Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / A mecÃnica quÃntica desempenha um papel fundamental na descriÃÃo e entendimento dos fenÃmenos naturais. De fato, os fenÃmenos que ocorrem em uma escala muito pequena (atÃmica ou sub-atÃmica) nÃo podem ser corretamente explicados fora do contexto da mecÃnica quÃntica. AlÃm disso, existem muitos fenÃmenos em escala macroscÃpica que revelam o comportamento quÃntico da natureza. Nesse sentido, podemos dizer que a mecÃnica quÃntica à a base de todo nosso atual conhecimento sobre os fenÃmenos naturais. O estado de uma partÃcula em quÃntica à descrito matematicamente pela sua funÃÃo de onda Ψ(r,t) e a evoluÃÃo temporal de Ψ(r,t) à governada pela EquaÃÃo de SchrÃdinger dependente do tempo. Dessa forma, podemos enunciar que o problema fundamental da mecÃnica quÃntica consiste em solucionar a EquaÃÃo de SchrÃdinger numa situaÃÃo arbitrÃria. Neste trabalho, estudamos uma tÃcnica numÃrica de soluÃÃo da EquaÃÃo de SchrÃdinger dependente ou independente do tempo conhecida como Split Operator. Essa tÃcnica utiliza formas aproximadas para a exponencial da soma de operadores que nÃo comutam para implementar o operador evoluÃÃo temporal, permitindo reduzir o processo de soluÃÃo da EquaÃÃo de SchrÃdinger a sucessivos processos de simples multiplicaÃÃo e de soluÃÃo de sistemas de equaÃÃes lineares tridiagonais, que podem ser facilmente realizados por um computador. O formalismo da tÃcnica em coordenadas cartesianas foi estudado em detalhes, onde mostramos como aplicÃ-lo para sistemas com condiÃÃes de com torno periÃdicas ou com condiÃÃes de contorno finitas. Utilizamos essa forma da tÃcnica para estudar o comportamento de um elÃtron confinado numa regiÃo de energia potencial aleatÃria, onde nos deparamos com o fenÃmeno de LocalizaÃÃo de Anderson. AlÃm disso, desenvolvemos a tÃcnica Split Operator em coordenadas generalizadas, aplicando-a para estudar o problema de um elÃtron confinado na superfÃcie de um cilindro. Os resultados obtidos numericamente concordam muito bem com os resultados obtidos analiticamente, mostrando que a tÃcnica Split Operator em coordenadas generalizadas nos leva a resultados confiÃveis. / Quantum mechanics plays a fundamental role in the description and understanding of the natural phenomena. Actually, the phenomena that take place in atomic and subatomic scale can not be well explained without the quantum mechanics approach. Furthermore, there are a lot of phenomena in macroscopic scale that reveals the quantum behavior of nature. In this sense, we can say that quantum mechanics is fundamental for the understanding of all natural phenomena. In Quantum Mechanics the state of a particle is mathematically described by the wave function Ψ(r,t) and its time evolution is governed by time-dependent SchrÃdinger equation. Thus, we can state that the fundamental problem of quantum mechanics is to solve the SchrÃdinger Equation in an arbitrary situation. In this work, we study a numerical technique to solve the time-dependent and time-independent SchrÃdinger Equation known as Split Operator technique. This aproach uses approximations for the exponencial of sum of operators that do not commute in order to implement the time-evolution operator. It makes possible to reduce the solution of the SchrÃdinger equation to a successive processes of multiplication and solution of tridiagonal system of linear equations. It can be easily performed using a computer. The technique was studied in detail using cartesian coordinates, and we also explained how to use the technique with periodic or finite boundary conditions. We make use this technique to study the behavior of an electron subjected to a random potential. In this situation we face the Anderson Localization phenomena. Furthermore, we developed the Split Operator technique using generalized coordinates, and studied the problem of an electron confined to a cylinder surface. It was verified that the numerical results agree with the analytical ones. So we can conclude that the Split Operator technique using generalized coordinates produce reliable results.

This report presents an application developed for evaluating the possible benefits of using audial support in a visualization application. A hypothesis is presented where the idea is that sonification might help users perceive densities in data-sets with large amounts of data points. The application presents a scatterplot and a parallel coordinates plot. To both plots audial support is added where the amplitude of the sound is used for representing the amount of points in different areas of the plots. The method is evaluated through user studies where ability to find maximum points, finding equal densities and appreciation of the sounds is investigated. Quantitative and qualitative results show improvements when finding maximum points in tight clusters both in parallel coordinates and scatter plots. This is a first step when investigating this area of visualization spurring further research.

