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As a safe long-term management of nuclear wastes, deep geological repositories (DGRs) have been proposed or currently being constructed in several countries. The host rocks in DGRs are saturated with water after the geological disposal facilities (GDFs) are closed and sealed. Significant gas can be generated due to several processes, e.g., the metal corrosion, water radiolysis or microbial reaction of organic materials, etc. The generated gas is anticipated to span throughout the long-term disposal of waste, which may jeopardize the stability of host rocks. Correspondingly, the performance of GDF will be affected since the host rocks provide a final impediment to the radionuclide transport. As gas migration in saturated host rocks is a highly coupled hydro-mechanical (HM) process, either gas-induced micro-fracturing or macro-fracturing may contribute to the development of preferential gas pathways, which needs to be concerned to ensure the feasibility and safety of geological disposal. Current numerical studies on the gas migration behavior devoted to explaining the experimental phenomena in the gas injection tests conducted on the rock materials, in which some behaviors still cannot be well represented, i.e., gas induced fracturing, volulme dilation, anisotropic radial deformation. Therefore, to better represent the actual physical process of preferential gas flow, two modelling frameworks, i.e., macroscopic HM framework and two-scale HM framework, are proposed in the PhD study. For the macroscopic HM framework, a double porosity model is firstly developed based on the dual continuum method, in which the volumetric strains of the porous continuum (PC) and fractured continuum (FC) are work-conjugated to the respective effective stress level. The treatment in two types of porosity allows us to capture that the opening/closure of the fractures is caused by the interaction between the dilation of the PC and the dilation of the FPM, which is beneficial to describe the gas induced fracturing in an implicit way. Then, an enriched embedded fracture model (EFM) is proposed to address the mechanical behavior of fractures. A hyperbolic relation of fracture deformability is incorporated into the rock matrix, as a result the fractured rock shows a nonlinear elastic behavior, which can capture the stiffness degradation due to fracture opening. The equivalent continuum method is provided to derive the effective compliance tensor, which includes the transverse isotropic matrix and two fracture sets. Using the enriched EFM with a three-dimensional (3D) geometry is able to capture the anisotropic radial deformation during gas migration. Although the macroscopic HM framework is able to capture the major HM behaviors related to preferential gas flow, the development of gas dilatant pathways is still represented in an implicit way. Therefore, a two-scale HM framework is developed to explicitly simulate the development of preferential gas pathways. Initiating from the periodically distributed microstructures with microcracks, the asymptotic homogenization method is used to derive the macroscopic governing equations coupled with the normalized damage variable. The time-dependent damage evolution law is obtained from the microscopic mechanical energy analysis for evolving microcracks. Both time effect and size effect are incorporated in the damage model that will affect the overall HM behavior of rocks. The developed two-scale HM framework with single gas flow can qualitatively capture important behaviors, such as the discrete pathways, localized gas flow, unstabilized fracture branching. More specifically, the simulated results demonstrates that the inter-connection of fractures from gas inlet to outlet is a prerequisite for gas breakthrough, accompanied by large amounts of gas flowing out of the sample and a rapid drop in gas injection pressure. Incorporating water flow in the two-scale framework allows the model to quantitatively reproduce the experimental phenomena observed in the laboratory air injection tests, such as gas pressure evolution and mechanical deformation. More importantly, the model exlpaines that the significant differences in controlling gas breakthrough and mechanical deformation are resulting from the arbitrary nature of microstructural heterogeneities. To account for the gas-water interaction in the two-scale HM framework, a fully coupled two-phase flow and elaso-damage model is developed to simulate the laboratory and in-situ gas injection experiments. The model can quantitatively capture the experimental behaviors, e.g., gas pressure evolution and non-desaturation phenomenon. Furthermore, model results show that the highly localized fracture pathways are the major places where gas and water interacts each other, and as a result the rock is still kept fully saturated. As a whole, the obtained numerical results are synthesized and analyzed, the pros and cons of the developed models are discussed. To better improve the model performance, some recommendations are proposed for the future studies.

