Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2018-05-03T11:57:05Z No. of bitstreams: 2 Dissertação - Pedro Felipe Tavares do Amaral - 2018.pdf: 5863877 bytes, checksum: 084454dc18411f245114eb910cfa2474 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-05-03T13:20:55Z (GMT) No. of bitstreams: 2 Dissertação - Pedro Felipe Tavares do Amaral - 2018.pdf: 5863877 bytes, checksum: 084454dc18411f245114eb910cfa2474 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-05-03T13:20:55Z (GMT). No. of bitstreams: 2 Dissertação - Pedro Felipe Tavares do Amaral - 2018.pdf: 5863877 bytes, checksum: 084454dc18411f245114eb910cfa2474 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-02-05 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In the present work, studies about the nonlinear static and dynamic behavior of a spherical membrane are presented. This membrane is composed by a hyperelastic, incompressible homogeneous and isotropic material, which is defined by either of the two distinct constitutive models: Mooney-Rivlin or the Neo-Hookean model. The equilibrium equations are obtained from the large-strain theory, by utilizing a variational formulation and by subjecting the membrane to an uniformly distributed internal radial pressure differential. From the nonlinear static analysis, internal membrane tensions and strains are obtained. From the dynamic analysis, the frequency-amplitude relation, the linear stability analysis, the time response, bifurcation diagrams, resonance curves and basins of attraction are obtained. As a first step, there is an analysis on a membrane composed by the same experimental material, which is described by the two different constitutive models presented in this work. It is observed that the dynamic responses are considerably distinct, due to the difference between the geometrical nonlinearities that each constitutive model insert on the equilibrium equation. The Neo-Hookean model has a lower pre-stretching limit, and its attraction basins are more eroded and irregular than the Mooney-Rivlin, that is still stable on regions of larger vibration amplitudes. Then, the influence of the Mooney-Rivlin parameter (α) is evaluated, and it is found that this parameter is the main source of the differences between the constitutive models, modifying the stability, nonlinear vibrations and also influencing on the loss or gain of the global rigidity of the membrane. / Neste trabalho são apresentados estudos dos comportamentos não lineares, estático e dinâmico, de uma membrana de geometria esférica composta por um material hiperelástico, incompressível, homogêneo e isotrópico definido por um entre esses dois modelos constitutivos: Mooney-Rivlin ou Neo-Hookeano. As equações de equilíbrio são obtidas a partir da teoria de grandes deformações, utilizando uma formulação variacional e considerando a membrana esférica submetida a uma pressão interna na direção radial uniformemente distribuída. A partir da análise não linear estática, encontram-se as tensões e as extensões radiais da membrana e da análise dinâmica obtêm-se as relações frequência-amplitude, a análise não linear da estabilidade, as respostas no tempo, os diagramas de bifurcação, as curvas de ressonância e as bacias de atração da membrana. Primeiramente, analisa-se a membrana composta por um mesmo material experimental e descrita pelos dois modelos hiperelásticos avaliados nesta dissertação. Observa-se que as respostas dinâmicas são consideravelmente distintas entre si devido à diferença entre as não linearidades geométricas que cada modelo constitutivo insere na equação de equilíbrio, sendo que o modelo Neo-Hookeano apresenta menor limite de pré-carregamento com bacias de atração mais erodidas e menos uniformes quando comparado ao modelo de Mooney-Rivlin, que ainda apresenta estabilidade em regiões de maior amplitude de vibração. Posteriormente, avalia-se a influência do parâmetro do material do tipo Mooney-Rivlin (α), que é a principal fonte das diferenças entre os modelos constitutivos, na estabilidade e nas vibrações não lineares da membrana esférica, observando-se que o parâmetro influência na perda ou no ganho de rigidez global do problema.