Este trabalho é composto de duas partes distintas, ambas dentro de um mesmo tema: núcleos positivos definidos sobre variedades. Na primeira delas fornecemos uma caracterização para os núcleos contínuos, isotrópicos e positivos definidos a valores matriciais sobre um espaço compacto 2-homogêneo. Utilizando-a, investigamos a positividade definida estrita destes núcleos, apresentando inicialmente algumas condições suficientes para garantir tal propriedade. No caso em que o espaço 2-homogêneo não é uma esfera, descrevemos uma caracterização definitiva para a positividade definida estrita do núcleo. Neste mesmo caso, para núcleos a valores no espaço das matrizes de ordem 2, apresentamos uma caraterização alternativa para a positividade definida estrita do núcleo via os dois elementos na diagonal principal da representação matricial do núcleo. Na segunda parte, nos restringimos a núcleos positivos definidos escalares sobre os mesmos espaços e determinamos condições necessárias e suficientes para a positividade definida estrita de um produto de núcleos positivos definidos sobre um mesmo espaço compacto 2-homogêneo. Apresentamos ainda uma extensão deste resultado para núcleos positivos definidos sobre o produto cartesiano de um grupo localmente compacto com uma esfera de dimensão alta, mantendo-se a isotropia na componente esférica. / In this work we present a characterization for the continuous, isotropic and positive definite matrix-valued kernels on a compact two-point homogeneous space. After that, we consider the strict positive definiteness of the kernels, describing some independent sufficient conditions for that property to hold. In the case the space is not a sphere, one of the conditions becomes necessary and sufficient for the strict positive definiteness of the kernel. Further, for 22- matrix-valued kernels on a compact two-point homogeneous space which is not a sphere, we present a characterization for the strict positive definiteness of the kernels based upon the main diagonal elements in its matrix representation. In the last part of this work, we restrict ourselves to scalar kernels and determine necessary and sufficient conditions in order that the product of two continuous, isotropic and positive definite kernels on a compact two-point homogeneous space be strictly positive definite. We also discuss the extension of this result for kernels defined on a product of a locally compact group and a high dimensional sphere.

This thesis deals with different computational techniques related to some classes of nonlinear response regimes of engineering interest. The work is mainly divided into two parts. In the first part different numeric-analytic integration techniques for nonlinear oscillators are developed. In the second part, procedures for handling arbitrarily large rotations are addressed and a few novel developments are reported in the process. To begin the first part, we have proposed an explicit numeric-analytic technique, based on the Adomian decomposition method, for integrating strongly nonlinear oscillators. Numerical experiments suggest that this method, like most other numerical techniques, is versatile and can accurately solve strongly nonlinear and chaotic systems with relatively larger step-sizes. It is then demonstrated that the procedure may also be effectively employed for solving two-point boundary value problems with the help of a shooting algorithm. This has been followed up with the derivation and numerical exploration of variants of a recently developed numeric-analytic technique, the multi-step transversal linearization (MTrL), in the context of nonlinear oscillators of relevance in engineering dynamics. A considerable generalization and improvement over the original form of a MTrL strategy is achieved in this study. Finally, we have used the concept of MTrL method on the nonlinear variational (rate) equation corresponding to a nonlinear oscillator and thus derive another family of numeric-analytic techniques, presently referred to as the multi-step tangential linearization (MTnL). A comparison of relative errors through the MTrL and MTnL techniques consistently indicate a superior quality of approximation via the MTrL route. In the second part of the thesis, a scheme for numerical integration of rigid body rotation is proposed using only rudimentary tensor analysis. The equations of motion are rewritten in terms of rotation vectors lying in same tangent spaces, thereby facilitating vector space operations consistent with the underlying geometric structure of rotation. One of the most important findings of this part of the dissertation is that the existing constant-preserving algorithms are not necessarily accurate enough and may not be ideally applicable to cases wherein numerical accuracy is of primary importance. In contrast, the proposed rotation-algorithms, the higher order ones in particular, are significantly more accurate for conservative rotational systems for reasonably long time. Similar accuracy is expected for dissipative rotational systems as well. The operators relating rotation variables corresponding to different tangent spaces are also investigated and this should provide further insight into the understanding of rotation vector parametrization. A rotation update is next proposed in terms of rotation vectors. This update, employed along with interpolation of relative rotations, gives a strain-objective and path independent finite element implementation of a geometrically exact beam. The method has the computational advantage of requiring considerably less nodal variables due to the use of rotation vector parametrization. We have proposed a new isoparametric interpolation of nodal quaternions for computing the rotation field within an element. This should be a computationally efficient alternative to the interpolation of local rotations. It has been proved that the proposed interpolation of rotation leads to the objectivity of strain measures. Several numerical experiments are conducted to demonstrate the frame invariance, path-independence and other superior aspects of the present approach vis-`a-vis the existing methods based on the rotation vector parametrization. It is emphasized that, in order to develop an objective finite element formulation, the use of relative rotation is not mandatory and an interpolation of total rotation variables conforming with the rotation manifold should suffice.

