First published in the Bulletin of the American Mathematical Society in Vol.74, 1968, published by the American Mathematical Society

Orientador: Michael John Brennan / Banca: Fabricio César Lobato de Almeida / Banca: Gianluca Gatti / Título em portugues: Efeitos da vibração em linha férrea induzida pela passagem de trens em dispositivo de captação de energia / Resumo: Com avanços em tecnologia, e com a necessidade em buscar soluções para reduzir efeitos do aquecimento global, tornou captação de energia uma área de pesquisa popular. O particular interesse deste projeto é a extração de energia a partir de vibrações em ambientes no qual possui aplicação em ambientes hostis ou em áreas remotas. Este tipo de dispositivo possui a capacidade de alimentar sistemas microeletrônicos que utilizam pouca energia, por exemplo sensores de monitoramento da saúde estrutural, sensores sem fio, radio comunicação, etc. Neste trabalho, uma investigação é conduzida para determinar a quantidade de energia que pode ser extraída a partir de vibrações devido a passagem do trem. Um estudo é conduzido para investigar o design dos parâmetros ótimos para um extrator de energia submetido a vibrações induzidas por trens passando com diferentes velocidades. Dados de vibração de dois locais no Reino Unido é utilizado para este propósito. Uma expressão analítica aproximada para energia extraída por um extrator linear submetido a excitação periódica de tempo limitado é avaliado utilizando os componentes harmônicos das vibrações em um dormente. Os resultados são comparados com os obtidos através da análise numérica. Também, o comportamento de um extrator de energia linear submetido a vibrações induzidas por diversos trens passantes, é avaliado para trens com uma faixa de velocidade observado nos dados mensurados em Steventon / Abstract: With advances in technology, and with the need to seek for solutions to reduce the effects of global warming, makes energy harvesting a popular research topic. The particular interest in this project is the harvesting of energy from ambient vibrations, which has applications in hostile environments or in remote areas. This type of device has the capacity feed microelectromechanical systems that use a low power, for example sensors for structural health monitoring, wireless sensors, radio communications, etc. In this work, an investigation is conducted to determine how much energy can be scavenged from vibrations due the passage of a train. A study is conducted to investigate the optimum parameters design of an energy harvester subject to vibrations induced by trains passing at different speeds. Vibration Data from two sites in the United Kingdom is used for this purpose. An approximate analytical expression for energy harvested from a linear harvester subject to a time-limited periodic excitation is evaluated using the harmonic components of the sleeper vibrations. The results are compared with those obtained through numerical analysis. Also, the behaviour of the linear energy harvester subject to vibrations induced by several passing trains is evaluated for ranges of speeds observed in measurement data sets at Steventon site / Mestre

With advances in technology and the increasing use of power electronic components in the design of household and industrial equipment, harmonic distortion has become one of the major power quality problems in power systems. Identifying the harmonic sources and quantifying the contributions of these harmonic sources provides utility companies with the information they require to effectively mitigate harmonics in the system. This thesis proposes the use of observers for harmonic estimation and harmonic source identification. An iterative observer algorithm is designed for performing harmonic estimation in measured voltage or current signals taken from a power distribution system. The algorithm is based on previous observer designs for estimating the power system states at the fundamental frequency. Harmonic estimation is only carried out when the total harmonic distortion (THD) exceeds a specified threshold. In addition, estimation can be performed on multiple measurements simultaneously. Simulations are carried out on an IEEE distribution test feeder. A number of scenarios such as changes in harmonic injections with time, variations in fundamental frequency and measurement noise are simulated to verify the validity and robustness of the proposed iterative observer algorithm. Furthermore, an observer-based algorithm is proposed for identifying the harmonic sources in power distribution systems. The observer is developed to estimate the system states for a combination of suspicious nodes and the estimation error is analysed to verify the existence of harmonic sources in the specified node combinations. This method is applied to the identification of both single and multiple harmonic sources. The response of the observer-based algorithm to time varying load parameters and variations in harmonic injections with time is investigated and the results show that the proposed harmonic source identification algorithm is able to adapt to these changes. In addition, the presence of time delay in power distribution system measurements is taken into consideration when identifying harmonic sources. An observer is designed to estimate the system states for the case of a single time delay as well as multiple delays in the measurements. This observer is then incorporated into the observer-based harmonic source identification algorithm to identify harmonic sources in the presence of delayed measurements. Simulation results show that irrespective of the time delay in the measurements, the algorithm accurately identifies the harmonic sources in the power distribution system.

The research presented in this dissertation primarily focuses on providing analytical frequency-domain equations that use the system and controller parameters to accurately characterize the power conversion harmonics resulting from the deployment of hysteresis current-controlled inverters within the ac network. In addition, the ac and dc harmonic interactions under both ideal system conditions (constant dc excitation and pure sinusoidal ac voltages) and non-ideal system conditions (harmonic terms are added to the dc and ac sources) are derived for the fixed- and variable-band hysteresis current control. The spectral characteristics, such as frequency orders, spectral magnitude and bandwidth, are given in terms of line and control parameters, a development not only useful in analyzing the harmonic output sensitivity to line and controller parameter variations, but also in filter and system design. Various simulation studies compared results obtained from the developed models to those obtained from the Fourier analysis of MATLAB/Simulink output with very good agreement. The developed models proved their reliability and improved numerical efficiency in harmonic studies compared to those performed using time-domain simulations.

We extend the theory of singular integral operators and multiplier theorems to the setting of anisotropic Hardy spaces. We first develop the theory of singular integral operators of convolution type in the anisotropic setting and provide a molecular decomposition on Hardy spaces that will help facilitate the study of these operators. We extend two multiplier theorems, the first by Taibleson and Weiss and the second by Baernstein and Sawyer, to the anisotropic setting. Lastly, we characterize the Fourier transforms of Hardy spaces and show that all multipliers are necessarily continuous.

