O Estado de São Paulo possui uma extensa malha rodoviária que atravessa diferentes compartimentos geológicos e geomorfológicos. Os taludes presentes nestas rodovias podem apresentar diferentes processos de instabilização a depender destes condicionantes. Na busca do entendimento da deflagração destes processos em taludes de corte, a presente pesquisa é baseada no estudo da influência da forma de escoamento superficial, da geometria dos taludes e dos tipos de perfis de alteração dos solos. Para este estudo foi escolhida uma área de 13,6 km² localizada na Rodovia Luís Augusto de Oliveira (SP-215), entre os quilômetros 170 e 183, nos municípios de São Carlos, Ibaté e Ribeirão Bonito em SP. A pesquisa foi realizada em duas escalas, de semi-detalhe e de detalhe. Na primeira foram definidas quatro classes de potencial de instabilização para os setores no entorno dos taludes utilizando como base os condicionantes críticos cartografados nos mapas temáticos (declividades maiores que 15%, perfil de encosta côncavo, direção de escoamento superficial coincidente com o mergulho do talude e de uso e ocupação de cultura), além da altura dos setores. A definição do potencial de instabilização foi realizada considerando os condicionantes de forma isolada e de forma conjunta (fazendo uso do somatório ponderado). Os potenciais de instabilização definidos pelos dois métodos foram validados em relação a disposição das cicatrizes de escorregamento em campo. Os potenciais de instabilização alto e muito alto, definidas a partir dos condicionantes críticos considerados de forma conjunta, coincidiram com os locais com escorregamento. Na segunda escala de análise foi feita análise da estabilidade de seções geológico-geotécnicas dos taludes de corte, utilizando do método determinístico de Bishop Simplificado. Uma segunda validação do potencial de instabilização foi feito comparando as classes com os valores de fatores de segurança (FS) obtidos das análises de estabilidade (feitas com os parâmetros de resistência dos solos da retroanálise e os mínimos obtidos nas referências). Os FS mostraram-se compatíveis com as classes definidas, principalmente os FS obtidos das análises de estabilidade feitas com os parâmetros de resistência obtidas nas retroanálises. A metodologia de investigação proposta de potencial de instabilização apresentou resultados relevantes no estudo de estabilidade de taludes de corte em condições de relevo suave, como ocorre na área de estudo. / São Paulo State has an extensive road network that crosses different geological and geomorphological compartments. The slopes present in these highways can have different instability processes depending on their conditions. In the search for better understanding the deflagration processes in cutting slopes, the present research is based on the study of the influence of the surface runoff, the slope geometry, and the soil alteration profile. For this study, an area of 13.6 km² was selected, which is located on the Luís Augusto de Oliveira Highway (SP-215), between the kilometers 170 and 183, in São Carlos, Ibaté and Ribeirão Bonito cities in SP. The research was carried out in two scales (semi-detail and detail). In the semi-detail scale, four classes of instability potential were defined for the sectors around the slopes. The index was defined using as a reference the critical conditioners outlined in the thematic maps (such as slope bigger than 15%, concave slope profile, runoff direction coincident with slope dip and land use and occupation), as well as the height of the sectors. The definition of the instability potential was performed considering the conditioners by themselves and in a joint manner (using the weighted summation). The instability potentials defined by the two methods were validated in relation to the landslides scars disposition in the field. The high and very high instability potentials classes, which were defined considering the conditioners together, coincided with the landslides scars. The detail scale of analysis corresponded to stability analysis of geological-geotechnical sections of cut slopes using the Simplified Bishop\'s deterministic method. A second validation of the instability potential was made comparing the classes with the safety factor (FS) values obtained in the stability analyzes (made with the soil resistance parameters from retroanalysis and with the minimums parameters obtained in the references). The FS were compatible with the defined classes, mainly the FS from the stability analysis made with the resistance parameters obtained in the retroanalysis. The proposed research methodology of instability potential presented relevant results in the study of stability of cut slopes under conditions of gentle relief, as occurs in the study area.

In this thesis we modify an existing model for the spread of resistant bacteria in a hospital. The existing model does not account for some of the trends seen in the data found in literature. The new model takes some of these trends into account. For the new model, we examine issues relating to identifiability, sensitivity analysis, parameter estimation, uncertainty analysis, and equilibrium stability.