Diese Dissertation ist dem Studium temperierter Distributionen mittels mikrolokaler Methoden gewidmet. Die fundamentale Größe der mikrolokalen Analysis, die Wellenfrontmenge, wird durch zwei analoge Konzepte ersetzt, die den pseudo-differentiellen SG- und Shubin-Kalkülen zugeordnet sind. Die Eigenschaften dieser globalen Wellenfrontmengen werden studiert und ferner werden unterschiedliche Möglichkeiten, diese globalen Singularitäten zu charakterisieren, untersucht, insbesondere mittels der FBI-Transformation. Zahlreiche Konstruktionen, die den klassischen Wellenfrontmengenbegriff beinhalten, werden in den globalen Kontext übersetzt, insbesondere Rechenoperationen mit temperierten Distributionen wie etwa (getwistete) Produkte, Pull-backs und Paarungen, für die mikrolokale Existenzkriterien angegeben werden. Als eine Anwendung wird eine Klasse von temperierten Oszillatorintegralen eingeführt, welche durch inhomogene Phasenfunktionen und Amplituden aus SG-Symbolklassen parametrisiert werden. Die SG-Wellenfrontmengen dieser Distributionen werden untersucht und es stellt sich heraus, dass diese durch eine Verallgemeinerung der Menge stationärer Punkte der Phasenfunktionen beschränkt werden. In diesem Kontext wird eine Verallgemeinerung des klassischen Begriffs einer konischen Lagrange-Untermannifaltigkeit des T*R^d vorgenommen und diese Objekte werden auf ihre Parametrisierungseigenschaften untersucht. Es stellt sich heraus, dass jedes solche Objekt lokal als die Menge der stationären Punkte einer SG-Phasenfunktion realisiert werden kann. Als weitere Anwendung werden einige Konstruktionen der axiomatischen Quantenfeldtheorie, die Distributionen beinhalten, im temperierten Kontext realisiert.

