Utilizando a representação funcional de schrodinger e um ansatz gaussiano simples, obtemos um conjunto de equações finitas para a matéria e gravitação em espaços homogêneos e inomogêneos. / Using the formalism of functional Schrödinger representation and a simple Ansatz, we obtain a set of finite equations to the matter and gravitation in homogeneous and inhomogeneous spaces.

My dissertation focuses on the existence of metrics of non-positive curvature for the simplicial complexes constructed recently by Tom Brady and Daan Krammer for the braid groups and other Artin groups of finite type. In particular, for each Artin group of finite type, there is a recently constructed finite simplicial Eilenberg-Mac Lane space known as its Brady-Krammer complex. The Brady-Krammer complexes are highly symmetric objects. Prior work on the relationship between the Brady-Krammer complexes and the theory of CAT(0)spaces has produced some positive results in low-dimensions. More specifically, the Brady-Krammer complexes of dimension at most 3 have been shown to support piecewise Euclidean metrics of non-positive curvature. Similarly, the 4dimensional Brady-Krammer complexes of type A4 and type B4 also support such metrics. In every instance, the metrics assigned respect all of the symmetries alluded to above. The main results of my dissertation show that this pattern does not extend to the Brady-Krammer complexes of type F4 and D4. These are the first negative results known about the curvature of these Brady-Krammer complexes. The proofs of my main theorems involve a combination of combinatorial results and computer calculations. These negative results are particularly striking since Ruth Charney, John Meier and Kim Whittlesey have shown that a particular complex closely related to each Brady-Krammer complex admits an asymmetric metric satisfying a weak version of non-positive curvature. Thus, one corollary of my results is that the weak asymmetric version of a CAT(0) metric (initially defined by Mladen Bestvina) is strictly weaker than the traditional version.

The first ocean general circulation models developed in the late sixties were based on finite differences schemes on structured grids. Many improvements in the fields of engineering have been achieved since three decades with the developments of new numerical methods based on unstructured meshes. Some components of the first models may now seem out of date and new second generation models are therefore under study, with the aim of taking advantage of the potential of modern numerical techniques such as finite elements. In particular, unstructured meshes are believed to be more efficient to resolve the large range of time and space scales present in the ocean. Besides the classical continuous finite element or finite volume methods, another popular new trend in engineering applications is the Discontinuous Galerkin (DG) method, i.e. discontinuous finite elements presenting many interesting numerical properties in terms of dispersion and dissipation, errors convergence rates, advection schemes, mesh adaptation, etc. The method is especially efficient at high polynomial orders. The motivation for this PhD research is therefore to investigate the use of the high-order DG method for geophysical flow modeling. A first part of the thesis is devoted to the mesh adaptation using the DG method. The inter-element jumps of the fields are used as error estimators. New mesh size fields or polynomial orders are then derived and local h- or p-adaptation is performed. The technique is applied to standard benchmarks and computations in more realistic domains as the Gulf of Mexico. A second part deals with the use of the high order DG method with high-order representation of geometrical features. On one hand, a method is proposed to deal with complex representations of the coastlines. Computations are performed using high-order mappings around the Rattray island, located in the Great Barier Reef. Numerical results are then compared to in-situ measurements. On the other hand, a new method is proposed to deal with curved manifolds in order to represents oceanic or atmospheric flows on the sphere. The approach is based on the use of a local high-order non-orthogonal basis, and is equivalent to the use of vectorial shape and test functions to represent the vectorial conservation laws on the manifold's surface. A method is finally proposed to analyze the dispersion and dissipation properties of any numerical scheme on any kind of grid, possibly unstructured. The DG method is then compared to other techniques as the mixed non-conforming linear elements, and the impact of unstructured meshes is studied.

