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Orientadores: Helena Judith Nussenzveig Lopes, Milton da Costa Lopes Filho / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-10T07:01:21Z (GMT). No. of bitstreams: 1 Faria_JosianeCristinadeOliveira_D.pdf: 915381 bytes, checksum: 33fbbc86d823554534cbe546850e707d (MD5) Previous issue date: 2008 / Resumo: As equações semigeostrocas, introduzidas por Hoskins e Bretherton em 1972 em [20], sao um conjunto de equacoes que modelam fluxos atmosfericos/ oceanicos de larga escala. Elas possuem uma formulação em variaveis duais que se presta ao tratamento analítico. Alguns autores estudaram esta formulação, veja, por exemplo, [3], [14], [22], [12], [21],em particular obtendo existencia de solucões fracas em espaços de medidas. Contudo, ha dificuldades em converter soluções fracas da formulação dual em soluções fracas na formulação original, e portanto de interpretar fisicamente as soluções obtidas. Em [11], Culled e Feldman provaram a existencia de soluções Lagrangeanas para o sistema semigeostrofico em coordenadas fisicas com vorticidade potencial em Lp, p > 1. No presente trabalho estendemos os resultados de Cullen e Feldman para o caso limite p = 1 e estudamos o comportamento de sequencias de soluções Lagrangeanas correspondentes a uma sequencia de vorticidades potenciais iniciais convergindo fortemente em L1. Provamos que tais soluções Lagrangeanas convergem em L1 loc. Exibimos um contra-exemplo que sugere que nosso resultado não pode ser estendido para o espaço das medidas de Radon / Abstract: The semigeostrophic equations, which were introduced by Hoskins and Bretherton in 1972 in [20], are a set of equations that model large-escale atmospheric/ocean ows. They have a formulation in dual variables which can be analytically treated. Some authors studied these equations in dual variables, see for instance [3], [14], [22], [12], [21], particularly it is obtained existence of weak solutions in the space of Radon measures. In [11], Cullen and Feldman proved existence of Lagrangian solutions for the semigeostrophic system in physical variables with initial potential vorticity in Lp, p > 1. In the present work we extend Cullen and Feldman's result to the limit case p = 1 and we study the behavior of sequences of Lagrangian solutions corresponding to a sequence of initial potential vorticities converging strongly in L1. We prove that these Lagrangian solutions converge in L1 loc. However, there is difficulties in to turn weak solutions in dual formulations into solutions in original formulation, and therefore there is dificulties in to interpret the obtained solutions physically. We show by means of a counterexample that our result cannot be extended to the space of Radon measures / Doutorado / Matematica - Analise / Doutor em Matemática

Transformadores de potência, como produtos não seriados, estão sujeitos a uma série de possíveis desvios de processo. As divergências que transformadores podem apresentar em relação ao seu projeto original podem ter consequências em sua capacidade de suportar carregamentos mecânicos que lhe serão aplicados. Seu transporte da fábrica às subestações elétricas é um dos principais eventos durante o qual suas estruturas são carregadas. Este trabalho foca em descrever e analisar um transformador de potência genérico em um modelo bidimensional, sob o ponto de vista da Mecânica Analítica e da análise de variabilidades com o objetivo de identificar parâmetros importantes à integridade estrutural do equipamento, especialmente aqueles relacionados ao modo de falha de destacamento das chapas do núcleo nos step laps. O modelo numérico do transformador consiste na representação de corpos rígidos conectados entre si por elementos de rigidez e amortecimento, tendo o conjunto do núcleo ferromagnético particularmente mais detalhado de modo a descrever o atrito existente em suas junções. A avaliação dos esforços nesses locais é feita por meio do método dos multiplicadores de Lagrange, ao considerar o atrito como uma restrição ao movimento, sendo que as forças e momentos limites para que ocorra o deslizamento planar das chapas do núcleo são determinados utilizando-se Newton-Raphson ou outras técnicas de otimização. / Power transformers, as non serialized products, are subject to a number of process deviations. The divergences that transformers present from their original design may have consequences on their ability to withstand mechanical loads which will be applied on them. Their transportation from workshop to power plants is one of the main events their structures are loaded. This work focuses on describing and analyzing a generic power transformer in a two-dimensional model, under the sight of Analytical Mechanics and Structural Reliability in order to identify important parameters related to their structural integrity, especially those concerning the failure mode of dismantling of the ferromagnetic core in the step-lap joints. The numerical model of the transformer consists of a representation of rigid bodies, connected to each other by stiness and damping elements, having the assembly of the ferromagnetic core more detailed in order to describe the friction present on their step-lap joint. The evaluation of friction in these locations is made using the Lagrange Multipliers Method, by considering it as a movement restriction, and the limit values of forces and moments to which the planar sliding of the core sheets occurs, damaging the behavior of the electric machine, are determined using Newton-Raphson and Optimization Methods.

