The studies of particles advected by tubulent flows is an active area of research across many streams of sciences and engineering, which include astrophysics, fluid mechanics, statistical physics, nonlinear dynamics, and also chemistry and biology. Advances in experimental techniques and high performance computing have made it possible to investigate the properties these particles advected by fluid flows at very high Reynolds numbers. The main focus of this thesis is to study the statistics of Lagrangian tracers and heavy inertial particles in hydrodynamic and magnetohydrodynamic (MHD) turbulent flows by using direct numerical simulations (DNSs). We also study the statistics of particles in model stochastic flows; and we compare our results for such models with those that we obtain from DNSs of hydrodynamic equations. We uncover some of aspects of the statistical properties of particle trajectories that have not been looked at so far. In the last part of the thesis we present some results that we have obtained by solving the three-dimensional Euler equation by using a new method based on the Cauchy-Lagrange formulation. This thesis is divided into 6 chapters. Chapter 1 contains an introduction to the background material that is required for this thesis; it also contains an outline of the problems we study in subsequent Chapters. Chapter 2 contains our study of “Persistence and first-passage time problems with particles in three-dimensional, homogeneous, and isotropic turbulence”. Chapter 3 is devoted to our study of “Universal Statistical Properties of Inertial-particle Trajectories in Three-dimensional, Homogeneous, Isotropic, Fluid Turbulence”. Chapter 4 deals with “Time irreversibility of Inertial-particle trajectories in Homogeneous, Isotropic, Fluid Turbulence”. Chapter 5 contains our study of the “Statistics of charged inertial particles in three-dimensional magnetohydrodynamic (MHD) turbulence”. Chapter 6 is devoted to our study of “The Cauchy-Lagrange method for the numerical integration of the threedimensional Euler equation”.

We investigate classically (iso)spinning topological soliton solutions in (2+1)- and (3+1)-dimensional models; more explicitly isospinning lump solutions in (2+1) dimensions, Skyrme solitons in (2+1) and (3+1) dimensions and Hopf soliton solutions in (3 +1) dimensions. For example, such soliton types can be used to describe quasiparticle excitations in ferromagnetic quantum Hall systems, can model spin and isospin states of nuclei and may be candidates to model glueball configurations in QCD.Unlike previous work, we do not impose any spatial symmetries on the isospinning soliton configurations and we explicitly allow the isospinning solitons to deform and break the symmetries of the static configurations. It turns out that soliton deformations clearly cannot be ignored. Depending on the topological model under investigation they can give rise to new types of instabilities, can result in new solution types which are unstable for vanishing isospin, can rearrange the spectrum of minimal energy solutions and can allow for transitions between different minimal-energy solutions in a given topological sector. Evidently, our numerical results on classically isospinning, arbitrarily deforming solitons are relevant for the quantization of classical soliton solutions.

L'emboutissage est une technique de mise en forme des tôles métalliques. L'emboutissage est généralement suivi par un phénomène de retour élastique de la tôle emboutie. Le phénomène de retour élastique correspond à une modification de la géométrie de la tôle après enlèvement de la charge d'emboutissage. L'écrouissage du matériau est l'un des facteurs les plus importants qui influence ce phénomène. Dans cette thèse, l'écrouissage de différentes tôles dédiées à l'emboutissage a été étudié en utilisant la technique d'indentation instrumentée. Cette technique permet d'obtenir la loi d'écrouissage d'un matériau à partir de la mesure de l'évolution de l'enfoncement d'une bille dans le matériau testé en fonction de l'effort appliqué sur cette bille. Trois aspects essentiels de l'écrouissage ont été étudiés : La variation de la loi d'écrouissage dans l'épaisseur de la tôle, le niveau d'écrouissage atteint par la tôle après déformation plastique et le type d'écrouissage. Le test d'indentation instrumentée a permis de caractériser chacun de ces aspects influençant le retour élastique. Cet outil peut ainsi être utile dans une démarche d'amélioration de la prédiction du phénomène de retour élastique en emboutissage. / Stamping is a forming technique of the metal sheets. Stamping is generally followed by a springback phenomenon of the stamped sheet metal. The phenomenon of springback corresponds to a modification of the geometry of the sheet after removal of the load. One of the most important factors influencing springback is the work-hardening of the material. In this thesis, the work-hardening of different sheet metals used for stamping process was investigated using the instrumented indentation technique. This technique allows obtaining the work-hardening law of a material from the measurement of the evolution of the penetration depth of a ball in the tested material as a function of the applied force on the ball. Three major aspects of the work-hardening were studied: The variation of the work-hardening law in the thickness of the sheet, the level of work-hardening obtained after plastic deformation and the type of the work-hardening. The instrumented indentation test allows characterizing each of these aspects influencing springback. This tool can thus be useful in a process of improving the prediction of the springback phenomenon in stamping.

