Nesta dissertação, definimos a geometria hiperbólica usando o disco de Poincaré (D2) e o semiplano superior (H2) com as respectivas propriedades. Além disso, apresentamos algumas funções e relações importantes da geometria hiperbólica; conceituamos as superfícies de Riemann, analisando suas propriedades e representações; estudamos o espaço de Teichmüller com a devida decomposição em calças. Esses temas são ferramentas necessárias para atingir o objetivo da dissertação: definir as coordenadas de Fenchel Nielsen como um sistema de coordenadas locais do espaço de Teichmüller Tg. / In this dissertation, we defined the hyperbolic geometry using the Poincares disk (D2) and upper half-plane (H2) with its properties. Besides, we presented some functions and important relations of the hyperbolic geometry; we conceptualize the Riemann surfaces, analyzing its properties and representations; we studied the Teichmüller Space with proper decomposition pants. These themes are essential tools to reach the goal of the work: The definition of the Fenchel Nielsen coordenates as local coordinate system of the Teichmüller space Tg.

O desempenho metrológico de uma Máquina de Medir a Três Coordenadas (MM3C) está relacionado com a sua capacidade de medir peças com a precisão requerida ou desejada. No entanto, como todo instrumento de medição, essas máquinas possuem erros que afetam as medições gerando o que se convencionou chamar de erros volumétricos. Tais erros podem ser obtidos através de modelos matemáticos que descrevem como os erros individuais de todos os componentes da MM3C se combinam por todo o volume de trabalho. Atualmente, no modelamento dos erros, adota-se a independência entre os erros individuais, entretanto, se analisada a geometria estrutural da máquina, verifica-se que existe dependência entre os erros de retilineidade e os erros angulares. O objetivo deste trabalho é expressar o erro angular em função do erro de retilineidade, possibilitando assim minimizar o número de calibrações necessárias e, consequentemente, o tempo de máquina parada requerido para o levantamento do seu comportamento metrológico. Para que se pudesse atingir o objetivo proposto, foram levantados os erros de retilineidade e os angulares de uma Máquina de Medir a Três Coordenadas da marca Brown & Sharp do tipo Ponte Móvel. Com esses dados e o conhecimento da geometria da máquina, os erros angulares foram equacionados, calculados e comparados com os obtidos experimentalmente. / The metrological performance of a Three Coordinate Measuring Machines (CMM) is related to the capacity of measuring workpieces with a required precision. As every measurement instrument, these machines undergo the effects of internal and external factors that affect the measurement, generating what has been denominated as volumetric errors. Such errors can be obtained through a mathematical model that simulates how the individual errors of the CMM are combined and propagated to any point within the machine working volume. Usually, the independence among the individual errors is adopted when the machine error model is built. However, if the machine geometry is analyzed, the dependence between the straightness error and the angular error can be noted. The objective of this work is to express the angular error as a function of the straightness error. The formulation proposed in this work to express this correlation minimizes the number of calibrations necessary to evaluate the machine behavior. A Brown & Sharp Moving Bridge Coordinate Measuring Machine was used for the experimental evaluation. With this data set and knowing the machine geometry, a mathematical expression relating straightness and angular error was obtained. The calculated error values were then compared with the errors experimentally measured.

