Cheung Sing Leung = 頻散耗散系統中的本征矢量展開式 / 張承亮. / Thesis submitted in: October 2003. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves [141]-[144]). / Text in English; abstracts in English and Chinese. / Cheung Sing Leung = Pin san hao san xi tong zhong de ben zheng shi liang zhan kai shi / Zhang Chengliang. / Abstract --- p.i / Acknowledgments --- p.iv / Contents --- p.v / List of Figures --- p.ix / List of Tables --- p.xiii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Physical Motivation --- p.1 / Chapter 1.2 --- Review of Ohmic Damping Formalism --- p.3 / Chapter 1.3 --- Outline of Thesis --- p.11 / Chapter Chapter 2. --- Critical Point and Perturbation around Critical Points --- p.13 / Chapter 2.1 --- Introduction and Example --- p.13 / Chapter 2.2 --- Basis Vectors near and at Critical Point --- p.16 / Chapter 2.2.1 --- Properties of Jordan block basis --- p.20 / Chapter 2.3 --- Example of Damped Oscillator --- p.24 / Chapter 2.4 --- Perturbation around Critical Points --- p.25 / Chapter 2.4.1 --- Behavior of other Jordan blocks --- p.27 / Chapter 2.4.2 --- Summary on generic and non-generic behaviors around the critical point --- p.28 / Chapter Chapter 3. --- Fast Mode and Constrained Systems --- p.34 / Chapter 3.1 --- Introduction --- p.34 / Chapter 3.2 --- Model A: Damped System with Special Mass --- p.36 / Chapter 3.2.1 --- Limiting case ε= 0 --- p.38 / Chapter 3.2.2 --- Eigenvalue convergence --- p.40 / Chapter 3.3 --- Model B: Damped System with Outgoing-wave Condition --- p.44 / Chapter 3.3.1 --- Matching criteria --- p.46 / Chapter 3.4 --- Model C: Discrete Wave Equation with Outgoing-wave Condition --- p.46 / Chapter 3.4.1 --- Matching criteria in the N →∞ limit in wave element example --- p.48 / Chapter Chapter 4. --- Dispersive Dissipative Systems --- p.56 / Chapter 4.1 --- Introduction --- p.56 / Chapter 4.1.1 --- Relation between dispersion and dissipation --- p.58 / Chapter 4.2 --- Previous Works on Dispersive Dissipative Systems --- p.59 / Chapter 4.3 --- Damped Systems with Dispersion --- p.62 / Chapter 4.4 --- Initial-value Problem --- p.65 / Chapter Chapter 5. --- Dispersive Linear-space Formalism --- p.72 / Chapter 5.1 --- Low-dimensional System --- p.72 / Chapter 5.1.1 --- State space and evolution --- p.72 / Chapter 5.1.2 --- Inner product and bilinear map --- p.76 / Chapter 5.1.3 --- Metric --- p.78 / Chapter 5.2 --- Generalization of Metric for N = 1 and Arbitrary M --- p.81 / Chapter 5.3 --- Generalization of the Formalism to Arbitrary N and M --- p.82 / Chapter Chapter 6. --- Properties of Dispersive Systems --- p.86 / Chapter 6.1 --- Initial-value Problem Revisited --- p.86 / Chapter 6.1.1 --- Worked example --- p.88 / Chapter 6.2 --- Weak Dispersion --- p.91 / Chapter 6.2.1 --- Eigenvalues --- p.91 / Chapter 6.2.2 --- Decoupling --- p.93 / Chapter 6.2.3 --- Perturbation around the decoupling limit --- p.94 / Chapter 6.3 --- Connection between Dispersive and Ohmic Systems --- p.96 / Chapter 6.3.1 --- Illustrative example --- p.97 / Chapter 6.3.2 --- Conditions --- p.99 / Chapter 6.3.3 --- "Illustration of N =1, M = 2 case" --- p.100 / Chapter 6.3.4 --- Numerical example --- p.101 / Chapter Chapter 7. --- Conclusion --- p.105 / Chapter Appendix A. --- Perturbation Around Critical Points --- p.107 / Chapter A.1 --- Genericity --- p.107 / Chapter A.1.1 --- Example --- p.110 / Chapter A.2 --- Non-genericity --- p.111 / Chapter A.2.1 --- First-order non-genericity --- p.111 / Chapter A.2.1.1 --- Example --- p.113 / Chapter A.2.1.2 --- Special case --- p.114 / Chapter A.2.2 --- Second-order non-genericity --- p.117 / Chapter A.2.2.1 --- Example --- p.118 / Chapter A.2.2.2 --- Special case --- p.120 / Chapter A.2.3 --- Third-order non-genericity --- p.123 / Chapter A.2.3.1 --- Example --- p.125 / Chapter A.2.3.2 --- Special case --- p.128 / Chapter Appendix B. --- Numerical Detail of Initial-value Problem --- p.134 / Chapter B.1 --- Numerical Algorithm --- p.134 / Chapter B.2 --- Description of Extracted Components --- p.135 / Chapter Appendix C. --- Vandermonde Matrix --- p.137 / Chapter C.1 --- Introduction --- p.137 / Chapter C.2 --- Algorithm --- p.138 / Chapter C.3 --- Example --- p.138 / Chapter C.4 --- Proof of Alogrithm --- p.139 / Bibliography --- p.141
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324841 |
| Date | January 2004 |
| Contributors | Cheung, Sing Leung., Chinese University of Hong Kong Graduate School. Division of Physics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, xii, 140 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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