Tidal bores are surge waves propagating upstream rivers as the tide rushes into estuaries. They induce large turbulences and mixing of the river and estuary flow of which effects remain scarcely studied. Herein, tidal bores are investigated experimentally and numerically with an idealised model of positive surges propagating upstream an initially steady flow. The experimental work estimated flow changes and typical turbulent length scale evolution induced by undular bores with and without breaking roller. The bore passage was associated with large free surface and flow velocity fluctuations, together with some variations of the integral turbulent scales. Coherent turbulent structures appeared in the wake of leading wave near the bed and moved upward into the water column during the bore propagation. The numerical simulations were based on previous experimental work on undular bores. Some test cases were realised to verify the accuracy of the numerical methods. The results gave access to the detailed flow evolution during the bore propagation. Large velocity reversals were observed close to the no-slip boundaries. In some configurations, coherent turbulent structures appeared against the walls in the wake of the bore front.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-10T14:58:33Z No. of bitstreams: 1 franciscodelgaudiooliveirafigeuiredo.pdf: 778762 bytes, checksum: 462fd065a0a2a277102c64e0a2ecf79c (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-23T11:51:06Z (GMT) No. of bitstreams: 1 franciscodelgaudiooliveirafigeuiredo.pdf: 778762 bytes, checksum: 462fd065a0a2a277102c64e0a2ecf79c (MD5) / Made available in DSpace on 2018-01-23T11:51:06Z (GMT). No. of bitstreams: 1 franciscodelgaudiooliveirafigeuiredo.pdf: 778762 bytes, checksum: 462fd065a0a2a277102c64e0a2ecf79c (MD5) Previous issue date: 2017-03-02 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / As exigências de localidade, positividade dos estados e positividade da energia dão origem a comportamentos ruins dos campos quânticos em distâncias pequenas (singularidadesUV). Quando tenta-se construir campos quânticos para partículas de spin s ≥ 1 que satisfazem esse princípios fundamentais, acaba-se ganhando interações não-renormalizaveis. Para spins um e dois, existem campos, no contexto de teorias de calibre, com o mesmo bom comportamento UV que o campo escalar para spin zero. Entretanto, é necessária a introdução de um espaço de estados não-físico, assim como campos não-físicos (ghosts). Motivado por trabalhos anteriores, nós investigamos campos quânticos, para bósons massivos de spin arbitrário, possuindo o mesmo comportamento UV que o campo escalar (s = 0), porém que agem num espaço de Hilbert sem ghosts e são covariantes por transformações de Poincaré. Esses campos, entretanto, não possuem mais localização pontual, estando localizados, ao invés, em semi-retas no espaço de Minkowski que se extendem em direções tipo-luz (strings tipo-luz). / The combined requirements of locality, positivity of states and positivity of energy lead to bad short distance behaviour of quantum fields (UV singularities). When one tries to build quantum fields for particles of spin s ≥ 1 that still satisfy these fundamental principles, one ends up with non-renormalizable interactions. For spin one and two, there exist fields in the context of gauge theory with the same good UV behaviour as the scalar field for spin zero. However, for this one has to introduce an unphysical state space, as well as unphysical fields (ghosts). Motivated by previous works, we begin to investigate quantum fields, for massive bosons of any spin, that have the same good UV behaviour as the scalar field (s = 0), act in a Hilbert space without ghosts and are Poincaré covariant. These fields are, however, no longer point-local, being localized instead on semi-infinite lines in Minkowski space extending to lightlike infinity (lightlike strings).

Este trabalho é composto de duas partes distintas, ambas dentro de um mesmo tema: núcleos positivos definidos sobre variedades. Na primeira delas fornecemos uma caracterização para os núcleos contínuos, isotrópicos e positivos definidos a valores matriciais sobre um espaço compacto 2-homogêneo. Utilizando-a, investigamos a positividade definida estrita destes núcleos, apresentando inicialmente algumas condições suficientes para garantir tal propriedade. No caso em que o espaço 2-homogêneo não é uma esfera, descrevemos uma caracterização definitiva para a positividade definida estrita do núcleo. Neste mesmo caso, para núcleos a valores no espaço das matrizes de ordem 2, apresentamos uma caraterização alternativa para a positividade definida estrita do núcleo via os dois elementos na diagonal principal da representação matricial do núcleo. Na segunda parte, nos restringimos a núcleos positivos definidos escalares sobre os mesmos espaços e determinamos condições necessárias e suficientes para a positividade definida estrita de um produto de núcleos positivos definidos sobre um mesmo espaço compacto 2-homogêneo. Apresentamos ainda uma extensão deste resultado para núcleos positivos definidos sobre o produto cartesiano de um grupo localmente compacto com uma esfera de dimensão alta, mantendo-se a isotropia na componente esférica. / In this work we present a characterization for the continuous, isotropic and positive definite matrix-valued kernels on a compact two-point homogeneous space. After that, we consider the strict positive definiteness of the kernels, describing some independent sufficient conditions for that property to hold. In the case the space is not a sphere, one of the conditions becomes necessary and sufficient for the strict positive definiteness of the kernel. Further, for 22- matrix-valued kernels on a compact two-point homogeneous space which is not a sphere, we present a characterization for the strict positive definiteness of the kernels based upon the main diagonal elements in its matrix representation. In the last part of this work, we restrict ourselves to scalar kernels and determine necessary and sufficient conditions in order that the product of two continuous, isotropic and positive definite kernels on a compact two-point homogeneous space be strictly positive definite. We also discuss the extension of this result for kernels defined on a product of a locally compact group and a high dimensional sphere.

