Dans cette thèse nous avons proposé un modèle robuste permettant d’expliquer la propagation de bulles dans des systèmes composés de plusieurs cavités de taille micrométrique. Notre modèle s’applique d’abord à deux cavités placées côte à côte, où l’une d’entre elle contient une bulle vibrante provoquant le mouvement de la paroi séparant les deux cavités. Un système d’équations modélisant ce système a été établi. Nous montrons que le choix des conditions initiales contrôle le déclenchement de l’onde de cavitation. En effet, le déphasage entre la vibration de la bulle et de la membrane vibrante donne les conditions nécessaires et suffisantes pour expliquer les observations expérimentales. En s’appuyant sur les résultats théoriques, nous avons développé un modèle macroscopique numérique, très phénoménologique, permettant la propagation de bulles de cavitation et la formation de clusters de bulle. / In this thesis, a robust model is proposed towards explaining bubbles propagation within systems composed by several micrometric cavities. Our first model is based on two cavities placed side by side, one of which contains a vibrating bubble which sets into motion the wall separating the two cavities. A system of equations modeling this system is proposed. It has been proved that the choice of the initial conditions controls the cavitation wave initiation. Indeed, the phase shifts between the bubble vibration and the vibrating membrane gives the necessary and sufficient conditions to explain the experimental observations. In this framework, we have developed a phenomenological and numerical macroscopic model, allowing the propagation of cavitation bubbles and the formation of bubble clusters.

La2Mo2-yWyO9 (y = 1.0 to 2.0) oxides were synthesized by conventional solid state route and studied by XRD, TC-XRD and DTA. A phase diagram of the series was proposed. The thermodynamically stable phases at room temperature are: for 1.0≤ y ≤1.2 a cubic β-La2Mo2O9 type solid solution, for 1.3≤ y ≤1.575 a biphasic mixture of β-La2Mo2O9 type + α-La2W2O9 type phases, and for 1.6≤ y ≤2.0 a triclinic α-La2W2O9 type solid solution. Inhomogeneous distribution of W is suspected in the biphasic samples. It is clear that the compounds above y =1.2 are not suitable for SOFC applications.Cationic diffusion studies were performed using SIMS on La2Mo2O9 (LMO)/La0.8Sr0.2MnO3-δ (LSM) annealed couples. Rod shaped LaMnO3 grains were observed on LMO pellet and SrMoO4 type phases were seen to be growing on LSM pellet. Hypotheses for possible reaction mechanisms are presented. Bulk diffusion coefficients of Sr and Mn in LMO and of Mo in LSM are extrapolated to be around 1x10-20 cm2.s-1 and 1x10-15 cm2.s-1, respectively, at 800oC. Similar diffusion studies were performed by depositing Mn and Sr cation rich solutions on LMO pellets and Mo rich solution on LSM pellet. Mn solution was observed to be forming, upon annealing, LaMnO3 single crystals on the surface of the LMO pellet. Mo in LSM and Sr in LMO diffusion coefficients appear to be much higher than in LMO/LSM couple experiments, namely around 1-2x10-10cm2.s-1 at 1150°C. Because of the reactivity, LMO/LSM couple is not desirable for SOFC applications, unless an appropriate buffer layer separates them.The stability of LMO and W-LMO was studied under reductive atmospheres. Successive structural changes from LMO to La7Mo7O30 (7730), an amorphous reduced phase La2Mo2O7-δ, and partial decomposition to metallic Mo were observed as a function of oxygen loss. The pO2 stability domain of La2Mo2-yWyO9 did not appear to change with W content, but the reduction kinetics varied with y. At reverse, the stability limit of the 7730 phase was found to be dependent on W content. The amorphous reduced phase can accommodate a wide range of oxygen stoichiometry (7-δ from 6.69 to 6.20), but its stability vs. pO2 is questioned. Resistivity measurements performed on a low compacity crack-free amorphous La2Mo2O7-δ sample showed significant increase in the conductivity (> 1 S.cm-1 at 1000 K) relative to La2Mo2O9, with a pseudo activation energy 0.255eV. It is postulated that n-type electronic conductivity arises from partial reduction of hexavalent Mo6+ to a mixture of Mo3+ and Mo4+.