The frictional behavior of soil-construction material interfaces is of significant importance in geotechnical engineering applications such as retaining structures, pile foundations, geosynthetic liners, and trenchless technologies. Since most failures initiate and develop on the interfaces, special attention is required to predict the capacity of these weak planes in the particular application. Pipe-jacking and microtunneling technologies are being more widely used over the past decade and there is significant interest to predict the jacking forces and jacking distances achievable in order to achieve more efficient design and construction. This study focuses on the evaluation of the frictional characteristics and factors affecting the shear strength of pipe-soil interfaces. Eight different pipes made from fiber reinforced polymer (FRP), polycrete, steel, concrete, and vitrified clay were tested in the experimental program. For this purpose, a new apparatus was designed to conduct conventional interface direct shear testing on pipes of different curvature. This device allows coupons cut from actual conduits and pipes to be tested in the laboratory under controlled conditions. The apparatus includes a double-wall shear box, the inner wall of which is interchangeable to allow for testing against surfaces of different curvatures. By considering a narrow width section, the circular interface of pipes was approximated with a surface along the axial direction and the boundary is defined by the inner box. Roughness tests were performed using a stylus profilometer to quantify the surface characteristics of the individual pipes and relate these to the interface shear behavior. The surface topography showed different degrees of variability for the different pipes. To extend the range of roughness values tested and force the failure to occur in the particulate media adjacent to the interface, two artificial pipe surfaces were created using rough sandpapers. Interface shear tests were performed using the new apparatus with air-pluviated dense specimens of Ottawa 20/30 sand. Additional tests were performed using Atlanta blasting sand to evaluate the effect of particle angularity. The effect of normal stress and relative density were also examined. The interface strength was shown to increase with surface roughness and finally reach a constant value above a certain critical roughness value, which corresponded to the internal strength of the soil itself. This represented the failure location moving from the interface into the soil adjacent to the interface. Both the strength and the shearing mechanism were thus affected by the surface topography. It was also shown that the interface shear strength was affected by particle angularity, relative density and normal stress.

ABSTRACT EXPERIMENTAL ANALYSIS OF CURVED LAMINATED GLASS BEAM Uzhan, Tevfik M.S., Department of Engineering Sciences Supervisor: Prof. Dr. M. Z&uuml / lf&uuml / ASik May 2010, 33 Pages In this thesis, experimental studies are carried out on curved laminated glass beams to form a database for the scientists who may like to test their mathematical models. Beams which are only free to rotate and constrained in radial direction at both ends are tested to make the data available for further calculations. Test setup is prepared to minimize error that could occur due to test setup and data readings. Material testing machine and 4 channel data collecting machine are used to measure the signals at the strain gauges located over the glass beam. Within the range of force applied to the specimens, laminated curved beam shows linear behavior without any fracture. Data collected from the specimens are in conformance with each other. Results obtained from experiments are compared with the results obtained from the mathematical model developed by ASik and Dural (2006). As it is observed from the graphs presented, experimental results from the tests and numerical results from the mathematical model are in good agreement.

My dissertation focuses on the existence of metrics of non-positive curvature for the simplicial complexes constructed recently by Tom Brady and Daan Krammer for the braid groups and other Artin groups of finite type. In particular, for each Artin group of finite type, there is a recently constructed finite simplicial Eilenberg-Mac Lane space known as its Brady-Krammer complex. The Brady-Krammer complexes are highly symmetric objects. Prior work on the relationship between the Brady-Krammer complexes and the theory of CAT(0)spaces has produced some positive results in low-dimensions. More specifically, the Brady-Krammer complexes of dimension at most 3 have been shown to support piecewise Euclidean metrics of non-positive curvature. Similarly, the 4dimensional Brady-Krammer complexes of type A4 and type B4 also support such metrics. In every instance, the metrics assigned respect all of the symmetries alluded to above. The main results of my dissertation show that this pattern does not extend to the Brady-Krammer complexes of type F4 and D4. These are the first negative results known about the curvature of these Brady-Krammer complexes. The proofs of my main theorems involve a combination of combinatorial results and computer calculations. These negative results are particularly striking since Ruth Charney, John Meier and Kim Whittlesey have shown that a particular complex closely related to each Brady-Krammer complex admits an asymmetric metric satisfying a weak version of non-positive curvature. Thus, one corollary of my results is that the weak asymmetric version of a CAT(0) metric (initially defined by Mladen Bestvina) is strictly weaker than the traditional version.

The paper presents a method for generating curved surfaces of 3D finite element meshes by mesh refinement starting with a very coarse grid. This is useful for parallel implementations where the finest meshes should be computed and not read from large files. The paper deals with simple geometries as sphere, cylinder, cone. But the method may be extended to more complicated geometries. (with 45 figures)

