O presente trabalho apresenta resultados objetivando classificar folheaÃÃes de codimensÃo 1 em variedades Riemannianas cujas folhas tem curvatura mÃdia constante. O principal resultado à o teorema de Barbosa-Kenmotsu-Oshikiri([3]), Teorema: Seja M uma variedade Riemanniana compacta com curvatura de Ricci nÃo negativa e F um folheaÃÃo de codimensÃo 1 e classe C3 de M, transversalmente orientÃvel, cujas folhas tem curvatura mÃdia constante. EntÃo, qualquer folha de F à uma subvariedade totalmente geodÃsica de M. AlÃm disso, M à localmente um produto Riemanniano de uma folha de F e uma curva normal e a curvatura de Ricci na direÃÃo normal Ãs folhas à zero. O resultado anterior nÃo pode ser estendido para o caso onde M à nÃo compacta. Uma folheaÃÃo contra-exemplo pode ser construÃda a partir de uma funÃÃo f que nÃo satisfaz a conjectura de Bernstein. No final, sÃo apresentados resultados recentes sobre os problemas abordados e uma prova da desigualdade de Heinz-Chern / In this paper, we work showing results aiming classify foliations of codimension-one in Riemannian manifolds whose leaves have constant mean curvature. The main result is the theorem by Barbosa-Kenmotsu-Oshikiri([3]). Theorem: LetM be a compact Riemannian manifold with nonnegative Ricci curvature e F, a codimensiononeC3-foliation of M whose leaves have constant mean curvature. The any leaf of F is totally geodesic submanifold of M. Futhermore M is locally a Riemannian product of a leaf of F and a normal curve,and the Ricci curvature in the direction normal to the leaves is zero. The previous result can not be extended for the case where M is not compact. A foliation counterexample can be built from a function f that does not satisfy the Bernsteinâs conjecture. At the end, they are present recent results about the boarded problems and a proof of the Heinz-Chern inequality.

This thesis is about some extensions of the ideas and techniques used in integrable field theories to deal with non-integrable theories. It is presented in two parts. The first part deals with gauge theories in 3 and 4 dimensional space-time; we propose what we call the integral formulation of them, which at the end give us a natural way of defining the conserved charges that are gauge invariant and do not depend on the parametrisation of space-time. The definition of gauge invariant conserved charges in non-Abelian gauge theories is an open issue in physics and we think our solution might be a first step into its full understanding. The integral formulation shows a deeper connection between different gauge theories: they share the same basic structure when written in the loop space. Moreover, in our construction the arguments leading to the conservation of the charges are dynamical and independent of the particular solution. In the second part we discuss the recently introduced concept called quasi-integrability: one observes soliton-like configurations evolving through non-integrable equations having properties similar to those expected for integrable theories. We study the case of a model which is a deformation of the non-linear Schr¨odinger equation consisting of a more general potential, connected in a way with the integrable one. The idea is to develop a mathematical approach to treat more realistic theories, which is in particular very important from the point of view of applications; the NLS model appears in many branches of physics, specially in optical fibres and Bose-Einstein condensation. The problem was treated analytically and numerically, and the results are interesting. Indeed, due to the fact that the model is not integrable one does not find an infinite number of conserved charges but, instead, a set of infinitely many charges that are asymptotically conserved, i.e., when two solitons undergo a scattering process the charges they carry before the collision change, but after the collision their values are recovered. / Essa tese discute algumas extensões de ideias e técnicas usadas em teorias de campos integráveis para tratar teorias que não são integráveis. Sua apresentação é feita em duas partes. A primeira tem como tema teorias de calibre em 3 e 4 dimensões; propomos o que chamamos de equação integral para uma tal teoria, o que nos permite de maneira natural a construção de suas cargas invariantes de calibre, e independentes da parametrização do espaço-tempo. A definição de cargas conservadas in variantes de calibre em teorias não-Abelianas ainda é um assunto em aberto e acreditamos que a nossa solução pode ser um primeiro passo em seu entendimento. A formulação integral mostra uma conexão profunda entre diferentes teorias de calibre: elas compartilham da mesma estrutura básica quando formuladas no espaço dos laços. Mais ainda, em nossa construção os argumentos que levam `a conservação das cargas são dinâmicos e independentes de qualquer solução particular. Na segunda parte discutimos o recentemente introduzido conceito de quasi-integrabilidade: em (1 + 1) dimensões existem modelos não integráveis que admitem soluções solitonicas com propriedades similares `aquelas de teorias integráveis. Estudamos o caso de um modelo que consiste de uma deformação (não-integrável) da equação de Schrödinger não-linear (NLS), proveniente de um potencial mais geral, obtido a partir do caso integrável. O que se busca é desenvolver uma abordagem matemática sistemática para tratar teorias mais realistas (e portanto não integráveis), algo bastante relevante do ponto de vista de aplicações; o modelo NLS aparece em diversas áreas da física, especialmente no contexto de fibra ótica e condensação de Bose-Einstein. O problema foi tratado de maneira analítica e numérica, e os resultados se mostram interessantes. De fato, sendo a teoria não integrável não é encontrado um conjunto com infinitas cargas conservadas, mas, pode-se encontrar um conjunto com infinitas cargas assintoticamente conservadas, i.e., quando dois solitons colidem as cargas que eles tinham antes tem os seus valores alterados, mas após a colisão, os valores inicias, de antes do espalhamento, são recobrados.