Com o crescimento industrial e tecnológico nas últimas décadas, as indústrias passaram a oferecer produtos customizados, ou seja, desenvolvidos com tolerâncias geométricas cada vez mais apertadas e geometrias cada vez mais complexas. Com isso, as máquinas de medir por coordenadas (MMC) vêm tornando-se instrumentos essenciais no ambiente industrial. A MMC é extremamente versátil o que possibilita a medição das mais diversas características geométricas e dimensionais. Padrões para calibração de MMC foram sugeridos e colocados em uso através dos anos, com a finalidade de utilizá-los em testes de aceitação e verificação periódica dos erros e da incerteza de medição de MMC. Novos artefatos para a calibração indireta de MMC visam melhorar os procedimentos de calibração para uso em sistemas de compensação de erros. Diante do exposto acima, este trabalho tem como objetivo desenvolver um procedimento de calibração indireta de MMC com o esquadro de esferas aliado a um modelo reduzido de sintetização de erros (MRSE) para uso em um Sistema de Compensação de Erros. O procedimento possibilita maior rapidez na obtenção dos valores e comportamentos dos erros quando comparado com outros procedimentos de calibração indireta. O procedimento proposto tem como vantagem o uso de um esquadro de esferas para medir todos os termos das equações das componentes do erro volumétrico, nas direções X, Y e Z de uma MMC. / With the technological and industrial growth in recent decades, the industries began to offer customized products, that is, products that fit individual specifications and often present increasingly tight tolerances and increasingly complex geometries. Therefore, the coordinate measuring machines (CMMs) have become an essential tool in the industrial environment. The CMM is very versatile since it allows the measurement of several geometric and dimensional features at once. Different standards for the calibration of CMMs were suggested and put into use through the years. This type of standard is traditionally used in acceptance tests and periodic verifications of the CMMs and in the evaluation of measurement uncertainties. New artifacts for indirect calibration of CMMs are proposed to allow the development of better procedures of error evaluation and compensation. Considering the above, this work aims to develop a procedure for indirect calibration of CMMs using a mechanical ball square combined with a reduced model of synthesis of Errors (MRSE). As a result, a compensation system for CMM errors is obtained. The procedure allows a faster evaluation of the values and behaviors of errors when compared with other indirect calibration procedures. Additionally, the proposed procedure has the advantage of using a single artifact to measure all the components of the volumetric error in the directions X, Y and Z of a CMM.

Com o crescimento industrial e tecnológico nas últimas décadas, as indústrias passaram a oferecer produtos customizados, ou seja, desenvolvidos com tolerâncias geométricas cada vez mais apertadas e geometrias cada vez mais complexas. Com isso, as máquinas de medir por coordenadas (MMC) vêm tornando-se instrumentos essenciais no ambiente industrial. A MMC é extremamente versátil o que possibilita a medição das mais diversas características geométricas e dimensionais. Padrões para calibração de MMC foram sugeridos e colocados em uso através dos anos, com a finalidade de utilizá-los em testes de aceitação e verificação periódica dos erros e da incerteza de medição de MMC. Novos artefatos para a calibração indireta de MMC visam melhorar os procedimentos de calibração para uso em sistemas de compensação de erros. Diante do exposto acima, este trabalho tem como objetivo desenvolver um procedimento de calibração indireta de MMC com o esquadro de esferas aliado a um modelo reduzido de sintetização de erros (MRSE) para uso em um Sistema de Compensação de Erros. O procedimento possibilita maior rapidez na obtenção dos valores e comportamentos dos erros quando comparado com outros procedimentos de calibração indireta. O procedimento proposto tem como vantagem o uso de um esquadro de esferas para medir todos os termos das equações das componentes do erro volumétrico, nas direções X, Y e Z de uma MMC. / With the technological and industrial growth in recent decades, the industries began to offer customized products, that is, products that fit individual specifications and often present increasingly tight tolerances and increasingly complex geometries. Therefore, the coordinate measuring machines (CMMs) have become an essential tool in the industrial environment. The CMM is very versatile since it allows the measurement of several geometric and dimensional features at once. Different standards for the calibration of CMMs were suggested and put into use through the years. This type of standard is traditionally used in acceptance tests and periodic verifications of the CMMs and in the evaluation of measurement uncertainties. New artifacts for indirect calibration of CMMs are proposed to allow the development of better procedures of error evaluation and compensation. Considering the above, this work aims to develop a procedure for indirect calibration of CMMs using a mechanical ball square combined with a reduced model of synthesis of Errors (MRSE). As a result, a compensation system for CMM errors is obtained. The procedure allows a faster evaluation of the values and behaviors of errors when compared with other indirect calibration procedures. Additionally, the proposed procedure has the advantage of using a single artifact to measure all the components of the volumetric error in the directions X, Y and Z of a CMM.

