Oil shale industry in Estonia is looking at other mining technologies as alternative to strip mining and room and pillar mining methods. One such alternative to the room and pillar method is the punch-longwall mining method. Enefit Kaevandused AS, one of the major oil shale companies in Estonia, plans to employ this technology in exploiting some of its resources in the near future. This thesis examines the different stability problems related to the planned punch-longwall mining project in Narva oil shale mine. Determining optimal chain pillar dimensions and stability of the punch-longwall highwall slope are the main objectives of this project. Rock mechanical analyses have been done and recommendations are made based on the rock mechanical aspect of the mining process. Taavi Lõhmuste is responsible for the chain pillar stability analysis and Ott Oisalu for the punch-longwall highwall slope stability analysis. It is essential to understand the geology of a certain area in order to make accurate stability assessments. Because of the previously stated requirements, the geology of Estonian oil shale deposit is examined in the first part of the thesis in order to determine the geological and rock mechanical conditions to set the foundation for further analyses. In conclusion, for the part of the highwall slope, a properly designed barrier pillar plays a key role in the stability of the slope. After reviewing and analyzing the results of both highwall slope numerical models, it can be stated that the minimum length for the barrier pillar that still will yield in stable highwall slope is 65 meters. For the part of the chain pillars, in conclusion, it can be determined that optimal chain pillar dimensions that should be suitable, from the stability standpoint, are 6x6 meters for 3-entry system and 7x7 meters for 2-entry system (length x width).

Modelling in cardiac electrophysiology results in a complex system of partial differential equations (PDE) describing the propagation of the electrical wave in the heart muscle coupled with a highly nonlinear system of ordinary differential equations (ODE) describing the ionic activity in the cardiac cells. This system forms the widely accepted bidomain model or its slightly simpler version, the monodomain model. To a large extent, the stiffness of the whole model depends on the choice of the ionic model, which varies in terms of complexity and realism. These simulations require accurate and, depending on the ionic model used, possibly very stable numerical methods. At this time, solving these models numerically requires CPU time of around one day per heartbeat. Therefore, it is necessary to use the most efficient method for these simulations. This research focuses on the comparison and analysis of several time-stepping methods: explicit or semi-implicit, operator splitting, deferred correction and Rush-Larsen methods. The goal is to find the optimal method for the ionic model used. For our analysis, we used the monodomain model but our results apply to the bidomain model as well. We compare the methods for three ionic models of varying complexity and stiffness: the Mitchell-Schaeffer models with only 2 variables, the more realistic Beeler-Reuter model with 8 variables, and the stiff and very complex ten Tuscher-Noble-Noble-Panfilov (TNNP) models with 17 variables. For each method, we derived absolute stability criteria of the spatially discretized monodomain model and verified that the theoretical critical time steps obtained closely match the ones in numerical experiments. Convergence tests were also conducted to verify that the numerical methods achieve an optimal order of convergence on the model variables and derived quantities (such as speed of the wave, depolarization time), and this in spite of the local non-differentiability of some of the ionic models. We looked at the efficiency of the different methods by comparing computational times for similar accuracy. Conclusions are drawn on the methods to be used to solve the monodomain model based on the model stiffness and complexity, measured respectively by the most negative eigenvalue of the model's Jacobian and the number of variables, and based on strict stability and accuracy criteria.

Impulsive differential equations are useful for modelling certain biological events. We present three biological applications showing the use of impulsive differential equations in real-world problems. We also look at the effects of stability on a reduced two-dimensional impulsive HIV system. The first application is a system describing HIV induction-maintenance therapy, which shows how the solution to an impulsive system is used in order to find biological results (adherence, etc). A second application is an HIV system describing the interaction between T-cells, virus and drugs. Stability of the system is determined for a fixed drug level in three specific regions: low, intermediate and high drug levels. Numerical simulations show the effects of varying drug levels on the stability of a system by including an impulse. We reduce these two models to a two-dimensional impulsive model. We show analytically the existence and uniqueness of T-periodic solutions, and show how stability changes when varying the immune response rate, the impulses and a certain nonlinear infection term. The third application shows how seasonal changes can be incorporated into an impulsive differential system of Rift Valley Fever, and looks at how stability may differ when impulses are included. The analysis of impulsive differential systems is crucial in developing more realistic mathematical models for infectious diseases.