Philosophiae Doctor - PhD / Numerical approximations of multiscale problems of important applications in ecology are investigated. One of the class of models considered in this work are singularly perturbed (slow-fast) predator-prey systems which are characterized by the presence of a very small positive parameter representing the separation of time-scales between the fast and slow dynamics. Solution of such problems involve multiple scale phenomenon characterized by repeated switching of slow and fast motions, referred to as relaxationoscillations, which are typically challenging to approximate numerically. Granted with a priori knowledge, various time-stepping methods are developed within the framework of partitioning the full problem into fast and slow components, and then numerically treating each component differently according to their time-scales. Nonlinearities that arise as a result of the application of the implicit parts of such schemes are treated by using iterative algorithms, which are known for their superlinear convergence, such as the Jacobian-Free Newton-Krylov (JFNK) and the Anderson’s Acceleration (AA) fixed point methods.

Cette thèse a pour but l’étude de la rotation de l’écoulement des grandes échelles dans deux configurations. La première configuration se concentre sur l’effet de la rotation de l’écoulement sur une flamme laminaire. Elle est stabilisée dans le sillage d’un cylindre. La rotation de l’écoulement est introduite en faisant tourner le cylindre autour de son axe. La simulation numérique directe (Direct Numerical Simulation (DNS)) montre que la rotation du cylindre rompt la symétrie des deux branches de la flamme. La fonction de transfert de flamme (Flame Transfer Function (FTF)), obtenue grâce à l’inversion de Wiener-Hopf, indique qu’un faible taux de rotation réduit le gain de la FTF et donc la flamme devient presque insensible aux perturbations acoustiques à une fréquence donnée. De plus, il est démontré que cette diminution du gain est due à une interférence destructive des fluctuations de chaleur produites par les deux branches de la flamme. La fréquence à laquelle le gain de la FTF devient presque nul est ajustable par la vitesse de rotation du cylindre. Cette étude suggère que le contrôle de la symétrie de la flamme pourrait être un outil de contrôle en boucle ouverte des instabilités thermoacoustiques. Dans le cas de la deuxième configuration, la rotation de l’écoulement est induite par une instabilité hydrodynamique, aussi nommée Precessing Vortex Core (PVC) dans un système d’injection de carburant industriel. Des expériences et des simulations aux grandes échelles (Large Eddy Simulation (LES)) montrent que l’écoulement non-réactif dans l’injecteur pri- maire peut être décomposé en une contribution moyenne et un PVC. Cette instabilité hydro- dynamique est étudiée par l’analyse de stabilité linéaire (Linear Stability Analysis (LSA)) en utilisant deux approches différentes (locale et BiGlobale). Les résultats de l’expérience, de la LES et de la LSA démontrent que le montage d’une tige centrale à l’intérieur de l’injecteur stabilise le PVC. De plus, le même injecteur industriel est étudié dans le cas d’un écoule- ment réactif par LES. Les résultats démontrent que la flamme stabilise le PVC. L’analyse de stabilité BiGlobal montre que le gradient de densité dans le front moyen de la flamme a un effet important sur l’amortissement du PVC. Enfin, l’impact de la tige centrale est également étudié pour le cas réactif. La tige centrale impacte marginalement la forme globale de la flamme, mais a un effet positif sur l’accrochage de la flamme dans la zone de combustion pauvre. En comparant deux cas par LSA, celui avec la tige et celui sans la tige, les résultats suggèrent que la tige augmente considérablement l’amortissement du PVC. Cela pourrait causer une diminution de la turbulence dans l’écoulement et empêcher l’extinction de la flamme et donc expliquer l’influence bénéfique de la tige sur la stabilisation de la flamme. / This thesis investigates large scale flow rotation in two configurations. In the first, the effect of flow rotation on a laminar flame is investigated. The flame is anchored in the wake of a cylindrical bluff body. The flow rotation is introduced by turning the cylinder along its axis. It is shown by Direct Numerical Simulation (DNS), that the cylinder rotation breaks the symmetry of both flame branches. Flame Transfer Function (FTF) measurements performed by the Wiener-Hopf Inversion suggest, that low rotation rates lead to deep gaps in the gain and the flame becomes almost insensitive to acoustic perturbation at a specific frequency. It furthermore is demonstrated that this decrease in gain of the FTF is due to destructive interference of the heat release signals caused by the two flame branches. The frequency at which the gain becomes almost zero can be adjusted by tuning the cylinder rotation rate. The study suggests that controlling the symmetry of the flame could be a tool of open-loop control of thermoacoustic instabilities.