O método da Coordenada Geradora é uma poderosa ferramenta para gerar funções de base. Sua última versão, chamada de método da Coordenada Geradora polinomial, permite a geração de funções de base mais eficientes e precisas a um baixo custo computacional. Nesta tese, além da geração de funções de base para os átomos do primeiro período da Tabela Periódica, uma estratégia de selecionar expoentes da própria função de base para posteriormente refiná-los, com o intuito de gerar funções de polarização e difusas, é apresentada e testada em cálculos de propriedades eletrônicas de átomos e moléculas. / Ab initio electronic structure calculations for atoms and especially for molecules are mostly carried out within the finite basis set expansion method in the Hartree-Fock theory by Roothaan. The search for ever more efficient basis sets has been a constant quest and here we show a new alternative to develop efficient Gaussian-Type Functions (GTF) basis sets for atomic and molecular calculations by employing the Polynomial Generator Coordinate Hartree-Fock method.

Conjuntos de funções de base Gaussianos são desenvolvidos para os átomos da primeira fila dos metais de transição Sc - Zn. Esses conjuntos de base foram construídos por meio do método da Coordenada Geradora Hartree-Fock (GCHF - Generator Coordinate Hartre-Fock) baseado em uma expansão polinomial de grau 3 para discretizar as equações Griffin-Wheeler-Hartree-Fock. Neste procedimento, a maneira na qual as equações são discretizadas está baseada em uma malha de pontos flexíveis não igualmente espaçada para cada uma das simetrias orbitais requeridas para descrever os átomos estudados, a diferença do método GCHF original é que a malha é igualmente espaçada para todas as simetrias. Inicialmente, foi gerado um conjunto de base balanceado consistindo de 23s17p13d funções gaussianas primitivas. A partir deste, um conjunto padrão de qualidade 7Z na valência foi construído e, posteriormente, enriquecido com grupos de funções de polarização e gerando assim:pGCHF - 7Z - 2f 1g, pGCHF - 7Z - 3f 2g e pGCHF - 7Z - 3f 2g1h. Energias atômicas Hartree-Fock para os dois estados eletrônicos de menor energia, para os átomos do Sc - Zn, foram calculadas com nossos conjuntos e comparadas com valores da energia numérica. Os resultados apresentaram um erro máximo de 1.02 mHartree, demostrando a capacidade desta expansão polinomial no desenvolvimento de conjuntos de base acurados para átomos dos metais de transição (MT) 3d. Cálculos em nível da Teoria do Funcional da Densidade (DFT - Density Functional Theory), utilizando nove diferentes funcionais, foram realizados com nossos conjuntos de base. A energia eletrônica total e propriedades incluíndo: geometrias otimizadas, cumprimentos de ligação e, frequências vibracionais, foram examinadas para um conjunto de sistemas moleculares (hidretos, dicloretos, dímeros, trímeros e óxidos de metais de transição). Os resultados são comparados com valores teóricos obtidos com conjuntos de base cc-pVnZ (n= Q ou 5) e com valores experimentais, quando disponiveís na literatura. Os resultados mostram que os valores de energia total cc-pV5Z, podem ser atingidos com nossos conjuntos de base com um menor número de funções de polarização. Outros cálculos moleculares dão resultados aproximados com valores experimentais e valores de referência DFT/cc-pV5Z. O ponto mais importante para ser mencionado é que os conjuntos de base da coordenada geradora requerem somente uma pequena fração de tempo computacional para alcançar a convergência, quando comparados com cálculos DFT/cc-pVQZ e DFT/cc-pV5Z. / Gaussian basis set functions have been constructed for the atoms of the first row of the transition metals from Sc to Zn. These basis sets were built by means of the Generator Coordinate Hartree-Fock (GCHF) method based on a polynomial expansion of degree 3 for the discretization of the Grifin-Wheler-Hartree-Fock equations. In this procedure, the equations were discretized through a mesh which is not equally spaced for each one of the orbital symmetries required to describe the atoms studied in this work, differently from the original method, in which the mesh is equally spaced for all symmetries. At first, it was generated a minimal basis set consisting of 23s17p13d primitive functions. Starting with this pattern set was construted a set of 7Z quality in the valence and then, this one was enriched with polarization functions classified as: 2f1g, 3f2g y 3f2g1h, which originated 3 sets of basis functions namely: pGCHF-7Z-2f1g, pGCHF-7Z-3f2g y pGCHF-7Z-3f2g1h. Hartree-Fock energies for the atoms Sc-Zn were calculated with our basis sets, for the two electronic states with the lowest energy and compared with values of numerical energy. The maximum error presented for the results was 1.02mH, showing the ability of this polynomial expansion to create accurate basis sets for atoms of third-rows transition metals. Density Functional Theory (DFT) calculations using a set of nine functionals were realized with our basis sets. The total electronic energy and properties such as: optimized geometries, bond distances and vibrational frequencies were calculated for a set of molecules (hydrides, dichlorides, dimers, trimmers and oxides). The obtained values were compared with theoretical values obtained with calculations using the basis set cc-pVnZ and with some experimental values found in the literature. The outcomes showed that reference values of the total electronic can be reproduced by ours basis sets, although ours have a less degree of polarization. Other molecular calculations yield results very close to experimental values and reference theorical values calculated with DFT/cc-pV5Z. The most important point to be mentioned here is that our generator coordinate basis sets require only a tiny fraction of the computational time when compared to DFT/cc-pV5Z calculations.

