Resumen: En esta tesis doctoral se presentan tres modelos matemáticos que describen el comportamiento de dos enfermedades parasitarias con vector de transmisión; de los cuales dos modelos están dedicados a la Toxoplasmosis donde se explora la dinámica de la enfermedad a nivel de la población humana y de gatos domésticos. Los gatos juegan un papel de agentes infecciosos del Toxoplasma gondii. La dinámica cualitativa del modelo es determinada por el umbral básico de reproducción, R0. Si el parámetro R0 < 1, entonces la solución converge al punto de equilibrio libre de la enfermedad. Por otro lado, si R0 > 1, la convergencia es al punto de equilibrio endémico. Las simulaciones numéricas ilustran diferentes dinámicas en función del parámetro umbral R0 y muestra la importancia de este parámetro en el sector salud. Finalmente la Babesiosis bovina se modela a partir de cinco ecuaciones diferenciales ordinarias, que permiten explicar la influencia de los parámetros epidemiológicos en la evolución de la enfermedad. Los estados estacionarios del sistema y el número básico de reproducción R0 son determinados. La existencia del punto endémico y libre de enfermedad se expone, puntos que dependen del R0, ratificando la importancia del parámetro umbral en la salud publica. Objetivo: Construir modelos matemáticos epidemiológicos aplicados a enfermedades parasitarias (Toxoplasmosis y Babesiosis) con vector de transmisión. Metodología: Para la construcción de los modelos matemáticos epidemiológicos es necesario representar la enfermedad a partir de modelos de flujo, permitiendo ver la dinámica de la población entre los diferentes estadíos de la enfermedad, dichos movimientos son analizados a partir de sistemas dinámicos, análisis matemático y métodos numéricos; con estas herramientas es posible hacer un estudio detallado del modelo, permitiendo calcular parámetros umbrales que dominan la dinámica de la enfermedad y a su vez simular escenarios reales e hipotéticos. / Aranda Lozano, DF. (2011). Modeling of parasitic diseases with vector of transmission: toxoplasmosis and babesiosis bovine [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/11539 / Palancia

Apresenta-se uma metodologia para análise de interação solo-estrutura aplicada ao estudo da estabilidade global de estruturas de concreto armado sobre fundações profundas. A metodologia de análise de interação solo-estrutura consiste num processo iterativo no qual, inicialmente, determinam-se as reações da superestrutura, considerando os apoios indeslocáveis. Com estas reações, por meio do programa EDRR, calculam-se os deslocamentos dos blocos de fundação. Com as reações e estes deslocamentos calcula-se os coeficientes das molas que substituirão os apoios fixos da superestrutura, cujas reações são recalculadas. Repete-se o processo até que as reações de duas iterações consecutivas sejam aproximadamente iguais. O programa EDRR (estaqueamento, deslocamento horizontal, recalque, rotação), elaborado em linguagem FORTRAN, determina os esforços no estaqueamento através de análise matricial considerando a reação horizontal do solo. Os deslocamentos horizontais e rotações são calculados através da teoria de viga sobre apoio elástico, enquanto os recalques no maciço de solos são calculados considerando o efeito de grupo através da continuidade do meio. Através de exemplos de casos reais, com medida de recalques, demonstra-se a eficiência da metodologia na previsão dos recalques. Além disso, procura-se mostrar que os recalques influenciam na estabilidade global da superestrutura. / This work presents a methodology for the analysis of soil-structure interaction applied to the study of the global stability of reinforced concrete structures on deep foundations. The soil-structure interaction methodology consists of an iterative process in which, at the beginning, the superstructure support reactions are computed, assuming fixed supports. Using the computed reactions, with aid of the EDRR program, foundation cap displacements are computed. Then, with the computed support reactions and displacements, spring coefficients, which will replace the fixed supports, are calculated. The process is repeated until reactions determined in two consecutive iterations are close to each other. The EDRR program, written in FORTRAN language, computes the forces at the top of piles by means of matrix analysis, taking into account the horizontal soil reaction. Horizontal linear displacements and rotations are computed using the elastic foundation beam theory, and soil mass settlements are computed taking into account the group effect considering the mass continuity. Thro ugh real case examples, with settlement monitoring, the proposed methodology efficiency is demonstrated. Furthermore, the influence of settlements on the structure global stability is shown.