[pt] O trabalho desenvolveu uma metodologia de solução numérica de escoamentos em geometrias complexas, numa formulação incompressível e bi-dimensional. As equações de conservação são discretizas com o emprego da técnica de volumes finitos em coordenadas não ortogonais. Esta técnica mapeia o espaço real num espaço transformado, no qual as fronteiras do domínio de cálculo coincidem com as fronteiras do domínio físico. Os componentes contravariantes da velocidade foram empregados como variáveis dependentes nas equações de conservação de quantidade de movimento. Estas equações foram obtidas em coordenadas não ortogonais pela manipulação algébrica das equações discretizadas para os componentes cartesianos. Este procedimento, que emprega um sistema de coordenadas auxiliar fixo localmente, evita o surgimento dos diversos termos oriundos da curvutura e da não ortogonalidade da malha, que seriam obtidos caso fosse empregada a análise tensorial para a derivação destas equações. O ocoplamento pressão-velocidade é feito utilizando SIMPLEC. O conjunto de equações algébricas resultante é resolvido por um esquema de solução segregado, no qual é empregado um esquema de solução linha-a-a linha(TDMA), com um processo de correção por blocos para acelerar a convergência. A metodologia desenvolvida foi utilizada para solução de diversos problemas visando analisar o seu desempenho. Foram estudados os seguintes casos-escoamento laminar entre dois cilindros, convecção natural entre dois cilidros excêntricos, escoamento induzido numa cavidade trapezoidal pelo movimento de suas bases, escoamento laminar num canal, escoamento axi-simétrico num duto com estrangulamento.Tendo em vista os bons resultados obtidos para testes, pode-se concluir que as opções realizadas para a confeção do esquema desenvolvido foram corretas, pois geraram um algoritimo efeciente e versátil. / [en] A solution method for bi-dimensional incompressibible fluid flow problems in complex geometrics is developed in this work. The method solves the conservation equations in nonorthogonal coordinate system using the finite volumes technique. The contravariant velocities are kept as dependent variables in the momentum equations. These equations are obtained by an algebric manipulation of the discretization equations written in locally fixed coordinate system. This producedure avoids the treatment of the extra terms if the discretization equations for the curvilinear velocities are obtained in the conventional manner. The coupling of pressure and velocities are performed by the SIMPLEC algorithm. The set of algebric equations are solved using an iterative method in conjunction with coefficient update for linerization. In the computer implementation of the proposed scheme a line-by-line algorithm (TDMA) has been employed with a block corretion procedure to enhance the convergence. The method is tested by solving a variety of problems. The problems include-flow between two concentric rotating cylinders, natural convection in an eccentric annuli, driven flow in a trapezoidal cavity with moving lids, laminar flow in a channel, exismetric flow in duct with reduced cross section and laminar and turbulent flow through a tube with an axisimetric constriction. The objetive of these tests is to establish the validity of the proposed scheme and demonstrate its applicability to a wide variety of problems.

The thesis is engaged with making documentation of the parish building of the Roman Catholic Church in the South – Moravian village Pavlov. The purpose of this work is practical measuring of the object in the terrain using geodetic methods, calculation of the measured values and the following performance of designs for the appropriate reconstruction of historic building. The text section describes the various preparatory, surveying and office works. The main output of this work is design documentation. It includes a thematic map of the building area, drawing floor plans of the first, second floor and roof truss, fasade views and sections of the building.

This work contains a few basic terms of analytical geometry. We mention some of ray-triangle intersection computation algorithms and present some use-case examples. We discuss capabilities of CUDA, optimization techniques of this architecture and implementation with focus on given issues. Algorithms of ray-triangle intersection are tested and results are discussed.

The purpose of these studies was to measure the drag coefficient of a small model submarine to add data to a Reynolds number study. First, a laser Doppler velocimeter (LDV) was used to measure the flow characteristics of the Mississippi State University water tunnel. The velocity and turbulence intensity profiles were measured for a range of freestream velocities of 8.6 m/s to 10.7 m/s. Several wake velocity profiles were taken for a model submarine at downstream distances of x/d = 10 to x/d = 28, with a freestream velocity of 8.6 m/s. A formula for the drag coefficient that uses only mean velocity measurements in the wake was derived for an axisymmetric body using the assumptions of a self-similar wake and a power law behavior of the wake scales. The experimental drag coefficient results are compared to computational fluid dynamic (CFD) solutions.

No description available.

