In this study, theoretical and experimental approaches were combined, using Arabidopsis as the studied species. The multi-scale model incorporates the following, existing sub-models: a phenology model that can predict the flowering time of plants grown in the field, a gene circuit of the circadian clock network that regulates flowering through the photoperiod pathway, a process-based model describing carbon assimilation and resource partitioning, and a functional-structural module that determines shoot structure for light interception and root growth. First, the phenology model was examined on its ability to predict the flowering time of field plantings at different sites and seasons in light of the specific meteorological conditions that pertained. This analysis suggested that the synchrony of temperature and light cycles is important in promoting floral initiation. New features were incorporated into the phenology model that improved its predictive accuracy across seasons. Using both lab and field data, this study has revealed an important seasonal effect of night temperatures on flowering time. Further model adjustments to describe phytochrome (phy) mutants supported the findings and implicated phyB in the temporal gating of temperature-induced flowering. The improved phenology model was next linked to the clock gene circuit model. Simulation of clock mutants with different free-running periods highlighted the complex mechanism associated with daylength responses for the induction of flowering. Finally, the carbon assimilation and functional-structural growth modules were integrated to form the multi-component, whole-plant model. The integrated model was successfully validated with experimental data from a few genotypes grown in the laboratory. In conclusion, the model has the ability to predict the flowering time, leaf biomass and ecosystem exchange of plants grown under conditions of varying light intensity, temperature, CO2 level and photoperiod, though extensions of some model components to incorporate more biological details would be relevant. Nevertheless, this meso-scale model creates obvious application routes from molecular and cellular biology to crop improvement and biosphere management. It could provide a framework for whole-organism modelling to help address global issues such as food security and the energy crisis.

<div>Electronics have now become a part of our daily life and therefore the reliability of microelectronics cannot be overlooked. As the Moore's law era comes to an end, various new system-level innovations (e.g., 3D packaging, evolution of packaging material to molding compounds) with constant scaling of transistors have resulted in increasingly complicated integrated circuits (ICs) configurations. The reliability modeling of complex ICs is a nontrivial concern for a variety of reasons. For example, ever since 2004, self-heating effect (SHE) has become an important reliability concern for ICs. Currently, many groups have developed thermal predictive models for transistors, circuits, and systems. In order to describe SHE self-consistently, the modeling framework must account for correlated self-heating within the ICs. This multi-scales nature of the self-consistency problem is one of the difficult factors poses an important challenge to self-consistent modeling. In addition, coupling between different physical effects within IC further complicates the problem.</div><div><br></div><div>In this thesis, we discuss three challenges, and their solutions related to an IC's reliability issues. We (i) generalize the classical effective medium theory (EMT) to account for anisotropic, heterogeneous system; (ii) develop computationally efficient a physics-based thermal compact model for a packaged ICs to predict junction temperature in the transistor based on the EMT model, and image charge theory. Our thermal compact model bridges different length scales among the sources and rest of the system. Finally (iii) propose the modeling framework of electrical chip package interaction (CPI) due to charge transport within mold compounds by coupling moisture diffusion, electric distribution, and ions transport. The proposed modeling framework not only addresses the three major modeling challenges discussed earlier, but also provides deep and fundamental insights regarding the performance and reliability of modern ICs. </div>

Heart failure occurs when the heart is not capable to pump blood at a sufficient rate to meet the demands of the body. Depending on the health of the heart, doctors may recommend a heart transplant, but finding a suitable donor is often a long duration process and the patient might be at an advance condition or the patient is not adequate for a heart transplant. In such cases Ventricular assist devices (VAD) are implemented. The purpose of a VAD is to aid the heart to pump the correct amount of blood, by doing so it relives the load that is put on the heart while giving the patient a chance for recovery. This study focuses on observing the hemodynamic effects of implementing a left ventricular assist device (LVAD) along the aortic arch and main arteries. Thrombi creation and transportation is other subject included in the study, due to the fact that thrombi can obstruct blood flow to critical arteries, manly carotid and vertebral. Occlusion of these can lead to a stroke with devastating effects on the neurocognitive functions and even death. A multi-scale CFD analysis a patient specific geometry model is used as well as a lumped system which provides the correct conditions in order to simulate the whole cardiovascular system. The main goal of the study is to understand the difference in flow behavior created by the unsteady pulsatile boundary conditions. The model described in this work has a total cardiac output of 7.0 Liters/ minute, this for a healthy heart. Two cardiac output splits are used to simulate heart failure conditions. The first split consists of 5 Liters/minute flowing through the LVAD cannula and 2 Liters/minute via the aortic root. The second scenario is when heart iv failure is critical, meaning that zero flow is being output by the left ventricle, thus a split of 7 Liter/minute trough the LVAD cannula and 0 Liters/minute traveling through the aortic root. A statistical analysis for the thrombi motion throughout the patient aortic arch was performed in order to quantify the influence that pulsatile flow has on the particles being track. Spherical particles of 2mm, 4mm and 5mm were released and accounted in the statistical analysis for each of the two split configurations. The study focuses on particles that escaped on the outlet boundaries of the upper arteries (Right Carotid, Left Carotid, and Vertebral). Results exhibit the statistical comparison of means for each particle diameter as well as for the overall probability for the steady and unsteady flow condition.