Dans cette étude nous considérons l'interaction entre une onde de choc et une couche limite turbulente sur un écoulement transsonique sur une bosse d'un point de vue expérimentale et théorique.Des mesures expérimentales ont permis de montrer que l'interaction est caractérisée par la coexistence de deux fréquences caractéristiques distinctes, mais l'origine des oscillations est controversée. Des simulations numériques permettent une description de l'écoulement moyen, mais ne sont pas capables de reproduire le comportement instable de l'interaction. Nous proposons d'abord une étude de stabilité globale: une décomposition en valeurs propres de l'opérateur de Navier-Stokes linéarisé indique que l'interaction est un phénomène stable, et la dynamique de l'écoulement ne peut pas être décrite par un mode global instable.Nous considérons ensuite une approche linéarisée, où la réceptivité de l'écoulement à un forçage externe est analysée à travers une décomposition en valeurs singulières du Résolvant global. Cette nouvelle approche est proposée afin d'expliquer le processus de sélection de fréquence dans cet écoulement, et montre que l'interaction filtre et amplifie le bruit résiduel existant.La même approche est enfin appliquée sur un cas d'écoulement transsonique autour d'un profil d'aile, qui peut présenter des oscillations périodiques de l'onde de choc. La décomposition en valeurs propres de opérateur de Navier-Stokes linéarisé est capable de décrire la dynamique du choc, tandis que la décomposition en valeurs singulières du Résolvant global peut indiquer la présence des instabilité convectives. / A transonic interaction between a shock wave and a turbulent boundary layer is experimentally and theoretically investigated. The configuration is a channel flow over a bump, where a shock wave causes the separation of the boundary layer and a recirculating bubble is observed downstream of the shock foot.The mean flow is experimentally investigated by means of PIV, then different techniques allows to identify the main unsteadiness of this shock-wave/boundary-layer interaction. As recognised in similar configurations, the flow presents two distinguished characteristic frequencies, whose origins are still unknown.Numerical simulations are performed solving RANS equations. Results are in good agreement with the experimental mean flow, but the approach fails to predict the unsteady. The solution of RANS equations is then considered as a base flow, and a global stability analysis is performed. Eigenvalue decomposition of the Navier-Stokes operator indicates that the interaction is stable, and the dynamics cannot be described by unstable global modes.A linearised approach based on a singular-value decomposition of the Resolvent is then proposed: the noise-amplifier behaviour of the flow is highlighted by the linearised approach. Medium-frequency perturbations are shown to be the most amplified in the mixing layer, whilst the shock wave behaves as a low-pass filter.The same approach is then applied to a transonic flow over a profile, where the flow can present high-amplitude shock oscillations. The stability analysis can describe both the buffet phenomenon when an unstable mode is present, and the convective instabilities responsible of medium-frequency unsteadiness.

No description available.