Polarized helium-3 is used as a contrast agent for lungs magnetic resonance imaging that has recently reached the pre-clinical applications. One method to hyperpolarize 3He is the metastability exchange optical pumping (MEOP). Optical pumping is performed in standard conditions at low pressure (~ 1 mbar) and low magnetic field (~ 1 Gauss). In this work, the complete update of a low field polarizer dedicated to small animal lungs imaging is presented. The implementation of a new 10 W laser, new peristaltic compressor and others components resulted in a production of 3-4 scc/min for a polarization between 30 to 40%. Images of rat lungs made with better resolution and a new dynamic radial sequence are presented as a validation of the system. Since few years, MEOP has also been studied at higher pressures and higher magnetic fields in small sealed cells. It showed that, thanks to hyperfine decoupling effect induced by high magnetic field, it was also possible to efficiently polarize at higher pressure (67 mbar). Experiments done at 4.7 and 1.5 T are reported in this work. The first ones show a benefic (higher polarization values) and a negative effect (lower production rates) of the magnetic field. The seconds highlight the advantage of using an annular beam shape of the laser that matches the distribution of 23S state atoms at higher pressure. Nuclear polarization values of 66.4% at 32 mbar and 31% at 267 mbar were obtained in 20 mL sealed cells and a 10 times increase in the production rate compare to best standard conditions. These promising results were the first motivation for building a high-field polarizer working inside MRI scanner in hospital. The design and the construction of such a polarizer are described in detail in the last part of the dissertation. The polarizer produces hyperpolarize 3He at 30-40% with a 4 times higher flow than the low field polarizer (10-15 scc/min). The first good quality human lungs images made in Poland with healthy volunteers are the main result of this work.

Dans cette thèse, nous étudions le comportement asymptotique précis à basse température de l’événement de sortie d'un domaine métastable $Omegasubset mathbb R^d$ (point de sortie et temps de sortie) pour le processus de Langevin sur amorti. En pratique, le processus de Langevin sur amorti peut par exemple simuler l'évolution des positions des atomes d'une molécule ou la diffusion d'impuretés interstitielles dans un cristal. Nos résultats principaux concernent le comportement asymptotique précis de la distribution de la loi du point de sortie de $Omega$. Dans la limite d'une petite température, ces résultats permettent de justifier l'utilisation de la formule d'Eyring-Kramers pour modéliser les événements de sortie de $Omega$. La loi d'Eyring-Kramers est par exemple utilisée pour calculer les taux de transition entre les états d'un système dans un algorithme de Monte-Carlo cinétique afin de simuler efficacement les différents états visités par le système. L'analyse repose de manière essentielle sur la distribution quasi stationnaire associée au processus de Langevin sur amorti dans $Omega$. Nos preuves utilisent des outils d'analyse semi-classique. La thèse se décompose en trois chapitres indépendants. Le premier chapitre (rédigé en français) est une introduction aux résultats obtenus. Les deux autres chapitres (rédigées en anglais) sont consacrés aux énoncés mathématiques / This thesis is dedicated to the study of the sharp asymptotic behaviour in the low temperature regime of the exit event from a metastable domain $Omegasubset mathbb R^d$ (exit point and exit time) for the overdamped Langevin process. In practice, the overdamped Langevin dynamics can be used to describe for example the motion of the atoms of a molecule or the diffusion of interstitial impurities in a crystal. The obtention of sharp asymptotic approximations of the first exit point density in the small temperature regime is the main result of this thesis. These results justify the use of the Eyring-Kramers law to model the exit event. The Eyring-Kramers law is used for example to compute the transition rates between the states of a system in a kinetic Monte-Carlo algorithm in order to sample efficiently the state-to-state dynamics. The cornerstone of our analysis is the quasi stationary distribution associated with the overdamped Langevin dynamics in $Omega$. The proofs are based on tools from semi-classical analysis. This thesis is divided into three independent chapters. The first chapter (in French) is dedicated to an introduction to the mathematical results. The other two chapters (in English) are devoted to the precise statements and proofs