Ce travail porte sur le couplage des déformations d'une bulle avec son sillage et sa trajectoire dans plusieurs configurations. Un formalisme de type eulérien-lagrangien permet d'écrire le problème sur un domaine mouvant faiblement déformé par rapport à la configuration de référence. Grâce à cette approche, il est possible d'étudier dans un cadre linéaire le couplage entre les déformations d'une bulle et les effets hydrodynamiques. En appliquant ce formalisme, on peut dans un premier temps calculer l'écoulement de base autour de la bulle et sa géométrie d'équilibre, et dans un second temps développer une approche de stabilité globale prédisant les seuils d'instabilité et les propriétés des modes d'oscillation. Afin de développer cette méthode, des résultats sur les oscillations linéaires de bulles et de gouttes dans un fluide au repos et sans influence de la gravité sont tout d'abord présentés et comparés à des résultats théoriques existants. Puis, le principe du formalisme eulérien-lagrangien est illustré en prenant pour problème modèle l'équation de la chaleur formulée sur un domaine arbitrairement déformé. Ce principe est ensuite appliqué aux équations de Navier-Stokes, aboutissant à une version linéarisée autour d'un domaine de référence incluant de manière complète les couplages entre déformations de la géométrie et perturbations de l'écoulement. On met en oeuvre sur le système obtenu une méthode itérative de Newton donnant accès à l'état de base, c'est-à-dire à l'écoulement stationnaire autour de la bulle et à sa forme d'équilibre. Ce même système permet par la suite d'effectuer une analyse de stabilité globale de l'écoulement autour d'une bulle qui se déforme. L'algorithme développé est d'abord appliqué au cas d'une bulle piégée dans un écoulement d'étirement, permettant de décrire des formes d'équilibre dans des régimes stables et instables. Le cas de la bulle en ascension dans un fluide pur est ensuite abordé. Une étude paramétrique est conduite, couvrant une vaste gamme de liquides allant de l'eau pure à des huiles de silicone très visqueuses. Les états de base calculés par la méthode de Newton ainsi que les seuils d'instabilité des sillages sont en bon accord avec les résultats expérimentaux. Dans les cas des liquides très peu visqueux, notre approche décrit de manière plus précise les effets visqueux dans les couches limites et donne des résultats plus satisfaisants que les approches numériques existantes. Elle confirme par ailleurs que la déformation de la bulle joue un rôle mineur dans ces gammes de paramètres. Pour les liquides plus visqueux en revanche, on observe un couplage plus fort entre déformation et sillage. / This works deals with the coupling between time-dependent deformation, wake dynamics and path characteristics of a gas bubble in different configurations. An Eulerian-Lagrangian formalism is sought to formulate this problem in a moving domain having a small deformation compared to the reference configuration. This approach allows us to study the linear coupling between bubble deformations and hydrodynamic effects. This formalism makes it possible to first compute the base flow around a bubble and the corresponding steady shape, then to develop a global stability approach aimed at predicting the threshold of path instability and the properties of bubble oscillation modes. To develop this method, we first compute the linear oscillations of bubbles and drops in a quiescent fluid without gravity and compare them to existing theory. Then, the premise of the Eulerian-Lagrangian formalism is illustrated using a model equation, namely the heat equation written in an arbitrarily deformed domain. The same formalism is applied to the NavierStokes equations, yielding a linearized version of these equations in the neighbourhood of a reference domain, including the two-way coupling between shape deformations and perturbations of the base flow. With this system of equations at hand, we implement a Newton method that provides the steady state, i.e. the base flow around the bubble and its geometry. The same system allows us to carry out a global stability analysis of the flow past a deformable bubble. We first consider the situation where the bubble is trapped in a straining flow, for which we compute stable and unstable equilibrium shapes. We finally tackle the case of a buoyancy-driven bubble rising in a pure liquid. A parametric study is carried out over a wide range of liquids, from pure water to high-viscosity silicon oils. Steady states computed with the Newton method and instability thresholds are found to be in good agreement with experimental observations. For low-viscosity fluids, our approach captures the viscous effects that take place in the boundary layer better than existing computational approaches, yielding predictions for the onset of path instability in better agreemnt with observations. Furthermore, it confirms that time-dependent bubble deformations play a minor part for such liquids. In contrast, a stronger coupling between shape and path instabilities is observed in high-viscosity fluids