Made available in DSpace on 2015-10-06T13:02:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-07-24. Added 1 bitstream(s) on 2015-10-06T13:19:18Z : No. of bitstreams: 1 000849610.pdf: 1060639 bytes, checksum: f7f529a2c97b379eced359bb7ae14e34 (MD5) / Com avanços em tecnologia, e com a necessidade em buscar soluções para reduzir efeitos do aquecimento global, tornou captação de energia uma área de pesquisa popular. O particular interesse deste projeto é a extração de energia a partir de vibrações em ambientes no qual possui aplicação em ambientes hostis ou em áreas remotas. Este tipo de dispositivo possui a capacidade de alimentar sistemas microeletrônicos que utilizam pouca energia, por exemplo sensores de monitoramento da saúde estrutural, sensores sem fio, radio comunicação, etc. Neste trabalho, uma investigação é conduzida para determinar a quantidade de energia que pode ser extraída a partir de vibrações devido a passagem do trem. Um estudo é conduzido para investigar o design dos parâmetros ótimos para um extrator de energia submetido a vibrações induzidas por trens passando com diferentes velocidades. Dados de vibração de dois locais no Reino Unido é utilizado para este propósito. Uma expressão analítica aproximada para energia extraída por um extrator linear submetido a excitação periódica de tempo limitado é avaliado utilizando os componentes harmônicos das vibrações em um dormente. Os resultados são comparados com os obtidos através da análise numérica. Também, o comportamento de um extrator de energia linear submetido a vibrações induzidas por diversos trens passantes, é avaliado para trens com uma faixa de velocidade observado nos dados mensurados em Steventon / With advances in technology, and with the need to seek for solutions to reduce the effects of global warming, makes energy harvesting a popular research topic. The particular interest in this project is the harvesting of energy from ambient vibrations, which has applications in hostile environments or in remote areas. This type of device has the capacity feed microelectromechanical systems that use a low power, for example sensors for structural health monitoring, wireless sensors, radio communications, etc. In this work, an investigation is conducted to determine how much energy can be scavenged from vibrations due the passage of a train. A study is conducted to investigate the optimum parameters design of an energy harvester subject to vibrations induced by trains passing at different speeds. Vibration Data from two sites in the United Kingdom is used for this purpose. An approximate analytical expression for energy harvested from a linear harvester subject to a time-limited periodic excitation is evaluated using the harmonic components of the sleeper vibrations. The results are compared with those obtained through numerical analysis. Also, the behaviour of the linear energy harvester subject to vibrations induced by several passing trains is evaluated for ranges of speeds observed in measurement data sets at Steventon site

When intense laser pulses interact with an atomic or solid target, high order harmonics of the fundamental laser frequency are generated. In the case of atoms, this highly nonlinear optical process is initiated by ionization and terminated by the energetic recollision and recombination of the ionized electron with its correlated ion. In this thesis I demonstrate, both theoretically and experimentally, that high harmonics from bulk crystals can originate from the recollision of electrons with their associated holes, similarly to the atomic case, but where ionization is replaced by excitation of electron-hole pairs that accelerate within the material. This model is first derived from a quantum-mechanical theory of the solid-laser interaction, and then confirmed experimentally in ZnO and Si crystals. Despite the link I establish between high harmonic generation in solids and gases, there are notable dissimilarities. These include: a generalized motion of electrons and holes in their respective bands and its consequences, a more prominent role of dephasing and enhanced sensitivity to perturbing fields. These aspects are investigated throughout this thesis. Finally, I develop a method that exploits the recollision mechanism to reconstruct the momentum-dependent band structure of solids.

Orbital angular momentum (OAM) is a property of light that is widely used for applications in bioimaging, optical communication and optical manipulation, but is mainly limited to the infrared and visible spectra. Developing a table-top source of Extreme Ultraviolet (XUV) light containing an arbitrary amount of OAM is yet to be achieved. We accomplish this by exploiting high-harmonic generation (HHG), a process whereby an infrared pump beam produces high order harmonics. We experimentally demonstrate the conservation of OAM in HHG by measuring harmonics of order n containing n times the OAM of the pump (n = 11, 13, 15 in our experiment). These results agree with our theoretical model. We also show theoretically how to manipulate the HHG process to impart an arbitrary amount of OAM to the di fferent harmonics. We hence show the way to a table-top and flexible source of XUV light containing orbital angular momentum.

Many results in real and complex analysis are the consequence of mean value properties and theorems. This is the case for harmonic and holomorphic functions as well. The mean value property builds the foundation for several properties of each set of functions. Using this property one can derive more properties like the maximum principle for harmonic functions and the maximum modulus principle for holomorphic functions. These results are then used to show other properties. The goal is to compare the theorems and proofs for harmonic and holomorphic functions and to understand why the results seem to be similar.

In this thesis we study complex harmonic functions of the form f where f is the sum of a nonconstant analytic and a nonconstant anti-analytic function of one variable. The Fundamental Theorem of Algebra does not apply to such functions, so we ask how many zeros a complex harmonic function can have and where those zeros are located. This thesis focuses on the complex harmonic family of polynomials p_c where p_c is the sum of z+(c/2)z^2 and the conjugate of (c/(n-1))z^(n-1)+(1/n)z^n. We first establish properties of the critical curve, which separates orientation preserving and reversing regions. These properties are then used to show the sum of the orders of the zeros of p_c is -n. In turn, we use this to show p_c has n+2 zeros when 04 and n+4 zeros when c>4, n>5. The total number of zeros of p_c changes when zeros interact with the critical curve, so we investigate where zeros occur on the critical curve to understand how the number of zeros of p_c changes for c between 1 and 4.