Ce travail de thèse porte sur les instabilités dans les structures minces hyperélastiques. Nous analysons les mécanismes de sélection du motif de flambement dans un solide prismatique fortement pré-contraint. Pour ce système, le modèle de poutre classique d'Euler-Bernoulli n'est pas pertinent du fait de cette forte précontrainte et il est nécessaire de recourir à une description 3-d pour expliquer l'apparition de modes instables de petite longueur d'onde. Notre analyse, fondée sur la théorie de l'élasticité finie incrémentale, montre que la longueur typique du motif de flambement est sélectionnée par l'importance relative de la pré-contrainte et du rapport d'aspect du solide prismatique. Nous nous interrogeons ainsi sur les limites du modèle classique et proposons une piste de réflexion pour la construction de nouveaux modèles. Celle-ci repose sur un développement à deux échelles combiné aux équations d'équilibre du système formulées sous forme faible. Il est alors facile de résoudre les équations exactes à chaque ordre, ce qui donne accès à la cinématique complète du système. Nous mettons en œuvre cette méthode pour l'exemple simple d'un barreau homogène en compression, ce qui nous permet d'établir le modèle classique d'Euler-Bernoulli à partir des équations de l'élasticité 3-d. La dernière partie de ce travail de thèse porte sur l'étude du flambement de systèmes invariants d'échelle : l'étude expérimentale et numérique de la compression d'un prisme à base triangulaire met en lumière une transition inédite d'un mode de flambement étendu vers des motifs localisés. / This Ph.D. work deals with buckling instabilities arising in thin hyper-elastic structures. We focus on instabilities arising in a prismatic solid submitted to finite incompatible pre-strains. We observe that the traditional 1-d Euler-Bernoulli beam model is not applicable to such a system because of the finite inhomogeneous pre-stress. The latter triggers short-wavelength instabilities that are note described by the classical 1-d models. We rely on the 3-d elasticity theory and propose a quantitative criterion on the ratio between the pre-stress and the cross-sectional aspect-ratio of the prismatic solid, that predicts the typical wavelength of the buckling pattern. This work questions the validity of classical 1-d models and suggests that extensions of these models are possible. We propose a method for the systematic derivation of reduced models. It relies on asymptotic expansions of the variational formulation of the equilibrium equations, starting from the complete expression of the energy. In this framework, kinematics can be entirely determined by solving the exact equations, order by order. We successfully apply this method to a homogeneous and isotropic beam submitted to a homogeneous compression and recover the classical Euler-Bernoulli beam model. In a last part of the manuscript we investigate the transition from extended wrinkling to localized creasing in a scale-invariant system made of a prismatic solid with a triangular cross-section, both experimentally and numerically.

Neste trabalho foram estudadas instabilidades magnetohidrodinâmicas (MHD) utilizando um novo sistema bolométrico que foi instalado no tokamak TCABR para medidas da evolução temporal da potência irradiada. Este novo sistema conta com 24 cordas verticais, capazes de mapear toda uma secção poloidal da coluna de plasma com resolução espacial de aproximadamente 2 cm e uma resolução temporal de 20 µs. Como se sabe, as instabilidades MHD degradam o connamento do plasma e modicam a topologia das superfícies magnéticas, causando a perda da energia do plasma. Por conta disso, compreender essas instabilidades é fundamental para o sucesso dos futuros reatores de fusão nuclear. As perturbações (oscilações) causadas pelas instabilidades MHD modulam diversos parâmetros macroscópicos do plasma como a densidade, a temperatura e a potência irradiada. Então, utilizando o diagnóstico bolométrico, é possível medir as oscilações no perl de potência irradiada e, a partir deles, extrair informações importantes para determinar a origem e as características de tais instabilidades. No tokamak TCABR, as instabilidades foram caracterizadas através da análise espectral dos 24 sinais provenientes do novo sistema bolométrico. Para auxiliar a caracterização das instabilidades, um programa foi desenvolvido em Matlab para simular as medidas das perturbações no perl de potência irradiada. Através do mesmo procedimento de análise espectral, os resultados simulados foram comparados aos experimentais de forma que os parâmetros simulados, como largura e posição das ilhas magnéticas, fossem