Orientador: José Mario Martínez Pérez / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T09:19:13Z (GMT). No. of bitstreams: 1 Prudente_LeandrodaFonseca_D.pdf: 1307430 bytes, checksum: 6ac8a3a70af28dce0b2cd6d839b227ef (MD5) Previous issue date: 2012 / Resumo: Algoritmos de programação não-linear práticos podem convergir para pontos inviáveis mesmo quando o problema a ser resolvido é viável. Quando isso ocorre, é natural que o usuário mude o ponto inicial e/ou parâmetros algorítmicos e reaplique o método na tentativa de encontrar uma solução viável e ótima. Desta forma, o ideal é que um algoritmo não só seja eficiente em encontrar soluções viáveis, mas também que detecte rapidamente quando ele está fadado a convergir para um ponto inviável. Na tentativa de atingir esse objetivo, apresentamos modificações em um algoritmo baseado em Lagrangiano aumentado de modo que, no caso de convergência para um ponto inviável, os subproblemas são resolvidos com tolerâncias moderadas e, mesmo assim, as propriedades de convergência global são mantidas. Experimentos numéricos são apresentados / Abstract Practical Nonlinear Programming algorithms may converge to infeasible points even when the problem to be solved is feasible. When this occurs, it is natural for the user to change the starting point and/or algorithmic parameters and reapply the method in an attempt to find a feasible and optimal solution. Thus, the ideal is that an algorithm is eficient not only in finding feasible solutions, but also in quickly detecting when it is fated to converge to an infeasible point. In pursuit of this goal, we present modifications of an algorithm based on Augmented Lagrangians so that, in the case of convergence to an infeasible point, the subproblems are solved with moderate tolerances and, even then, the global convergence properties are maintained. Numerical experiments are presented / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Context. Fluid simulations are an important part for enhancing the visualization of games, movies and other graphical applications. Fluid simulations can be achieved in different type of context ranging between slow, high-quality simulations which is mainly used for movies, to fast lower-quality simulations which is primarily used for real-time applications such as games. Objectives. The goal was to compare the visual appearance of a Lagrangian method and a semiLagrangian method when it came to realistic appearance.  Methods. Identical scenes of water being rendered are made for both the Lagrangian and the semiLagrangian algorithm. This is later measured by using a user study which will provide the result of which method that provides a more realistic appearance Results. The result of the tests showed that the visual realism between the semi-Lagrangian and Lagrangian were different depending on the scene environment.  Conclusions. The conclusion of the data presented in the result yields that the Lagrangian and semiLagrangian looks very much alike and there is no real realistic difference between the methods, some scene yields a vast majority of votes in the favor of one method.

The existence and uniqueness of Lagrangian invariant subspaces of Hamiltonian matrices is studied. Necessary and sufficient conditions are given in terms of the Jordan structure and certain sign characteristics that give uniqueness of these subspaces even in the presence of purely imaginary eigenvalues. These results are applied to obtain in special cases existence and uniqueness results for Hermitian solutions of continuous time algebraic Riccati equations.

There are two types of structures in human body, solid organs and hollow membrane like organs. Brain, liver and other soft tissues such as tendons, muscles, cartilage etc., are examples of solid organs. Colon and blood vessels are examples of hollow organs. They greatly differ in structure and mechanical behavior. Deformation of these types of structures is an important phenomena during the process of medical simulation. The primary focus of this project is on deformation of soft tissues. These kind of soft tissues usually undergo large deformation. Deformation of an organ can be considered as mechanical response of that organ during medical simulation. This can be modeled using continuum mechanics and FEM. The primary goal of any system, irrespective of methods and models chosen, it must provide real-time response to obtain sufficient realism and accurate information. One such example is medical training system using haptic feedback. In the past two decades many models were developed and very few considered the non-linear nature in material and geometry of the solid organs. TLED is one among them. A finite element formulation proposed by Miller in 2007, known as total Lagrangian explicit dynamics (TLED) algorithm, will be discussed with respect to implementation point of view and deploying GPU acceleration (because of its parallel nature to some extent) for both pre-processing and actual computation.