MSc (Applied Mathematics) / Department of Mathematics and Applied Mathematics / In this study, we develop a multiscale model of soil transmitted helminths in humans with a special reference to hookworm infection. Firstly, we develop a single scale model that comprises of five between host scale populations namely; susceptible humans, infected humans, eggs in the physical environment, noninfective worms in the physical environment and infective worms in the physical environment. Secondly, we extend the single scale model to incorporate within-host scales namely; infective larvae within-host, immature worms in small intestine, mature worm population and within-host egg population which resulted to a multiscale model. The models are analysed both numerically and analytically. The models are epidemiologically and mathematically well posed. Numerical simulation results show that there is a bidirectional relationship between the between-host and within-host scales. This is in agreement with the sensitivity analysis results, we noted that the same parameters that reduce reproductive number R0 are the same parameters that reduce the infective worms endemic equilibrium point. From the comparative effectiveness of hookworm interventions analysis results, we notice that any intervention combination that include wearing shoes controls and reduces the spread of the infection. The modelling framework developed in this study is vigorous to be applicable to other soil transmitted helminths infections / NRF

Solicitud de envío manuscrito de artículo científico. / El presente trabajo propone 4 alternativas de codificadores inspirados en el codificador MPEG-1, capa I, descrito en el estándar ISO/IEC 11172-3. El problema que se intenta resolver es el de requerir definir un modelo psicoacústico explícitamente para lograr codificar audio, reemplazándolo por redes neuronales. Todas las alternativas de codificador están basadas en redes neuronales convolucionales multiescala (MCNN) que emulan el modelo psicoacústico 1 del codificador mencionado. Las redes tienen 32 entradas que corresponden a las 32 subbandas del nivel de presión sonora (SPL – sound pressure level), y una única salida que corresponde a una de las 32 subbandas de o bien la relación señal a máscara (SMR) o bien el vector de asignación de bits. Es decir, un codificador está compuesto de un conjunto de 32 redes neuronales. La validación empleó los 10 primeros segundos de 15 canciones elegidas aleatoriamente de 10 géneros musicales distintos. Se comparó la calidad de las señales de audio generadas por cada codificador contra la de MPEG-1, capa I, mediante la métrica de ODG. El codificador cuya entrada es el SPL y cuya salida es la SMR, planteado por Guillermo Kemper, obtuvo los mejores resultados al realizar la comparación para 96 kbps y 192 kbps. El codificador denominado “SBU1” obtuvo los mejores resultados para 128 kbps. / The present work proposes 4 encoder alternatives, inspired in the MPEG-1, layer I encoder described in the ISO/IEC 11172-3 standard. The problem addressed here is the requirement of explicitly defining a psychoacoustic model to code audio, instead replacing it by neural networks. All the proposals are based on multiscale convolutional neural networks (MCNN) that emulate the psychoacoustic model 1 of the referred encoder. The networks have 32 inputs that map the 32 subbands of the sound pressure level (SPL), and a single output that corresponds to each of the 32 subbands of either the signal-to-mask ratio (SMR) or the bit allocation vector. Thus, an encoder is composed of a set of 32 neural networks. The validation process took the first 10 seconds of 15 randomly chosen songs of 10 different musical genres. The audio signal quality of the proposed encoders was compared to that of the MPEG-1, layer I encoder, using the ODG metric. The encoder whose input is the SPL and whose output is the SMR, proposed by Guillermo Kemper, yielded the best results for 96 kbps and 192 kbps. The encoder named “SBU1” had the best results for 128 kbps. / Tesis