Recentemente introduzida no mercado, a liga à base de titânio β-metaestável Ti-5Al-5V-5Mo3Cr-1Zr (Ti-55531) é um material estrutural para aplicações nos setores automotivo e aéreo, além de compor peças para centrífugas. A presente Dissertação de Mestrado tem como objetivo o estudo in situ das transformações de fase em estado sólido da liga Ti-55531 durante o envelhecimento a diferentes temperaturas e condições iniciais por meio de refinamento Rietveld. A ênfase do projeto será a análise qualitativa e quantitativa das principais fases presentes nesta liga, em especial aquelas β de estrutura cúbica de corpo centrado, alfa (α) e ômega (ω) de estrutura hexagonal e martensita (α\'\') de estrutura ortorrômbica. Os padrões de difração desta liga para os diferentes tempos de envelhecimento foram obtidas com o auxílio da técnica de difração de raio-X de alta energia in situ utilizando luz síncrotron, enquanto que as respectivas análises das imagens dos anéis de difração a partir destes experimentos foram realizadas com o auxílio do programa de integração e calibração instrumental FIT2D e do programa de análise de materiais usando difração (do inglês MAUD). / Recently introduced, the new Ti-55531 titanium based alloy has been developed aiming structural applications such as the automotive and aerospace ones. The present Thesis is focused on the assessment of Ti-55531 alloy in situ solid state transformations during ageing at diferente temperatures as well as initial conditions. In this sense, the study emphasis will deal with both quantitative and qualitative analysis of the main constitutive phases found in the alloy, namely the body-centered cubic β, both hexagonal α and ω and the martensitic α\'\', this one orthorhombic, by means of Rietveld refinement. Concerning the data, it was obtained by high energy X-ray diffraction (HEXRD) technique in a synchrotron light source facility. All the Debye-Scherrer rings resulting from these in situ experiments were analyzed by both FIT2D and MAUD software.

A discrete analogue of the Witten Laplacian on the n-dimensional integer lattice is considered. After rescaling of the operator and the lattice size we analyze the tunnel effect between different wells, providing sharp asymptotics of the low-lying spectrum. Our proof, inspired by work of B. Helffer, M. Klein and F. Nier in continuous setting, is based on the construction of a discrete Witten complex and a semiclassical analysis of the corresponding discrete Witten Laplacian on 1-forms. The result can be reformulated in terms of metastable Markov processes on the lattice. / In dieser Arbeit wird auf dem n-dimensionalen Gitter der ganzen Zahlen ein Analogon des Witten-Laplace-Operatoren eingeführt. Nach geeigneter Skalierung des Gitters und des Operatoren analysieren wir den Tunneleffekt zwischen verschiedenen Potentialtöpfen und erhalten vollständige Aymptotiken für das tiefliegende Spektrum. Der Beweis (nach Methoden, die von B. Helffer, M. Klein und F. Nier im Falle des kontinuierlichen Witten-Laplace-Operatoren entwickelt wurden) basiert auf der Konstruktion eines diskreten Witten-Komplexes und der Analyse des zugehörigen Witten-Laplace-Operatoren auf 1-Formen. Das Resultat kann im Kontext von metastabilen Markov Prozessen auf dem Gitter reformuliert werden und ermöglicht scharfe Aussagen über metastabile Austrittszeiten.

Much experimental evidence shows that the cytoskeleton is a downstream target and effector during cell death in numerous neurodegenerative diseases, including Parkinson's, Huntington's, and Alzheimer's diseases. However, recent evidence indicates that cytoskeletal dysfunction can also trigger neuronal death, by mechanisms as yet poorly understood. We studied a mathematical model of cytoskeleton-induced neuron death in which assembly control of the neuronal cytoskeleton interacts with both cellular stress levels and cytosolic free radical concentrations to trigger neurodegeneration. This trigger mechanism is further modulated by the presence of cell interactions in the form of a diffusible toxic factor released by dying neurons. We found that, consistent with empirical observations, the model produces one-hit exponential and sigmoid patterns of cell dropout. In all cases, cell dropout is exponential-tailed and described accurately by a gamma distribution. The transition between exponential and sigmoidal is gradual, and determined by a synergetic interaction between the magnitude of fluctuations in cytoskeleton assembly control and by the degree of cell coupling. We concluded that a single mechanism involving neuron interactions and fluctuations in cytoskeleton assembly control is compatible with the experimentally observed range of neuronal attrition kinetics. We also studied the transit of neurons through states intermediate between initial viability and cell death. We found that the stochastic flow of neuron fate, from viability to cell death, self-organizes into two distinct temporal phases. There is a rapid relaxation of the initial neuron population to a more disordered phase that is long-lived, or metastable, with respect to the time scales of change in single cells. Strikingly, cellular egress from this metastable phase follows the one-hit kinetic pattern of exponential decline now established as a principal hallmark of cell death in neurodegenerative disorders. Intermediate state metastability may therefore be an important element in the systems biology of one-hit neurodegeneration. Further, we studied the full spatiotemporal dynamics of death factor pulses released from dying neurons to emphasize the effects of the cell-to-cell coupling strength on neuron death rates. The rate of neuron cell loss monotonically increased with increased diffusion-dependent intercellular communication. Death factor diffusion effects may therefore be important moderators of one-hit neurodegeneration.

