O objetivo deste projeto é o desenvolvimento de transdutores de RF tipo gaiola (birdcage coil) e sela (saddle coil), com desenho especial inovador, que mantém elementos com comprimento elétrico constante, para um campo magnético de 2 Tesla. Este transdutor deve permitir o estudo e também o desenvolvimento de novas metodologias em imagens e espectroscopia por RMN de pequenos primatas como marmosets, exigidos pela interação deste grupo com o programa CInAPCe (Cooperação Interinstitucional de Apoio a Pesquisas sobre o Cérebro). Essas bobinas também se destinam ao uso em metodologias de imagens e espectroscopia ?in vivo? por Ressonância Magnética Nuclear (RMN), que utilizem pulsos de RF caracterizados como Pulsos Adiabáticos. Outra perspectiva é a continuação do desenvolvimento de bobinas de RF que operam segundo as características de bobinas de superfície, que pode resultar deste trabalho. Os resultados nos mostram que para as dimensões e freqüência utilizadas, a interação entre os condutores que compõe os transdutores é mais relevante do que a perda de fase da corrente elétrica devido às diferenças no comprimento elétrico. O cruzamento entre os condutores consiste num bom desenho alternativo, melhorando a homogeneidade de campo de RF e a relação sinal/ruído. / The purpose of the present work is the development of birdcage- and saddlelike RF transducers which were based on a special and innovative approach. The aim of this design is to keep constant the electromagnetic length of its elements, for a magnetic field intensity of 2 Tesla. These resonators will allow both the study and the development of new imaging and spectroscopy methods addressed to the NMR research on small primates such as marmosets. Such studies are part of the cooperation between this group and other participants of the CInAPCe program, Portuguese acronym for Inter-institutional Cooperation to Support Brain Research. Other perspective is the continuing development of RF coils whose characteristics are similar to surface coils, also designed for anatomic specific studies of imaging and in vivo NMR spectroscopy that take advantage from the use of RF pulses characterized as Adiabatic Pulses. From the results it could be verified that, for the frequency and dimensions used, the interaction between the conductive paths present in the transducers is more significant than the electric current phase losses due to differences in electric path. The crossing of the conductive paths constitute a good alternative design, improving the RF field homogeneity and the signal to noise ratio.

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.

Snap-through is a striking instability in which an elastic object rapidly jumps from one state to another. It is seen in the leaves of the Venus flytrap plant and umbrellas flipping on a windy day among many other examples. Similar structures that snap-through are used to generate fast motions in soft robotics, switches in micro-scale electronics and artificial heart valves. Despite the ubiquity of snap-through in nature and engineering, its dynamics is usually only understood qualitatively. In this thesis we develop analytical understanding of this dynamics, focussing on how the mathematical structure underlying the snap-through transition controls the timescale of instability. We begin by considering the dynamics of 'pull-in' instabilities in microelectromechanical systems (MEMS) - a type of snap-through caused by electrostatic forces in which the motions are dominated by fluid damping. Using a lumped-parameter model, we show that the observed time delay near the pull-in transition is a type of critical slowing down - a so-called 'bottleneck' due to the 'ghost' of a saddle-node bifurcation. We obtain a scaling law describing this slowing down, and, in the process, unify a large range of experiments and simulations that exhibit delay phenomena during pull-in. We also investigate the pull-in dynamics of MEMS microbeams, extending the lumped-parameter approach to incorporate the details of the beam geometry. This provides a model system in which to understand snap-through of a continuous elastic structure due to external loading. We develop a perturbation method that systematically exploits the proximity to pull-in to reduce the governing equations to a simpler evolution equation, with a structure that highlights the saddle-node bifurcation. This allows us to analyse the bottleneck dynamics in detail, which we compare with previous experimental and numerical data. The remainder of the thesis is concerned with the dynamics of snap-through in macroscopic systems. In particular, we explore the extent to which dissipation is required to explain anomalously slow snap-through. Considering an elastic arch as an archetype of a snapping system, we use the perturbation method developed earlier to show that two bottleneck regimes are possible, depending delicately on the relative importance of external damping. In particular, we show that critical slowing down occurs even in the absence of damping, leading to a new scaling law for the snap-through time that is confirmed by elastica simulations and experiments. In many real systems material viscoelasticity is present to some degree. Finally, we examine how this influences the snap-through dynamics of a simple truss-like structure. We present a regime diagram that characterises when the timescale of snap-through is controlled by viscous, elastic or viscoelastic effects.

The limiting behavior of weighted paths associated with the semidefinite program (SDP) map $X^{1/2}SX^{1/2}$ was studied and some applications to error bound analysis and superlinear convergence of a class of primal-dual interior-point methods were provided. A new approach for solving large-scale well-structured sparse SDPs via a saddle point mirror-prox algorithm with ${cal O}(epsilon^{-1})$ efficiency was developed based on exploiting sparsity structure and reformulating SDPs into smooth convex-concave saddle point problems. An iterative solver-based long-step primal-dual infeasible path-following algorithm for convex quadratic programming (CQP) was developed. The search directions of this algorithm were computed by means of a preconditioned iterative linear solver. A uniform bound, depending only on the CQP data, on the number of iterations performed by a preconditioned iterative linear solver was established. A polynomial bound on the number of iterations of this algorithm was also obtained. One efficient ``nearly exact' type of method for solving large-scale ``low-rank' trust region subproblems was proposed by completely avoiding the computations of Cholesky or partial Cholesky factorizations. A computational study of this method was also provided by applying it to solve some large-scale nonlinear programming problems.

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.