There is currently worldwide pressure to establish Marine Protected Area (MPA) networks which are self-sustaining and will persistently protect habitats and species. In order for MPA networks to be effective, the species targeted for conservation must be able to disperse between protected areas and maintain a gene-flow necessary for population sustainability and persistence. This warrants new research on how to quantify and map faunal dispersal to ensure that protection will be effective and sustainable. Population genetic methods have merit, with the ability to track parentage and gene flow between areas directly. However the costs, quantity of samples, and time required to genetically quantify dispersal for multiple species make these approaches prohibitive as the only method of assessment, especially in relatively inaccessible offshore waters. Dispersal modelling is now becoming more accessible and may fulfil immediate needs in this field (although ground truthing will be necessary in the future). There have been very few dispersal modelling studies focussed on deep sea or offshore areas, predominantly due to the lack of high resolution hydrodynamic models with sufficient geographic extent away from shore. Current conclusions have been drawn based on shallow water coastal studies, informing offshore MPA network size and spacing. However the differences between these two environments may mean that dispersal abilities are not comparable. Deep water receives less influence from wind and weather, and the scales are vastly different in terms of a) the depth ranges covered, b) the planktonic larval durations (PLDs) of animals, and c) the geographic areas concerned as a consequence. Global hydrodynamic models with reasonable resolution are now becoming more accessible. With the outputs from these models, and freely available particle simulators, it is becoming more practical to undertake offshore deep water dispersal studies. This thesis aims to undertake an analysis of these accessible modelling tools within a deep sea context. The guidelines which are currently available to dispersal modellers are yet to encompass the needs of deep water modellers which may require some additional considerations given the extended depth range covered and the different hydrodynamic drivers away from the air/sea interface. Chapter 1 reviews the larval dispersal process, the factors which may affect dispersal success, and those which should be incorporated into future predictions of dispersal. The current methods for assessing larval dispersal are explored covering genetics, elemental tagging and modelling approaches with an extended look at modelling considerations. Existing marine conservation policy is also touched on in the context of connectivity and larval dispersal. Chapter 2 is designed to inform future deep sea modellers on how to parameterise and understand a dispersal model. As models appear as a ‘black box’ to the majority of users, sensitivity tests can offer a way of scaling model inputs and tempering expectations from model outputs. A commonly used model pairing (the HYCOM hydrodynamic model and the Connectivity Modeling System) is assessed, using parameters which link to the temporal and spatial scales of mixing in the modelled system: timestep of particle tracer, horizontal and vertical positioning of release points, release frequency of larvae, and temporal range of simulation. All parameters were shown to have a decreased sensitivity with depth, with patterns reflecting local watermass structure. Future studies observing similar hydrodynamic conditions seeking to optimise their model set up would be advised to stratify their model release locations with depth. A means to incorporate all sensitivity test results into optimal input parameters for future studies is demonstrated. Chapter 3 investigates whether dispersal models provide any advantage over a “sphere of influence” estimate based on average current speeds and PLDs: there is no use pursuing dispersal modelling if the outputs are too erroneous to provide any advantage over a back-of-the-envelope calculation. This chapter examines the outputs of two dispersal models driven by two different hydrodynamic models in order to observe the variability in prediction between models. This model comparison revealed a greater disparity between hydrodynamic model predictions than has been previously understood by ecologists. The two models compared (POLCOMS and HYCOM) may equally be considered as suitable to promote realism in the study region, but slight differences in resolution and numerical error handling resulted in dispersal predictions from which opposing conclusions can be drawn. This chapter therefore emphasises the necessity for model ground truthing before predictions can be trusted. Chapter 4 assimilates the findings of the previous chapters and applies their advice to a study of MPA network dispersal connectivity. Using the hydrodynamic model which performed best in chapter 3 (HYCOM), a simulation was undertaken for cold water coral (Lophelia pertusa (Linnaeus 1758)) larval dispersal between already established MPAs in the NE Atlantic. As larval characters have only been observed ex situ, dispersal was simulated using two null models (passive and active vertical migration) and averaged to provide an intermediate prediction. A method for assessing dispersal within MPAs and MPA networks is offered based on the intermediate prediction, as well as a network wide assessment of the difference in dispersal patterns for passive and active larvae. It was found that the existing network performs well at supplying larvae to non-networked sites, but performs poorly at supplying other MPAs. The ‘best’ MPAs were central to the network and facilitated the traverse of regional gaps in suitable habitat. The ‘worst’ MPAs were peripheral to the network and small in size. Network-wide passive and active dispersal matrices had no significant difference between them. However site specific variability in the effect of vertical migration was detected subject to variability in local topographic barriers to dispersal, only some of which could be surmounted with vertical migration. All chapters aim to inform future deep sea dispersal modellers, and encourage exploration of this tool in other contexts, as well as marine conservation. The thesis cautions against the transplantation of shallow water assumptions to deep water environments, and advocates region specific studies and mandatory ground truthing of predictions. An upcoming study will ground truth the findings of this thesis with both genetic and oceanographic data, allowing the accuracy of study results to be quantified.

