published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

The goal of this research project is to determine the fractal nature, if any, which surface water waves exhibit when viewed on a microscopic scale. Due to the relatively recent development of this area of mathematics, a brief introduction to the study of fractal geometry, as well as several examples of fractals, are included in this paper. From that point, this paper addresses the specific situation of a surface wave as it nears the breaking point and attempts to detect the fractal structure of a wave at this given point when viewed on a microscopic scale. This is done from both a physical standpoint based on observations at the Hinsdale Wave Facility at Oregon State University and at Cape Perpetua, Oregon on the Pacific Coast, and from a theoretical standpoint based on a spring model. / Graduation date: 1992

by Chong, Cheung-Yu = 開放球腔中波動之二分量理論 / 莊翔宇. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 84-87). / Text in English; abstracts in English and Chinese. / by Chong, Cheung-Yu = Kai fang qiu qiang zhong bo dong zhi er fen liang li lun / Zhuang Xiangyu. / Abstract --- p.i / Acknowledgments --- p.iii / Contents --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Open Cavities and Quasinormal Modes --- p.1 / Chapter 1.2 --- Completeness of Quasinormal Modes --- p.3 / Chapter 1.3 --- Objective and Outline of this Thesis --- p.5 / Chapter 2 --- Waves in One-Dimensional Open Cavities I: Completeness --- p.6 / Chapter 2.1 --- Quasinormal Modes of One-Dimensional Open Cavities --- p.6 / Chapter 2.2 --- Green's Function Formalism --- p.7 / Chapter 2.2.1 --- Construction of the Green's Function --- p.8 / Chapter 2.2.2 --- Conditions for Completeness --- p.9 / Chapter 2.2.3 --- Quasinormal Mode Expansion of the Green's Function --- p.10 / Chapter 2.3 --- Two-Component Formalism --- p.11 / Chapter 2.3.1 --- Overcompleteness --- p.11 / Chapter 2.3.2 --- Two-Component Expansion --- p.11 / Chapter 2.3.3 --- Linear Space Structure --- p.13 / Chapter 3 --- Waves in One-Dimensional Open Cavities II: Time-Independent Problems --- p.16 / Chapter 3.1 --- Perturbation Theory --- p.16 / Chapter 3.1.1 --- Formalism I: Green's Function Formalism --- p.17 / Chapter 3.1.2 --- Formalism II: Two-Component Formalism --- p.20 / Chapter 3.2 --- Diagonalization Method --- p.23 / Chapter 3.2.1 --- Formalism I: One-Component Expansion --- p.24 / Chapter 3.2.2 --- Formalism II: Green's Function Formalism --- p.25 / Chapter 3.2.3 --- Formalism III: Two-Component Formalism --- p.28 / Chapter 3.2.4 --- Numerical Example --- p.29 / Chapter 4 --- Waves in Open Spherical Cavities I: Completeness --- p.34 / Chapter 4.1 --- Quasinormal Modes of Open Spherical Cavities --- p.34 / Chapter 4.2 --- Green's Function Formalism --- p.36 / Chapter 4.2.1 --- Construction of the Green's Function --- p.37 / Chapter 4.2.2 --- Conditions for Completeness --- p.37 / Chapter 4.2.3 --- Quasinormal Mode Expansion of the Green's Function --- p.38 / Chapter 4.3 --- Two-Component Formalism --- p.39 / Chapter 4.3.1 --- Evolution Formula --- p.40 / Chapter 4.3.2 --- Two-Component Expansion --- p.48 / Chapter 4.3.3 --- Outgoing-Wave Boundary Condition --- p.49 / Chapter 4.3.4 --- Numerical Example --- p.51 / Chapter 4.3.5 --- Linear Space Structure --- p.52 / Chapter 5 --- Waves in Open Spherical Cavities II: Time-Independent Prob- lems --- p.57 / Chapter 5.1 --- Perturbation Theory --- p.57 / Chapter 5.1.1 --- Formalism I: Green's Function Formalism --- p.57 / Chapter 5.1.2 --- Formalism II: Two-Component Formalism --- p.60 / Chapter 5.2 --- Diagonalization Method --- p.61 / Chapter 5.2.1 --- Formalism I: One-Component Expansion --- p.61 / Chapter 5.2.2 --- Formalism II: Green's Function Formalism --- p.63 / Chapter 5.2.3 --- Formalism III: Two-Component Formalism --- p.64 / Chapter 5.2.4 --- Numerical Example --- p.65 / Chapter 6 --- Numerical Evolution of Outgoing Waves in Open Spherical Cav- ities --- p.73 / Chapter 6.1 --- Formulation of the Problem --- p.74 / Chapter 6.2 --- Derivation of the Boundary Condition --- p.75 / Chapter 6.3 --- Boundary Condition without High Derivatives --- p.76 / Chapter 6.4 --- Numerical results --- p.78 / Chapter 6.5 --- Discussion --- p.79 / Chapter 7 --- Conclusion --- p.82 / Chapter 7.1 --- Summary of Our Work --- p.82 / Chapter 7.2 --- Future Developments --- p.83 / Bibliography --- p.84

Sound propagation in a waveguide is greatly dependent on the acoustic properties of the boundaries. The effect of these properties can be described by a bottom reflection coefficient RB, and surface reflection coefficient RS. Two methods for estimating reflection coefficients are used in this research. The first, the ratio method, is based on the variations of the Green's function with depth utilizing the ratio of the wavenumber spectra at two depths. The second, the pole method, is based on the wavenumbers of the modal peaks in the spectrum at a particular depth. A method to invert for sound speed and density is also examined. Estimates of RB and RS based on synthetic data by the ratio method were very close to their predicted values, especially for higher frequencies and longer apertures. The pole method returned less precise estimates though with longer apertures, the estimates were better. Using experimental data, results of the pole method as well a geoacoustic inversion technique based on them were mixed. The ratio method was used to estimate RS based on the actual data and returned results close to the predicted phase of p. / by Alexander Conrad. / Vita. / Thesis (M.S.C.S.)--Florida Atlantic University, 2010. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.