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / In the last two decades, multiple input multiple output (MIMO) wireless systems have been subject of intense research due to the theoretical promise of the proportional increase of the communications channel capacity as the number of antennas increases. This outstanding property supposes an efficient use of spatial diversity at both the transmitter and receiver. An important and not well explored path towards improving MIMO system performance using spatial diversity takes into account the interactions among the antennas and the (physical) propagation medium. By understanding these interactions, the transmit and receive antenna arrays can be designed to best âmatchâ the propagation medium so that the link quality and capacity can be further improved in a MIMO system. In this work, we consider the use of spherical harmonics and tensor decompositions in the problem of MIMO channel modeling and estimation. The use of spherical harmonics allows to represent the radiation patterns of antennas in terms of coefficients of an expansion, thus decoupling the transmit and receive antenna array responses from the physical propagation medium. By translating simple propagation-motivated channel models with polarization information into the spherical harmonics domain, we study how propagation parameters themselves and antenna configurations affect MIMO performance in terms of capacity and correlation. A second part of this work addresses the problem of estimating directional MIMO channels in the spherical harmonics domain using tensor decompositions. Considering both single-scattering and double-scattering propagation scenarios, we make use of the parallel factor (PARAFAC) and PARATUCK-2 decompositions, respectively, to estimate the propagating spherical modes, from which the directions of arrival (DoA) and directions of departure (DoD) can be extracted. Finally, we propose and compare two methods for optimizing the coefficients of the spherical harmonics expansion of an antenna array for a prespecified MIMO channel response. / Nas Ãltimas dÃcadas, sistemas de comunicaÃÃo sem fio de mÃltiplas antenas (MIMO - Multiple Input Multiple Output) tÃm sido objetos de intensas pesquisas devido à promessa teÃrica do aumento proporcional da capacidade com o aumento do nÃmero de antenas. Esta propriedade excepcional supÃe um uso eficiente da diversidade espacial no transmissor e receptor. Um caminho importante e nÃo bem explorado no sentido de melhorar o desempenho de sistemas MIMO usando diversidade espacial leva em conta a interaÃÃo entre as antenas e meio de propagaÃÃo (fÃsico). AtravÃs da compreensÃo dessas interaÃÃes, arranjos de antenas de recepÃÃo e transmissÃo podem ser projetados para melhor "casar" com o meio de propagaÃÃo, tal que a qualidade do link de comunicaÃÃo e capacidade possam ser melhoradas em um sistema MIMO. Neste trabalho, consideramos o uso de harmÃnicos esfÃricos e decomposiÃÃes tensoriais no problema de modelagem de canal MIMO e estimaÃÃo. O uso de harmÃnicos esfÃricos permite representar os padrÃes de radiaÃÃo de antenas em termos de coeficientes de uma expansÃo, assim desacoplando as respostas dos arranjos de antenas (transmissoras e receptoras) do meio de propagaÃÃo fÃsica. Traduzindo modelos simples de canais baseados em propagaÃÃo, com informaÃÃes de polarizaÃÃo, para o domÃnio dos harmÃnicos esfÃricos, estudamos como os parÃmetros de propagaÃÃo si e configuraÃÃes especÃficas de antenas afetam o desempenho do sistema MIMO em termos de capacidade e de correlaÃÃo. A segunda parte deste trabalho aborda o problema de estimar canais direcionais MIMO no domÃnio dos harmÃnicos esfÃricos usando decomposiÃÃes por tensores. Considerando tanto cenos de espalhamento simples e de duplo espalhamento, fazemos uso das decomposiÃÃes PARAFAC e PARATUCK2, respectivamente, para estimar os modos esfÃricos propagantes, a partir das quais as direÃÃes de chegada (DoA) e as direÃÃes de saÃda (DoD) podem ser extraÃdas. Finalmente, propomos e comparamos dois mÃtodos de otimizaÃÃo dos coeficientes da expansÃo em harmÃnicos esfÃricos de arranjos de antenas para respostas de canais MIMO prÃ-especificados .

Orientador: Carlos Lenz Cesar / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física "Gleb Wataghin" / Made available in DSpace on 2018-08-18T09:30:54Z (GMT). No. of bitstreams: 1 Moreira_WendelLopes_D.pdf: 1772489 bytes, checksum: 3d4e37a805f4c66c447aea58b93692b8 (MD5) Previous issue date: 2010 / Resumo: Desde 1908, quando Mie apresentou expressões analíticas para os campos espalhados por uma partícula esférica sob incidência de uma onda eletromagnética plana, generalizações para esta expansão têm se mostrado incompletas. Isto se deve à presença de certos termos com dependência radial nos coe cientes de forma do feixe quando expandido em termos de funções de onda esféricas vetoriais. Aqui mostramos pela primeira como cancelar estes termos, permitindo expressões analíticas para os coe cientes para um campo eletromagnético completamente arbitrário. Damos tambem vários exemplos deste novo método, que também é muito apropriado para cálculos numéricos. Obtemos deste modo, expressões analíticas para feixes de Bessel e para os modos de guias de onda metálicos retangulares e cilíndricos. Estes resultados são extremamente relevantes para o incremento na velocidade de cálculo das forças de radiação atuando sobre uma partícula esférica, colocada em um campo eletromagnético arbitrário, com por exemplo, em pinças ópticas / Abstract: Since 1908, when Mie reported analytical expressions for the elds scattered by a spherical particle upon incidence of an electromagnetic plane-wave, generalizing his analysis to the case of an arbitrary incident wave has proved elusive. This is due to the presence of certain radially-dependent terms in the equation for the beam-shape coecients of the expansion of the electromagnetic elds in terms of vector spherical wave functions. Here we show for the rst time how these terms can be canceled out, allowing analytical expressions for the beam shape coecients to be found for a completely arbitrary incident eld. We give several examples of how this new method, which is well suited to numerical calculation, can be used. Analytical expressions are found for Bessel beams and the modes of rectangular and cylindrical metallic waveguides. The results are highly relevant for speeding up calculation of the radiation forces acting on spherical particles placed in an arbitrary electromagnetic eld, such as in optical tweezers / Doutorado / Física / Doutor em Ciências

Neste trabalho estudamos diferentes noções de diferenciabilidade para funções definidas na esfera unitária S^n-1 de R^n, n>=2. Em relação à derivada usual, encontramos condições necessárias e/ou suficientes para que uma função seja diferenciável até uma ordem fixada. Para as outras duas, a derivada forte de Laplace-Beltrami e a derivada fraca, apresentamos algumas propriedades básicas e procuramos condições que garantam a equivalência destas com a diferenciabilidade usual. / In this work we study different notions of differentiability for functions defined on the unit sphere S^n-1 of R^n, n>=2. With respect to the usual derivative, we find necessary and/or sufficient conditions in order that a function be differentiable up to a fixed order. As for the other two, the strong Laplace-Beltrami derivative and the weak derivative, we present some basic properties about them and search for conditions that guarantee the equivalence of them with the previous one.

Dada uma ação isométrica livre do grupo binário tetraedral G sobre esferas de dimensão ímpar, obtemos uma decomposição celular finita explícita para as formas espaciais esféricas tetraedrais, fazendo uso do conceito de região (ou domínio) fundamental. A estrutura celular deixa explícita uma descrição do complexo de cadeias sobre o grupo G. Como aplicações, utilizamos o complexo de cadeias e a interpretação geométrica do produto cup para calcular o anel de cohomologia da forma espacial esférica tetraedral em dimensão três, e também calculamos a torção de Reidemeister destes espaços para uma determinada representação de G / Given a free isometric action of a binary tetrahedral group G on odd dimensional spheres, we obtain an explicit finite cellular decomposition of the tetrahedral spherical space forms, using the concept of fundamental domain. The cellular structure gives an explicit description of the associated cellular chain complex over the group G. As applications we use the chain complex and the geometric interpretation of the cup product to calculate the cohomology ring of the tetrahedral spherical space form in three dimension, and also compute the Reidemeister torsion of these spaces for a determined representation of G

Nesta tese, investigamos a geometria de curvas no 3-espaço e no 4-espaço de Minkowski usando a teoria de singularidades, mais especificamente, a teoria de contato. Para isto, estudamos as famílias de funções altura e de funções distância ao quadrado sobre as curvas. Os conjuntos discriminantes e conjuntos de bifurcação destas famílias são ferramentas essenciais para o desenvolvimento deste trabalho. Para curvas no 3-espaço de Minkowski, estudamos seus conjuntos focais e conjunto de bifurcação da família de funções distância ao quadrado sobre estas curvas para investigar o que acontece próximo de pontos tipo luz. Estudamos também os conjuntos focais e conjuntos de bifurcação esféricos de curvas nos espaços de Sitter do 3-espaço e do 4-espaço de Minkowski. Definimos imagens normal Darboux pseudo-esféricas de curvas sobre uma superfície tipo tempo no 3-espaço de Minkowski e estudamos as singularidades e propriedades geométricas destas imagens normal Darboux. Além disso, investigamos a relação da imagem normal Darboux de Sitter (hiperbólica) de uma curva tipo espaço em S21 com a superfície tipo luz ao longo desta curva tipo espaço. Definimos as superfícies horoesférica e dual hiperbólica de curvas tipo espaço no espaço de Sitter S31 e estudamos estas superfícies usando técnicas da teoria de singularidades. Damos uma relação entre estas superfícies do ponto de vista de dualidades Legendrianas. Finalmente, consideramos curvas sobre uma hipersuperfície tipo espaço no 4-espaço de Minkowski e definimos a superfície hiperbólica desta curva. Estudamos a geometria local da superfície hiperbólica e da curva hiperbólica, que é definida como sendo o local das singularidades da superfície hiperbólica. / We study in this thesis the geometry of curves in Minkowski 3-space and 4-space using singularity theory, more specifically, the contact theory. For this we study the families of height functions and of the distance square functions on the curves. The discriminant sets and bifurcation sets of these families are essential tools in our work. For curves in Minkowski 3-space, we study their focal sets and the bifurcation set of the family of the distance square functions on these curves in order to investigate what happens near the lightlike points. We also study the spherical focal sets and bifurcation sets of curves in the de Sitter space in Minkowski 3-space and 4-space. We define pseudo-spherical normal Darboux images of curves on a timelike surface in Minkowski 3-space and study the singularities and geometric properties of these normal Darboux images. Furthermore, we investigate the relation of the de Sitter (hyperbolic) normal Darboux image of a spacelike curve in S21 with the lightlike surface along this spacelike curve. We define the horospherical and hyperbolic dual surfaces of spacelike curves in de Sitter space S31 and study these surfaces using singularity theory technics. We give a relation between these surfaces from the view point of Legendrian dualities. Finally, we consider curves on a spacelike hypersurface in Minkowski 4-space and define the hyperbolic surface of this curve. We study the local geometry of the hyperbolic surface and of the hyperbolic curve that is defined as being the locus of singularities of the hyperbolic surface.

Nous considérons la fonction zêta d’Epstein des réseaux euclidiens pour étudier le problème des minima de la hauteur du tore plat associé à un réseau. La hauteur est définie comme la dérivée au point s = 0 de la fonction zêta spectrale du tore, fonction qui coïncide, à un facteur près, avec la fonction zêta d’Epstein du réseau dual du réseau donné. Nous donnons dans cette dissertation une condition suffisante pour qu’un réseau donné soit un point critique de la hauteur. En particulier, en utilisant la théorie des designs sphériques, nous montrons qu’un réseau qui a des 2-designs sphériques sur toutes ses couches est un point critique de la hauteur. Nous donnons un algorithme pour tester si un réseau donné satisfait cette condition de 2-designs, et nous donnons des tables de résultats en dimension jusqu’à 7. Ensuite, nous montrons qu’un réseau qui réalise un minimum local de la hauteur est nécessairement irréductible. Enfin, nous nous intéressons à certains tores définis sur les corps de nombres quadratiques imaginaires, et nous prouvons une formule qui donne leur hauteur comme limite d’une suite de hauteurs de tores complexes discrets. / In this thesis we consider the Epstein zeta function of Euclidean lattices, in order to study the problem of the minima of the height of the flat torus associated to a lattice. The height is defined as the first derivative at the point s = 0 of the spectral zeta function of the torus ; this function coincides, up to a factor, with the Epstein zeta function of the dual lattice of the given lattice. We describe a sufficient condition for a given lattice to be a stationary point of the height. In particular, by means of the theory of spherical designs, we show that a lattice which has a spherical 2-design on every shell is a stationary point of the height. We give an algorithm to check whether a given lattice satisfies this 2-design condition or not, and we give some tables of results in dimension up to 7. Then, we show that a lattice which realises a local minimum of the height is necessarily irreducible. Finally, we deal with some tori defined over the imaginary quadratic number fields, and we show a formula which gives their height as a limit of a sequence of heights of discrete complex tori.

The aim for this thesis is to develop a foundation for a compression system for animated mesh sequences, specifically under dynamic change of mesh geometry and topology. Compression of mesh sequences is of special interest in the game industry and this particular thesis is a part of an ongoing series of projects at EA DICE. One of the primary challenges when creating a mesh compression system is creating a matching bijective subset of the mesh surfaces between two subsequent frames in the animation to guide remeshing of the sequence. This thesis describes a method for producing a bijective set of matching mesh patches between two meshes along with an error metric that captures the quality of the matching in terms of shape similarity and distortion. Theory of mathematical topology and tensor algebra used in methods for high performance scientific digital 3D-image recognition are here adopted to extract similar local features between meshes. Techniques for creating parametrizations of mesh patches are combined with techniques for matching point clouds and deforming mesh geometry under energy minimization in order to produce a matching set of patches. The presented algorithm successfully creates bijective sets of matched patches for subsequent meshes in a sequence as well as measures the error for the matchings. Results show an average matching set size of approximately 25% of the mesh areas over a sequence of meshes. This suggests that the data size of such a sequence could potentially be reduced by 25%.

This thesis presents the results of computer simulation studies of the structure, dynamics, and deformation of cross-linked polymer gels. Obtaining a fundamental understanding of the interrelation between the detailed structure and the properties of polymer gels is a challenge and a key issue towards designing materials for specific purposes. A new off-lattice method for constructing a closed network is presented that is free from defects, such as looping chains and dangling ends. Using these model networks in Brownian dynamics simulations, I show results for the structure and dynamics of bulk gels and describe a novel approach using spherical boundary conditions as an alternative to the periodic boundary conditions commonly used in simulations. This algorithm was also applied for simulating the diffusion of tracer particles within a static and dynamic network, to illustrate the quantitative difference and importance of including network mobility for large particles, as dynamic chains facilitate the escape of particles that become entrapped. I further investigate two technologically relevant properties of polymer gels: their stimuli-responsive behaviour and their mechanical properties. The collapse of core-shell nanogels was studied for a range of parameters, including the cross-linking degree and shell thickness. Two distinct regimes of gel collapse could be observed, with a rapid formation of small clusters followed by a coarsening stage. It is shown that in some cases, a collapsing shell may lead to an inversion of the core-shell particle which exposes the core polymer chains to the environment. This thesis also explores the deformation of bimodal gels consisting of both short and long chains, subject to uniaxial elongation, with the aim to understand the role of both network composition as well as structural heterogeneity on the mechanical response and the reinforcement mechanism of these materials. It is shown that a bimodal molecular weight distribution alone is sufficient to strongly alter the mechanical properties of networks compared to the corresponding unimodal networks with the same number-average chain length. Furthermore, it is shown that heterogeneities in the form of high-density short-chain clusters affect the mechanical properties relative to a homogeneous network, primarily by providing extensibility.

Cieľom tejto práce je priniesť detailný pohľad na doterajší prieskum v oblasti sférických videí. Konkrétne sa táto práca zameriava na problém tvorby videa s normálnym zorným poľom zo sférického videa pre potreby zobrazovania. Prináša tiež implementáciu niektorých dostupných metód. Doteraz boli predstavené tri metódy v štyroch článkoch, ktoré riešia tento problém. Všetky priniesli zaujímavé výsledky a táto práca sa dvomi z nich zaoberá hlbšie. Táto práca tiež prináša základnú metódu využívajúcu overené metódy automat- ického orezu obrazu. Táto metóda je využitá na porovnanie so skúmanými metódami, u ktorých zvýrazní ich vylepšenia ale aj nedostatky. Na základe porovnania metód pomocou užívateľského experimentu táto práca usudzuje, že najlepšou zo skúmaných metód pre túto úlohu je upravená varianta metódy od Pavel et al. [14], predstavená v tejto práci.