In Part I we are dealing with effective description of Yang-Mills theories based on gauge-invarint variables. For pure Yang-Mills we study the spin-charge separation varibles. The dynamics in these variables resembles the Skyrme-Faddeev model. Thus the spin-charge separation is an important intermediate step between the fundamental Yang-Mills theory and the low-energy effective models, used to model the low-energy dynamics of gluons. Similar methods may be useful for describing the Electroweak sector of the Standard Model in terms of gauge-invariant field variables called supercurrents. We study the geometric structure of spin-charge separation in 4D Euclidean space (paper III) and elaborate onconnection with gravity toy model. Such reinterpretation gives a way to see how effective flat background metric is created in toy gravity model by studying the appearance of dimension-2 condensate in the Yang-Mills (paper IV). For Electroweak theory we derive the effective gauge-invariant Lagrangian by doing the Kaluza-Klein reduction of higher-dimensional gravity with 3-brane, thus making explicit the geometric interpretation for gauge-invariant supercurrents. The analogy is then made more precise in the framework of exact supergravity solutions. Thus, we interpret the Higgs effect as spontaneous breaking of Kaluza-Klein gauge symmetry and this leads to interpretation of Higgs field as a dilaton (papers I and II). In Part II of the thesis we study rather simple field theories, called “geometric” or “instantonic”. Their defining property is exact localization on finite-dimensional spaces – the moduli spaces of instantons. These theories allow to account exactly for non-linearity of space of fields, in this respect they go beyond the standard Gaussian perturbation theory. In paper V we show how to construct a geometric theory of chiral boson by embedding it into the geometric field theory. In Paper VI we elaborate on the simplest geometric field theory – the supersymmetric Quantum Mechanics and construct new non-perturbative topological observables that have a transparent meaning both in geometric and in the Hamiltonian formalisms. In Paper VII we are motivated by making perturbations away from the simple instantonic limit. For that we need to carefully define the observables that are quadratic in momenta and develop the way to compute them in geometric framework. These correspond geometrically to bivector fields (or, in general, the polyvector fields). We investigate the local limit of polyvector fields and compare the geometric calculation with free-field approach.

This thesis is motivated by the necessity to understand the flow structure of turbulent flows in bends encountered in many technical applications such as heat exchangers, nuclear reactors and internal combustion engines. Flows in bends are characterised by strong secondary motions in terms of counter-rotating vortices (Dean cells) set up by a centrifugal instability. Specifically the thesis deals with turbulent flows in 90° curved pipes of circular cross-section with and without an additional motion, swirling or pulsatile, superposed on the primary flow.  The aim of the present thesis is to study these complex flows in detail by using time-resolved stereoscopic particle image velocimetry to obtain the three-dimensional velocity field, with complementary hot-wire anemometry and laser Doppler velocimetry measurements. In order to analyse the vortical flow field proper orthogonal decomposition (POD) is used. The so called ``swirl-switching'' is identified and it is shown that the vortices instantaneously, ``rock'' between three states, viz. a pair of symmetric vortices or a dominant clockwise or counter-clockwise Dean cell. The most energetic mode exhibits a single cell spanning the whole cross-section and ``rolling'' (counter-)clockwise in time. However, when a honeycomb is mounted at the inlet of the bend, the Dean vortices break down and there is strong indication that the ``swirl-switching'' is hindered. When a swirling motion is superimposed on the incoming flow, the Dean vortices show a tendency to merge into a single cell with increasing swirl intensity. POD analysis show vortices which closely resemble the Dean cells, indicating that these structures co-exist with the swirling motion. In highly pulsating turbulent flow at the exit of a curved pipe, the vortical pattern is diminished or even eliminated during the acceleration phase and then re-established during the deceleration. In order to investigate the effect of pulsations and curvature on the performance of a turbocharger turbine, highly pulsating turbulent flow through a sharp bend is fed into the turbine. Time-resolved pressure and mass-flow rate measurements show that the hysteresis loop in the pressure-ratio-mass-flow plane, may differ significantly between straight and curved inlets, however the mean operating point is only slightly affected. / <p>QC 20140523</p>

An investigation of information loss in black hole spacetimes is performed. We demon- strate that the definition of particles as energy levels of the Harmonic oscillator will not have physical significance in general and is thus not a good instrument to study the ra- diation of black holes. This is due to the ambiguity of the choice of coordinates on the phase space of the quantum field. We demonstrate how to identify quantum states in the functional Schr ̈dinger picture. o We demonstrate that information is truly lost in the case of a Vaidya black hole (a black hole formed from null dust) if we neglect back reaction. This is done by quantizing the constrained classical system of a Klein-Gordon field in a Vaidya background. The interaction picture of quantum mechanics can be applied to this system. We find a physically well motivated vacuum state for a spherically symmetric space- time with an extra conformal Killing vector. We also demonstrate how to calculate the response of a particle detector in the a LeMaitre-Tolman-Bondi spacetime with a self- similarity. Finally, some of the claims and confusion surrounding Unruh radiation, Hawking radiation and the equivalence principle are investigated and shown to be false.