Eigenvector expansion in dispersive dissipative systems.

• Other Authors: Cheung, Sing Leung.
• Format: Others
• Language: English; Chinese
• Published: 2004
• Subjects: Eigenvectors
• Online Access: http://library.cuhk.edu.hk/record=b5891990; http://repository.lib.cuhk.edu.hk/en/item/cuhk-324841

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