Le phénomène d’interaction onde de choc/couche limite (CL) est omniprésent en aérodynamique. De manière générale, il génère des oscillations basses fréquences qui peuvent être néfastes pour les machines. L’exemple typique est le tremblement de l’onde de choc sur profil d’aile en régime transsonique, dangereux car il peut exciter les modes de structure de l’aile et potentiellement la rompre. Ce type de phénoménologies a été largement étudié en condition de CL amont turbulente, ce qui a donné lieu à des scénarios physiques crédibles et des méthodologies d’étude efficaces, notamment les analyses de stabilité sur champs turbulents moyennés (RANS). Toutefois la technologie laminaire, c’est-à-dire l’utilisation de CL laminaires en vue de réduire la consommation des aéronefs représente un nouveau challenge scientifique sur cette problématique. La physique est en effet fortement impactée par la nature laminaire de la CL, notamment du fait de la faible résilience de celle-ci aux gradients de pression adverses et à la transition turbulente. Cette thèse a ainsi porté les méthodes d’analyse de stabilité sur champ RANSpour les situations de CL laminaire. L’originalité et l'apport de l’étude résident dans la prise en compte des modèles de transition dans l’approchelinéarisée sur champ RANS. Les modèles utilisés (RANS et transition) ont donc été linéarisés afin de réaliser des études de stabilité en perturbant toutes les variables aérodynamiques. La validation de la méthode a été réalisée par comparaison avec des résultats expérimentaux et de simulation (LES) sur deux conifurations d'application. La première configuration est le cas de la réflexion d’un choc oblique sur une plaque plane. La deuxième est celle du choc droit à l’extrados d’un profil en condition transsonique. Ces deux cas sont en condition de CL laminaire à l'amont du choc.Des analyses de stabilité et de résolvent ont été réalisées.Ces approches ont permis de caractériser le comportement d’oscillateur/amplificateur des écoulements en question et d'analyser la physique des instationnarités observées dans les expériences.Le cas de la réflexion de choc est caractérisé par trois fréquences. L'analyse de stabilité montre que celles-ci ne correspondent pas à des modes globaux instables mais à une dynamique d'amplificateur de l'écoulement. L'analyse de résolvent identifie bien ces trois fréquences. L’analyse des réponses optimales, couplée à une analyse de stabilité locale, a ensuite permis de proposer des scénarios physiques de ces dynamiques.Dans le cas du choc droit sur profil en régime transsonique, l'écoulement apparaît globalement instable. Deux modes d'instabilité sont identifiés. Le premier à basse fréquence correspond au phénomène de tremblement observé en conditions turbulentes. Le deuxième apparaît à plus haute fréquence, et correspond à un mode d'oscillation de la bulle de séparation présente sous le pied de choc.Plus largement, la thèse permet de suggérer que certaines dynamiques dans ce type d’interaction procèdent de mécanismes similaires liés à la respiration de la bulle de séparation laminaire. / The shock wave boundary layer (BL) interaction phenomenon is ubiquitous in aerodynamic. In general this interaction generates some low frequency oscillations which can be disastrous for the machines. The typical example is the buffet phenomenon on an airfoil in transonic conditions. Buffet is dangerous since its low frequency can excite the structural modes of the airfoil and break it. The phenomenology has been wildly studied when the incoming BL is turbulent. These studies have derived several credible scenarii and efficient methodologies to capture its dynamic, especially the stability analysis tools on an averaged turbulent flow (RANS). However laminar technologies, the use of laminar BL to reduce the fuel consumption of planes, represent a new scientific challenge on this problematic. In fact, the physic of the interaction is importantly impacted by the laminar nature of the BL especially because of its weak resilience to an adversed pressure gradient and of the transition to turbulence.The thesis deals with the methodologies for the stability analysis on a RANS base flow in the case of a laminar BL. The originality and the contribution of this work have been to take into account a transition criteria in the linearised dynamic on a RANS base flow. The model used (RANS and transition) have then been linearized in order to make a stability analysis which take into account all the aerodynamic varaibles. The validation of this methodology has been made by comparison to expermient and simulation (LES) on two configurations of application. The first one is a weak reflected shock wave on a flat plate. The second one is the strong shock around an airfoil in a transonic regime. In both cases the incoming BL is laminar.Stability and resolvent analysis have been made. These approches have been able to caratirized the ocillator/noise amplifier behavior of the flow and to enabled a physical analysis of the unsteadinesses observed in the experiments.The case of the reflected shock wave is caracterized by three frequencies. The stability analysis shows that they don't correspond to globally unstable modes but to a noise amplifier behavior of the flow. The resolvent analysis identifies the three frequencies. The analysis of the optimal response, coupled with a local stability analysis, enables to proposed physical scenarii of these dynamics.In the case of the strong shock on an airfoil in transonic regime, the flow is globally unstable. Two unstable modes have been identified. The first one, at low frequency, correspond to the buffet phenomenon also observed in the turbulent case. The second one appears at higher frequency and correspond to the oscillation of the separation bubble formed at the feet of the shock.More generally, this thesis suggests that some dynamics of these two interactions result from the same mecanism linked to the breathing motion of the laminar separation bubble.

