Firman So. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves [159]-160). / Text in English; abstracts in English and Chinese. / Firman So. / Abstract --- p.i / Acknowledgement --- p.iii / Contents --- p.iv / List of Figures --- p.vii / List of Tables --- p.xii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Derivation of the Fokker-Planck Equation --- p.4 / Chapter 2.1 --- Brownian Motion --- p.4 / Chapter 2.2 --- Non-Linear Langevin Equation --- p.7 / Chapter 2.3 --- Conditional Probability Density --- p.9 / Chapter 2.4 --- Kramers-Moyal Expansion --- p.11 / Chapter 2.5 --- Fokker-Planck Equation --- p.13 / Chapter Chapter 3. --- Method & Solution of the One-variable Fokker-Planck Equation with Time-Independent Coefficients --- p.15 / Chapter 3.1 --- Stationary Solution --- p.16 / Chapter 3.2 --- Ornstein-Ulhenbeck Process: An Exactly Solvable Fokker-Planck Equation --- p.17 / Chapter 3.3 --- Eigenfunction Expansion --- p.19 / Chapter 3.4 --- Ornstein-Ulhenbeck process by Eigenfunction Expansion --- p.29 / Chapter 3.5 --- Eigenfunctions and Eigenvalues of Inverted Potentials --- p.30 / Chapter 3.6 --- Kramers' Escape Rate --- p.32 / Chapter Chapter 4. --- Diffusion in Potential Wells --- p.36 / Chapter 4.1 --- Symmetric Double-Well Potential --- p.36 / Chapter 4.2 --- Asymmetric Bistable Potential --- p.61 / Chapter Chapter 5. --- Stochastic Resonance --- p.100 / Chapter 5.1 --- Introduction --- p.100 / Chapter 5.2 --- Probability Density........................... --- p.101 / Chapter 5.3 --- Power Spectrum of the Autocorrelation Function of x --- p.113 / Chapter 5.4 --- Stochastic Resonance --- p.120 / Chapter Chapter 6. --- Colored Noise --- p.124 / Chapter 6.1 --- Introduction --- p.124 / Chapter 6.2 --- Approximation Schemes for the Colored Noise Problem --- p.125 / Chapter 6.3 --- Stationary Probability Density of the Colored Noise Driven Bistable System --- p.132 / Chapter 6.4 --- Escape Rate in the Presence of Colored Noise --- p.140 / Chapter Chapter 7. --- Conclusion --- p.146 / Appendix A --- p.149 / Chapter A.1 --- State-Dependent Diagonalization Method --- p.149 / Chapter A.2 --- Infinite-Square-Well Basis Diagnalization --- p.153 / Chapter A.3 --- Solving the Fokker-Planck equation --- p.156 / References
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_322785 |
| Date | January 1999 |
| Contributors | So, Firman., 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, xi, 160 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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