Periodic steady-state analysis plays an important role in both theoretical topics and numerical simulations. It has been applied to numerous fields such as electronics, economics, biology, chemistry and so on. Particularly in electronics it is the basis of microwave and radio frequency (RF) circuit simulation. Although the topic has been studied for decades, periodic steady-state analysis still remains a difficulty in certain aspects including the analysis of the exact analytical formulas of limit cycles, as well as fast and accurate approximation of periodic steady states with unknown frequencies. In this thesis, two innovative methods are proposed in order to overcome two difficulties in the field of periodic steady-state analysis accordingly: on the one hand, a limit cycle identification method is developed to provide a robust method for computation of the exact analytical formulas of limit cycles. The method can be further extended to a wide range of nonlinear systems by the technique called state immersion. On the other hand, a method for highly accurate periodic steady-state approximation based on harmonic balancing is proposed. It combines the robustness of Macaulay matrix approach for small size polynomial root(s) finding, and the efficiency of a guided global optimization for higher order approximations. Thus, it is capable of computing approximations of periodic steady states with a high accuracy. Together, the two methods establish a reliable framework where highly accurate periodic steady-state analysis for a wide range of nonlinear systems can be performed. / published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Includes bibliographical references (p. 177-185).

No description available.

Thesis (Ph.D.)--City University of Hong Kong, 2005. / "Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy" Includes bibliographical references (leaves 121-133)

No description available.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 113-114).

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 Western Australia, 2007.

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 11, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Dr. Carmen Chicone Vita. Includes bibliographical references.