Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-09T17:18:20Z No. of bitstreams: 1 JACQUELINE FÉLIX DE BRITO - DISSERTAÇÃO PPGMAT 2005..pdf: 538695 bytes, checksum: cd410bf0dae8b3cd679e8abc8feef00b (MD5) / Made available in DSpace on 2018-07-09T17:18:20Z (GMT). No. of bitstreams: 1 JACQUELINE FÉLIX DE BRITO - DISSERTAÇÃO PPGMAT 2005..pdf: 538695 bytes, checksum: cd410bf0dae8b3cd679e8abc8feef00b (MD5) Previous issue date: 2005-12 / Neste trabalho, mostramos a existência de soluções para a seguinte classe de problemas elípticos: (Para ver a formula ou equação recomendamos o download da dissertação). As principais ferramentas utilizadas são os Teoremas de Deformação, Passo da Montanha e Ponto de Sela. / In this work, we show the existence of solutions for the following class for elliptic problem: (To see the formula or equation we recommend downloading the dissertation). (To see the formula or equation we recommend downloading the dissertation).

Neste trabalho consideramos sistemas elípticos de tipo hamiltoniano, envolvendo o operador Laplaciano, com uma parte linear dependendo de dois parâmetros e uma perturbação sublinear. Obtemos a existência de pelo menos duas soluções quando a parte linear está perto da ressonância (este fenômeno é chamado de quase ressonância). Mostramos também a existência de uma terceira solução, quando a quase ressonância é em relação ao primeiro autovalor do operador Laplaciano. No caso ressonante obtemos resultados análogos, adicionando mais uma perturbação sublinear. Os sistemas estão associados a funcionais fortemente indefinidos, e as soluções são obtidas através do Teorema de Ponto de Sela e aproximação de Galerkin. / In this work we consider elliptic systems of hamiltonian type, involving the Laplacian operator, a linear part depending on two parameters and a sublinear perturbation. We obtain the existence of at least two solutions when the linear part is near resonance (this phenomenon is called almost-resonance). We also show the existence of a third solution when the almost-resonance is with respect to the first eigenvalue of the Laplacian operator. In the resonant case, we obtain similar results, with an additional sublinear term. These systems are associated with strongly indefinite functionals, and the solutions are obtained by Saddle Point Theorem and Galerkin approximation.

Cette thèse s’intéresse au développement d’un contrôleur sûre et robuste en tant que partie intégrante d’un pancréas artificiel. Plus précisément, nous sommes intéressés à contrôler la partie du traitement usuel qui a pour but d’équilibrer la glycémie du patient. C’est ainsi que le développement d’une commande prédictive nonlinéaire robuste basée sur la résolution d’un problème de point selle a été envisagé. Afin de valider les performances du contrôleur dans une situation réaliste, des simulations numériques en utilisant une plate-forme de tests validée par la FDA sont envisagées.Dans une première partie, nous présentons une extension de la classique commande prédictive nonlinéaire dont le but est d’assurer le contrôle robuste de systèmes décrits par des équations différentielles ordinaires non linéaires dans un cadre échantillonné. Ce contrôleur, qui calcule une action de contrôle adéquate en considérant la solution d’un problème de point selle, est appelé saddle point model predictive controller (SPMPC). En utilisant cette commande, il est prouvé que le système converge en temps fini dans un espace borné et, en supposant une certaine structure dans le problème, qu’il est pratiquement stable entrée-état. Ensuite, nous nous sommes intéressés à la résolution numérique. Pour ce faire, nous proposons une méthode de résolution inspirée de la méthode du Langrangien augmenté et qui fait usage de modèles adjoints.Dans un deuxième temps, nous considérons l’application de ce contrôleur au problème du contrôle artificiel de la glycémie. Après une phase de modélisation, nous avons retenu deux modèles : un modèle simple qui est utilisé pour développer la commande et un modèle complexe qui est utilisé comme un simulateur réaliste de patients. Ce dernier est nécessaire pour valider notre approche de contrôle. Afin de calculer une entrée de commande adéquate, la commande SPMPC a besoin de l’état complet du système. Or, les capteurs ne peuvent fournir qu’une valeur du glucose sanguin. C’est pourquoi le développement d’un observateur est envisagé. Ensuite, des simulations sont réalisées. Les résultats obtenus témoignent de l’intérêt de l’approche retenue. En effet, pour tous les patients, aucune hypoglycémie n’a été observée et le temps passé en état hyperglycémique est suffisamment faible pour ne pas être dommageable. Enfin, l’intérêt d’étendre l’approche de commande SPMPC au problème de contrôle de systèmes décrits par des équations différentielles retardées non linéaires dans un cadre échantillonné est formellement investigué. / This thesis deals with the design of a robust and safe control algorithm to aim at an artificial pancreas. More precisely we will be interested in controlling the stabilizing part of a classical cure. To meet this objective, the design of a robust nonlinear model predictive controller based on the solution of a saddle point optimization problem is considered. Also, to test the controller performances in a realistic case, numerical simulations on a FDA validated testing platform are envisaged.In a first part, we present an extension of the usual nonlinear model predictive controller designed to robustly control, in a sampled-data framework, systems described by nonlinear ordinary differential equations. This controller, which computes the best control input by considering the solution of a constrained saddle point optimization problem, is called saddle point model predictive controller (SPMPC). Using this controller, it is proved that the closed-loop is Ultimately Bounded and, with some assumptions on the problem structure, Input-to State practically Stable. Then, we are interested in numerically solving the corresponding control problem. To do so, we propose an algorithm inspired from the augmented Lagrangian technique and which makes use of adjoint model.In a second part, we consider the application of this controller to the problem of artificial blood glucose control. After a modeling phase, two models are retained. A simple one will be used to design the controller and a complex one will be used to simulate realistic virtual patients. This latter is needed to validate our control approach. In order to compute a good control input, the SPMPC controller needs the full state value. However, the sensors can only provide the value of blood glucose. That is why the design of an adequate observer is envisaged. Then, numerical simulations are performed. The results show the interest of the approach. For all virtual patients, no hypoglycemia event occurs and the time spent in hyperglycemia is too short to induce damageable consequences. Finally, the interest of extending the SPMPC approach to consider the control of time delay systems in a sampled-data framework is numerically explored.

