Cho, Chi Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 63-65). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

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by Chan Kam Wai Clifford. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 105-108). / Text in English; abstracts in English and Chinese. / by Chan Kam Wai Clifford. / Abstract --- p.i / Acknowledgements --- p.iii / Contents --- p.iv / List of Figures --- p.vii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Motivations of the Project --- p.1 / Chapter 1.2 --- Historical Background --- p.1 / Chapter 1.3 --- Objective and Outline of Thesis --- p.3 / Chapter Chapter 2. --- Reviews on One-dimensional Dynamical Cavity --- p.4 / Chapter 2.1 --- Formalism --- p.4 / Chapter 2.2 --- Methods of Solution --- p.6 / Chapter 2.2.1 --- Phase Construction (R function) --- p.6 / Chapter 2.2.2 --- Instantaneous Mode Expansion --- p.12 / Chapter 2.2.3 --- Transformation Method --- p.15 / Chapter 2.3 --- Numerical Results --- p.15 / Chapter 2.3.1 --- Some Results using R function --- p.16 / Chapter 2.3.2 --- Some Results using Instantaneous Mode Decomposition --- p.24 / Chapter 2.3.3 --- Remarks on the Numerical Scheme used in Transformation Method --- p.28 / Chapter 2.3.4 --- "Comparisons of Results obtained by Phase Construction, In- stantaneous Mode Decomposition and Transformation" --- p.28 / Chapter 2.4 --- Conclusion --- p.30 / Chapter Chapter 3. --- Fixed-point Analysis for the One-dimensional Cavity --- p.31 / Chapter 3.1 --- Introduction --- p.31 / Chapter 3.2 --- What are the fixed-points? --- p.32 / Chapter 3.3 --- Characteristics of Fixed-points --- p.36 / Chapter 3.4 --- Fixed-points and Geometric Resonance --- p.39 / Chapter Chapter 4. --- Electromagnetic Field in an Undulating Spherical Cavity --- p.44 / Chapter 4.1 --- Classical Electromagnetic field theory --- p.44 / Chapter 4.2 --- Boundary Conditions --- p.46 / Chapter 4.3 --- The Motion of Cavity Surface --- p.47 / Chapter Chapter 5. --- Methods of Solution and Results to the Spherical Cavity --- p.48 / Chapter 5.1 --- Introduction --- p.48 / Chapter 5.2 --- Mode Decomposition and Transformation Method revisited --- p.49 / Chapter 5.2.1 --- Mode Decomposition --- p.49 / Chapter 5.2.2 --- Transformation Method --- p.50 / Chapter 5.2.3 --- Remarks on the use of Instantaneous Mode Expansion and Transformation Method --- p.51 / Chapter 5.3 --- The Ge(z) function --- p.52 / Chapter 5.3.1 --- The Ge(z) function as a solution of the scalar wave equation --- p.52 / Chapter 5.3.2 --- Numerical Results --- p.54 / Chapter 5.4 --- The Me(z) function --- p.60 / Chapter 5.4.1 --- Formalism --- p.60 / Chapter 5.4.2 --- Comparison of Me(z) with Ge(z) --- p.62 / Chapter 5.4.3 --- Numerical Results --- p.63 / Chapter 5.5 --- Conclusions and Discussions --- p.93 / Chapter 5.5.1 --- Geometric Resonances --- p.93 / Chapter 5.5.2 --- Harmonic Resonances --- p.94 / Chapter Chapter 6. --- Conclusion --- p.95 / Appendix A. Electromagnetic Field in Spherical Cavity --- p.97 / Chapter A.1 --- Field Strength --- p.97 / Chapter A.2 --- Field Energy --- p.98 / "Appendix B. Construction of Ψe(r,t) by G(z)" --- p.100 / Appendix C. The Arbitrary Part GH(z) of Ψe(r，t) --- p.103 / Bibliography --- p.105