La fragmentation d’enveloppes métalliques en expansion dynamique intéresse tant l’industrie civile que celle de la défense. Pour les deux domaines d’application, il s’agit de pouvoir prédire la taille et la vitesse des fragments, résultant de la destruction des enveloppes, afin de mesurer les conséquences que ceux-ci peuvent avoir sur des structures de sécurité. Les modèles de prédiction existants étudient le développement d’un défaut au sein du matériau et arrivent à déterminer une taille caractéristique des fragments. Néanmoins, ces modèles nécessitent une hypothèse dont la validité est remise en cause lorsque la vitesse de déformation est importante. Dans ce travail, nous proposons un nouveau modèle analytique pour des cylindres (sollicitation en traction plane) permettant de s’affranchir de cette hypothèse et d’étudier l’influence du défaut initial en suivant son évolution. Le modèle développé est comparé avec succès à des résultats issus de simulations numériques par éléments finis. Nos travaux permettent notamment de préciser les cadres d’application et de validité des approches classiques. Comme résultats majeurs, la nouvelle approche permet d’analyser les évolutions des perturbations aux faibles déformations mais aussi d’estimer le temps d’apparition des premières décharges élastiques, synonymes de strictions localisées. / This work deals with the fragmentation of dynamically expanding metal shells and covers a problem of interest for both civil and military industries. For both fields of application, it is crucial to predict the size and the speed of fragments, resulting from the destruction of shells in order to measure the consequences that it could have on structures. Current models study the growth of a defect within the material and are able to determine a characteristic size of fragments. Nevertheless, these models require a hypothesis whose validity is questionable when the rate of deformation is important. In this work, we propose a new analytical model for cylinders (equivalent to the dynamic extension of a plate) to overcome this hypothesis and study the influence of the initial defect by following its time evolution. The model is compared successfully with results performed with a finite element method. Our work notably expands the framework of classical linear stability analyses. As a major outcome, the proposed approach is able to track the evolution of a perturbation even for small plastic strain, when the flow may be stable. In addition it is shown that the present approach can predict accurately the time where the elastic unloading is observed in finite element simulations.

This thesis presents a discussion of design tools for analysing block stability around a tunnel. First, it was determined that joint length and field stress have a significant influence on estimating block stability. The results of calculations using methods based on kinematic limit equilibrium (KLE) were compared with the results of filtered DFN-DEM, which are closer to reality. The comparison shows that none of the KLE approaches– conventional, limited joint length, limited joint length with stress and probabilistic KLE – could provide results similar to DFN-DEM. This is due to KLE’s unrealistic assumptions in estimating either volume or clamping forces. A simple mechanism for estimating clamping forces such as continuum mechanics or the solution proposed by Crawford-Bray leads to an overestimation of clamping forces, and thus unsafe design. The results of such approaches were compared to those of DEM, and it was determined that these simple mechanisms ignore a key stage of relaxation of clamping forces due to joint existence. The amount of relaxation is a function of many parameters, such as stiffness of the joint and surrounding rock, the joint friction angle and the block half-apical angle. Based on a conceptual model, the key stage was considered in a new analytical solution for symmetric blocks, and the amount of joint relaxation was quantified. The results of the new analytical solution compared to those of DEM and the model uncertainty of the new solution were quantified. Further numerical investigations based on local and regional stress models were performed to study initial clamping forces. Numerical analyses reveal that local stresses, which are a product of regional stress and joint stiffness, govern block stability. Models with a block assembly show that the clamping forces in a block assembly are equal to the clamping forces in a regional stress model. Therefore, considering a single block in massive rock results in lower clamping forces and thus safer design compared to a block assembly in the same condition of in-situ stress and properties. Furthermore, a sensitivity analysis was conducted to determine which is  the most important parameter by assessing sensitivity factors and studying the applicability of the partial coefficient method for designing block stability. It was determined that the governing parameter is the dispersion of the half-apical angle. For a dip angle with a high dispersion, partial factors become very large and the design value for clamping forces is close to zero. This suggests that in cases with a high dispersion of the half-apical angle, the clamping forces could be ignored in a stability analysis, unlike in cases with a lower dispersion. The costs of gathering more information about the joint dip angle could be compared to the costs of overdesign. The use of partial factors is uncertain, at least without dividing the problem into sub-classes. The application of partial factors is possible in some circumstances but not always, and a FORM analysis is preferable. / QC 20111201