ajustados aos experimentais. Através dessa metodologia de análise, que combina simulação e experimento, foi possível caracterizar diversas instabilidades como o precursor dos dentes de serra e ilhas magnéticas de modos m = 2 e m = 3. / In this dissertation, magnetohydrodynamic (MHD) instabilities were investigated using a new bolometric system that was installed in the TCABR tokamak for radiation power measurements. This diagnostic is composed by 24 vertical chords that provide a full view of the poloidal cross section of the plasma column and provides spatial and temporal proles with approximately 2 cm space and 20 µs time resolution. As it is well known, the MHD instabilities degrade the plasma connement and modify the magnetic topology, leading to energy loss from the plasma. Therefore, the understanding of these instabilities is essential for the success of the controlled thermonuclear fusion reactors. The MHD instabilities also cause perturbations (oscillations) in various macroscopic parameters, such as plasma density, temperature, and radiated power. Therefore, the oscillations in the radiated power prole measured by the bolometric diagnostic system provide a possibility to investigate the origin and features of the instabilities. In the TCABR tokamak, the instabilities were characterized by spectral analysis of the 24 vertical chords of the bolometric signals. In addition, a Matlab program was developed to simulate the integral characteristic of the oscillations in the radiated power measured by the bolometric system. The spectral analysis of the simulated signals is then compared with the spectral analysis of the bolometric signals. The simulated parameters, island width and radial position, were then adjusted to t the experimental spectrum results. Using this method of analysis, which combines experiment and simulation, it was possible to characterize various instabilities, such as sawtooth precursor and m = 2 and m = 3 magnetic islands.

Ce manuscrit présente une étude couplée, numérique et théorique, portant sur les écoulements tournants transitionnels et turbulents. L'accent y est mis sur la formation de structures macroscopiques cohérentes au sein de l'écoulement, générées par des procédés rendus fortement tri-dimensionnels par la présence des couches limites sur les disques et le long des parois cylindriques extérieure (carter) et/ou intérieure (moyeu). La complexité de ces écoulements pose de véritables difficultés en recherche fondamentale mais les résultats de ces travaux ont aussi une importance non négligeable pour les machines industrielles tournantes, depuis les disque-durs jusqu'aux turbopompes spatiales, la conception de ces dernières étant la motivation première pour ces travaux de thèse. Ce travail peut être divisé en deux sous-parties. Dans un premier temps, les cavités industrielles sont modélisées par de simples cavités rotor/stator lisses pour y étudier la dynamique de l'écoulement. Comme les campagnes expérimentales sur les machines industrielles ont révélé de dangereux phénomènes instationnaires en leur sein, l'accent est mis sur l'obtention et l'étude des fluctuations de pression dans les écoulements modèles. Ensuite, les SGE de trois configurations de turbine industrielle réelle sont réalisées pour étudier les fluctuations de pression in situ et appliquer les diagnostiques éprouvés sur les géométries modèles. / This thesis provides a numerical and theoretical investigation of transitional and turbulent enclosed rotating flows, with a focus on the formation of macroscopic coherent flow structures. The underlying processes are strongly threedimensional due to the presence of boundary layers on the discs and on the walls of the outer (resp. inner) cylindrical shroud (resp. shaft). The complexity of these flows poses a great challenge in fundamental research however the present work is also of importance for industrial rotating machinery, from hard-drives to space engines turbopumps - the design issues of the latter being behind the motivation for this thesis. The present work consists of two major investigations. First, industrial cavities are modeled by smooth rotor/stator cavities and therein the dominant flow dynamics is investigated. For the experimental campaigns on industrial machinery revealed dangerous unsteady phenomena within the cavities, the emphasis is put on the reproduction and monitoring of unsteady pressure fluctuations within the smooth cavities. Then, the LES of three configurations of real industrial turbines are conducted to study in situ the pressure fluctuations and apply the diagnostics already vetted on academic problems.