La batterie lithium ion est la technologie de stockage d’énergie la plus répandue dans l'industrie automobile. Assurer sa haute efficacité, sa puissance, sa capacité, sa sécurité et son endurance présente un défi pour plusieurs chercheurs et industriels. En effet, une batterie est un système complexe renfermant plusieurs composants et soumis à divers risques de dégradations d’origines chimiques, mécaniques et électriques, se manifestant même dans les conditions normales de fonctionnement. Cependant, la batterie devrait assurer ses fonctions pour un grand nombre de cycles de charge et de décharge et continuer à servir sans que ces dégradations influencent sa performance globale. L’une des dégradations principales et inévitables est son gonflement qui induit une discontinuité électrique et une perte de sa capacité.En effet, le gonflement est un phénomène multi-physique qui fait intervenir l’électrochimie, la mécanique et la thermique. D’une part, une batterie lithium-ion est basée sur l’échange réversible de l’ion lithium entre une électrode positive et une électrode négative. Le processus d’insertion de l’ion dans les particules de l’électrode aboutit à un changement volumique significatif réversible de la batterie pour chaque cycle de charge/décharge. Cette variation de volume mène à la formation de contraintes quand la batterie est maintenue dans un pack rigide empêchant ou limitant sa déformation. D’autre part, la formation d’une couche à l’interface particule-électrolyte (SEI) suite aux réactions parasites se produisant à l’échelle de l’électrode constitue une cause principale d’un gonflement supplémentaire irréversible et de vieillissement de la batterie.Ainsi, le gonflement doit être pris en compte pendant la phase du dimensionnement mécanique de la batterie. Il est donc indispensable d’avoir un outil numérique fiable capable de prédire ce comportement mécanique pendant toutes les phases de fonctionnement de la batterie et de permettre aux concepteurs d’améliorer sa structure.Ce travail rentre dans le cadre d’une collaboration entre l’ENSTA ParisTech et le constructeur automobile Renault suite à un besoin industriel de comprendre et de maîtriser le gonflement des batteries utilisées dans les véhicules électriques et hybrides. Pour répondre à ce besoin, un modèle multi-physique et multi-échelle fondé sur la théorie de la thermodynamique des processus irréversibles, sur l’endommagement et sur la théorie de l’homogénéisation est développé. Il permet de décrire et de prédire la déformation d’une batterie lithium ion pendant son fonctionnement. Le modèle tient compte des phénomènes mécaniques, électrochimiques et thermiques qui se produisent à l’échelle locale des électrodes afin de calculer la déformation mécanique au niveau macroscopique de la batterie. / Lithium ion battery is the most popular energy storage technology in the automotive industry. Ensuring high efficiency, power, capacity, safety and endurance is a challenge for many researchers and manufacturers. Indeed, a battery is a complex system containing several components and subject to various risks of chemical, mechanical and electrical damage, manifesting even under normal operating conditions. However, the battery should perform its functions for a large number of charge and discharge cycles and continue to serve without these risks influencing its overall performance. One of the main and inevitable damage is its swelling, which induces an electrical discontinuity and a loss of its capacity.Indeed, swelling is a multi-physics phenomenon that involves electrochemistry, mechanics and heat. On the one hand, a lithium-ion battery is based on the reversible exchange of the lithium ion between a positive electrode and a negative electrode. The process of inserting the ion into the particles of the electrode results in a significant reversible volume change of the battery for each charge / discharge cycle. This variation in volume leads to the formation of stresses when the battery is held in a rigid pack preventing or limiting its deformation. On the other hand, the formation of a layer at the particle-electrolyte interface (SEI) following parasitic reactions occurring at the electrode scale is a major cause of irreversible additional swelling and aging of the drums.Thus, the swelling must be taken into account during the mechanical sizing phase of the battery. It is therefore essential to have a reliable numerical tool able to predict this mechanical behavior during all phases of battery operation and to allow designers to improve its structure.This work is part of a collaboration between ENSTA ParisTech and the car manufacturer Renault following an industrial need to understand and control the swelling of batteries used in electric and hybrid vehicles. To meet this need, a multi-physics and multi-scale model based on the theory of the thermodynamics of irreversible processes, mechanical damage theory and the homogenization theory is developed. It allows to describe and predict the deformation of a lithium ion battery during its operation. The model takes into account the mechanical, electrochemical and thermal phenomena that occur at the local scale of the electrodes in order to calculate the mechanical deformation at the macroscopic level of the battery.