Computational Neuroscience deals with spatio-temporal scales which vary considerably.For example interactions at synaptic contact regions occur on the scale of nanometers and nanoseconds to milliseconds (micro-scale) whereas networks of neurons can measure up to millimeters and signals are processed on the scale of seconds (macro-scale). Whole-cell calcium dynamics models (meso-scale) mediate between the multiple spatio-temporal scales. Of crucial importance is the calcium propagation mediated by the highly complex endoplasmic reticulum network. Most models do not account for the intricate intracellular architecture of neurons and consequently cannot resolve the interplay between structure and calcium-mediated function. To incorporate the detailed cellular architecture in intracellular Calcium models, a novel mesh generation methodology has been developed to allow for the efficient generation of computational meshes of neurons with a three-dimensionally resolved endoplasmic reticulum. Mesh generation routines are compiled into a versatile and fully automated reconstruct-and-simulation toolbox for multi-scale physics to be utilized on high-performance or regular computing infrastructures. First-principle numerical simulations on the neuronal reconstructions reveal that intracellular Calcium dynamics are effected by morphological features of the neurons, for instance a change of endoplasmic reticulum diameter leads to a significant spatio-temporal variability of the calcium signal at the soma. / Math & Science Education

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Une approche couplée prenant en compte l’interaction de la plasticité cristalline et de la diffusion d’hydrogène a été établie et utilisée pour étudier le transport de l’hydrogène dans les agrégats polycristallins synthétiques de l’acier 316L avec des géométries de grains and des orientations cristallographiques différentes. Les champs mécaniques calculés à l’aide du code ZeBuLoN sont transférés dans un code de diffusion développé dans le cadre de ce travail. Une nouvelle formulation associée à un nouveau schéma numérique permet un calcul qui présente une bonne convergence. Les résultats des simulations montrent la redistribution de l’hydrogène dans les polycristaux due à la présence des hétérogénéités des contraintes hydrostatiques à l’échelle intragranulaire. L’effet de la vitesse de déformation a été quantitativement obtenu. Afin d’enrichir l’approche continue, un intérêt particulier est porté sur le rôle des joints de grains. Des simulations numériques d’un modèle atomique plan par plan ont été développées et appliquées aux bicristaux et aux structures de type ”bambou”. Les effets de puits ou de barrière induits par la présence des joints de grains sont clairement démontrés dans le cas du nickel pur. Pour reproduire ces effets dans les simulations de diffusion avec le modèle continue, une approche originale de simulation”multi-échelles” de la diffusion au joint de grain a été développée, et un nouveau régime de diffusion au joint de grain a été modélisé. / In the present work, we establish a one-way coupled crystal plasticity – hydrogen diffusion analysis and use this approach to study the hydrogen transport in artificial polycrystalline aggregates of 316L steel with different grain geometries and crystallographic orientation. The data about stress/strain fields computed at the microstructure scaleutilizing the crystal plasticity concept are transferred to the in-house diffusion code which was developed using a new numerical scheme for solving parabolic equations. In the case of initial uniform hydrogen content, the heterogeneity of the mechanical fields is shownto induce a redistribution of hydrogen in the microstructure. The effect of strain rate is clearly revealed. In the second part, hydrogen transport across grain boundaries is investigatedconsidering the specific diffusivity and segregation properties of these interfaces. Using a discrete atomic layer model, the retarding impact of grain boundaries is demonstrated on bicrystals and bamboo type membranes with and without external mechanical loading. To reproduce the effects observed in the atomistic simulations into the crystal plasticity – hydrogen diffusion model, a new physically based multi-scale method is proposed. Using this new approach we study the effect of grain boundary trapping kinetics on hydrogen diffusion and reveal a new grain boundary diffusion regime which has notbeen reported before.