Les chocs sans collision sont omniprésents dans l'Univers, notamment dans les restes de supernova, et sont formés via diverses instabilités plasmas dépendant essentiellement de la vitesse et de la magnétisation des flux de plasmas. La description de tels chocs nécessite une approche cinétique, tant analytique que numérique.Dans cette thèse, nous avons étudié, au travers de simulations Particle-In-Cell (PIC), les processus sous-jacents par lesquels les instabilités rentrent en compétition les unes avec les autres. Nous avons montré que la diminution du rapport des masses entre ions et électrons, souvent utilisée en simulations numériques pour accélérer la dynamique des chocs, peut avoir de fortes conséquences sur le transfert d'énergie entre particules durant la phase non-linéaire des instabilités.Ces dernières, comme l'instabilité acoustique ionique (IAI) amènent sous certaines conditions à la formation de chocs électrostatiques, pouvant donner naissance à la formation de trous dans l'espace des phases, se propageant dans la région aval du choc, et accélérant ce dernier. L'ajout d'un champ magnétique externe conduit à un changement de médiation du choc, pouvant varier entre l'IAI et les ondes magnéto-soniques lente ou rapide en fonction de l'obliquité entre le champ magnétique et la normale au choc. De plus, nous avons montré que l'orientation du champ magnétique permet de choisir entre une dispersion convexe ou concave des ondes plasma conduisant à la création d'ondes précurseurs dans les régions amont ou aval du choc.Ces chocs magnétisés se trouvent être correctement représentés par le modèle magnétohydrodynamique (MHD) tant qu'ils restent laminaire et que leur potentiel dans la région aval n'est pas suffisamment grand pour réfléchir les particules du milieu amont.Nous avons montré que même pour des chocs sous critiques, une fraction d'ions réfléchis, ne pouvant pas être représentés par la MHD, est suffisante à la croissance d'ondes solitaires en amont du choc, conduisant à l’accélération de ce dernier, mais pas à un processus d'auto-reformation comme pour les chocs super critiques.Bien que les échelles spatio-temporelles soient très différentes, les lois d'échelle rendent possible l'étude de tels phénomènes en laboratoire. Nos études numériques ont été faites dans un cadre de type tube à choc pouvant être testé expérimentalement.A ce titre, nous proposons dans cette thèse une expérience sur la création d'îlots magnétiques, formés par l’interaction de plasmas générés par l'irradiation de cibles par laser baignant dans un champ magnétique externe, et conduisant à la formation de tels chocs.Enfin, nous avons démontré expérimentalement et numériquement la formation de chocs électromagnétiques sans collisions par le biais de l'instabilité de Weibel stimulée par l'instabilité de batterie Biermann, conduisant à l'accélération de particules par le mécanisme de Fermi. Ce nouveau type d'expérience pourrait expliquer l'origine du rayonnement cosmique provenant des restes de supernova. / Collisionless shocks are ubiquitous in the Universe, especially in the supernova remnants, and are formed via various plasma instabilities mainly depending on the speed and magnetization of plasma flows. The description of such shocks requires a kinetic approach, both analytical and numerical.In this thesis, we have studied, through Particle-In-Cell (PIC) simulations, the underlying processes by which instabilities compete with each other.We have shown that the reduction of the ion-to-electron mass ratio, often used in numerical simulations to accelerate the dynamics of shocks, can have strong consequences on the energy transfer between particles during the non-linear phase of instabilities.These instabilities, like the ionic acoustic instability (IAI) lead under certain conditions to the formation of electrostatic shocks, which can give rise to phase space holes formation, propagating in the downstream shock region, and accelerating the shock.The addition of an external magnetic field leads to different shock mediation, which can vary between the IAI to the slow or fast magneto-sonic waves as a function of the obliquity between the magnetic field and the shock normal.Furthermore, we have shown that the orientation of the magnetic field makes it possible to choose between a convex or concave dispersion of the plasma waves leading to the creation of precursor waves in the upstream or downstream shock regions.These magnetized shocks are correctly represented by the magnetohydrodynamic (MHD) model as long as they remain laminar and their potential in the downstream region is not large enough to reflect the particles of the upstream medium.We have shown that even for sub-critical shocks, a fraction of reflected ions, which cannot be modeled by the MHD, is sufficient for the growth of solitary waves upstream of the shock, leading to the acceleration of the latter, but not to a process of 'self-reformation' as for super-critical shocks.Although spatio-temporal scales are very different, scaling laws make possible the study of such phenomena in the laboratory. Our numerical studies have been done in the context of shock tubes that can be experimentally tested.As such, we propose in this thesis an experiment on the creation of magnetic islands, formed by the interaction of plasmas generated by the irradiation of laser targets bathed in an external magnetic field, leading to the formation of such shocks.Finally, we experimentally and numerically demonstrated the formation of collisionless electromagnetic shocks through the Weibel instability stimulated by theBiermann Battery instability, and leading to particle acceleration by the Fermi mechanism.This new type of experiment could explain the origin of cosmic radiation from supernova remnants.