Thesis (M.A. in Cultural Resources Management)--Sonoma State University, 2005. / Includes bibliographical references (p. 112-127) and abstract.

Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-03-03Bitstream added on 2014-06-13T20:27:28Z : No. of bitstreams: 1 bronzi_ma_me_sjrp.pdf: 904425 bytes, checksum: 2344eb35a112034c2f1741b2e229f1ec (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Estudamos intersecções homoclínicas de variedades estável e instável de pontos peródicos. Toda intersecção homoclínica produz um comportamento curioso na dinâmiôa. Nosso modelo de tal fenômeno é a famosa ferradura de Smale, a qual é um conjunto hiperbólico para um difeomorfismo. Além disso, estudamos dinâmica não hiperbólica cuja perda de hiperbolicidade é divido à tangências homoclínicas. Elas tem um papel central na teoria de sistemas dinâmicos. O desdobramento de uma tangência homoclínica produz dinâmicas muito interessantes. Neste trabalho estudamos a criação de cascatas de bifurcações de duplicação de período e um esquema de renormalização para uma tangência homoclínica. / We study homoclinic intersection of stable and unstable manifolds of periodic points. Every homoclinic intersection produce a intricate behavior of the dynamics. Our model of such phenomena is the so called Smalesþs horseshoe, which is a hyperbolic set for a di eomorphism. We also study non hyperbolic dynamics whose lack of hyperbolicity is due to homoclinic tangencies. They play a central role in the theory of dynamical systems. The unfolding of a homoclinic tangency produce many interesting dynamics. In this work we study creation of cascade of period doubling bifurcations and a renormalization scheme for a homoclinic tangency.

abstract: The holomorphic embedding method (HEM) applied to the power-flow problem (HEPF) has been used in the past to obtain the voltages and flows for power systems. The incentives for using this method over the traditional Newton-Raphson based nu-merical methods lie in the claim that the method is theoretically guaranteed to converge to the operable solution, if one exists. In this report, HEPF will be used for two power system analysis purposes: a. Estimating the saddle-node bifurcation point (SNBP) of a system b. Developing reduced-order network equivalents for distribution systems. Typically, the continuation power flow (CPF) is used to estimate the SNBP of a system, which involves solving multiple power-flow problems. One of the advantages of HEPF is that the solution is obtained as an analytical expression of the embedding parameter, and using this property, three of the proposed HEPF-based methods can es-timate the SNBP of a given power system without solving multiple power-flow prob-lems (if generator VAr limits are ignored). If VAr limits are considered, the mathemat-ical representation of the power-flow problem changes and thus an iterative process would have to be performed in order to estimate the SNBP of the system. This would typically still require fewer power-flow problems to be solved than CPF in order to estimate the SNBP. Another proposed application is to develop reduced order network equivalents for radial distribution networks that retain the nonlinearities of the eliminated portion of the network and hence remain more accurate than traditional Ward-type reductions (which linearize about the given operating point) when the operating condition changes. Different ways of accelerating the convergence of the power series obtained as a part of HEPF, are explored and it is shown that the eta method is the most efficient of all methods tested. The local-measurement-based methods of estimating the SNBP are studied. Non-linear Thévenin-like networks as well as multi-bus networks are built using model data to estimate the SNBP and it is shown that the structure of these networks can be made arbitrary by appropriately modifying the nonlinear current injections, which can sim-plify the process of building such networks from measurements. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2017

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).

O objetivo deste projeto é o desenvolvimento de transdutores de RF tipo gaiola (birdcage coil) e sela (saddle coil), com desenho especial inovador, que mantém elementos com comprimento elétrico constante, para um campo magnético de 2 Tesla. Este transdutor deve permitir o estudo e também o desenvolvimento de novas metodologias em imagens e espectroscopia por RMN de pequenos primatas como marmosets, exigidos pela interação deste grupo com o programa CInAPCe (Cooperação Interinstitucional de Apoio a Pesquisas sobre o Cérebro). Essas bobinas também se destinam ao uso em metodologias de imagens e espectroscopia ?in vivo? por Ressonância Magnética Nuclear (RMN), que utilizem pulsos de RF caracterizados como Pulsos Adiabáticos. Outra perspectiva é a continuação do desenvolvimento de bobinas de RF que operam segundo as características de bobinas de superfície, que pode resultar deste trabalho. Os resultados nos mostram que para as dimensões e freqüência utilizadas, a interação entre os condutores que compõe os transdutores é mais relevante do que a perda de fase da corrente elétrica devido às diferenças no comprimento elétrico. O cruzamento entre os condutores consiste num bom desenho alternativo, melhorando a homogeneidade de campo de RF e a relação sinal/ruído. / The purpose of the present work is the development of birdcage- and saddlelike RF transducers which were based on a special and innovative approach. The aim of this design is to keep constant the electromagnetic length of its elements, for a magnetic field intensity of 2 Tesla. These resonators will allow both the study and the development of new imaging and spectroscopy methods addressed to the NMR research on small primates such as marmosets. Such studies are part of the cooperation between this group and other participants of the CInAPCe program, Portuguese acronym for Inter-institutional Cooperation to Support Brain Research. Other perspective is the continuing development of RF coils whose characteristics are similar to surface coils, also designed for anatomic specific studies of imaging and in vivo NMR spectroscopy that take advantage from the use of RF pulses characterized as Adiabatic Pulses. From the results it could be verified that, for the frequency and dimensions used, the interaction between the conductive paths present in the transducers is more significant than the electric current phase losses due to differences in electric path. The crossing of the conductive paths constitute a good alternative design, improving the RF field homogeneity and the signal to noise ratio.