Cette thèse a pour objectif de modéliser le couplage fluide-structure pouvant survenir dans les faisceaux tubulaires des réacteurs nucléaires. Leurs simulations numériques directes étant hors de portée, on met en œuvre une approche multi-échelle: il s'agit de tirer profit du coût modeste d'une description macroscopique, et à la fois, de la précision des informations microscopiques. Vis-à-vis des modèles existants, le travail de développement se focalise sur la prise en compte de la convection dans le calcul des champs hydrodynamiques, mais surtout, sur la possibilité de restituer des réponses vibratoires variées au sein d'un même faisceau. L'homogénéisation aboutit à un système d'équations gouvernant les Interactions Fluide-Solide à une échelle macroscopique. Ces équations sont couplées par une source en quantité de mouvement, traduisant les charges hydrodynamiques exercées sur une structure donnée. Cette force à modéliser représente une loi de fermeture du problème homogénéisé, mettant en jeu des coefficients a priori inconnus. Une méthode d'estimation est proposée à partir des champs microscopiques obtenus par simulation directe sur un domaine réduit et représentatif du large système de référence. Les capacités prédictives du modèle homogénéisé sont évaluées en comparaison avec des données de référence, issues de calculs numériques directs microscopiques. Chaque système considéré présente une variété de réponses en déplacement que le modèle homogénéisé restitue avec un accord satisfaisant. Cette approche multi-échelle semble être un bon compromis entre le coût des réalisations numériques et la précision attendue des données vibratoires et hydrodynamiques. / Vibration of tubes arrays is a matter of safety assessments of nuclear reactor cores or steam generators. Such systems count up thousands of slender-bodies immersed in viscous flow, involving multi-physics mechanisms caused by nonlinear dynamic interactions between the fluid and the solid materials. Direct numerical simulations for predicting these phenomena could derive from continuum mechanics, but require expensive computing resources. Therefore, one alternative to the costly micro-scale simulations consists in describing the interstitial fluid dynamics at the same scale as the structures one. Such approach rely on homogenization techniques intended to model mechanics of multi-phase systems. Homogenization results in coupled governing equations for the fluid and solid dynamics, whose solution provides individual tubes displacements and average fluid fields for each periodic unit cell. An hydrodynamic force term arises from the formulation within this set of homogenized equations: it depends on the micro-scale flow in the vicinity of a given tube-wall, but needs to be estimated as a function of the macro-scale fields in order to close the homogenized problem. The fluid force estimation relies on numerical micro-scale solutions of fluid-solid interactions over a tube array of small size. The multi-scale model is assessed for arrays made up of hundreds tubes, and is compared with solutions coming from the numerical micro-scale simulations. The macro-scale solution reproduces with good agreement the averaged solution of the micro-scale simulation, indicating that the homogenization method and the hydrodynamic force closure are suitable for such tube array configurations.

Le virus de l’hépatite E (HEV) est un agent zoonotique dont les porcs représentent le principal réservoir dans les pays industrialisés. Le présent projet de recherche a combiné études épidémiologiques, modélisation mathématique et sciences sociales pour proposer des leviers de réduction du risque d’exposition humaine au HEV par consommation de produits à base de porc. Deux essais expérimentaux et une étude en conditions naturelles ont mis en évidence le rôle majeur des co-infections immunomodulatrices dans la dynamique de l’infection par le HEV chez le porc, ces pathogènes intercurrents conduisant à une infection chronique par le HEV et à un risque augmenté de présence du virus dans le foie, le sang et les muscles des animaux abattus. Le développement d’un modèle intra-élevage, stochastique, individu-centré et multi-pathogènes, a permis de dégager des pistes de maîtrise à la fois zootechniques et sanitaires pour réduire la prévalence du virus en élevage. En complément, la conception d’un modèle inter-troupeaux a rendu possible l’analyse des facteurs de diffusion du virus dans un réseau d’élevages français. L’ensemble de ces mesures de gestion du HEV a été soumis à l’avis des organisations publiques et privées et des acteurs individuels de la filière porcine (éleveurs, conseillers, vétérinaires) par des approches de sciences humaines et sociales. Finalement, ce projet transversal et multi-disciplinaire a permis de définir des axes d’action tangibles et réalisables de gestion du HEV dans la filière porcine tout en apportant des contributions méthodologiques significatives en épidémiologie et en modélisation. / Hepatitis E virus (HEV) is a zoonotic pathogen whose main reservoir in industrialised countries is pigs. This research project combined epidemiological studies, mathematical modelling and social sciences to propose levers for reducing the risk of human exposure to HEV through the consumption of pork products. Two experimental trials and one study under natural conditions highlighted the major role of immunomodulating co-infections on the dynamics of HEV infection in pigs, as these intercurrent pathogens led to chronic HEV infection and an increased risk of the virus in the liver, blood and muscles of slaughtered animals. The development of a within-herd, stochastic, individual-based and multi-pathogen model has made it possible to identify both zootechnical and sanitary control measures to reduce the prevalence of the virus on farms. In addition, the design of a between-herd model has enabled to analyse the factors responsible for the spread of the virus in a network of French farms. All these HEV control measures have been submitted for the opinion of public and private organisations and individual players in the pig sector (farmers, farming advisors, veterinarians) through social science approaches. Finally, this transversal and multidisciplinary project made it possible to define tangible and achievable lines of action for the management of HEV in the pig sector while making significant methodological contributions in epidemiology and modelling.