AbstractThe overall safety of dams depend on several stipulations. One of them is global stability of the dam, which is addressed with approaches like that in (RIDAS, 2017) (the Swedish power companies’ guidelines for dam safety). When designing a new dam, two global failure modes; sliding and overturning should be considered according to RIDAS. However, this is a simplification and other failure modes may exist, such as the combination of sliding and overturning failure. In this combined mode, the dam typically starts to overturn slightly, then as it looses its contact in the upstream area of the footprint, the dam starts to slide. This combined failure mode is yet to be fully addressed in design codes.One additional failure mode that may occur is an internal failure which is caused by material failure of the dam or where existing cracks govern the failure mode. Reinforced concrete structures are expected to crack and hence it likely that such failure mode may occur. The objective of this report is to understand the behavior of a pre-cracked buttress dam under typical loading conditions, and to analyze potential internal failure modes caused by these cracks. Moreover, the validity of using RIDAS design criteria for evaluating the safety of cracked concrete buttress dams will be examined. Finally, this report will study the influence of various possible cracks to study if these are critical and influence the overall dam safety.The stated objectives were investigated by performing analytical calculations and FE-analyses for three different geometries, where each geometry was analyzed with and without pre-existing cracks. The analytical calculations were carried out using MATLAB, to study the two global failure modes suggested by RIDAS: sliding and overturning for the selected geometries. FE-analyses were performed using BRIGADE Plus 6.2 software, where all geometries were studied for all potential global failure modes, including a combination of sliding and overturning failure modes. When comparing results of uncracked and cracked sections, whether it was obtained analytically or by FE-analyses, the influence of cracks in reducing the overall safety of the structure could be clearly highlighted. Moreover, the results comparing analytical solution using RIDAS and FE-analysis did not follow a uniform pattern, therefore, no concrete results could be concluded and further studies to develop more detailed analytical calculation methods were suggested. Finally, the cracks develop between the inspection gangway and the front-plate was proven to have larger influence on the residual mass of the dam, and thus, the overall safety of the dam.

"Safety is a value, not just a Priority" Geomechanically stable underground excavations require continuous assessment of rock mass behavior for maximizing safety. Optimizing pillar design is essential for preventing hazardous incidents and improving production in room-and-pillar mines. Maintaining regional and global stability is complicated for underground carbonate or stone deposits, where extensive fracture networks and groundwater flow become leading factors for generating unsteady ground conditions including karsts. A sudden encounter with karst cavities during mine advance may lead to safety issues, including ground collapse and outflow of unconsolidated sediments and groundwater. The presence of these eroded zones in pillars may cause their failure and poses a risk to the lives of miners apart from disrupting the pre-planned mining operations. A pervasive presence of joints and fractures plays a primary role in promoting structurally controlled failures in stone mines, which accelerates upon interaction with the karst cavities. The prevalent empirical and analytical approaches for pillar design ignore the geotechnical complexities such as the spatial density of discontinuities, karst voids, and deviation from the design during short-range mine planning. With the increasing market demand for limestone products, mining organizations, as well as enforcement agencies, are investing in research for increasing the efficiency of extracting valuable resources. While economical productivity is essential, preventing risks and ensuring the safety of miners remains the cardinal objective of mining operations. According to the Mine Safety and Health Administration (MSHA), since 2000, about 31% of occupational fatalities at all underground mines in the United States are caused due to ground collapse, which rises to 39% for underground stone mines. The objective of this study is to provide a reliable and methodological approach for pillar design in underground room-and-pillar hard rock mines for safe and efficient ore recovery. The numerical modeling techniques, implemented for a case study stone mine, could provide a pragmatic framework to assess the effect of karsts on rock mass behavior, and design future pillars detected with voids. The research uses data acquired from using remote sensing techniques, such as LiDAR