Ce travail étudie les stratégies de contrôle des limites pour l'analyse de stabilité et la stabilisation d'un système hyperbolique de premier ordre couplé à des conditions limites dynamiques non linéaires. La modélisation d'un écoulement à l'intérieur d'un tube (phénomène de transport de fluide) avec une stratégie de contrôle des limites appliquée dans une installation expérimentale physique est considérée comme une étude de cas pour évaluer les stratégies proposées. Dans le contexte des systèmes de dimension finie, des outils de contrôle classiques sont appliqués pour traiter des systèmes hyperboliques de premier ordre ayant des conditions limites données par le couplage d'un modèle dynamique de colonne de chauffage et d'un modèle statique de ventilateur. Le problème de suivi de cette dynamique complexe est abordé de manière simple en considérant des approximations linéaires, des schémas de différences finies et une action intégrale conduisant à un système linéaire à temps discret augmenté avec une dimension dépendant de la taille d'échelon de la discrétisation dans l'espace. Par conséquent, pour la contrepartie dimensionnelle infinie, deux stratégies sont proposées pour résoudre le problème de contrôle de frontière des systèmes hyperboliques de premier ordre couplé à des conditions de frontière dynamique non linéaires. Le premier se rapproche de la dynamique du système hyperbolique de premier ordre par un retard pur. La stabilité convexe et les conditions de stabilisation des systèmes quadratiques non linéaires retardés d'entrée incertaine sont proposées sur la base de la théorie de la stabilité de Lyapunov-Krasovskii (LK) qui sont formulées en termes de contraintes de l'inégalité matricielle linéaire (LMI) avec des variables supplémentaires lâches (introduites par le lemme de Finsler ). Ainsi, des fonctions strictement de Lyapunov sont utilisées pour dériver une approche basée sur LMI pour la stabilité de la frontière régionale robuste et la stabilisation des systèmes hyperboliques de premier ordre avec une condition de frontière définie au moyen d'un système dynamique non linéaire quadratique. Les conditions de stabilité et de stabilisation proposées pour LMI sont évaluées en tenant compte de plusieurs exemples universitaires et de l'écoulement à l'intérieur d'une étude de cas. / This work studies boundary control strategies for stability analysis and stabilization of first-order hyperbolic system coupled with nonlinear dynamic boundary conditions. The modeling of a flow inside a pipe (fluid transport phenomenon) with boundary control strategy applied in a physical experimental setup is considered as a case study to evaluate the proposed strategies. Firstly, in the context of finite dimension systems, classical control tools are applied to deal with first-order hyperbolic systems having boundary conditions given by the coupling of a heating column dynamical model and a ventilator static model. The tracking problem of this complex dynamics is addressed in a simple manner considering linear approximations, finite difference schemes and an integral action leading to an augmented discrete-time linear system with dimension depending on the step size of discretization in space. Hence, for the infinite dimensional counterpart, two strategies are proposed to address the boundary control problem of first-order hyperbolic systems coupled with nonlinear dynamic boundary conditions. The first one approximates the first-order hyperbolic system dynamics by a pure delay. Then, convex stability and stabilization conditions of uncertain input delayed nonlinear quadratic systems are proposed based on the Lyapunov-Krasovskii (L-K) stability theory which are formulated in terms of Linear Matrix Inequality (LMI) constraints with additional slack variables (introduced by the Finsler's lemma). Thus, strictly Lyapunov functions are used to derive an LMI based approach for the robust regional boundary stability and stabilization of first-order hyperbolic systems with a boundary condition defined by means of a nonlinear quadratic dynamic system. The proposed stability and stabilization LMI conditions are evaluated considering several academic examples and also the flow inside a pipe as case study.

[pt] O Aterro Metropolitano de Jardim Gramacho (AMG) é o local que recebe desde 1976 os resíduos sólidos gerados pelas atividades domésticas, além das comerciais e industriais da área metropolitana do Rio de Janeiro. Atualmente no AMG vem se desenvolvendo projetos de aterramento até o ano 2012, portanto, a estabilidade dos taludes do maciço cresce em importância e a presente dissertação está dirigida a compreender aspectos da análise de estabilidade do AMG. Nesse sentido, faz-se ênfase no comportamento da resistência dos materiais, fundamentalmente da fundação que é uma argila muito mole. Na área do AMG tem campanhas de ensaios do campo durante vários anos e em quantidade menor os ensaios laboratoriais. Neste trabalho são feitas atividades como a coleta e interpretação das sondagens desde 1992 até a campanha do ano 2009, esta informação é introduzida numa modelagem estratigráfica tridimensional, deles são gerados perfis bidimensionais para as análises de estabilidade, Outra atividade é interpretar informação do campo, ensaios de laboratório da campanha 2009 e realizar ensaios complementares na argila do local (compressão triaxial drenada e não drenada, cisalhamento direto e adensamento com medição do creep). A totalidade da informação é discutida obtendo correlações da resistência não drenada em base da teoria do estado critico. Os parâmetros geotécnicos do lixo são obtidos através das referências na literatura e retro-análises de taludes movimentados no local. Finalmente se avalia a estabilidade do AMG pelos métodos de equilíbrio limite e tensão deformação em termos de tensões totais e efetivas até chegar às geometrias finais projetadas. / [en] The Metropolitan Landfill Jardim Gramacho (AMG) is the site since 1976 that receives solid waste generated by domestic activities, also of commercial and industrial metropolitan area of Rio de Janeiro. Currently in AMG is developing projects ground to the year 2012, so the stability of slopes of the massive gains in importance and this dissertation is aimed at understanding aspects of the stability analysis of the AMG. Thus, it is an emphasis on the behavior of resistance of materials, primarily from a foundation that is very soft clay. In the area of AMG has field test in explorations for several years and fewer laboratory tests. This work made activities such as collection and interpretation of surveys from 1992 to the exploration of 2009, this information is entered into a three-dimensional stratigraphic modeling, their profiles are generated for the two-dimensional stability analysis, Another activity is to interpret information from field trials Campaign 2009 laboratory and perform additional tests on the clay site (triaxial drained and undrained, direct shear and consolidation with measurement of creep). The totality of the information obtained is discussed correlations of resistance undrained in the base of critical state theory. The geotechnical parameters of garbage are obtained through the references in the literature and analysis of retro-crowded slopes at the site. Finally it assesses the stability of the AMG methods of limit equilibrium and stress-strain curves in terms of total stresses and effective to reach the final designed geometry.