by Li Kam Shun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaf 65). / Chapter CHAPTER 1 --- Soliton Solutions of the Nonisospectral and Variable Coefficient Korteweg-de Vries Equation / Chapter §1.1 --- Introduction --- p.4 / Chapter §1.2 --- Inverse Scattering --- p.6 / Chapter §1.3 --- N-Soliton Solution --- p.11 / Chapter §1.4 --- One-Soliton Solutions --- p.15 / Chapter §1.5 --- Two-Soliton Solutions --- p.18 / Chapter §1.6 --- Oscillating and Asymptotically Standing Solitons --- p.23 / Chapter CHAPTER 2 --- Asymptotic Behaviour of Nonsoliton Solutions of the Nonisospectral and Variable Coefficient Korteweg-de Vries Equation / Chapter §2.1 --- Introduction --- p.31 / Chapter §2.2 --- Main Results --- p.36 / Chapter §2.3 --- Lemmas --- p.39 / Chapter §2.4 --- Proof of the Main Results --- p.59 / References --- p.65

by Ho Yum Bun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 93-94). / Text in English; abstracts in English and Chinese. / by Ho Yum Bun. / List of Figures --- p.3 / Abstract --- p.9 / Chinese Abstract --- p.10 / Acknowledgement --- p.11 / Chapter 1 --- Introduction --- p.12 / Chapter 1.1 --- Motivation --- p.12 / Chapter 1.2 --- What is Sonoluminescence? --- p.13 / Chapter 1.3 --- The Main Task of this Project --- p.13 / Chapter 1.4 --- Organization of this Thesis --- p.13 / Chapter 2 --- Reviews on One-dimensional Dynamical Cavity Problem --- p.15 / Chapter 2.1 --- Introduction --- p.15 / Chapter 2.2 --- Formulation --- p.15 / Chapter 2.3 --- Moore's R Function Method --- p.18 / Chapter 2.4 --- Mode Expansion Method --- p.19 / Chapter 2.5 --- Transformation method --- p.20 / Chapter 2-6 --- Summary --- p.21 / Chapter 3 --- Numerical Results For One-dimensional Dynamical Cavity Prob- lem --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Evolution of a Cavity System --- p.23 / Chapter 3.3 --- Motion of the Moving Mirror --- p.23 / Chapter 3.4 --- R(z) Function --- p.24 / Chapter 3.4.1 --- Construction of R(z) Function --- p.24 / Chapter 3.4.2 --- Numerical R(z) Function --- p.27 / Chapter 3.5 --- Results --- p.27 / Chapter 3.5.1 --- Results with Moore's R(z) Function Method --- p.27 / Chapter 3.5.2 --- Results with the Mode Expansion Method --- p.29 / Chapter 3.5.3 --- Results with the Transformation Method --- p.36 / Chapter 3.6 --- Summary --- p.36 / Chapter 4 --- Spherical Dynamical Cavity Problem --- p.37 / Chapter 4.1 --- Introduction --- p.37 / Chapter 4.2 --- Formulation --- p.37 / Chapter 4.3 --- Motion of a Moving Spherical Mirror --- p.39 / Chapter 4.4 --- Summary --- p.40 / Chapter 5 --- The G(z) Function Method --- p.41 / Chapter 5.1 --- Introduction --- p.41 / Chapter 5.2 --- G(z) Function --- p.42 / Chapter 5.2.1 --- Ideas of Deriving the G(z) Function --- p.42 / Chapter 5.2.2 --- Formalism --- p.42 / Chapter 5.2.3 --- Initial G(z) Function --- p.45 / Chapter 5.3 --- Construction of the G(z) Function --- p.46 / Chapter 5.3.1 --- Case I : l=0 --- p.46 / Chapter 5.3.2 --- Case II : l > 0 --- p.49 / Chapter 5.4 --- Asymptotic Series Solution of G(z) --- p.50 / Chapter 5.5 --- Application to Resonant Mirror Motion --- p.52 / Chapter 5.6 --- Regularization of G(z) --- p.58 / Chapter 5.7 --- Behaviors of the Fields --- p.58 / Chapter 5.7.1 --- z vs tf Graph --- p.61 / Chapter 5.7.2 --- Case 1: l= 0 --- p.61 / Chapter 5.7.3 --- "Case2: l= 1,2" --- p.62 / Chapter 5.7.4 --- Case 3: l= 3 --- p.73 / Chapter 5.7.5 --- Section Summary --- p.73 / Chapter 5.8 --- Summary --- p.73 / Chapter 6 --- Three-dimensional Mode Expansion Method and Transforma- tion Method --- p.75 / Chapter 6.1 --- Introduction --- p.75 / Chapter 6.2 --- Mode Expansion Method --- p.75 / Chapter 6.2.1 --- Formalism --- p.75 / Chapter 6.2.2 --- Application of Floquet's Theory --- p.78 / Chapter 6.2.3 --- Results --- p.80 / Chapter 6.3 --- The Transformation Method --- p.80 / Chapter 6.3.1 --- The Method --- p.80 / Chapter 6.3.2 --- Numerical Schemes --- p.86 / Chapter 6.3.3 --- Results --- p.89 / Chapter 6.4 --- Summary --- p.89 / Chapter 7 --- Conclusion --- p.90 / Chapter 7.1 --- The One-dimensional Dynamical Cavity Problem --- p.90 / Chapter 7.2 --- The Dynamical Spherical Cavity Problem --- p.91 / Chapter 7.3 --- Numerical Methods --- p.91 / Chapter 7.4 --- Further Investigation --- p.92 / Bibliography --- p.93