and Ground-penetrating Radar surveys, to map the excavation characteristics. Discontinuum modeling was valuable for analyzing the pillar strength in the presence of discontinuities and cavities, as well as estimating a safe design standard. Discrete Fracture Networks, created using statistical information from discontinuity mapping, were employed to simulate the joints pervading the rock mass. This proposed research includes the calibration of rock mass properties to translate the effect of discontinuities to continuum models. Continuum modeling proved effective in analyzing regional stability along with characterizing the redistributed stress regime by imitating the excavation sequence. The results from pillar-scale and local-scale analyses are converged to optimize pillar design on a global scale and estimate the feasibility of secondary recovery in stone mines with a dominating discontinuity network and karst terrane. Stochastic analysis using finite volume modeling helped evaluate the performance of modified pillars to assist production while maintaining safety standards. The proposed research is valuable for improving future design parameters, excavation practices, and maintaining a balance between an approach towards increased safety while enhancing production. / Doctor of Philosophy / "The most valuable resource to come back out of a mine is a miner" – Anonymous. The United States accounted for 27% of the global limestone market share which was valued at US$58.5 billion in 2020 [148]. It is projected to reach a target of US$65.3 billion in 2027, growing even in midst of the COVID-19. As surface reserves deplete, much of the mineral demand gap is supplemented by mining underground deposits. Underground mines extract minerals from deep within the earth compared to surface mines. As a result, the miners experience a greater number of accidents in a constricted environment because of roof/tunnel collapse, fewer escape routes, ventilation, explosions, or inundation. According to the Mine Safety and Health Administration (MSHA), about 15% of all underground mine injuries in the US were caused by rockfalls since 1983. The majority of underground stone deposits are mined using the room-and-pillar mining method, which resembles a chessboard design where the light squares are mined, and the dark squares are left as rock pillars to support the tunnels. Limestone, a carbonate rock, contains a lot of fractures and joints (discontinuities). Erosion of rocks due to continuous water flow through the fractures leads to the formation of cavities known as karsts. Interaction of karsts with the prevalent fracture network increases rockfall risk during mining. The collapse of voids along with an inrush of filled rock-clay-water sludge can harm miners' lives, damage machinery, and stop further operations. Literature is scarce on topics that quantify the risk and disruption posed by these cavities in underground mines. Most rock classification systems cannot classify their effect because of the unpredictability and extensive analysis required. The objective of this research is to provide a reliable and methodological approach for designing pillars in underground hard rock mines for ensuring a safe working environment and efficient mineral recovery. This research starts with analyzing the strength of pillars, in which karst cavities were discovered while mining. The safety concerns often lead the miners to not excavate around the cavities and leave valuable resources unmined. Data from ground-penetrating radar and laser scanning surveys were used to characterize the voids and map the discontinuities. Discrete-element numerical modeling was used to simulate the pillars as an assembly of blocks jointed by the discontinuities. The simulation results help us understand the instability issues in the karst-ridden pillars and ways to improve upon the existing design. The findings were used to modulate the parameters for regional-scale models using finite volume modeling for less computationally intensive analyses and simulating rock as a continuum. The continuum models were highly effective in analyzing the instability issues due to the prevalent karstic network. This helps understand any alternative scenario that could have been implemented to optimize ore recovery while preventing risks. The results from the single pillar and regional analyses are combined to optimize pillar design on a global mine scale. This dissertation focuses on improving hazard mitigation in mines with unpredicted anomalies like karsts. Although this research is based on a specific mine site, it empowers the operators to explore the presented techniques to increase safety in all underground mines. The suggested methodology will help devise better strategies for handling instability issues without jeopardizing the mine operations. The primary motivation is to keep the underground miners safe from hazardous situations while fulfilling the secondary objective of maximizing mineral production.