O objetivo deste trabalho e desenvolver um instrumento computadorizado para análise da superfície anterior da córnea humana, gerando para isto, um mapa topográfico bidimensional em código de cores. Utilizando a córnea como um espelho esférico convexo, projeta-se anéis luminosos sobre sua superfície e aquisiciona-se com uma câmera a imagem por ela refletida. Esta imagem e digitalizada e armazenada em um microcomputador para posterior processamento. Através de técnicas de computação gráfica e processamento de imagens digitais, extrai-se da imagem as informações necessárias para construção da topografia desejada. Por fim, a topografia e apresentada em forma de mapas coloridos, sendo cada cor associada a uma determinada dioptria, transmitindo ao médico oftalmologista uma noção exata da superfície da córnea do paciente em análise. / The main goal of this work is to develop a computerized instrument for the analysis of the anterior portion of the human cornea, which displays its result in topographic color maps. Approximating the cornea to a spherical convex mirror, and by projecting a known pattern over it, the reflected image is captured and stored. By means of computer graphics technology and image processing, the necessary information for mathematical calculations is extracted. The resulting maps are color-coded in accordance to the degree of power of each corneal region, that is, to the diopter value. The ophthalmologist can then make important diagnostics and surgery tactics from the analysis of these topographic maps.

A teoria das transforma»ções de superfícies de curvatura constante começou, no fim do século XIX, com o trabalho [3] de A.V. Bäcklund e, em seguida, recebeu importantes contribuições por parte de diversos geômetras, entre eles, L. Bianchi e C. Guichard (veja, por exemplo, [5, 6, 7, 17]). Nessa dissertação apresentamos alguns dos mais importantes resultados desse tópico da geometria diferencial que estão relacionados às superfícies de curvatura média (ou gaussiana não nula) constante. Tais superfícies estão associadas a soluções de equações diferenciais parciais de segunda ordem e não lineares. A interpretação analítica da teoria das transformações de superfícies de curvatura constante nos capacita obter soluções dessas equações diferenciais parciais a partir de uma outra dada, mediante integração de um sistema de equações diferenciais, chamado transformação de Bäcklund. Então, os teoremas de permutabilidade fornecem uma \"fórmula de superposição\" para a construção algébrica de novas soluções / The theory on transformations of surfaces with constant curvature begins, in the late nineteen century, with the article [3] of A.V. Bäcklund and, after, received important contributions from various geometricians, among others, L. Bianchi and C. Guichard (see, for example, [5, 6, 7, 17]). In this dissertation we outline some of the most important results on the theory of surfaces of constant mean (or gaussian) curvature. Such surfaces are associated to the solutions of nonlinear partial differential equations of second order. The analytic interpretation of the theory on transformations of constant curvature surfaces provides a method of obtaining, from a given solution of these partial differential equations, a new solution of the same equation, by integrating a system of differential equations, called Bäcklund transformation. Then, the permutability theorems give a \"superposition formula\" to construct, algebraically, new solutions

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.

This thesis deals with factors influencing the average speed on Czech roads. Curvature and inclination of the slopes were selected among the main factors influencing the average speed. Until now, these factors have been considered at discrete intervals, not as continuous functions. The function for calculating the curvature is based on ČSN 73 6101, where the equation with all variables is directly defined. The functional relationship for the movement of vehicles in sloping terrain was created from data from scientific articles. Therefore, an algorithm was implemented in this thesis, which can automatically evaluate the average speed on the road network. Python was used to implement this algorithm. Furthermore, there is a testing section for travel times, which is validated using route planners and also supported by extensive field research. Testing took place in GIS using network analysis methods. Testing has shown that the inclusion of curvature and inclination will significantly improve the calculation of travel times. key words: network analyst, curvature, gis, algorithm

No description available.