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In numerical multiscale methods, one relies on a coupling between macroscopic model and a microscopic model. The macroscopic model does not include the microscopic properties that the microscopic model offers and that are vital for the desired solution. Such microscopic properties include parameters like material coefficients and fluxes which may variate microscopically in the material. The effective values of this data can be computed by running local microscale simulations while averaging the microscopic data. One desires the effect of the microscopic coefficients on a macroscopic scale, and this can be done using classical homogenisation theory. One method in the homogenization theory is to use local elliptic cell problems in order to compute the homogenized constants and this results in <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Clambda%20/R" data-classname="equation_inline" data-title="" /> error where <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Clambda" data-classname="equation" /> is the wavelength of the microscopic variations and <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?R" data-classname="mimetex" data-title="" /> is the size of the simulation domain. However, one could greatly improve the accuracy by a slight modification in the homogenisation elliptic PDE and use a filter in the averaging process to get much better orders of error. The modification relates the elliptic PDE to a parabolic one, that could be solved and integrated in time to get the elliptic PDE's solution.   In this thesis I apply the modified elliptic cell homogenization method with a qth order filter to compute the homogenized diffusion constant in a 2d Poisson equation on a rectangular domain. Two cases were simulated. The diffusion coefficients used in the first case was a deterministic 2d matrix function and in the second case I used stochastic 2d matrix function, which results in a 2d stochastic differential equation (SDE). In the second case two methods were used to determine the expected value of the homogenized constants, firstly the multi-level Monte Carlo (MLMC) and secondly its generalization multi-index Monte Carlo (MIMC). The performance of MLMC and MIMC is then compared when used in the process of the homogenization.   In the homogenization process the finite element notations in 2d were used to estimate a solution of the Poisson equation. The grid spatial steps were varied in a first order differences in MLMC (square mesh) and first order mixed differences in MIMC (which allows for rectangular mesh).

The objective of this dissertation centers on gaining a better understanding of the structure - property - performance relations of nickel and copper through the advanced multiscale theoretical framework and integrated computational methods. The goal of this dissertation also includes to combine material science and computational mechanics to acquire a transformative understanding of how the different crystal orientations, size scales, and penetration velocities affect plastic deformation and damage behavior of metallic materials during high strain rate (> 103s-1) processes. A multiscale computational framework for understanding plasticity and shearing mechanisms of metallic materials during the high rate process was developed, which for the first time reveals micromechanical insights on how different crystal orientations, size scales, and penetration velocities affect the atomistic simulations which render structure property information for plasticity, shearing and damage mechanisms. The contributions of this dissertation include: (1) Comprehensive understanding of the plasticity and shearing mechanisms between the nickel penetrator and copper target under high strain rates (2) Development of a multiscale study of a nickel penetrator striking a copper plate by employing macroscale simulations and atomistic simulations to better understand the micromechanisms. (3) An essential description of how different crystal orientations, size scales, and strain rates affect the plasticity and shearing mechanisms.

This project aims to investigate the orientation of plasma jet fronts in Earth's magnetotail using multi-spacecraft measurement data. The orientations are estimated by applying minimum variance analysis (MVA) and multi-spacecraft timing analysis for finding normal vectors to the jet fronts as they pass over the spacecraft. An agreement between the two analysis methods is found when applied to a data set of fronts. The obtained results are compared to measurements of the ion bulk velocities of the fronts, where a discrepancy is found. Limitations of the analysis are addressed and alternative approaches are presented. / I detta projekt undersöks riktningen hos fronter till plasma-jetstrålar i jordens magnetsvans genom analysering av mätdata från en samling rymdfarkoster. Riktningarna uppskattas genom att applicera minimum variance analysis (MVA) samt multi-spacecraft timing för att hitta normalvektorer till fronterna som passerar rymdfarkosterna. De två metoderna uppnår liknande resultat när de tillämpas på en uppsättning fronter. De erhållna normalvektorerna jämförs även med riktningen av uppmätta jonhastigheter från rymdfarkosterna där en tydlig skillnad förekommer. Begränsningar av analysmetoden påpekas och förslag på alternativa tillvägagångssätt läggs fram.

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