O presente trabalho tem como objetivo desenvolver processos analíticos e programas computacionais para avaliação da estabilidade global e pré-dimensionamento de pórticos planos em concreto pré-moldado com base na garantia da estabilidade global. Em relação à avaliação da estabilidade global, são propostas duas expressões. A primeira está relacionada à expressão do limite do parâmetro de estabilidade aplicada a pórticos planos em concreto pré-moldado. A segunda expressão tem o objetivo determinar o deslocamento horizontal de topo de pórticos planos em concreto pré-moldado de um pavimento. A expressão do limite alternativo do parâmetro de estabilidade é deduzida a partir dos valores obtidos da relação entre o deslocamento horizontal médio e de topo de 1320 pórticos. A expressão é função do fator de restrição da ligação, contemplando, dessa forma, os efeitos causados pela semirrígidez das ligações no comportamento da estabilidade global desse sistema estrutural. A equação de determinação do deslocamento horizontal de topo de pórticos planos em concreto pré-moldado de um pavimento é deduzida com base no método dos deslocamentos. Em relação ao pré-dimensionamento de pórticos planos em concreto pré-moldado, são propostos processos analíticos para o pré-dimensionamento dos pilares de pórticos de um pavimento com ligação semirrígida e de pórticos de múltiplos pavimentos com ligações rígidas e articuladas. Os processos analíticos são constituídos pela expressão da rigidez equivalente de estabilidade de pórticos, desenvolvida através das equações do parâmetro de estabilidade e do seu limite alternativo. O trabalho ainda apresenta o Programa de Avaliação da Estabilidade Global e Pré-dimensionamento de Pórticos Planos em Concreto Pré-moldado, denominado PRE-MOLDIM. O programa é constituído por quatro módulos. O primeiro módulo realiza a avaliação da estabilidade global e verificação da deslocabilidade lateral de pórticos planos em concreto pré-moldado. O segundo módulo tem o objetivo de definir as dimensões mínimas dos pilares em função da garantia da estabilidade global e do deslocamento lateral admissível. O terceiro módulo define o valor da rigidez das ligações necessário para que sejam atendidos os quesitos de estabilidade global e deslocamento lateral admissível. O quarto módulo realiza o dimensionamento da armadura de continuidade de uma típica ligação viga-pilar em concreto pré-moldado. O dimensionamento da armadura de continuidade é realizado em função da garantia da estabilidade global e do deslocamento lateral admissível de pórticos planos em concreto pré-moldado. A aplicação dos processos analíticos e programas computacionais em exemplos comprovaram, de forma satisfatória, o desempenho de suas funções. Os valores obtidos pela expressão alternativa do limite do parâmetro de estabilidade são compatíveis com o limite do coeficiente \'gama\'z. Os valores do deslocamento de topo de pórticos de um pavimento com ligações semirrígidas, obtidos pelo processo analítico, são próximos dos valores obtidos pela simulação numérica. Os pilares pré-dimensionados pelos processos analíticos conseguem garantir de forma satisfatória estabilidade global dos pórticos planos em concreto pré-moldado. / The present work aims to develop analytical processes and computer programs for the evaluation of global stability and preliminary design of plane frames in precast concrete based on ensuring global stability. Regarding the evaluation of global stability, two analytical expressions are proposed. The first is related to the expression of the limit of the stability parameter applied to plane frames in precast concrete. The second expression has the objective to determine the horizontal displacement of the top of plane frames in precast concrete for a floor. The expression of the alternative stability limit of the parameter is deduced from the values obtained from the relationship between the average and the top horizontal displacement of 1320 frames. The expression is a function of the limiting factor of the connection, thus contemplating the effects caused by the semi-rigidity of the connection on the global stability behavior of this structural system. The equation for determining the horizontal displacement of the top of plane frames in precast concrete pavement is obtained based on the displacement method. Regarding the preliminary design of plane frames in precast concrete, analytical procedures are proposed for the preliminary design of column of an one store frame with semi-rigid connection and a multiple store frames with rigid and articulated connections. The analytical processes are constituted by the expression of equivalent stiffness of frame stability, developed through the equations of the stability parameter and its alternative limit. The work also presents the Program of Global Stability Evaluation and Preliminary Design of Plane Frames in Precast Concrete, called PRE-MOLDIM. The program consists of four modules. The first module performs the evaluation of global stability and verification of lateral plane frames displaceability in precast concrete. The second module aims to set minimum dimensions for the pillars due to guarantee the global stability and check the allowable lateral displacement. The third module defines the value of the connections stiffness so the matter of global stability and allowable lateral displacement are satisfied. The fourth module performs the design of continuity armor of a typical beam-column connection in precast concrete. The design armour continuity is made on the basis of ensuring the global stability and lateral displacement allowable plane frames in precast concrete. The application of analytical processes and computer programs in examples proved satisfactorily, the performance of its functions. The values obtained by the alternative expression of the limit of stability parameter are compatible with the limit of the coefficient \'gama\'z. The offset values top venting a pavement with semi-rigid connections, obtained by the analytical process, are close to the values obtained by numerical simulation. The preliminary designed pillars by analytical processes can ensure a satisfactory global stability of the plane frames in precast concrete.