An explicit algebraic Reynolds stress model (EARSM) based ona pressure strain rate model including terms tensoriallynonlinear in the mean velocity gradients is developed in orderto improve predictions for .ows with strong curvature and/orrotation. This work has been carried out in the context of acollaborative international project on high-lift aerodynamics.For 2D mean .ows the nonlinear terms can easily be accountedfor in the model formulation. This is not the case for 3D mean.ows and approximations making the 2D and 3D mean .owformulations consistent are suggested. The proposed EARSM, theparent-EARSM and the corresponding di.erential Reynolds stressmodels (DRSM) are tested for spanwise rotating channel .ow andaxially rotating pipe .ow. The model predictions are comparedto experimental and DNS data. The nonlinear extensions areshown to have a signi.cant e.ect on the .ow predictions,somewhat less pronounced for the DRSM though. The turbulentdi.usion modelling in the EARSM computations is important forthe rotating pipe. It is shown that by using a Daly and Harlowdi.usion model, turbulence levels in good agreement withexperiments and DRSM can be achieved. However, by using asimpler e.ective eddy viscosity based di.usion model theturbulence kinetic energy levels are drastically overpredicted.Finally the proposed EARSM is tested on a standard high-liftcon.guration. The EARSM predictions are compared withexperiments and the predictions made by the standard K - ωtwo-equation model. Descriptors:Turbulence model, nonlinear modelling,streamline curvature, high-lift aerodynamics.

This paper presents results of an experimental investigation to study the structural performance and deformability of a concrete bridge deck reinforced with corrosion resistant reinforcing (CRR) bars, i.e., bars that exhibit improved corrosion resistance when embedded in concrete as compared to traditional black steel. Flexural tests of one-way slabs were conducted to simulate negative transverse flexure over a bridge girder as assumed in the commonly employed strip design method. The bar types studied were Grade 60 (uncoated), epoxy-coated reinforcing (ECR, Grade 60), Enduramet 32 stainless steel, 2304 stainless steel, MMFX2, and glass fiber reinforced polymer (GFRP). The experimental program was designed to evaluate how a one-to-one replacement of the Grade 60 with CRR, a reduction of concrete top clear cover, and a reduction in bar quantities in the bridge deck top mat influences flexural performance at service and ultimate limit states. Moment-curvature predictions from the computer-based sectional analysis program Response 2000 were consistent with the tested results, demonstrating its viability for use with high strength and non-metallic bar without a defined yield plateau.    Deformability of the concrete slab-strip specimens was defined with ultimate-to-service level ratios of midspan deflection and curvature. The MMFX2 and Enduramet 32 one-to-one replacement specimens had deformability consistent with the Grade 60 controls, demonstrating that bridge deck slabs employing high strength reinforcement without a defined yield plateau can still provide sufficient ductility at an ultimate limit state. A reduction in bar quantity and cover provided acceptable levels of ductility for the 2304 specimens and MMFX2 reinforced slabs. / Master of Science

A Doppler LIght Detection And Ranging (LIDAR or lidar) system is studied for the application of measuring train ground speed in a non-contacting manner, as an alternative to the current train speed measurement devices such as wheel-mounted tachometers or encoders. The ability to accurately measure train speed and distance is a critical part of monitoring track geometry conditions. Wheel-mounted tachometer speed measurements often fluctuate due to wheel vibrations, change in wheel diameter, or wheel slip affecting the measurement accuracy.  Frequent calibrations are needed to account for changes in wheel diameter due to wear.  Additionally, the high levels of vibrations at the wheel can cause occasional mechanical failure of the encoder.   This thesis examines LIDAR as a non-contact train speed measurement device as a direct retrofit for wheel-mounted encoders. LIDAR uses Doppler technology to accurately measure train speed. The LIDAR system consists of two laser sensors and can be installed on either the car body or the truck on the underside of the train. The sensors measure the true ground speed of each rail, from which the track curvature can then be assessed based on the difference between the right and left rail speeds. The LIDAR train speed, distance, and curvature results are then evaluated against encoder readings and other conventional train measurement devices. Various tests were performed, including field-testing onboard a track geometry railcar operated by Norfolk Southern for evaluating the efficacy, accuracy, and durability of the LIDAR system; and laboratory tests on a 40-foot rail panel for assessing the ability to obtain measurements at super low speeds. The test results indicate that when compared with other conventional means used by the railroad industry, LIDAR is capable of accurately measuring train speed and distance from speeds as slow as 0.3 mph and up to 100 mph.  Additionally, the curvature  measurements proved to be as accurate as Inertial Measurement Units (IMUs) that are commonly used in track geometry measurement railcars. / Master of Science