Earth-abundant first-row transition metals have seen a renaissance in chemistry in recent years due to their relatively low toxicity and cost in comparison to precious metals. Furthermore open-shell transition metal complexes exhibit useful one-electron redox processes which contrasts to their heavier d block anologues. This thesis aims to synthesize and analyse the structure and reactivity of low-coordiante first-row transition metal complexes of from groups 7-9 with an aim to utilize these species in catalysis. The divalent compound [Co{N(SiMe3)2}2] reacts with the primary phosphines PhPH2 in the presence of an NHC ligand (IMe4) to yield the phosphinidene bridged dimer [(IMe4)2Co(µ-PMes)]2. The complex has interesting magnetic properties due to strong antiferromagnetic coupling between the two cobalt(II) centres. Increasing the steric bulk of the NHC yielded carbene-phosphinidene adducts (NHC·PAr). This transformation was shown to be catalytic. The structure and reactivity of complexes of the type [(NHC)xMn{(N(SiMe3)2}2] were investigated. The complexes exhibit similar structural properties to their iron and cobalt analogues; however their reactivity has been shown to differ. The addition of primary phosphines to complexes of the type [(NHC)xMn{N(SiMe3)2}2] yielded a range of manganese phosphide complexes. [Mn{N(SiMe3)2}2] also reacts with imidazolium salts at elevated temperatures to yield heteroleptic manganese NHC complexes. The reaction of [Mn{N(SiMe3)2}2] with IPr·HCl afforded the abnormal carbene complex [(aIPr)Mn{N(SiMe3)2}µ-Cl]2. A new monoanionic bidentate ligand is reported which has shown to be a useful ligand system to stabilize three-coordiante iron(II) complex. The reaction of [(L)Fe(Br)] with mesitylmagnesium Grignard or n-butyllithium yield the iron hydrocarbyls [(L)Fe(Mes)] and [(L)Fe(nBu)] with the latter being stable to β-hydrogen elimination. Finally [(L)Fe(nBu)] has been utilized as a pre-catalyst in the hydrophosphination of internal alkynes, showing selectivity for the E-isomeric vinylphosphine.

