The limits of current micro-scale technology is approaching rapidly. As the technology is going toward nano-scale devices, physical phenomena involved are fundamentally different from micro-scale ones [1], [2]. Principles in classical physics are no longer powerful enough to explicate the phenomena involved in nano-scale devices. At this stage, quantum mechanic sheds some light on those topics which cannot be described by classical physics. The primary focus of this research work is the development of an analysis technique for understanding the behavior of strongly perturbed harmonic oscillators. Developing ``auxiliary'' boundary value problems we solve monomially perturbed harmonic oscillators. Thereby, we assume monomial terms of arbitrary degree and any finite coefficient desired. The corresponding eigenvalues and eigenvectors can be utilized to solve more complex anharmonic oscillators with non polynomial anharmonicity or numerically defined anharmonicity. A large number of numerical calculations demonstrate the robustness and feasibility of our technique. Particular attention has been paid to the details as have implemented the underlying formula. We have developed iterative expressions for the involved integrals and the introduced ``Universal Functions.'' The latter are applications and adaptations of a concept which was developed in 1990's to accelerate computations in the Boundary Element Method.

Thesis (PhD)--University of South Australia, 1997

by Leung Pui-tang. / Parallel title in Chinese characters. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1988. / Bibliography: leaves 92-94.

Chee Shiu Chung = 阻尼振子的線空間結構與哈密頓理論 / 朱兆中. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 88). / Text in English; abstracts in English and Chinese. / Chee Shiu Chung = Zu ni zhen zi de xian kong jian jie gou yu ha mi dun li lun / Zhu Zhaozhong. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Conservative Systems --- p.4 / Chapter 2.1 --- General Formalism --- p.4 / Chapter 2.2 --- One Simple Harmonic Oscillator --- p.7 / Chapter 2.3 --- Two Coupled Harmonic Oscillators --- p.9 / Chapter 3 --- Dissipative Systems --- p.12 / Chapter 3.1 --- Elimination of Bath --- p.12 / Chapter 3.2 --- One Oscillator with Dissipation --- p.16 / Chapter 3.3 --- Two Oscillators with Dissipation --- p.19 / Chapter 4 --- Eigenvector Expansion and Bilinear Map --- p.21 / Chapter 4.1 --- Formalism --- p.21 / Chapter 4.2 --- Inner Product and Bilinear Map --- p.23 / Chapter 4.3 --- Normalization and Phase --- p.25 / Chapter 4.4 --- Matrix Representation --- p.25 / Chapter 4.5 --- Duality --- p.28 / Chapter 5 --- Applications and Examples of Eigenvector Expansion --- p.31 / Chapter 5.1 --- Single Oscillator --- p.31 / Chapter 5.2 --- Two Oscillators --- p.32 / Chapter 5.3 --- Uneven Damping --- p.33 / Chapter 6 --- Time Evolution --- p.36 / Chapter 6.1 --- Initial-Value Problem --- p.36 / Chapter 6.1.1 --- Green's Function --- p.37 / Chapter 6.2 --- Sum Rules --- p.39 / Chapter 7 --- Time-Independent Perturbation Theory --- p.41 / Chapter 7.1 --- Non-degenerate Perturbation --- p.41 / Chapter 7.2 --- Degenerate Perturbation Theory --- p.46 / Chapter 8 --- Jordan Block --- p.48 / Chapter 8.1 --- Jordan Normal Basis --- p.48 / Chapter 8.1.1 --- Construction of Basis Vectors --- p.48 / Chapter 8.1.2 --- Bilinear Map --- p.50 / Chapter 8.1.3 --- Example of Jordan Normal Basis --- p.55 / Chapter 8.2 --- Time Evolution --- p.56 / Chapter 8.2.1 --- Time Dependence of Basis Vectors --- p.56 / Chapter 8.2.2 --- Initial-Value Problem --- p.58 / Chapter 8.2.3 --- Green's Function --- p.59 / Chapter 8.2.4 --- Sum Rules --- p.60 / Chapter 8.3 --- Jordan Block Perturbation Theory --- p.61 / Chapter 8.3.1 --- Lowest Order Perturbation --- p.61 / Chapter 8.3.2 --- Higher-Order Perturbation --- p.65 / Chapter 8.3.3 --- Non-generic Perturbations --- p.66 / Chapter 8.4 --- Examples of High-Order Criticality --- p.66 / Chapter 8.4.1 --- Fourth-order JB --- p.67 / Chapter 8.4.2 --- Third-order JB --- p.74 / Chapter 8.4.3 --- Two Second-order JB --- p.79 / Chapter 9 --- Conclusion --- p.81 / Chapter A --- Appendix --- p.83 / Chapter A.l --- Fourier Transform and Contour Integration --- p.83 / Chapter B --- Degeneracy and Criticality --- p.86 / Bibliography --- p.88

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

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

A method is developed to predict the critical harmonic excitation of systems undergoing nonlinear oscillations. The method is based on the total energy approach which limits the system responses within a region bounded by a critical total energy in the phase space. Three one-degree-of-freedom nonlinear systems are investigated. Their governing ordinary differential equations are associated with a quadratic nonlinearity and/or a cubic nonlinearity. The study also is extended to a two-degree-of-freedom nonlinear system. The harmonic balance method is the analytical technique used in solving the nonlinear ordinary differential equations. In comparison with the approximate analytical solutions, numerical approaches are implemented. / Master of Science

No description available.

Yung Man Hong = 受歐姆阻尼振子和光學系統內的彼德曼因數及費曼圖展開 / 翁文康. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 95-99). / Text in English; abstracts in English and Chinese. / Yung Man Hong = Shou ou mu zu ni zhen zi he guang xue xi tong nei de Bideman yin shu ji Feiman tu zhan kai / Weng Wenkang. / Acknowledgement --- p.iii / Chapter 1 --- Overview --- p.1 / Chapter 1.1 --- The Langevin Equation --- p.1 / Chapter 1.2 --- Excess Noise in Lasers --- p.4 / Chapter 1.3 --- Non-orthogonality --- p.9 / Chapter 2 --- Bilinear Map and Eigenvector Expansion --- p.12 / Chapter 2.1 --- Introduction --- p.12 / Chapter 2.2 --- Mathematical Formalism --- p.14 / Chapter 2.3 --- Criticality and Divergence --- p.19 / Chapter 2.4 --- Perturbations and Cancellations --- p.25 / Chapter 3 --- Generalized Petermann Factor --- p.34 / Chapter 3.1 --- Introduction --- p.34 / Chapter 3.2 --- Petermann Factor in Optical Systems --- p.36 / Chapter 3.3 --- Generalized Petermann Factor --- p.41 / Chapter 3.4 --- Thermal Correlation Functions --- p.43 / Chapter 3.5 --- Fluctuation-Dissipation Theorem --- p.46 / Chapter 3.6 --- Weak Damping versus Near-Degeneracy --- p.49 / Chapter 4 --- Continuum Generalization --- p.56 / Chapter 4.1 --- Bilinear map --- p.56 / Chapter 4.2 --- Critical Points --- p.58 / Chapter 4.3 --- Semiclassical Laser Theory --- p.63 / Chapter 5 --- Diagrammatic Expansions --- p.71 / Chapter 5.1 --- Introduction --- p.71 / Chapter 5.2 --- Nonlinearly Coupled Oscillators --- p.72 / Chapter 5.3 --- Path Integral Method --- p.76 / Chapter 5.4 --- Feynman Diagram --- p.81 / Chapter 6 --- Conclusion --- p.87 / Chapter A --- Derivation of the Langevin equation --- p.89

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.