The broader research area investigated during this programme was conceived from a goal to contribute towards solving the challenge of food security in the 21st century through the reduction of crop loss and minimisation of fungicide use. This is aimed to be achieved through the introduction of an empirical approach to agricultural disease monitoring. In line with this, the SYIELD project, initiated by a consortium involving University of Manchester and Syngenta, among others, proposed a novel biosensor design that can electrochemically detect viable airborne pathogens by exploiting the biology of plant-pathogen interaction. This approach offers improvement on the inefficient and largely experimental methods currently used. Within this context, this PhD focused on the adoption of multidisciplinary methods to address three key objectives that are central to the success of the SYIELD project: local spore ingress near canopies, the evaluation of a suitable model that can describe spore transport, and multivariate analysis of the potential monitoring network built from these biosensors. The local transport of spores was first investigated by carrying out a field trial experiment at Rothamsted Research UK in order to investigate spore ingress in OSR canopies, generate reliable data for testing the prototype biosensor, and evaluate a trajectory model. During the experiment, spores were air-sampled and quantified using established manual detection methods. Results showed that the manual methods, such as colourimetric detection are more sensitive than the proposed biosensor, suggesting the proxy measurement mechanism used by the biosensor may not be reliable in live deployments where spores are likely to be contaminated by impurities and other inhibitors of oxalic acid production. Spores quantified using the more reliable quantitative Polymerase Chain Reaction proved informative and provided novel of data of high experimental value. The dispersal of this data was found to fit a power decay law, a finding that is consistent with experiments in other crops. In the second area investigated, a 3D backward Lagrangian Stochastic model was parameterised and evaluated with the field trial data. The bLS model, parameterised with Monin-Obukhov Similarity Theory (MOST) variables showed good agreement with experimental data and compared favourably in terms of performance statistics with a recent application of an LS model in a maize canopy. Results obtained from the model were found to be more accurate above the canopy than below it. This was attributed to a higher error during initialisation of release velocities below the canopy. Overall, the bLS model performed well and demonstrated suitability for adoption in estimating above-canopy spore concentration profiles which can further be used for designing efficient deployment strategies. The final area of focus was the monitoring of a potential biosensor network. A novel framework based on Multivariate Statistical Process Control concepts was proposed and applied to data from a pollution-monitoring network. The main limitation of traditional MSPC in spatial data applications was identified as a lack of spatial awareness by the PCA model when considering correlation breakdowns caused by an incoming erroneous observation. This resulted in misclassification of healthy measurements as erroneous. The proposed Kriging-augmented MSPC approach was able to incorporate this capability and significantly reduce the number of false alarms.

In this thesis we study the properties of Lagrangian matroids of dessins d'enfants (also known as maps on orientable surfaces) and their behaviour under the action of the absolute Galois group Gal(Q). We show that while the Lagrangian matroid of a dessin itself is not invariant under this action, some of its properties, namely its width and parity, are. We also study the partial duals of a dessin and their Lagrangian matroids and show that certain partial duals can always be defined over their field of moduli. We prove some results on the representations of Lagrangian matroids as well. A relationship between dessins, their partial duals and tropical curves arising from monodromy groups of dessins is observed.