Em epidemiologia matemática, muitos modelos de propagação de doenças infecciosas em populações têm sido analisados matematicamente e aplicados para doenças específicas. Neste trabalho um modelo de propagação de dengue é analisado considerando-se diferentes hipóteses sobre o tamanho da população humana. Mais precisamente, estamos interessados em verificar o impacto das variações populacionais a longo prazo no cálculo do parâmetro Ro e no equilíbrio endêmico. Vamos discutir algumas ideias que nortearam o processo de definição do parâmetro Ro a partir da construção do Operador de Próxima Geração. Através de um estudo qualitativo do modelo matemático, obtivemos que o equilíbrio livre de doença é globalmente assintoticamente estável se Ro é menor ou igual a 1 e instável se Ro>1. Para Ro>1, a estabilidade global do equilíbrio endêmico é provada usando um critério geral para estabilidade orbital de órbitas periódicas associadas a sistemas autônomos não lineares de altas ordens e resultados da teoria de sistemas competitivos para equações diferenciais ordinárias. Também foi desenvolvida uma análise de sensibilidade do Ro e do equilíbrio endêmico com relação aos parâmetros do modelo de propagação. Diversos cenários foram simulados a partir dos índices de sensibilidade obtidos nesta análise. Os resultados demonstram que, de forma geral, o parâmetro Ro e o equilíbrio endêmico apresentam considerável sensibilidade a taxa de picadas do vetor e a taxa de mortalidade do vetor. / In mathematical epidemiology many models of spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. In this work a dengue propagation model is analyzed considering different assumptions about the size of the human population. More precisely, we are interested to verify the impact of population long-term variations in the calculation of the parameter Ro and endemic equilibrium. We will discuss some ideas that guided the parameter setting process Ro from the construction of the Next Generation Operator. Through a qualitative study of the mathematical model, we found that the disease-free equilibrium is globally asymptotically stable if Ro is less or equal than 1 and unstable if Ro> 1. For Ro> 1 the global stability of the endemic equilibrium is proved using a general criterion for orbital stability of periodic orbits associated with nonlinear autonomous systems of higher orders and results of the theory of competitive systems for ordinary differential equations. Also a sensitivity analysis of the Ro and the endemic equilibrium with respect to the parameters of the propagation model was developed. Several scenarios were simulated from the sensitivity index obtained in this analysis. The results demonstrate that in general the parameter Ro and the endemic equilibrium are the most sensitive to the vector biting rate and the vector mortality rate.