Cette thèse présente les trois approches : analytique, expérimentale et numérique développées pour étudier le comportement d'une hydrolienne à membrane ondulante. Cette technologie, portée par l'entreprise EEL Energy, est basée sur les déformations périodiques d'une structure flexible pré-contrainte. Des convertisseurs d'énergie, positionnés de part et d'autre du système, sont actionnés par le mouvement d'ondulation.Analytiquement, la membrane est représentée par un modèle linéaire de poutre à une dimension et l'écoulement par un fluide potentiel 3D. L'action du fluide sur la membrane est évaluée par la théorie des corps élancés. L'énergie est dissipée de façon continue sur la longueur de la membrane. Expérimentalement, un prototype à l'échelle 1/20ième a été développé, des micro-vérins permettent de simuler l'énergie produite. Les essais avec le prototype1/20ième ont permis de valider le concept d'hydrolienne à membrane ondulante et le mode de récupération d'énergie. Un modèle numérique 2D éléments finis a été mis au point. Chaque élément constitutif de la membrane y est reproduit, la dissipation d'énergie est réalisée par des éléments dissipatifs mais la loi d'amortissement est limitée à un amortissement linéaire en vitesse.La comparaison des résultats issus de ces trois modèles a permis de valider leur bonne capacité à reproduire le comportement de la membrane sans conversion d'énergie. La dissipation d'énergie appliquée avec le modèle analytique se distingue clairement des deux autres modèles de part sa localisation mais aussi par la loi d'amortissement utilisée. Les autres modèles sont cohérents entre eux et si on ne parvient pas à corréler les résultats de puissance dissipée, le comportement du système et la répartition de la puissance dissipée le long de la membrane sont semblables. Ces trois approches ont permis de mettre en avant les paramètres clés dont dépend le comportement de la membrane et l'étude paramétrique démontre la complémentarité et l'intérêt du développement conjoint des modèles dans un souci industriel d'optimisation du système. Le développement d'un prototype à l'échelle supérieure (1/6ème), devant faire le lien entre les essais en bassin et les essais en mer, a permis de travailler sur les effets d'échelle. Des différences de comportements sont observées entre ces deux prototypes mais elles sont dues en partie à des différences de conditions aux limites et en partie à des effets de confinements très importants. Pour évaluer la tenue sur le long terme du prototype, ses composants (composite, élastomère) ont été caractérisés précisément et des essais de vieillissement accéléré par température ainsi que des essais de fatigue ont été mis en place sur des échantillons de matière. / This manuscript presents three approaches : analytical, experimental and numerical, to study the behavior of a flexible membrane tidal energy convertor. This technology, developed by the EEL Energy company, is based on periodic deformations of a pre-stressed flexible structure. Energy convertors, located on each side of the device, are set into motion by the wave-like motion.In the analytical model, the membrane is represented by a linear beam model at one dimension and the flow by a 3 dimensions potential fluid. The fluid forces are evaluated by the elongated body theory. Energy is dissipated all over the length of the membrane. A 20th scale experimental prototype has been designed with micro-dampers to simulate the power take-off. Trials have allowed to validate the undulating membrane energy convertor concept. A numerical model has been developed. Each element of the device is represented and the energy dissipation is done by dampers element with a damping law linear to damper velocity.Comparison of the three approaches validates their ability to represent the membrane behavior without damping. The energy dissipation applied with the analytical model is clearly different from the two other models because of the location (where the energy is dissipated) and damping law. The two others show a similar behavior and the same order of power take off repartition but value of power take off are underestimated by the numerical model. These three approaches have allowed to put forward key-parameters on which depend the behavior of the membrane and the parametric study highlights the complementarity and the advantage of developing three approaches in parallel to answer industrial optimization problems.To make the link between trials in flume tank and sea trials, a 1/6th prototype has been built. To do so, the change of scale was studied. The behavior of both prototypes is compared and differences could be explained by differences of boundary conditions and confinement effects. To evaluated membrane long-term behavior at sea, a method of aging accelerated by temperature and fatigue tests have been carried out on prototype materials samples immerged in sea water.

Les mousses métalliques ont connu un essor important durant les dernières décennies. Leur capacité à supporter de très larges niveaux de déformation tout en transmettant de faibles contraintes les rend particulièrement adaptés à des solutions d'absorption d'énergie ou de protection contre des sollicitations intenses.Le comportement dynamique de ce type de matériau peut être influencé par les effets inertiels au niveau des parois ou des ligaments constituant son squelette (micro-inertie). Un modèle de comportement à base micromécanique a été développé pour prendre en compte les effets micro-inertiels sur le comportement macroscopique de mousses à porosités fermées. Le modèle proposé repose sur la procédure d'homogénéisation dynamique introduite par Molinari et Mercier (2001). Par cette approche, les effets micro-inertiels apparaissent sous la forme d'un terme supplémentaire dans le tenseur des contraintes, appelé contrainte dynamique. À partir de comparaisons avec des données extraites de la littérature, il est ainsi démontré qu'inclure les effets micro-inertiels permet d'obtenir une meilleure description de la réponse des mousses sous choc.L'influence d'une épaisseur de mousse localisée entre un explosif et une enveloppe cylindrique a ensuite été étudiée en suivant deux approches. La première, qui s'appuie sur les travaux de Gurney (1943), repose sur des considérations énergétiques. La seconde méthode permet d'aboutir à une description plus détaillée des tailles et vitesses de fragments. Elle repose sur la combinaison d'un modèle éléments finis pour décrire la propagation de l'onde de choc dans la mousse et l'expansion de l'enveloppe et d'un modèle de fragmentation de type Mott (1947). / Metallic foams have known a growing interest in the last decades. Their ability to undergo very large strains while transmitting only reasonable stress levels makes them particularly suitable for energy absorption applications and protection against intense solicitations. The dynamic behavior of metal foams is linked to inertial effects appearing at the walls and ligaments of the material microstructure (micro-inertia). A constitutive model has been developed to take micro-inertial effects into account when describing the macroscopic behavior of closed-cell foams submitted to dynamic loadings. The proposed approach was developed using the dynamic homogenization procedure introduced by Molinari and Mercier (2001). Within this framework, micro-inertial effects appear as an additional stress term, called dynamic stress. Comparisons with data from literature have showed that including micro-inertia effects allows one to achieve a better description of the foam response under shock loading.The influence of a foam layer placed between an explosive and a cylindrical casing has been investigated by following two approaches. The first one is based on energetic considerations, following the work of Gurney (1943). The second method allows one to obtain a more detailed description of fragment sizes and velocities. It relies on the combined use of a finite element model and a description of the shell fragmentation based on the work of Mott (1947).

In Europe, the deployment characteristics of frontal crash restraints are generally optimised to best protect an average young male, since a 50th percentile male dummy is used in a stylised frontal impact scenario. These single point restraint systems may not provide similar levels of effectiveness when the crash scenarios vary with respect to the regulatory and consumer crash test procedures. Previous research has demonstrated that varying restraint deployment characteristics according to occupant and crash variation can provide further injury reduction in frontal impacts. This thesis reports the investigation conducted to assess the potential real world injury reduction benefit of smart restraint systems in frontal impacts. The intelligent capability of the restraint was achieved by varying the seat belt load limiter (SBL) threshold, according to the frontal crash scenario. Real world accident data (CCIS) were analysed to identify the target population of vehicle occupants and frontal impact scenarios where employing smart load limiters could be most beneficial, particularly in reducing chest injury risk. From the accident sample, the chest was the most frequently injured body region at an AIS 2+ level in frontal impacts (7% of front seat occupants). The proportion of older vehicle front seat occupants (>64 years old) with AIS 2+ injury was also greater than the proportion of younger occupants. Additionally, older occupants were more likely to sustain seat belt induced serious chest injury in low and moderate speed frontal crashes. Numerical simulations using MADYMO software were conducted to examine the effect of varying the load limiter thresholds on occupant kinematics and injury outcome in frontal impacts. Generic baseline driver and front passenger numerical models were developed using a 50th percentile dummy and were adapted to accommodate a 5th and 95th percentile dummy. Simulations were performed where the load limiter threshold was varied in five frontal impact scenarios which were selected to cover as wide a range of real frontal crash conditions as possible. From the simulation results, it was found that for both the 50th and 95th percentile dummy in front seating positions (driver and passenger), the low SBL provided the best chest injury protection, without increasing the risk to other body regions. In severe impacts, the low SBL allowed the dummy to move further towards the front facia, thus increasing the chance of occupant hard contact with the vehicle interiors. The Smart load limiters predicted no injury risk reduction for the 5th percentile drivers, who are shorter and tend to sit closer to the steering wheel. The potential injury reduction of the smart load limiters was quantified by applying the estimated injury risk reduction from the simulation to the real world accident data sample. Thoracic injury predictions from the simulations were converted into injury probability values using AIS 2+ age dependent thoracic risk curves which were developed and validated based on a methodology proposed by Laituri et al. (2005). Real world benefit was quantified using the predicted relative AIS 2+ risk reduction and assuming an appropriate adaptive system was fitted to all the cars in the real world sample. When applying the AIS 2+ risk reduction findings to the weighted accident data sample, the risk of sustaining an AIS 2+ seat belt injury reduced from 1.3% to 0.9% for younger front seat occupants, 7.6% to 5.0% for middle aged front seat occupants and 13.1% to 8.6% for the older front seat occupants. The research findings clearly demonstrate a chest injury reduction benefit across all age groups when the load limiter characteristics are varied. It suggests that employing a smart load limiter in a vehicle would not only benefit older occupants but also middle aged and young occupants. The benefit does appear to be most pronounced for older occupants, since the older population is more vulnerable to chest injury. As the older population of car users is rapidly rising, the benefits of smarter systems can only increase in the future.

The work developed in this thesis focusses on the electrical activity of the heart, from the modeling of the action potential originating from cardiac cells and propagating through the heart, as well as its electrical manifestation at the body surface. The study is divided in two main parts: modeling the action potential, and numerical simulations. For modeling the action potential a dimensional and asymptotic analysis is done. The key advance in this part of the work is that this analysis gives the steps to reliably control the action potential. It allows predicting the time/space scales and speed of any action potential that is to say the shape of the action potential and its propagation. This can be done as the explicit relations on all the physiological constants are defined precisely. This method facilitates the integrative modeling of a complete human heart with tissue-specific ionic models. It even proves that using a single model for the cardiac action potential is enough in many situations. For efficient numerical simulations, a numerical method for solving the heart-torso coupling problem is explored according to a level set description of the domains. This is done in the perspective of using directly medical images for building computational domains. A finite element method is then developed to manage meshes not adapted to internal interfaces. Finally, an anisotropic adaptive remeshing methods for unstructured finite element meshes is used to efficiently capture propagating action potentials within complex, realistic two dimensional geometries.

The motion of shock waves is important in many fields of engineering and increasingly so with medical applications and applications to inertial confinement fusion technologies. The flow structures that moving shock waves create when they encounter a change in area is complex and can be difficult to understand. Previousresearchers have carried out experimental studies and many numerical studies looking at this problem in more detail. There has been a discrepancy between numerical and experimental work which had remained unanswered. One of the aims of this project is to try and resolve the discrepancy between numerical and experimental work and try to investigate what experimental techniques are suitable for work of this type and the exact way in which they should be applied. Most previous work has focused on sharp changes in geometry which induce immediate flow separation. In this project rounded corners will also be investigated and the complex flow features will be analyzed.Two geometries, namely a sharp 172 degree knife-edge and a 2.8 mm radius rounded corner will be investigated at three experimental pressure ratios of 4, 8 and 12 using air as the driver gas. This yields experimental shock Mach numbers of 1.28, 1.46 and 1.55. High-speed schlieren and shadowgraph photography with varying levels of sensitivity were used to qualitatively investigate the wave structures. Particle image velocimetry (PIV), pressure-sensitive paint (PSP) and traditional pressure transducers were used to quantify the flow field. Numerical simulations were performed using the commercial package Fluent to investigate the effect of numerical schemes on the flow field produced and for comparison with the experimental results. The sharp geometry was simulated successfully using an inviscid simulation while the rounded geometry required the addition of laminar viscosity. Reynolds number effects will be only sparsely referred to in this project as the flows under investigation show largely inviscid characteristics. As the flow is developing in time rather than in space, quotation of a distance-based Reynolds number is not entirely appropriate; however, Reynolds number based on the same spatial location but varying in time will be mentioned. The density-based diagnostics in this project were designed to have a depth of field appropriate to the test under consideration. This approach has been used relatively few times despite its easy setup and significant impact on the results. This project contains the first quantative use of PIV and PSP to shock wave diffraction. Previous studies have almost exclusively used density-based diagnostics which, although give the best impression of the flow field, do not allow for complete analysis and explanation of all of the flow features present. PIV measurements showed a maximum uncertainty of 5% while the PSP measurements showed an uncertainty of approximately 10%.The shock wave diffraction process, vortex formation, shear layer structure, secondary and even tertiary expansions and the shock vortex interaction were investigate. The experimental results have shown that using one experimental technique in isolation can give misleading results. Only by using a combination of experimental techniques can we achieve a complete understanding of the flow field and draw conclusions on the validity of the numerical results. Expanding the range of the experimental techniques currently in use is vital for experimental aerodynamic testing to remain relevant in an industry increasingly dominated by numerical research. To this end, significant research work has been carried out on extending the range of the PSP technique to allow for the capture of shock wave diffraction, one of the fastest transient fluid processes, and for applications to low-speed flow (< 20 ms−1).