Redes neurais artificias, tipo \"feedforward\", de duas camadas, foram utilizadas neste trabalho para fazer previsões das instabilidades de disruptura que surgem nas descargas de plasma do tokamak TEXT (E.U.A.), obtendo-se resultados bastante encorajadores. Verificou-se que uma arquitetura de rede, do tipo m:2m:m:1, onde m é dimensão de imersão do atrator do sistema dinâmico em estudo, costuma ser um bom chute inicial para a escolha da arquitetura ideal de trabalho, que costuma ser livre e, não raro, trabalhosa. Utilizando-se, em sinais de raios-X, uma rede neural artificial com arquitetura 15:30:15:1, por exemplo, conseguiu-se fazer previsões com uma antecipação de até 4 ms das instabilidades de disruptura, tempo quatro vezes maior do que o obtido utilizaudo-se sinais magnéticos das bobinas de Mirnov. Tal antecipação é bastante significativa e abre a possibilidade de, no futuro, utilizarem­se mecanismos de defesa da máquina, tais como injeção de partículas neutras (ou\"pellets\"), aplicação de campos magnéticos externos, etc, no sentido de se tentar evitar a ocorrência destas instabilidades, ou, pelo menos, minimizar os seus efeitos nocivos. Isto certamente contribuirá significativamente para a viabilização dos futuros reatores de fusão à plasma. Finalmente, o sistema de diagnóstico de raios-X de baixas energias do tokamak TCABR, que foi projetado e já se encontra em fase de instalação para fornecer sinais que servirão para alimentar a rede neural, também possibilitará a reconstrução tomográfica das regiões de mesma emissividade da coluna de plasma. A análise tomográfica, utilizando-se os sinais de dois conjuntos de detectores de raios-X moles, também será muito útil na investigação dos mecanismos físicos que dão surgimento às instabilidades de disruptura, além de permitir, ainda, a medida da temperatura eletrônica do plasma, através do método dos absorvedores. / Two-layer feedforward neural network has been used in this work to forecast the disruptive instabilities that occur in the TEXT tokamak plasma discharges. For this task, soft X-ray experimental signals were used with very promising results. It was verified that a neural net with an architecture of the type m:2m:m:1, where m is the embedding dimension of the atractor of dynamical system in focus, is usually a good initial guess in the searching process of finding the ideal architecture. A neural network with architecture 15:30:15:1 was capable, for example, to forecast the disruptive instabilities up to 4 ms in advance. This period of time is four time larger than the one obtained when magnetic signals from Mirnov coils were used. This forecasting time is quite significative and opens up the possibility of using defensive mechanisms, such as the injection of neutral particles (or pellets), the application of external magnetic fields, etc, with the objective of avoiding the occurrence of the disruptions or, at least, to minimize their harmful effects. This achievement certainly would be an important contribution to the development of the next generation fusion devices. Finally, the soft X-ray diagnostic system for the TCABR was projected and it is already being installed. This system will provide experimental signals that will be analyzed by neural networks and will be also used to identify, through tomografic image reconstructions, the regions of the plasma that have the same soft X-ray emissivity. The tomography analysis of the plasma, that will be carried out by using the signals of two soft X-ray detectors arrays, will be also very usefull for investigating the triggering mechanism of disruptions and will also allow the determination of the plasma electron temperature through the two foil absorbing method.