Il s’agit ici d’étudier un phénomène vibratoire ressenti par les utilisateurs d’un masque à oxygène au niveau de la fosse nasale. Le masque à oxygène intègre un régulateur qui envoie de l’oxygène en réponse à une demande de débit. Les vibrations prennent la forme de variations de pression à l’entrée du masque et leur origine est inconnue. Parmi les objectifs du travail de thèse, on essaiera de comprendre l’origine et de caractériser ce phénomène après une modélisation détaillée du régulateur, prenant en compte assez finement sa géométrie. Dans un deuxième temps, la stabilisation de la trajectoire dynamique de ce système sera étudiée par le biais de l’application du critère de Routh à un modèle linéarisé autour d’un point d’équilibre. Dans un troisième temps, quelques phénomènes dynamiques et physiques additionnels seront investis afin de pousser plus en avant la compréhension du fonctionnement du masque. Dans un quatrième temps et en guise d’ouverture, on prendra le temps d’évoquer des pistes supplémentaires pour l’étude de ce système. / The vibratory behavior of a regulated oxygen mask is studied here. The oxygen mask integrates a regulator which sends oxygen in response to a demand flow. The vibrations take the form of pressure variations in the mask volume, at the entry of the nasal ways, and their origin is unknown. Among the goals of this thesis work, we will try first to understand the origin and to characterize this phenomenon after a detailed modeling of the regulator, taking accurately into account its geometry. Second, the stabilization of the system’s dynamical trajectory will be studied by applying the Routh criterion to a linearized model around an equilibrium point. Third, some additional dynamical and physical phenomena will be investigated in order to push forward the understanding of the mask functionning. Fourth, and as an opening, time will be taken to mention supplementary tracks for the study of this system.

Philosophiae Doctor - PhD / Singularly perturbed problems have been studied extensively over the past few years from different perspectives. The recent research has focussed on the problems whose solutions possess interior layers. These interior layers appear in the interior of the domain, location of which is difficult to determine a-priori and hence making it difficult to investigate these problems analytically. This explains the need for approximation methods to gain some insight into the behaviour of the solution of such problems. Keeping this in mind, in this thesis we would like to explore a special class of numerical methods, namely, fitted finite difference methods to determine reliable solutions. As far as the fitted finite difference methods are concerned, they are grouped into two categories: fitted mesh finite difference methods (FMFDMs) and the fitted operator finite difference methods (FOFDMs). The aim of this thesis is to focus on the former. To this end, we note that FMFDMs have extensively been used for singularly perturbed two-point boundary value problems (TPBVPs) whose solutions possess boundary layers. However, they are not fully explored for problems whose solutions have interior layers. Hence, in this thesis, we intend firstly to design robust FMFDMs for singularly perturbed TPBVPs whose solutions possess interior layers and to improve accuracy of these approximation methods via methods like Richardson extrapolation. Then we extend these two ideas to solve such singularly perturbed TPBVPs with variable diffusion coefficients. The overall approach is further extended to parabolic singularly perturbed problems having constant as well as variable diffusion coefficients. / 2023-08-31

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23017号 / 理博第4694号 / 新制||理||1673(附属図書館) / 京都大学大学院理学研究科地球惑星科学専攻 / (主査)准教授 成瀬 元, 准教授 堤 昭人, 教授 生形 貴男 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM