O objetivo principal deste trabalho é apresentar um estudo sobre o Teorema de Borsuk-Ulam para forma espacial esférica homotópica. Em nosso trabalho consideramos X uma n-forma espacial esférica homotópica a qual admite uma ação livre de Zp, com p> 2 primo e f : X → Rk uma função contínua e, mostramos que sob determinada relação entre os números n e k, o conjunto A(f) dos pontos de coincidência de f é não vazio / The main objective of this work is to present a study about the Borsuk- Ulam Theorem for homotopic spherical space. In our work we consider X be a n-dimensional homotopic spherical space form which admits a free action of Zp, with p> 2 prime and f : X → Rk be a continuous map and we show that, under certain relations between the numbers n and k, the set A(f) is not empty

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-26T20:13:44Z No. of bitstreams: 1 alcidesfariasndrade.pdf: 803619 bytes, checksum: 302375f647c6bebde2042805b53cddc2 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-07T20:49:09Z (GMT) No. of bitstreams: 1 alcidesfariasndrade.pdf: 803619 bytes, checksum: 302375f647c6bebde2042805b53cddc2 (MD5) / Made available in DSpace on 2017-08-07T20:49:09Z (GMT). No. of bitstreams: 1 alcidesfariasndrade.pdf: 803619 bytes, checksum: 302375f647c6bebde2042805b53cddc2 (MD5) Previous issue date: 2011-08-25 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Estudamos um defeito tipo deslocação com simetria esférica. Encontramos a métrica para um meio contendo uma única deformação deste tipo. Para isso, calculamos o vetor deslocamento por meio da teoria linear da elasticidade e usando o esquema da teoria geométrica de defeitos, na qual o meio é caracterizado por objetos geométricos tais como curvatura e torção, encontramos as componentes do tensor métrico. Calculamos também outras quantidades geométricas como os tensores de Riemann e Ricci, e o escalar de curvatura bem como as componentes do tensor momento-energia. Em todas estas quantidades aparecem funções δ, indicando divergência na superfície onde está localizado o defeito. Fora desta superfície, o meio possui uma geometria euclideana. Resolvemos as equações geodésicas radial e no plano para a região externa ao defeito e observamos que, mesmo localizado, ele exerce influência sobre o movimento nesta região. / We study a dislocation defect with spherical symmetry. We find the metric for a medium containing a single deformation of this kind. For this, we calculate the displacement vector through the linear theory of elasticity and using the scheme of geometric theory of defects, in which the medium is characterized by geometric objects such as curvature and torsion, we find the components of the metric tensor. We calculate also other geometrical quantities as the Riemann and Ricci tensor, and the scalar curvature as well as the energy-momentum tensor. In these quantities, δ-functions show up, indicating divergence in the surface where the defect is located. Outside this surface, the medium has an Euclidean geometry. We solve the geodesic equations for the outer region to the defect and we observed, despite being located, its influence on the movement in this region.

Orientador: Ernesto Kemp / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-25T18:38:19Z (GMT). No. of bitstreams: 1 Silva_MarceloZimbres_D.pdf: 8568193 bytes, checksum: 2348942e48cd0c1c610715988bd1d2f6 (MD5) Previous issue date: 2014 / Resumo: Devido à ação do campo magnético cósmico, trajetórias de raios cósmicos provenientes de uma mesma fonte podem ser defletidas e dar origem a estruturas filamentares cujos eventos são ordenados de acordo com suas energias, os multipletos. Nesse trabalho, propomos um novo método para identificação de multipletos, baseado no uso de uma classe de funções definidas sobre a esfera, chamadas de wavelets esféricos. Para testar o método aplicamos a análise em dados simulados. Primeiramente usamos um fundo isotrópico, onde um multipleto pode ocorrer apenas ao acaso. Posteriormente fazemos a análise colocando um multipleto em uma posição aleatória no mesmo fundo isotrópico. Com isso calculamos erros de tipo I e II. O método também é aplicado em dados obtidos pelo Observatório Pierre Auger para eventos com energia E > 15 x10^{18}eV / Abstract: Due to the action of the intervening cosmic magnetic fields, the trajectories of ultra-high energy cosmic rays (UHECRs) can be deflected in such a way as to create clustered energy-ordered filamentary structures in the arrival directions of these particles, the so-called multiplets. In this work we propose a new method based on the spherical wavelet transform to identify multiplets in sky maps containing arrival directions of UHECRs. The method is illustrated in simulations with a multiplet embedded in isotropic backgrounds with different numbers of events, and on data from the Pierre Auger Observatory. The efficiency of the algorithm is assessed through the calculation of Type I and II erros / Doutorado / Física / Doutor em Ciências