In this paper, we identify sufficient conditions for Lyapunov Mean Square Stability (LMSS) of a contention-based network of first-order systems, with state-based schedulers. The stability analysis helps us to choose policies for adapting the scheduler threshold to the delay from the network and scheduler. We show that three scheduling laws can result in LMSS: constant-probability laws and additively increasing or decreasing probability laws. Our results counter the notions that increasing probability scheduling laws alone can guarantee stability of the closed-loop system, or that decreasing probability scheduling laws are required to mitigate congestion in the network. / <p>QC 20130116</p>

Magnetic shape memory alloys (MSMAs) are a class of active materials that de- form under magnetic and mechanical loading conditions. This work is concerned with the modeling of MSMAs constitutive responses. The hysteretic magneto-mechanical responses of such materials are governed by two major mechanisms which are variant reorientation and field induced phase transformation (FIPT). The most widely used material for variant reorientation is Ni2 MnGa which can produce up to 6% magnetic field induced strain (MFIS) under 5 MPa actuation stress. The major drawback of this material is a low blocking stress, which is overcome in the NiMnCoIn material system through FIPT. This magnetic alloy can exhibit 5% MFIS under 125 MPa actuation stress. The focus of this work is to capture the key magneto-thermo-mechanical responses of such mechanisms through phenomenological modeling. In this work a detailed thermodynamic framework for the electromagnetic interaction within a continuum solid is presented. A Gibbs free energy function is postulated after identifying the external and internal state variables. Material symmetry restrictions are imposed on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals whereas continuous symmetry is considered for polycrystalline materials. The constitutive equations are derived in a thermodynamically consistent way. A specific form of Gibbs free energy for FIPT is proposed and the explicit form of the constitutive equations is derived from the generalized formulation. The model is calibrated from experimental data and different predictions of magneto-thermo-mechanical loading conditions are presented. The generalized constitutive equations are then reduced to capture variant reorientation. A coupled magneto-mechanical boundary value problem (BVP) is solved that accounts for variant reorientation to investigate the influence of the demagnetization effect on the magnetic field and the effect of Maxwell stress on the Cauchy stress. The BVP, which mimics a real experiment, provides a methodology to correlate the difference between the externally measured magnetic data and internal magnetic field of the specimen due to the demagnetization effect. The numerical results show that localization zones appear inside the material between a certain ranges of applied magnetic field. Stability analysis is performed for variant reorientation to analyze these numerical observations. Detailed numerical and analytical analysis is presented to investigate these localization zones. Magnetostatic stability analysis reveals that the MSMA material system becomes unstable when localizations appear due to non-linear magnetization response. Coupled magneto-mechanical stability analysis shows that magnetically induced localization creates stress-localizations in the unstable zones. A parametric study is performed to show the constraints on material parameters for stable and unstable material responses.

Small signal stability has always been an important concern for analog designers. Recent advances such as the Loop Finder algorithm allows designers to detect and identify local, potentially unstable return loops without the need to identify and add breakpoints. However, this method suffers from extremely high time and memory complexity and thus cannot be scaled to very large analog circuits. In this research work, we first take an in-depth look at the loop finder algorithm so as to identify certain key enhancements that can be made to overcome these shortcomings. We next propose pole discovery and impedance computation methods that address these shortcomings by exploring only a certain region of interest in the s-plane. The reduced time and memory complexity obtained via the new methodology allows us to extend automatic stability checking to much larger circuits than was previously possible.

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