The objective of this study is to develop a high-fidelity physics-based flexible tire model that can be fully integrated into multibody dynamics computer algorithms for use in on-road and off-road vehicle dynamics simulation without ad-hoc co-simulation techniques. Despite the fact detailed finite element tire models using explicit finite element software have been widely utilized for structural design of tires by tire manufactures, it is recognized in the tire industry that existing state-of-the-art explicit finite element tire models are not capable of predicting the transient tire force characteristics accurately under severe vehicle maneuvering conditions due to the numerical instability that is essentially inevitable for explicit finite element procedures for severe loading scenarios and the lack of transient (dynamic) tire friction model suited for FE tire models. Furthermore, to integrate the deformable tire models into multibody full vehicle simulation, co-simulation technique could be an option for commercial software. However, there exist various challenges in co-simulation for the transient vehicle maneuvering simulation in terms of numerical stability and computational efficiency. The transient tire dynamics involves rapid changes in contact forces due to the abrupt braking and steering input, thus use of co-simulation requires very small step size to ensure the numerical stability and energy balance between two separate simulation using different solvers. In order to address these essential and challenging issues on the high-fidelity flexible tire model suited for multibody vehicle dynamics simulation, a physics-based tire model using the flexible multibody dynamics approach is proposed in this study. To this end, a continuum mechanics based shear deformable laminated composite shell element is developed based on the finite element absolute nodal coordinate formulation for modeling the complex fiber reinforced rubber tire structure. The assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches are introduced for alleviating element lockings exhibited in the element. Use of the concept of the absolute nodal coordinate formulation leads to various advantages for tire dynamics simulation in that (1) constant mass matrix can be obtained for fully nonlinear dynamics simulation; (2) exact modeling of rigid body motion is ensured when strains are zero; and (3) non-incremental solution procedure utilized in the general multibody dynamics computer algorithm can be directly applied without specialized updating schemes for finite rotations. Using the proposed shear deformable laminated composite shell element, a physics-based flexible tire model is developed. To account for the transient tire friction characteristics including the friction-induced hysteresis that appears in severe maneuvering conditions, the distributed parameter LuGre tire friction model is integrated into the flexible tire model. To this end, the contact patch predicted by the structural tire model is discretized into small strips across the tire width, and then each strip is further discretized into small elements to convert the partial differential equations of the LuGre tire friction model to the set of first-order ordinary differential equations. By doing so, the structural deformation of the flexible tire model and the LuGre tire friction force model are dynamically coupled in the final form of the equations, and these equations are integrated simultaneously forward in time at every time step. Furthermore, a systematic and automated procedure for parameter identification of LuGre tire friction model is developed. Since several fitting parameters are introduced to account for the nonlinear friction characteristics, the correlation of the model parameters with physical quantities are not clear, making the parameter identification of the LuGre tire friction model difficult. In the procedure developed in this study, friction parameters in terms of slip-dependent friction characteristics and adhesion parameter are estimated separately, and then all the parameters are identified using the nonlinear least squares fitting. Furthermore, the modified friction characteristic curve function is proposed for wet road conditions, in which the linear decay in friction is exhibited in the large slip velocity range. It is shown that use of the proposed numerical procedure leads to an accurate prediction of the LuGre model parameters for measured tire force characteristics under various loading and speed conditions. Furthermore, the fundamental tire properties including the load-deflection curve, the contact patch lengths, contact pressure distributions, and natural frequencies are validated against the test data. Several numerical examples for hard braking and cornering simulation are presented to demonstrate capabilities of the physics-based flexible tire model developed in this study. Finally, the physics-based flexible tire model is further extended for application to off-road mobility simulation. To this end, a locking-free 9-node brick element with the curvature coordinates at the center node is developed and justified for use in modeling a continuum soil with the capped Drucker-Prager failure criterion. Multiplicative finite strain plasticity theory is utilized to consider the large soil deformation exhibited in the tire/soil interaction simulation. In order to identify soil parameters including cohesion and friction angle, the triaxial soil test is conducted. Using the soil parameters identified including the plastic hardening parameters by the compression soil test, the continuum soil model developed is validated against the test data. Use of the high-fidelity physics-based tire/soil simulation model in off-road mobility simulation, however, leads to a very large computational model to consider a wide area of terrains. Thus, the computational cost dramatically increases as the size of the soil model increases. To address this issue, the component soil model is proposed such that soil elements far behind the tire can be removed from the equations of motion sequentially, and then new soil elements are added to the portion that the tire is heading to. That is, the soil behavior only in the vicinity of the rolling tire is solved in order to reduce the overall model dimensionality associated with the finite element soil model. It is shown that use of the component soil model leads to a significant reduction in computational time while ensuring the accuracy, making the use of the physics-based deformable tire/soil simulation capability feasible in off-road mobility simulation.