Final thesis on the design of the drive of a cutting mechanical two-point crank press with a nominal force of 6300 kN. After the theoretical definition of the area of mechanical crank presses and their drives at the beginning of the work, the actual design solution follows. The main idea of the design is the drive arrangement with the concurrent axis of the clutch shaft. The supplied torque is distributed on two longitudinally mounted drive units via a two-sided bevel gear. Solution of the construction design is aimed at enabling workspace variability while simultaneously unifying the maximum number of drive components. Drawing documentation of selected components and assemblies is the part of the thesis.

This presenting master’s thesis deals with a problem of digitaly controled room temperature using the software PLC. The result of this work was creating of an algorithm to control temperature on the requested leve ofl setpoint, minimizing operating costs of the building. The PLC softwares from different manufacturers were analyzed and compared with conventional PLC. The testing facility was disigned and used to control the temperature in the room and data visualization. Room temperature was regulated by PS controller or two point regulator.

Anorexia nervosa (AN) is a mental illnes manifesting itselg, among other signs, with impaired body schema and rejection of food. Principal focus of the thesis was to assess the discrimination treshold, ability to evaluate sensory perception and body self-concept in adolescent female patients hospitalised with anorexia nervosa. Our goal was to clarify and better understand the still not adequately described neurophysiological aspects of anorexia nervosa. The results were compared to control group; both groups comprised 18 girls, the average age of observed group being 14,7 ± 0,71 years and average age of control group being 15,3 ±0,71 years. Two-point discrimination was examined in three areas - arm, between shoulder blades and belly - with modified caliper. The Petrie test was used in sensory perception testing, while body self-concept was measured with BAT questionare. The examinations were performed in standardised conditions during similar day times. We found significant difference in two-point discrimination in the area between the shoulder blades with significance level α = 5 % and p-value p = 0,0001. A statistically significant difference was also observed in body self-concept with significance level α = 5 % and p-value p = 0,017. Thus we conclude that patients suffering from anorexia nervosa...

Design space exploration (DSE) is used to improve and understand engineering designs. Such designs must meet objectives and structural requirements. Design improvement is non-trivial and requires new DSE methods. Turbomachinery manufacturers must continue to improve existing engines to keep up with global demand. Two challenges of turbomachinery DSE are: the time required to evaluate designs, and knowing which designs to evaluate. This research addressed these challenges by developing novel surrogate and principal component analysis (PCA) based DSE methods. Node and PCA-based surrogates were created to allow faster DSE of turbomachinery blades. The surrogates provided static stress estimation within 10% error. Surrogate error was related to the number of sampled finite element (FE) models used to train the surrogate and the variables used to change the designs. Surrogates were able to provide structural evaluations three to five orders of magnitude faster than FEA evaluations. The PCA-based surrogates were then used to create a PCA-based design workflow to help designers know which designs to evaluate. The workflow used either two-point correlation or stress and geometry coupling to relate the design variables to principal component (PC) scores. These scores were projections of the FE models onto the PCs obtained from PCA. Analysis showed that this workflow could be used in DSE to better explore and improve designs. The surrogate methods were then applied to vibratory stress. A computationally simplified analysis workflow was developed to allow for enough fluid and structural analyses to create a surrogate model. The simplified analysis workflow introduced 10% error but decreased the computational cost by 90%. The surrogate methods could not directly be applied to emulation of vibration due to the large spikes which occur near resonance. A novel, indirect emulation method was developed to better estimate vibratory responses Surrogates were used to estimate the inputs to calculate the vibratory responses. During DSE these estimations were used to calculate the vibratory responses. This method reduced the error between the surrogate and FEA from 85% to 17%. Lastly, a PCA-based multi-fidelity surrogate method was developed. This assumed the PCs of the high and low-fidelities were similar. The high-fidelity FE models had tens of thousands of nodes and the low-fidelity FE models had a few hundred nodes. The computational cost to create the surrogate was decreased by 75% for the same errors. For the same computational cost, the error was reduced by 50%. Together, the methods developed in this research were shown to decrease the cost of evaluating the structural responses of turbomachinery blade designs. They also provided a method to help the designer understand which designs to explore. This research paves the way for better, and more thoroughly understood turbomachinery blade designs.