The Laplace-Beltrami operator corresponds to the Laplace operator on curved surfaces. In this paper, we consider an eigenvalue problem for the Laplace-Beltrami operator on subdomains of the unit sphere in $\R^3$. We develop a residual a posteriori error estimator for the eigenpairs and derive a reliable estimate for the eigenvalues. A global parametrization of the spherical domains and a carefully chosen finite element discretization allows us to use an approach similar to the one for the two-dimensional case. In order to assure results in the quality of those for plane domains, weighted norms and an adapted Clément-type interpolation operator have to be introduced.

Conventional interferometry is widely used to measure spherical and flat surfaces with nanometer level precision but is plagued by back reflections. We describe a new method of isolating the measurement surface by controlling spectral properties of the source (Spectrally Controlled Interferometry - SCI). Using spectral modulation of the interferometer's source enables formation of localized fringes where the optical path difference is non-zero. As a consequence it becomes possible to form white-light like fringes in common path interferometers, such as the Fizeau. The proposed setup does not require mechanical phase shifting, resulting in simpler instruments and the ability to upgrade existing interferometers. Furthermore, it allows absolute measurement of distance, including radius of curvature of lenses in a single setup with possibility of improving the throughput and removing some modes of failure.

No description available.

The submicron-aperture fiber point-diffraction interferometer (SFPDI) can be applied to realize the measurement of three-dimensional absolute displacement within large range, in which the performance of point-diffraction wavefront and numerical iterative algorithm for displacement reconstruction determines the achievable measurement accuracy, reliability and efficiency of the system. A method based on fast searching particle swarm optimization (FS-PSO) algorithm is proposed to realize the rapid measurement of three-dimensional absolute displacement. Based on the SFPDI with two submicron-aperture fiber pairs, FS-PSO method and the corresponding model of the SFPDI, the measurement accuracy, reliability and efficiency of the SFPDI system are significantly improved, making it more feasible for practical application. The effect of point-diffraction wavefront error on the measurement is analyzed. The error of point-diffraction wavefront obtained in the experiment is in the order of 1x10(-4). (the wavelength. is 532 nm), and the corresponding displacement measurement error is smaller than 0.03 mu m. Both the numerical simulation and comparison experiments have been carried out to demonstrate the accuracy and feasibility of the proposed SFPDI system, high measurement accuracy in the order of 0.1 mu m, convergence rate (similar to 90.0%) and efficiency have been realized with the proposed method, providing a feasible way to measure three-dimensional absolute displacement in the case of no guide rail.

Long span flat slab systems with internal spherical void formers have been used in Europe for a decade now. Cobiax® is the brand name of a successful system, recently introduced in South Africa. It is a bi-axial reinforced concrete flat slab system, with a grid of internal spherical void formers. The main advantage is the possibility of long spans due to the significant reduction in own weight, as well as the fast construction sequence with the use of flat slab formwork systems. Design requirements of SANS 10100:2000 are affected. Vertical shear capacity is a concern due to loss of aggregate interlock. Research in Germany proved a factor of 0.55 to be a conservative shear resistance reduction factor for Cobiax slabs. Theoretical and preliminary laboratory South African research suggests that a greater factor of 0.85 might be used when considering the shear capacity of the steel cages. These cages’ vertical legs also cross the cold joint caused by the two concrete pours required for Cobiax slabs, and proved to provide sufficient horisontal shear resistance if the correct cage diameters are used. Laboratory tests in Germany supported by theoretical calculations further showed reduced deflections for Cobiax slabs. Although stiffness and own weight are reduced due to the voids, Cobiax slabs had smaller absolute deflections than solid slabs with the same thickness. Cobiax research factors are safe to apply to SANS 10100-01:2000. The economy of Cobiax slabs was tested against that of coffer and post-tensioned slabs. Different span lengths and loads were considered. Based on 2007 material costs in South Africa, Cobiax slabs subject to the same loads and span lengths will be slightly more expensive than that of coffer slabs and post-tensioned slabs when considering only direct slab construction costs. Cobiax will be most appropriate where a flat soffit is required for high multi-storey buildings, requiring large spans with a light load application. Copyright / Dissertation (MEng)--University of Pretoria, 2010. / Civil Engineering / unrestricted