Much experimental evidence shows that the cytoskeleton is a downstream target and effector during cell death in numerous neurodegenerative diseases, including Parkinson's, Huntington's, and Alzheimer's diseases. However, recent evidence indicates that cytoskeletal dysfunction can also trigger neuronal death, by mechanisms as yet poorly understood. We studied a mathematical model of cytoskeleton-induced neuron death in which assembly control of the neuronal cytoskeleton interacts with both cellular stress levels and cytosolic free radical concentrations to trigger neurodegeneration. This trigger mechanism is further modulated by the presence of cell interactions in the form of a diffusible toxic factor released by dying neurons. We found that, consistent with empirical observations, the model produces one-hit exponential and sigmoid patterns of cell dropout. In all cases, cell dropout is exponential-tailed and described accurately by a gamma distribution. The transition between exponential and sigmoidal is gradual, and determined by a synergetic interaction between the magnitude of fluctuations in cytoskeleton assembly control and by the degree of cell coupling. We concluded that a single mechanism involving neuron interactions and fluctuations in cytoskeleton assembly control is compatible with the experimentally observed range of neuronal attrition kinetics. We also studied the transit of neurons through states intermediate between initial viability and cell death. We found that the stochastic flow of neuron fate, from viability to cell death, self-organizes into two distinct temporal phases. There is a rapid relaxation of the initial neuron population to a more disordered phase that is long-lived, or metastable, with respect to the time scales of change in single cells. Strikingly, cellular egress from this metastable phase follows the one-hit kinetic pattern of exponential decline now established as a principal hallmark of cell death in neurodegenerative disorders. Intermediate state metastability may therefore be an important element in the systems biology of one-hit neurodegeneration. Further, we studied the full spatiotemporal dynamics of death factor pulses released from dying neurons to emphasize the effects of the cell-to-cell coupling strength on neuron death rates. The rate of neuron cell loss monotonically increased with increased diffusion-dependent intercellular communication. Death factor diffusion effects may therefore be important moderators of one-hit neurodegeneration.

Proteins are important biological products with unique functions, annually produced at the hundreds of millions of dollars value on a worldwide basis. The application of crystallization for these materials primarily was led by structural biologists and crystallographers who are keen on obtaining large and well-ordered crystals for protein structure determination via X-ray diffraction. Usually for this, crystallization is done on a small scale by vapor diffusion using a supersaturated solution of the material. In the past decades, production crystallization has slowly received increasing attention for the large-scale recovery of proteins. Among the numerous products, an industrial enzyme (alpha-amylase) that is extensively involved in food processing and laundry products was chosen for examination due to the lack of relevant data in the literature and the potential industrial interest in crystallizing this material. The chosen alpha-amylase is a product of Genencor International (the Danisco division) and is derived from a genetically modified Bacillus licheniformis. In parallel to the underlying principles that govern the bulk crystallization of small molecules, the broad topics of investigation for this macromolecular material included determination of solubility, studies of nucleation thresholds, and investigation of crystal growth kinetics and special phenomena accompanying the crystallization process. All these studies were preceded by a series of characterization tests conducted for the material. On the whole, this study aimed to extend the existing fundamental knowledge of bulk crystallization for biological macromolecules. Specifically, it intended to enrich the solubility and crystallization kinetic data for the alpha-amylase. The experimental data of this study were all obtained at conditions in line with industrial practice, which included the use of moderate temperatures, mild pH conditions and simple inorganic salts ((NH4)2SO4, Na2SO4 and NaCl) in order for the findings to be transferred to the industry directly. In a 20 mM sodium phosphate buffer (with no added salts), alpha-amylase solubility increased with solvent temperature and had a minimum at pH between 6.4 and 7.1. A generalized equation (as a function of pH and temperature) was obtained to correlate the data. The three inorganic salts examined affected the alpha-amylase solubility in a different manner, both qualitatively and quantitatively. Evidently, the interaction effect of a salt varied with solution pH. This confirms the importance of studying solubility with the two or more condition parameters at the same time. With relevance to crystal growth, the metastable region of the material was relatively wide at (NH4)2SO4 and Na2SO4 concentrations corresponding to maximum solubility. For example, σSNT was 1.2  0.2 in solutions with 5 wt% ammonium sulfate at pH 7.0 and 25oC. A wide metastability range is useful for the practical operation of batch crystallizers as nucleation can be minimized. This range, however, diminished as the salt concentration increased beyond the maximum solubility points, imposing a limit on the range of salt concentration favorable for growth processes. In systems with no added salts at pH 7.0, the solution metastability was slightly higher at 10oC than at 40oC. This would suggest a future further examination of the salt system at a lower temperature, say of 10oC. To develop a batch crystallizer, the growth kinetic data of the material have to be known. Throughout the growth studies, the alpha-amylase crystals obtained were lozenge-shaped thin plates. Apparently, habit was not influenced by the crystallization conditions chosen. Similar to other proteins crystallized in bulk, the growth rate of alpha-amylase demonstrated a second-order dependence upon supersaturation. Importantly, the alpha-amylase demonstrated crystal growth rate dispersion (GRD) under all the conditions tested. To simplify the analysis of growth kinetic results, the seed crystals used were common history (CH) seeds whose growth rates are proportional to their sizes. The spread of growth rates (CV) was 0.54 for the unsieved CH seeds used. Due to GRD, growth rate coefficient data varied with crystal size. For instance, in solutions containing 5 wt% ammonium sulfate at pH 7.0 and 25oC, the growth rate coefficient for seed crystals initially at 20 m was 2.47 m/hr. This order of magnitude was equivalent to that of many other proteins. Although being small, industrial crystallization was feasible with these kinetics, as demonstrated by the sample design calculations included. To improve the design, it is recommended to further examine the solubility, metastability and growth kinetics of the above system at other temperatures to obtain a wider growth rate range. As the important phenomenon of growth rate dispersion has seldom been examined for protein and enzyme materials in the crystallization literature, this study is a significant contribution to this area.