This research work investigates the thermal performance of a film-cooled gas turbine endwall under two different mainstream flow conditions. In the first part of the research investigation, the effect of unsteady passing wakes on a film-cooled pitchwise-curved surface (representing an endwall without airfoils) was experimentally studied for heat transfer characteristics on a time-averaged basis. The temperature sensitive paint technique was used to obtain the local temperatures on the test surface. The required heat flux input was provided using foil heaters. Discrete film injection was implemented on the test surface using cylindrical holes with a streamwise inclination angle of 35? and no compound angle relative to the mean approach velocity vector. The passing wakes increased the heat transfer coefficients at both the wake passing frequencies that were experimented. Due to the increasing film cooling jet turbulence and strong jet-mainstream interaction at higher blowing ratios, the heat transfer coefficients were amplified. A combination of film injection and unsteady passing wakes resulted in a maximum pitch-averaged and centerline heat transfer augmentation of ? 28% and 31.7% relative to the no wake and no film injection case. The second part of the research study involves an experimental and numerical analysis of secondary flow and coolant film interaction in a high subsonic annular cascade with a maximum isentropic throat Mach number of ? 0.68. Endwall (platform) thermal protection is provided using discrete cylindrical holes with a streamwise inclination angle of 30? and no compound angle relative to the mean approach velocity vector. The surface flow visualization on the inner endwall provided the location of the saddle point and the three-dimensional separation lines. Computational predictions showed that the leading-edge horseshoe vortex was confined to approximately 1.5% of the airfoil span for the no film injection case and intensified with low momentum film injection. At the highest blowing ratio, the film cooling jet weakened the horseshoe vortex at the leading-edge plane. The passage vortex was intensified with coolant injection at all blowing ratios. It was seen that increasing average blowing ratio improved the film effectiveness on the endwall. The discharge coefficients calculated for each film cooling hole indicated significant non-uniformity in the coolant discharge at lower blowing ratios and the strong dependence of discharge coefficients on the mainstream static pressure and the location of three-dimensional separation lines. Near the airfoil suction side, a region of coalesced film cooling jets providing close to uniform film coverage was observed, indicative of the mainstream acceleration and the influence of three-dimensional separation lines.

No description available.

<div>The Subword Complexity of a character string refers to the number of distinct substrings of any length that occur as contiguous patterns in the string. The kth Subword Complexity in particular, refers to the number of distinct substrings of length k in a string of length n. In this work, we evaluate the expected value and the second factorial moment of the kth Subword Complexity for the binary strings over memory-less sources. We first take a combinatorial approach to derive a probability generating function for the number of occurrences of patterns in strings of finite length. This enables us to have an exact expression for the two moments in terms of patterns' auto-correlation and correlation polynomials. We then investigate the asymptotic behavior for values of k=a log n. In the proof, we compare the distribution of the kth Subword Complexity of binary strings to the distribution of distinct prefixes of independent strings stored in a trie. </div><div>The methodology that we use involves complex analysis, analytical poissonization and depoissonization, the Mellin transform, and saddle point analysis.</div>