在本文中， 我們將主要討論一種在求解一類波動方程反問題中很有價值的數值方法：線性化方法。 / 在介紹上述的數值方法之前， 我們將首先討論波動方程的一些重要的特質，主要包括四類典型的波動方程模型，方程的基本解和一般解，以及波動方程解的性質。 / 接下來，在本文的第二部分中，我們會首先介紹所求解的模型以及其反問題。此反問題主要研究求解波動方程[附圖]中的系數c. 線性化方法的主要思想在於將速度c分解成兩部分：c₁ 和c₂ ，並且滿足關系式：[附圖]，其中c₁ 是一個小的擾動量。另一方面，上述波動方程的解u 可以被線性表示：u = u₀ + u₁ ，其中u₀ 和u₁ 分別是一維問題和二維問題的解。相應的，我們將運用有限差分方法和傅利葉變換方法求解上述一維問題和二維問題，從而分別求解c₁ 和c₂ ，最終求解得到係數c. 在本文的最後，我們將進行一些數值試驗，從而驗證此線性化方法的有效性和可靠性。 / In this thesis, we will discuss a numerical method of enormous value, a linearized method for solving a certain kind of inverse wave equations. / Before the introduction of the above-mentioned method, we shall discuss some important features of the wave equations in the first part of the thesis, consisting of four typical mathematical models of wave equations, there fundamental solutions, general solutions and the properties of those general solutions. / Next, we shall present the model and its inverse problem of recovering the coefficient c representing the propagation velocity of wave from the wave equation [with mathematic formula] The linearized method aims at dividing the velocity c into two parts, c₀ and c₁, which satisfying the relation [with mathematic formula], where c₁ is a tiny perturbation. On the other hand, the solution u can be represented in the linear form, u = u₀ + u₁, where u₀ and u₁ are the solutions to one-dimensional problem and two- dimensional problem respectively. Accordingly, we can use the numerical methods, finite difference method and Fourier transform method to solve the one-dimensional forward problem and two-dimensional inverse problem respectively, thus we can get c₀ and c₁, a step before we recover the velocity c. In the numerical experiments, we shall test the proposed linearized numerical method for some special examples and demonstrate the effectiveness and robustness of the method. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Xu, Xinyi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 64-65). / Abstracts also in Chinese. / Chapter 1 --- Fundamental aspects of wave equations --- p.6 / Chapter 1.1 --- Introduction --- p.6 / Chapter 1.1.1 --- Four important wave equations --- p.6 / Chapter 1.1.2 --- General form of wave equations --- p.10 / Chapter 1.2 --- Fundamental solutions --- p.11 / Chapter 1.2.1 --- Fourier transform --- p.11 / Chapter 1.2.2 --- Fundamental solution in three-dimensional space --- p.14 / Chapter 1.2.3 --- Fundamental solution in two-dimensional space --- p.16 / Chapter 1.3 --- General solution --- p.19 / Chapter 1.3.1 --- One-dimensional wave equations --- p.19 / Chapter 1.3.2 --- Two and three dimensional wave equations --- p.26 / Chapter 1.3.3 --- n dimensional case --- p.28 / Chapter 1.4 --- Properties of solutions to wave equation --- p.31 / Chapter 1.4.1 --- Properties of Kirchhoff’s solutions --- p.31 / Chapter 1.4.2 --- Properties of Poisson’s solutions --- p.33 / Chapter 1.4.3 --- Decay of the solutions to wave equation --- p.34 / Chapter 2 --- Linearized method for wave equations --- p.36 / Chapter 2.1 --- Introduction --- p.36 / Chapter 2.1.1 --- Background --- p.36 / Chapter 2.1.2 --- Forward and inverse problem --- p.38 / Chapter 2.2 --- Basic ideas of Linearized Method --- p.39 / Chapter 2.3 --- Theoretical analysis on linearized method --- p.41 / Chapter 2.3.1 --- One-dimensional forward problem --- p.42 / Chapter 2.3.2 --- Two-dimensional forward problem --- p.43 / Chapter 2.3.3 --- Existence and uniqueness of solutions to the inverse problem --- p.45 / Chapter 2.4 --- Numerical analysis on linearized method --- p.45 / Chapter 2.4.1 --- Discrete analog of the inverse problem --- p.46 / Chapter 2.4.2 --- Fourier transform --- p.48 / Chapter 2.4.3 --- Direct methods for inverse and forward problems --- p.52 / Chapter 2.5 --- Numerical Simulation --- p.54 / Chapter 2.5.1 --- Special Case --- p.54 / Chapter 2.5.2 --- General Case --- p.59 / Chapter 3 --- Conclusion --- p.63 / Bibliography --- p.64

