-order models initiated the development of the First-Order Stokes (or Blatter-Pattyn) model which retains much of the accuracy of the full-Stokes model but is also cost-effective. This model has proven accurate for ice sheets and glaciers with frozen bedrocks, or no-slip basal boundary conditions. However, experimental evidence seems to be lacking regarding its accuracy under sliding, or stress-free, bedrock conditions (ice-shelf conditions). Hence, it became of interest to investigate this. Numerical experiments were set up by formulating the first-order Stokes equations as a variational finite element problem, followed by implementing them using the open-source FEniCS framework. Two types of geometries were used with both no-slip and slip basal boundary conditions. Specifically, experiments B and D from the Ice Sheet Model Intercomparison Project for Higher-Order ice sheet Models (ISMIP-HOM) were used to benchmark the model. Local model errors were investigated and a convergence analysis was performed for both experiments. The results yielded an inherent model error of about 0.06% for ISMIP-HOM B and 0.006% for ISMIPHOM D, mostly relating to the different types of geometries used. Errors in stress-free regions were greater and varied on the order of 1%. This was deemed fairly accurate, and probably enough justification to replace models such as the Shallow Shelf Approximation with the First-Order Stokes model in some regions. However, more rigorous tests with real-world geometries may be warranted. Also noteworthy were inconsistent results in the vertical velocity under slippery conditions (ISMIPHOM D) which could either be due to coding errors or an inherent problem with the decoupling of the horizontal and vertical velocities of the First-Order Stokes model. This should be further investigated. / Vissa klimatmodeller saknar fortfarande funktioner så som dynamisk modellering av istäcken på grund av dess höga beräkningskostnad, vilket resulterar låg noggrannhet och uppskattningar av t.ex. havsnivåhöjning. Behovet av enkla modeller med hög noggrannhet satte igång utvecklingen av den s.k. Första Ordningens Stokes (eller Blatter-Pattyn) modellen. Denna modell behåller mycket av noggrannheten i den mer exakta full-Stokes-modellen men är också väldigt kostnadseffektiv. Denna modell har visat sig vara noggrann för istäcken och glaciärer med frusna berggrunder eller s.k. no-slip randvillkor. Experimentella bevis tycks dock saknas med avseende på dess noggrannhet under glidning, eller stressfria, berggrundsförhållanden (t.ex. vid ishyllor). Därför ville vi undersöka detta. Numeriska experiment upprättades genom att formulera Blatter-Pattyn ekvatonerna som ett variationsproblem (via finita elementmetoden), följt av att implementera dem med hjälp av den öppna källkoden FEniCS. Två typer av geometrier användes med både glidande och stressfria basala randvillkor. Specifikt användes experiment B och D från Ice Sheet Model Intercomparison Project for Higher-Order ice sheet Models (ISMIP-HOM) för att testa modellen. Lokala fel undersöktes och en konvergensanalys utfördes för båda experimenten. Resultaten gav ett modellfel på ca 0,06 % för ISMIP-HOM B och 0,006 % för ISMIP-HOM D, vilka var mest relaterade till de olika typerna av geometrier som användes. Fel i stressfria regioner var större och varierade i storleksordningen 1 %. Detta ansågs vara ganska noggrant och sannolikt tillräckligt för att ersätta modeller så som Shallow Shelf Approximationen med Blatter-Pattyn-modellen i vissa regioner. Dock krävs mer noggranna tester med mer verkliga geometrier för att dra konkreta slutsatser. Också anmärkningsvärt var motsägande resultat i den vertikala hastigheten under glidande förhållanden (ISMIP-HOM D) som antingen kan ha berott på kodningsfel eller ett modelproblem som härstammar utifrån särkopplingen mellan den horizontella- och den vertikala hastigheten i Blatter-Pattyn-modellen. Detta bör undersökas vidare.

Um problema auxiliar crucial à análise do problema de Stokes Compressível é estudado via a técnica de potenciais de camada dupla em regiões Lipschitz através de um método primeiro utilizado por Verchota e subseqüentemente estendido ao caso parabólico por Brown e Shen. Desse modo, mediante a utilização e cálculo da condição de salto na fronteira é possível estabelecer a existência e unicidade da solução em apropriados espaços funcionais via o estudo de potenciais de camada. / An auxiliary problem crucial to the analysis of the compressible Stokes problem is studied by means of the technique of double layer in Lipschitz regions through a method first used by Verchota and subsequently extended to the parabolic case by Brown and Shen. In this way through the use and calculation of the boundary jump condition it is possible to establish the existence and unicity of the solution in appropriate function spaces via the study of boundary layer potentials.