Over the last decade there has been a worldwide increase in the use of retractable roofs for stadia. This increase has been based on the flexibility and better economic performance offered by venues featuring retractable roofs compared to those with traditional fixed roofs. With this increased interest an evolution in retractable roof systems has followed. This dissertation is concerned with the development of concepts for retractable roof systems. A review is carried out to establish the current state-of-the-art of retractable roof design. A second review of deployable structures is used to identify a suitable retractable structure for further development. The structure chosen is formed by a two-dimensional ring of pantographic bar elements interconnected through simple revolute hinges. A concept for retractable roofs is then proposed by covering the bar elements with rigid cover plates. To prevent the cover plates from inhibiting the motion of the structure a theorem governing the shape of these plate elements is developed through a geometrical study of the retractable mechanism. Applying the theorem it is found that retractable structures of any plan shape can be formed from plate elements only. To prove the concept a 1.3 meter diameter model is designed and built. To increase the structural efficiency of the proposed retractable roof concept it is investigated if the original plan shape can be adapted to a spherical surface. The investigation reveals that it is not possible to adapt the mechanism but the shape of the rigid cover plates can be adapted to a spherical surface. Three novel retractable mechanisms are then developed to allow opening and closing of a structure formed by such spherical plate elements. Two mechanisms are based on a spherical motion for the plate elements. It is shown that the spherical structure can be opened and closed by simply rotating the individual plates about fixed points. Hence a simple structure is proposed where each plate is rotated individually in a synchronous motion. To eliminate the need for mechanical synchronisation of the motion, a mechanism based on a reciprocal arrangement of the plates is developed. The plate elements are interconnected through sliding connections allowing them mutually to support each other, hence forming a self-supporting structure in which the motion of all plates is synchronised. To simplify the structure further, an investigation into whether the plate elements can be interconnected solely through simple revolute joints is carried out. This is not found to be possible for a spherical motion. However, a spatial mechanism is developed in which the plate elements are interconnected through bars and spherical joints. Geometrical optimisation of the motion path and connection points is used to eliminate the internal strains that occur in the initial design of this structure so a single degree-of-freedom mechanism is obtained. The research presented in this dissertation has hence led to the development of a series of novel concepts for retractable roof systems.

This thesis presents a practical approach to reduce the overall testing time in a spherical near-field (SNF) antenna measurement environment. The premise of this work is that the acquisition time is mostly dominated by the mechanical movement and the processing electronic. Moreover, it is assumed that the transformation time to go from the near-field domain to the far-field domain (NF-FF transform) is small compared to the acquisition time. Thus this operation can be done repeatedly while the acquisition is on-going without significantly affecting the overall test time. This situation allows to continuously evaluate the far-field (FF) of the antenna under test (AUT), so that certain decision functions based on the radiation pattern of the antenna can be monitored. Such decision functions are based on the antenna specification, such as the gain, the side lobe level, etc. We do not proceed with a complete scan of the measurement sphere but effectively allow the probe to follow a directed path under control of an acquisition rule, so that the sampled near-field (NF) datapoints constitute an acquisition map on the sphere. The acquisition can then be terminated based on decision function values, allowing the smallest amount of data needed to ensure accurate determination of the AUT performance measures.