Calculation of propagation constants in particulate matter is an important aspect of wave propagation analysis in engineering disciplines such as satellite comnnication, geophysical exploration, radio astronomy and material science. It is important to understand why different propagation constants produced by different theories are not applicable to a particular problem. Homogenization of the random media using effective medium theories yields the effective propagation constants by effacing the particulate, microscopic nature of the medium. The Maxwell-Gamet and Bruggeman effective medium theories are widely used but their limitations are not always well understood. In this thesis, some of the more complex homogenization theories will only be partially derived or heuristically constructed in order to avoid unnecessary mathematical complexity which does not yield additional physical insight. The intent of this thesis is to elucidate the nature of effective medium theories, discuss the theories' approximations and gain a better global understanding of wave propagation equations. The focus will be on the Maxwell-Garnet and Bruggeman theories because they yield simple relationships and therefore serve as anchors in a sea of myriad approximations. / Master of Science

Call number: LD2668 .T4 1985 B78 / Master of Science

This thesis investigates inversion techniques used to determine the geoacoustic properties of a shallow-water waveguide. The data used were obtained in the Shallow Water '06 Modal Mapping Experiment in which four buoys drifted over a system of subbottom channels. The method used was perturbative inversion using modal eigenvalues as input parameters, which were found using an autoregressive spectral estimator. This work investigates the differences between a "channel" region and a "no channel" region based on an inferred stratigraphic model. Inversions were performed on data from a single buoy both at individual frequencies and multiple frequencies simultaneously. Since the use of multiple frequencies and a certain set of constraints proved to be an effective method of inversion, the method was applied to data from the other three buoys as well. It is shown that the "channel" and "no channel" regions have significantly different sound speed profiles. / by Rebecca Weeks. / Thesis (M.S.C.S.)--Florida Atlantic University, 2010. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.