Cette thèse est consacrée à la modélisation mathématique de l'hématopoïèse et des maladies sanguines. Plusieurs modèles traitant d'aspects différents et complémentaires de l'hématopoïèse y sont étudiés.Tout d'abord, un modèle multi-échelle de l'érythropoïèse est analysé, dans lequel sont décrits à la fois le réseau intracellulaire, qui détermine le comportement individuel des cellules, et la dynamique des populations de cellules. En utilisant des données expérimentales sur les souris, nous évaluons les rôles des divers mécanismes de retro-contrôle en réponse aux situations de stress.Ensuite, nous tenons compte de la distribution spatiale des cellules dans la moelle osseuse, question qui n'avait pas été étudiée auparavant. Nous décrivons l'hématopoïèse normale à l'aide d'un système d'équations de réaction-diffusion-convection et nous démontrons l'existence d'une distribution stationnaire des cellules. Puis, nous introduisons dans le modèle les cellules malignes. Pour certaines valeurs des paramètres, la solution "disease-free" devient instable et une autre solution, qui correspond à la leucémie, apparaît. Cela mène à la formation d'une tumeur qui se propage dans la moelle osseuse comme une onde progressive. La vitesse de cette propagation est étudiée analytiquement et numériquement. Les cellules de la moelle osseuse échangent des signaux qui régulent le comportement cellulaire. Nous étudions ensuite une équation integro-différentielle qui décrit la communication cellulaire et nous prouvons l'existence d'une solution du type onde progressive en utilisant la théorie du degré topologique et la méthode de Leray et Schauder. L'approche multi-agent est utilisée afin d'étudier la distribution des différents types de cellules dans la moelle osseuse.Finalement, nous étudions un modèle de type "Physiologically Based Pharmacokinetics-Pharmacodynamics" du traitement de la leucémie par l'AraC. L'AraC agit comme chimiothérapie et induit l'apoptose de toutes les cellules proliférantes, saines et malignes. La pharmacocinétique donne accès à la concentration intracellulaire d'AraC. Cette dernière, à son tour, détermine la dynamique des populations cellulaires et, par conséquent, l'efficacité de différents protocoles de traitement. / This PhD thesis is devoted to mathematical modelling of haematopoiesis and blood diseases. We investigate several models, which deal with different and complementary aspects of haematopoiesis.The first part of the thesis concerns a multi-scale model of erythropoiesis where intracellular regulatory networks, which determine cell choice between self-renewal, differentiation and apoptosis, are coupled with dynamics of cell populations. Using experimental data on anemia in mice, we evaluate the roles of different feedback mechanisms in response to stress situations. At the next stage of modelling, spatial cell distribution in the bone marrow is taken into account, the question which has not been studied before. We describe normal haematopoiesis with a system of reaction-diffusion-convection equations and prove existence of a stationary cell distribution. We then introduce malignant cells into the model. For some parameter values the disease free solution becomes unstable and another one, which corresponds to leukaemia, appears. This leads to the formation of tumour which spreads in the bone marrow as a travelling wave. The speed of its propagation is studied analytically and numerically. Bone marrow cells exchange different signals that regulate cell behaviour. We study, next, an integro-differential equation which describes cell communication and prove the existence of travelling wave solutions using topological degree and the Leray-Schauder method. Individual based approach is used to study distribution of different cell types in the bone marrow. Finally, we investigate a Physiologically Based Pharmacokinetics-Pharmacodynamics model of leukaemia treatment with AraC drug. AraC acts as chemotherapy, inducing apoptosis of all proliferating cells, normal and malignant. Pharmacokinetics provides the evolution of intracellular AraC. This, in turn, determines cell population dynamics and, consequently, efficacy of treatment with different protocols.