No presente trabalho são avaliados os principais parâmetros de projeto na análise da estabilidade global de estruturas em concreto pré-moldado de múltiplos pavimentos, considerando a não-linearidade física (NLF), não-linearidade geométrica (NLG) e ligações semi-rígidas. Os sistemas estruturais analisados são constituídos por pórticos com ligação viga-pilar semi-rígida e pilares engastados na fundação. As ligações viga-pilar têm sua tipologia definida por chumbadores retos e capa de concreto moldado in loco com armadura de continuidade. A NLF é avaliada segundo a construção dos diagramas M x N x 1/r, onde foi considerado de forma consistente o efeito da força normal, da armadura passiva, da armadura ativa e a reologia do concreto. São propostas funções e definidos coeficientes redutores de rigidez que foram comparados com valores apontados em expressões normativas que contemplam de forma aproximada a NLF. A NLG é avaliada com o auxílio do programa ANSYS e na forma aproximada segundo o coeficiente z e o método da carga lateral fictícia (P-). Apresentam-se modelos analíticos de caracterização de rigidez e resistência de ligações viga-pilar ao momento fletor negativo e positivo. Na análise numérica é feito um estudo de caso completo de uma estrutura típica de múltiplos pavimentos em concreto pré-moldado com o auxílio do programa ANSYS, avaliando-se diferentes formas de consideração da NLF e da NLG. É analisada a distribuição de esforços na estrutura frente às combinações de ações utilizadas e os modelos de comportamento das ligações, para algumas variações de geometria e carregamento. Dentre as conclusões, pode ser citado que os coeficientes redutores obtidos segundo o diagrama M x N x 1/r divergem das indicações normativas para consideração simplificada de NLF. Quanto à consideração simplificada de análise NLG, o coeficiente z apresentou resultados melhores na previsão dos esforços de segunda ordem em relação aos obtidos por 0,95.z. / In this research it was evaluated the main design parameters in the analysis of global stability of multi-storey precast concrete framed structures considering the physical nonlinearity (PNL), geometric nonlinearity (GNL) and semi-rigid connections behavior. The structural systems considered are those consisting of frames with beam-to-column semi-rigid connection and columns inset in the foundation. The beam-to-column connections are defined by two dowels and cast-in-place concrete cap with longitudinal reinforced bars. The PNL is evaluated according the M x N x 1/r diagrams, where are considered the effect of normal force, the reinforcing steel, prestressing steel and creep. Functions are proposed and reducing stiffness coefficients are defined, with were compared with codes that include the approximated PNL. The GNL is evaluated according to ANSYS software by no approximate analisys and its approximate according to the coefficient z and (P-) method. This research presents an analytical model characterization of stiffness and strength of beam-to-column connections to the negative and positive bending moment. In the numerical analysis is made a full case study of a typical multi-storey precast concrete framed structure with the aid of the ANSYS software, evaluating different forms of consideration of the PNL and the GNL. It analysed the bending moment distribution according the combinations of actions used and the behavioral models of connections, for some variations at geometry and loading. The reduction coefficients of flexural rigidity obtained according the M x N x 1/r diagrams differ from normative indications for simplified account of PNL. In GNL simplified analysis, the coefficient z showed better results in predicting the second-order effects with respect to those obtained by the coefficient 0,95. z.

<p><b>In this dissertation we present the quantitative response of an epidemic of the so-called SIR-type, in a population consisting of a local component and a migrant component. Each component can be divided into three classes, the susceptible individuals, usually denoted by S, who are uninfected but may contract the disease, infected individuals (I) who are infected and can spread the disease to the susceptible individuals and the class (R) of recovered individuals. If a susceptible individual becomes infected, it moves into the infected class. An infected individual, at recovery, moves to the class R. Firstly we develop a model describing two interacting populations with vaccination. Assuming the vaccination rate in both groups or components are constant, we calculate a threshold parameter and we call it a vaccination reproductive number. This invariant determines whether the disease will die out or becomes endemic on the (in particular, local) population. Then we present the stability analysis of equilibrium points and the effect of vaccination. Our primary finding is that the behaviour of the disease free equilibrium depend on the vaccination rates of the combined population. We show that the disease free equilibrium is locally asymptotically stable if the vaccination reproductive number is less than one. Also our stability analysis show that the global stability of the disease free equilibrium depends on the basic reproduction number, not the vaccination reproductive number. If the vaccination reproductive number is greater than one, then the disease free equilibrium is unstable and there exists three endemic equilibrium points in our model. Two of these three endemic equilibria are so-called boundary equilibrium points, which means that the infection is only in one group of the population. The third one which we focus on is the general endemic point for the whole system. We derive a threshold condition that determines whether the endemic equilibria is locally asymptotically stable or not. Secondly, by assuming that the rate of vaccination in the migrant population is constant, we apply optimal control theory to find an optimal vaccination strategy in the local population. Our numerical simulation shows the effectiveness of the control strategy. This model is suitable for modeling the real life situation to control many communicable diseases. Models similar to the model used in the main contribution of our dissertation do exist in the literature. In fact, our model can be regarded as being in-between those of [Jia et al., Theoretical Population Biology 73 (2008) 437-448] and [Piccolo and Billings, Mathematical and Computer Modeling 42 (2005) 291-299]. Nevertheless our stability analysis is original, and furthermore we perform an optimal control study whereas the two cited papers do not. The essence of chapter 5 and 6 of this dissertation is being prepared for publication.</b></p>