Le processus de contact est l'un des systèmes de particules en interaction les plus étudiés. Il peut s'interpréter comme un modèlepour la propagation d'un virus dans une population ou sur un réseau. L'objectif de cette thèse est d'étudier la relation entre la structure locale du réseau et le comportement global du processus sur le réseau tout entier.Le cadre typique dans lequel on se place est celui d’une suite de graphes aléatoires $(G_n)$ convergeant localement vers un graphe limite $G$.On étudie alors le comportement asymptotique du temps d’extinction $tau_n$ du processussur $G_n$; lorsqu’initialement tous les individus sont infectés. Nous montrons sur plusieurs exemples qu’il existe unetransition de phase lorsque $lambda$ - le taux d'infection du processus - traverse une valeur critique $ lambda_c (G)$, qui ne dépend que de $G$.Plus précisément, pour certains modèles de graphes aléatoires comme le modèle de configuration, le graphe d'attachement préférentiel, le graphe géométrique aléatoire, le graphe inhomogène, nous montrons que $ tau_n $ est d'ordre soit logarithmique soit exponentiel; selon que $ lambda$ est soit inférieur ou supérieur à $lambda_c (G) $.De plus, dans certains cas, nous montrons des résultats de métastablité: en régime sur-critique, $ tau_n $ divisé par son espérance converge en loi vers une variable aléatoire exponentielle de moyenne $1$, et la densité des sites infectés reste stable (et non nulle) sur une période de temps d’ordre typiquement $tau_n$. / The contact process is one of the most studied interacting particle systems and is also often interpreted as a model for the spread of a virus in a population or a network. The aim of this thesis is to study the relationship of the local structure of the network and the global behavior of the contact process (the virus) on the whole network. Let $(G_n)$ be a sequence of random graphs converging weakly to a graph $G$. Then we study $tau_n$, the extinction time of the contact process on $G_n$ starting from full occupancy. We prove in some examples that there is a phase transition of $tau_n$ when $lambda$ - the infection rate of the contact process crosses a critical value $lambda_c(G)$ depending only on $G$. More precisely, for some models of random graphs, such as the configuration model, preferential attachment graph, random geometric graph, inhomogeneous graph, we show that $tau_n$ is of logarithmic (resp. exponential) order when $lambda < lambda_c(G)$ (resp. $lambda < lambda_c(G)$). Moreover, in some cases we also prove metastable results: in the super-critical regime, $tau_n$ divided by its expectation converges in law to an exponential random variable with mean $1$, and the density of the infected sites is stable for a long time.