Ces dernières décennies ont vu apparaître de nombreuses innovations dans le domaine de la combustion afin de réduire la consommation et les émissions polluantes. De nouveaux types d'injecteur, de type LPP - Lean Premixed Prevaporized, ont été mis au point permettant de diminuer le rapport combustible/air et visent à pré-vaporiser le carburant en amont de la combustion afin de mieux le mélanger à l'air issu du compresseur. Cette architecture permet une amélioration de la consommation et des émissions polluantes, mais rend les foyers annulaires plus sensibles à des phénomènes instationnaires qui perturbent le fonctionnement du système, accroissent les flux de chaleur vers les parois de la chambre, induisent des vibrations de structures, entrainent une fatigue cyclique des pièces mécaniques et dans des cas extrêmes conduisent à des dommages irréversibles. L'objectif est de poursuivre l'effort engagé au laboratoire EM2C sur ce thème et plus particulièrement sur celui de la dynamique de la combustion dans les chambres annulaires. La thèse concerne plus spécialement le cas où l'injection du combustible s'effectue sous forme liquide. La configuration reproduit sous forme idéalisée celle que l'on trouve en pratique dans les moteurs aéronautiques. La chambre, désignée sous le nom de MICCA-Spray, est équipée de 16 injecteurs swirlés pouvant être alimentés par un combustible liquide ou gazeux, permettant ainsi une combustion diphasique ou prémélangée. Le système possède des parois en quartz donnant un accès optique à la zone de flamme. Il est aussi équipé d'un ensemble de diagnostics tels des microphones, des photomultiplicateurs ainsi que des systèmes d'imagerie à haute cadence. / These last decades have seen many innovations in the field of combustion to reduce fuel consumption and pollutant emissions. New types of injector, for example LPP - Lean Premixed Prevaporized, have then been developed to reduce the fuel / air ratio and aim to pre-vaporize the fuel upstream of the combustion in order to mix it better with the air coming from the compressor. Unfortunately this architecture makes annular chambers more sensitive to unsteady phenomena which disturb the functioning of the system, increase the heat flows towards the walls of the chamber, induce vibrations of structures, cause cyclic fatigue of mechanical parts and in extreme cases lead to irreversible damage. The objective of this thesis is to continue the effort undertaken at the EM2C laboratory on this topic and more particularly on the dynamics of combustion in annular chambers comprising a set of injectors. The thesis concerns more particularly the case where the injection of the fuel takes place in liquid form. This configuration reproduces, in idealized form, what can be found in practice in aeronautical engines. It is also a configuration studied at the fundamental level. The chamber, known as MICCA-Spray, is equipped with 16 swirled injectors that can be powered by liquid or gaseous fuel, thus enabling two-phase or fully premixed combustion. The system has quartz walls giving optical access to the flame zone. It is also equipped with a set of diagnostics such as microphones, photomultipliers and high-speed imaging systems.

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. / Vita. / Includes bibliographies. / Ph.D.

This thesis presents an improved feedback system on HBT-EP and suppression of the fast rotating kink mode using this system. HBT-EP is an experimental tokamak at Columbia University designed to study the magnetohydrodynamic (MHD) instabilities in confined fusion. The most damaging instabilities are global long wavelength kink modes, which break the toroidal symmetry of the magnetic structure and lead to plasma disruption and termination. When a tokamak is surrounded by a close fitting conducting wall, then the single helicity linear dispersion relation of the kink instability has two ominating branches: one is the "slow mode", rotating at the time scale of wall time, known as resistive wall mode (RWM), the other is the fast mode, that becomes unstable near the ideal wall stability limit. Both instabilities are required to be controlled by the feedback system in HBT-EP. In this thesis, improvements have been made upon the previous GPU-based system to enhance the feedback performance and obtain clear evidence of the feedback suppression effect. Specifically, a new algorithm is implemented that maintains an accurate phase shift between the applied perturbation and the unstable mode. This prevents the excitation of the slow kink mode observed in previous studies and results in high gain suppression for fast mode control at all frequency for the first time. When the system is turned off, suppression is lost and the fast mode is observed to grow back. The feedback performance is tested with several wall configurations including the presence of ferritic material. This provides the first comparison of feedback control between the ferritic and stainless wall. The effect of plasma rotation on feedback control is tested by applying a static voltage on a bias probe. As the mode rotation being slowed by the radial current flow, a higher gain on the kink mode is required to achieve feedback suppression. The change in plasma rotation also modifies the plasma response to the external perturbation. The optimal phase shift for suppression changes with the modified response and these observations are consistent with the predictions of the single helicity model.