Robust preconditioners on block-triangular and block-factorized form for three types of linear systems of two-by-two block form are studied in this thesis. The first type of linear systems, which are dense, arise from a boundary element type of discretization of crack propagation problems. Numerical experiment show that simple algebraic preconditioning strategies results in iterative schemes that are highly competitive with a direct solution method. The second type of algebraic systems, which are sparse, indefinite and nonsymmetric, arise from a finite element (FE) discretization of the partial differential equations (PDE) that describe (visco)elastic glacial isostatic adjustment (GIA). The Schur complement approximation in the block preconditioners is constructed by assembly of local, exactly computed Schur matrices. The quality of the approximation is verified in numerical experiments. When the block preconditioners for the indefinite problem are combined with an inner iterative scheme preconditioned by a (nearly) optimal multilevel preconditioner, the resulting preconditioner is (nearly) optimal and robust with respect to problem size, material parameters, number of space dimensions, and coefficient jumps. Two approaches to mathematically formulate the PDEs for GIA are compared. In the first approach the equations are formulated in their full complexity, whereas in the second their formulation is confined to the features and restrictions of the employed FE package. Different solution methods for the algebraic problem are used in the two approaches. Analysis and numerical experiments reveal that the first strategy is more accurate and efficient than the latter. The block structure in the third type of algebraic systems is due to a fine-coarse splitting of the unknowns. The inverse of the pivot block is approximated by a sparse matrix which is assembled from local, exactly inverted matrices. Numerical experiments and analysis of the approximation show that it is robust with respect to problem size and coefficient jumps.

Submitted by (ana.araujo@ufrpe.br) on 2016-08-10T13:00:13Z No. of bitstreams: 1 Rejane dos Santos Brito.pdf: 1642561 bytes, checksum: 084711a62c79f703133a032643c8d19f (MD5) / Made available in DSpace on 2016-08-10T13:00:13Z (GMT). No. of bitstreams: 1 Rejane dos Santos Brito.pdf: 1642561 bytes, checksum: 084711a62c79f703133a032643c8d19f (MD5) Previous issue date: 2009-03-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / We make a review about Edgeworth, Lugannani-Rice, Daniels and Cordeiro-Ferrari asymptotic approximations. We use the Cordeiro-Ferrari asymptotic approximation to approximate the gamma distribution G(m;f ) by the exponential distribution with mean a. In a further application, based on the statistical proposed by them, we approximate the t-Student distribution with n degrees of freedom using the normal standard distribution. Moreover, we realize a study about the functionalities of the beta generalized distributions. We obtain moments of the generalized beta distributions using the Lauricella and Kampé de Fériet generalized functions. Beyond this, we propose a new generalized beta distribution called beta power. Finally, we realize some applications in regression models by logistic regression and further more using discriminant analysis. / Inicialmente, realiza-se uma revisão literária sobre as expansões assintóticas de Daniels, Edgeworth, Lugannani-Rice e Cordeiro-Ferrari. Mediante uso da expansão de Cordeiro- Ferrari, torna-se possível realizar um estudo correspondente a aproximação da distribuição gama G(m;f ) em função da distribuição exponencial com média a. E, ainda, numa outra aplicação, faz-se a aproximação da distribuição t-Student com n graus de liberdade em função da distribuição normal padrão. Além disso, apresenta-se um estudo correspondente às funcionalidades das distribuições beta generalizadas e, ainda, a obtenção dos momentos das distribuições beta generalizadas mediante as funções de Lauricella e generalizada de Kampé de Fériet. Propõe-se, ainda, a generalização da distribuição power como sendo uma nova distribuição beta generalizada. Por fim, realizam-se algumas aplicações em modelos de regressão, mediante regressão logística, bem como em modelos de análise discriminante.

The main focus of this work lies in the simulation of the deformation of mechanical components which consist of nonlinear elastic, incompressible material and that are subject to large deformations. Starting from a nonlinear formulation one can derive a discrete problem by using linearisation techniques and an adaptive mixed finite element method. This turns out to be a saddle point problem that can be solved via a Bramble-Pasciak conjugate gradient method. With some modifications the simulation can be improved.:1. Introduction 2. Basics 3. Mixed variational formulation 4. Solution method 5. Error estimation 6. LBB conditions 7. Improvement suggestions

Masters thesis of Liam Farrell, under the supervision of Dr. Duncan O'Dell. Successfully defended on August 26, 2021. / Caustics are regions created by the natural focusing of waves. Some examples include rainbows, spherical aberration, and sonic booms. The intensity of a caustic is singular in the classical ray theory, but can be smoothed out by taking into account the interference of waves. Caustics are generic in nature and are universally described by the mathematical theory known as catastrophe theory, which has successfully been applied to physically describe a wide variety of phenomena. Interestingly, caustics can exist in quantum mechanical systems in the form of phase singularities. Since phase is such a central concept in wave theory, this heralds the breakdown of the wave description of quantum mechanics and is in fact an example of a quantum catastrophe. Similarly to classical catastrophes, quantum catastrophes require some previously ignored property or degree of freedom to be taken into account in order to smooth the phase divergence. Different forms of spontaneous pair-production appear to suffer logarithmic phase singularities, specifically Hawking radiation from gravitational black holes. This is known as the trans-Planckian problem. We will investigate Hawking radiation formed in an analogue black hole consisting of a flowing ultra-cold Bose-Einstein condensate. By moving from an approximate hydrodynamical continuum description to a quantum mechanical discrete theory, the phase singularity is cured. We describe this process, and make connections to a new theory of logarithmic catastrophes. We show that our analogue Hawking radiation is mathematically described by a logarithmic Airy catastrophe, which further establishes the plausibility of pair-production being a quantum catastrophe / Thesis / Master of Science (MSc)