Xie Chunjing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 65-71). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Stability of Shock Waves in Viscous Conservation Laws --- p.10 / Chapter 1.1 --- Cauchy Problem for Scalar Viscous Conservation Laws and Viscous Shock Profiles --- p.10 / Chapter 1.2 --- Stability of Shock Waves by Energy Method --- p.15 / Chapter 1.3 --- Nonlinear Stability of Shock Waves by Spectrum Anal- ysis --- p.20 / Chapter 1.4 --- L1 Stability of Shock Waves in Scalar Viscous Con- servation Laws --- p.26 / Chapter 2 --- Propagation of a Viscous Shock in Bounded Domain and Half Space --- p.35 / Chapter 2.1 --- Slow Motion of a Viscous Shock in Bounded Domain --- p.36 / Chapter 2.1.1 --- Steady Problem and Projection Method --- p.36 / Chapter 2.1.2 --- Projection Method for Time-Dependent Prob- lem --- p.40 / Chapter 2.1.3 --- Super-Sensitivity of Boundary Conditions --- p.43 / Chapter 2.1.4 --- WKB Transformation Method --- p.45 / Chapter 2.2 --- Propagation of a Stationary Shock in Half Space --- p.50 / Chapter 2.2.1 --- Asymptotic Analysis --- p.50 / Chapter 2.2.2 --- Pointwise Estimate --- p.51 / Chapter 3 --- Nonlinear Stability of Viscous Transonic Flow Through a Nozzle --- p.58 / Chapter 3.1 --- Matched Asymptotic Analysis --- p.58 / Bibliography --- p.65

Zhang Hedan. / Thesis submitted in: September 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 78-81). / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Convex Scalar Conservation Laws --- p.9 / Chapter 2.1 --- Cauchy Problems and Weak Solutions --- p.9 / Chapter 2.2 --- Rankine-Hugoniot Condition --- p.11 / Chapter 2.3 --- Entropy Condition --- p.13 / Chapter 2.4 --- Uniqueness of Weak Solution --- p.15 / Chapter 2.5 --- Riemann Problems --- p.17 / Chapter 3 --- General Scalar Conservation Laws --- p.21 / Chapter 3.1 --- Entropy-Entropy Flux Pairs --- p.21 / Chapter 3.2 --- Admissibility Conditions --- p.22 / Chapter 3.3 --- Kruzkov Theory --- p.23 / Chapter 4 --- Elementary waves and Riemann Problems for Nonconvex Scalar Conservation Laws --- p.35 / Chapter 4.1 --- Basic Facts --- p.35 / Chapter 4.2 --- Riemann Solutions --- p.36 / Chapter 5 --- Asymptotic Behavior --- p.46 / Chapter 5.1 --- Periodic Asymptotic Behavior --- p.46 / Chapter 5.2 --- Asymptotic Behavior of Convex Conservation Law --- p.49 / Chapter 5.3 --- Asymptotic Behavior of Non-convex case --- p.52 / Chapter 5.3.1 --- L∞ Behavior --- p.53 / Chapter 5.3.2 --- Wave-Interactions and Asymptotic Behavior Toward Shock Waves --- p.55 / Bibliography --- p.78

Ye Mao. / "May 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 116-123). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Wang Hui Ying. / "June 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 67-72). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

In this paper we demonstrate a theorem of Well-Posedness Local and followed by Well-Posedness Global Equation Korteweg-de Vries in Sobolev spaces by making use of conservation laws of this equation, the properties of the group associated with it, and some estimates obtained by Kenig , Ponce and Vega in [6]. We also demonstrated the existence and stability of solitary wave type solutions for Equation Korteweg-de Vries, to obtain the result of stability we use the lemma Concentrated compactness of P. Lions, in part the result of good global placement is used in a critical, and the conservation laws for this equation, because using this technique to solve a variational minimization problem. Latter part of this thesis is based on the work of John Albert [20]. / Fundação de Amparo a Pesquisa do Estado de Alagoas / Neste trabalho demonstraremos um teorema de Boa Colocação Local e em seguida de Boa Colocação Global para a Equação Korteweg-de Vries nos espaços de Sobolev fazendo uso das leis de conservação desta equação, das propriedades do grupo associada a mesma e de algumas estimativas obtidas por Kenig, Ponce e Vega em [6]. Demonstraremos ainda a existência e estabilidade de soluções tipo ondas solitárias para a Equação Korteweg-de Vries, para obter o resultado de estabilidade usamos o Lema de Compacidade Concentrada de P. Lions, nesta parte o resultado de boa colocação global é utilizado de forma essencial, assim como as leis de conservação para esta equação, pois para utilizar esta técnica resolvemos um problema variacional de minimização. A última parte desta dissertação esta baseada no trabalho de Jonh Albert [20].