Protoplanetary discs, composed of gas and dust, usually surround young stellar objects and serve two main purposes: they determine the accretion of matter onto the central object and also represent sites of planet formation. The accretion proceeds through the transport of angular momentum outwards allowing the disc matter to fall towards the centre. A mechanism responsible for the transport can be turbulence, waves or other coherent structures originating from various instabilities in discs that could, in addition, play a role in the planet formation process. For an understanding of these instabilities, it is necessary to study perturbation dynamics in differentially rotating, or sheared media. Thus, this thesis focuses on new aspects in the perturbation dynamics in non-magnetised protoplanetary discs that arise due to their self-gravity and velocity shear associated with the disc’s differential rotation. The analysis is carried out in the framework of the widely employed local shearing box approximation. We start with 2D discs and then move on to 3D ones. In 2D discs, there are two basic perturbation types/modes – spiral density waves and vortices – that are responsible for angular momentum transport and that can also contribute to accelerating planet formation. First, in the linear regime, we demonstrate that the vortical mode undergoes large growth due to self-gravity and in this process generates density waves via shear-induced linear mode coupling phenomenon. This is noteworthy, because commonly only density waves are considered in self-gravitating discs. Then we investigate vortex dynamics in the non-linear regime under the influence of self-gravity by means of numerical simulations. It is shown that vortices are no longer well-organised and long-lived structures, unlike those occurring in non-self-gravitating discs. They undergo recurring phases (lasting for a few disc rotation periods) of formation, growth and eventual destruction. We also discuss the dust trapping capability of such transient vortices. Perturbation dynamics in 3D vertically stratified discs is richer, as there are more mode types. We first consider non-axisymmetric modes in non-self-gravitating discs and then only axisymmetric modes in the more complicated case when self-gravity is present. Specifically, in non-self-gravitating discs with superadiabatic vertical stratification, motivated by the recent results on the transport properties of incompressible convection, we show that when compressibility is taken into account, the non-axisymmetric convective mode excites density waves via the same shear-induced linear mode coupling mechanism mentioned above. These generated density waves transport angular momentum outwards in the trailing phase, and we suggest that they may aid and enhance the transport due solely to convection in the non-linear regime, where the latter becomes outward. In the final part of the thesis, we carry out a linear analysis of axisymmetric vertical normal modes in stratified self-gravitating discs. Although axisymmetric modes do not display shear-induced couplings, their analysis provides insight into how gravitational instabilities develop in the 3D case and their onset criterion. We examine how the structure of dispersion curves and eigenfunctions of 3D modes are influenced by self-gravity, which mode first becomes gravitationally unstable and thus determines the onset criterion and nature of the gravitational instability in stratified discs. We also contrast the more exact instability criterion obtained with our 3D model with that of density waves in 2D discs. Based on these findings, we discuss the origin of 3D behaviour of perturbations involving noticeable disc surface distortions, as seen in some numerical simulations of self-gravitating discs.

The subject of this thesis is to evaluate the main causes of instability in the foreign exchange market in selected countries. The first part is devoted to a summary of the basic theoretical knowledge about the foreign exchange market, its organization and operations of entities intended to hedge against exchange rate risk. The second part focuses on the exchange rate systems. The third chapter focuses on chosen economies, which are included in the final analysis. The main point of the analytical part is focused on the development of turnover on the foreign exchange market in selected countries in terms of the nature of the operations, currency and traded entities. The comparison of the dynamics and structure of the foreign exchange market turnover in selected countries, the system takes into account the applicable exchange rate. Sweden, Denmark, Hungary and Bulgaria were chosen for the analysis, performed during the period 2002 - 2011