Animal home range estimations are important for conservation planning and protecting the habitat of threatened species. The accuracy of home range calculations is influenced by the map projection chosen in a geographic information system (GIS) for data analysis. Different methods of projection will distort spatial data in different ways, so it is important to choose a projection that meets the needs of the research. The large number of projections in use today and the lack of distortion comparison between the various types make selecting the most appropriate projection a difficult decision. The purpose of this study is to quantify and compare the amount of area distortion in animal home range estimations when projected into a number of projected coordinate systems in order to understand how the chosen projection influences analysis. The objectives of this research are accomplished by analyzing the tracking data of four species from different regions in North and South America. The home range of each individual from the four species datasets is calculated using the Characteristic Hull Polygon method for home range estimation and then projected into eight projected coordinate systems of various scales and projection type, including equal area, conformal, equidistant, and compromise projections. A continental Albers Equal Area projection is then used as a baseline area for the calculation of a distortion measurement ratio and magnitude of distortion statistic. The distortion measurement ratio and magnitude calculations provide a measurement of the quantity of area distortion caused by a projection. Results show the amount distortion associated with each type of projection method and how the amount of distortion changes for a projection based on geographic location. These findings show how the choice of map projection can have a large influence on data analysis and illustrate the importance of using an appropriate PCS for the needs of a given study. Distorted perceptions can influence decision-making, so it is important to recognize how a map projection can influence the analysis and interpretation of spatial data.

<p>Crystallographic and spectroscopic studies have been performed of structures, coordination and chemical bonding for series of trivalent metal ions solvated by two oxygen-coordinating solvents, water and dimethyl sulfoxide (DMSO). The hydrated scandium(III) and lanthanoid(III) ions, La to Lu, are surrounded by tricapped trigonal prisms of aqua ligands in the isomorphous series of trifluoromethanesulfonates, [M(H₂O)_n](CF₃SO₃)₃. For the smallest ions, M = Er, Tm, Yb, Lu, Sc, the hydration numbers decrease, <i>n</i> = 8.96(5), 8.8(1), 8.7(1), 8.5(1), 8.0(1), respectively, with decreasing size of the ion. The crystal structures at ambient temperature indicate randomly distributed vacancies of the capping oxygen atoms, and ²H solid-state NMR of the diamagnetic [M(H₂O)_n](CF₃SO₃)₃, M = Sc, Lu, Y and La compounds revealed increasing mobility of the water ligands in the coordination sphere with increasing temperature, also for the fully nonahydrated La^III and Y^III ions. The stretching force constants of the Ln-O bonds, evaluated from vibrational spectroscopy, increased from 0.81 to 1.16 N cm^-1 for the Ln-6O trigonal prism in a smooth correlation with the bond distances from La to Lu. For the capping Ln-3O bonds the increase from 0.49 to 0.65 N cm^-1 reflects the increased ligand-ligand repulsion with decreasing ion size. This is also the reason for the water deficiency of the Er, Tm, Yb, Lu and Sc salts, and for [Sc(H₂O)_8.0](CF₃SO₃)₃ the repulsion induced a phase transition at about 185 K that, by low temperature crystallography, was found to distort the coordination of water molecules toward a monocapped trigonal prism around the scandium(III) ion.</p><p>All crystal structures of the octakis(dimethyl sulfoxide)lanthanoid(III) iodides comprise discrete [Ln(dmso)₈]³⁺ complexes surrounded by iodide ions. The lanthanum(III) and praseodymium(III) compounds crystallize in the orthorhombic space group <i>Pbca</i> with more efficient packing than for the heavier and smaller ions in the lanthanoid series, which crystallize in the monoclinic space group <i>P2</i>₁/<i>n</i>. The group 13 metal ions, aluminium(III), gallium(III), indium(III), thallium(III), and also scandium(III) of group 3, form crystalline hexakis(dimethyl sulfoxide) solvates in the space group <i>R</i> 3, with octahedral MO₆ coordination entities, which are increasingly compressed along one threefold axis for increasing ionic size. EXAFS measurements on the solvated ions display similar M-O bond distances in dimethyl sulfoxide solution as in the solid solvates. For all the solid dimethyl sulfoxide solvates the strength and nature of the metal-oxygen bond has been evaluated by normal coordinate analysis of vibrational spectra, and correlated with the S-O stretching vibrational mode.</p><p>Distortions from regular octahedral six coordination are discussed for the hydrated isoelectronic soft mercury(II) and thallium(III) ions in the solid bisaquamercury(II) and trisaquatallium(III) trifluoromethanesulfonates, in terms of pseudo Jahn-Teller effects (PJTE). Mercury(II), generally more strongly influenced by PJTE distortions, displays a 2 + 4 Hg-O coordination forming chains that are held together in sheets by hydrogen bonds and in layers by van der Waals interactions, which explain the fragile structure of the crystals.</p>