Le réseau de digues français s'étend sur 9000 km et protège moult enjeux humains et socio-économiques. Les surverses se produisent lorsque le niveau d'eau dépasse la crête de la digue et sont responsables de nombreuses ruptures d'ouvrages. La prévision des caractéristiques des brèches (vitesse de développement, taille finale et hydrogramme) reste délicate, d'autant que les effets de la dynamique de la rivière n'ont jamais été étudiés.Cette étude expérimentale est basée sur cinq essais réalisés en canal sur des modèles physiques de digue cohésifs. Les phases classiques du développement de brèches ainsi que le mécanisme de headcutting ont été observés. L'érosion s'est manifestée à trois échelles spatiales (grain, mm et cm) et la durée des essais a varié entre 1h30 et 10 jours selon les sols. Nous avons constaté que le développement d'une brèche et de la fosse d'érosion devient asymétrique en présence d'une vitesse longitudinale amont. Des essais géotechniques originaux menés à l'IRPHE ont permis de relever des différences importantes sur le mode et la cinétique d'érosion entre les sols testés, toujours en bon accord avec les observations menées sur les modèles de digues.Des essais en brèche de largeur fixe nous ont mis à jour l'émergence d'une hydraulique particulière dans la brèche lorsque le vitesse longitudinale incidente augmente (ressauts, recirculations) qui a un impact sur l'hydrogramme de brèche.Enfin, des simulations menées sous RUBAR20 ont permis de retrouver de nombreuses observations expérimentales tant sur le fonctionnement hydraulique des brèches que sur la sensibilité de la cinétique d'érosion à la contrainte critique d'érosion et à l'érodibilité. / France's embankment network stretches over 9000~km, protecting people and infrastructures. Overtopping occurs when water level rises above the embankment's crest, often leading to breach development. Reliable forecasting of breaches' characteristics (widening rate, final geometry and breach hydrograph) remains a challenging task. Furthermore, the effects of river dynamics have never been studied.This work is based on a campain of five overtopping tests performed on scaled homogeneous cohesive model embankments, carried out in an eight meters recirculated flume. The classical steps of dike breaching were observed, as wall as headcutting. Depending on soil type and water content, erosion occured at three distinct scales (sand grain, mm, cm) while the experiments' durations ranged from 1h30 to 250~h. Evidence was brought that river dynamics can result in a completely asymmetric development of both the breach and scour pit. Simple geotechnical tests showed notable differences on erosion modes and rates among tested soils, consistently with the flume experiments.The study of fixed-width breaches showed that distinguish hydraulic phenomena such as hydraulic jumps and recirculations arise when lateral flow speed increases on the river side, which comes with an important drop in breach flow.In addition, bidimensional numerical simulations offered a practical and satisfying way of modelling breach hydraulics. In particular, the strong surface deformation and important velocity gradients in the vicinity of the breach were well-rendered. Elements relative to breach formation sensitivity to erosion parameters (threshold stress and erodibility coefficient) are also provided.

Cosmological N-body simulations indicate that the dark matter haloes of galaxies should be generally triaxial. Yet, the presence of a baryonic disc is believed to modify the shape of the haloes. The goal of this thesis is to study how bar formation is affected by halo triaxiality and how, in turn, the presence of the bar influences the shape of the halo. We performed a series of collisionless and hydrodynamical numerical simulations, using elliptical discs as initial conditions. Triaxial halos tend to become more spherical and we show that part of the circularisation of the halo is due to disc growth, but part must be attributed to the formation of a bar. We find that the presence of gas in the disc is a more efficient factor than halo triaxiality in inhibiting the formation of a strong bar. / As simulações cosmológicas de N-corpos indicam que os halos de matéria escura das galáxias devem ser em geral triaxiais. Contudo, acredita-se que a presença de um disco bariônico seja capaz de alterar a forma do halo. O objetivo desta tese é o de estudar como a formação de barras é afetada pela triaxialidade do halo e como, por sua vez, a presença da barra influencia a forma do halo. Nós realizamos uma série de simulações numéricas acolisionais e hidrodinâmicas, utilizando discos elípticos como condições iniciais. Os halos triaxiais tendem a se tornar mais esféricos e nós mostramos que parte da circularização do halo é devida ao crescimento do disco, mas parte precisa ser atribuída à formação da barra. Notamos que a presença de gás no disco é um fator mais eficiente do que a triaxialidade do halo em inibir a formação de uma barra forte.