Geometry optimization is a key step in the computational modeling of chemical reactions because one cannot model a chemical reaction without first accurately determining the molecular structure, and electronic energy, of the reactants and products, along with the transition state that connects them. These structures are stationary points— the reactant and product structures are local minima, and the transition state is a saddle point with one negative-curvature direction—on the molecular potential energy surface. Over the years, many methods for locating these stationary points have been developed. In general, the problem of finding reactant and product structures is relatively straightforward, and reliable methods exist. Converging to transition states is much more challenging. Because of the difficulty of transition-state optimization, researchers have designed optimization methods specifically for this problem. These methods try to make good choices for the initial geometry, the system of coordinates used to represent the molecule, the initial Hessian, the Hessian updating method, and the step-size. The transition-state optimization method developed in this thesis required considering all of these methods. Specifically, a new method for finding an initial guess geometry was developed in chapter 2; good choices for a coordinate system for representing the molecule were explored in chapters 2 and 6; different choices for the initial Hessian are considered in chapter 5; chapters 3 and 4 present, and test, a sophisticated new method for updating the Hessian and controlling the step-size during the optimization. iv The methods created in the process of this research led to the development of Saddle, a general-purpose geometry optimizer for transition states and stable structures, with and without constraints on the molecular coordinates. Saddle can be run in conjunction with the Gaussian program or almost any other quantum chemistry program, and it converges significantly more often than the other traditional methods we tested. / Thesis / Doctor of Science (PhD)

This dissertation presents work conducted at the Center for Power Electronics Systems (CPES) at Virginia Polytechnic Institute and State University. Chapter 1 introduces the concept of impedance measurement, and discusses previous work on this topic. This chapter also addresses issues associated with impedance measurement. Chapter 2 introduces the analyzer architecture and the proposed algorithm. The algorithm involves locking on to the voltage vector at the point of common coupling between the analyzer and the system via a PLL to establish a D-Q frame. A series of sweeps are performed, injecting at least two independent angles in the D-Q plane, acquiring D- and Q-axis voltages and currents for each axis of injection at the point of interest. Chapter 3 discusses the analyzer hardware and the criteria for selection. The hardware built ranges from large-scale power level hardware to communication hardware implementing a universal serial bus. An eight-layer PCB was constructed implementing analog signal conditioning and conversion to and from digital signals with high resolution. The PCB interfaces with the existing Universal Controller hardware. Chapter 4 discusses the analyzer software. Software was written in C++, VHDL, and Matlab to implement the measurement process. This chapter also provides a description of the software architecture and individual components. Chapter 5 discusses the application of the analyzer to various examples. A dynamic model of the analyzer is constructed, considering all components of the measurement system. Congruence with predicted results is demonstrated for three-phase balanced linear impedance networks, which can be directly derived based on stationary impedance measurements. Other impedances measured include a voltage source inverter, Vienna rectifier, six-pulse rectifier and an autotransformer-rectifier unit. / Ph. D.

Over the last two decades there has been an increased use of three-phase AC power systems that may not be connected to the main power grid, such as the power systems on more-electric airplane and all-electric ships. Power-electronic converters are usually a significant part of these systems, which provide excellent performance. But their negative incremental impedance nature increases the possibility of system instability. A small-signal analysis that uses interface impedances defined in the synchronous frame is developed by Belkhayat at Purdue in the mid-90s to access the system stability. The system impedance varies with the operating point. Thus the impedance has to be obtained online at the desired operating point, on even in situ. Literature investigates its use with system models, but the lack of equipment to measure such impedance prevents its use in practical systems. Measurement of impedances of each component enables the prediction of system stability before building the real system. The impedance data can also be used to investigate the instability in the system after it is built. The capability of impedance measurement can save the cost and time of system integrators. After reviewing the state-of-the-art development of impedance measurement systems, the dissertation analyzes several systematical error sources in the system, which includes the signal processing and sampling circuits, the phase estimation for coordinate transformation and the injection device connection, and proposes the solution to reduce their influence. Improved algorithm and system architecture are proposed to increase the measurement speed and accuracy. Chirp signal is used as an excitation signal to extract impedances at a group of frequencies at one time. The use of both shunt current injection and series voltage injection improves the SNR of measured signal. Oversampling, cross-correlation and frequency domain averaging technique are used to further reduce the influence of noise. An instrument is built based on the proposed solution. A voltage source inverter is used to generate the perturbation. A PXI computer is used for real-time signal processing. A PC is used for data post processing and measurement process control. Software is developed to fully automate the measurement. The designed unit is tested with various linear and nonlinear load. The test result shows the validity of the proposed solution. / Ph. D.