Yim Man Yi = 亞擴散雙穩分數福克-普朗克系統的線性響應及隨機共振和有色噪音對雙穩系統所引起的效應 / 嚴敏儀. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 85-89). / Text in English; abstracts in English and Chinese. / Yim Man Yi = Ya kuo san shuang wen fen shu Fuke-Pulangke xi tong de xian xing xiang ying ji sui ji gong zhen he you se zao yin dui shuang wen xi tong suo yin qi de xiao ying / Yan Minyi. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Brownian motion and anomalous dynamics --- p.1 / Chapter 1.2 --- White and colored noises --- p.3 / Chapter 2 --- Linear response theory of sub diffusive Fokker-Planck systems --- p.6 / Chapter 2.1 --- Introduction to subdiffusive Fokker-Planck systems --- p.6 / Chapter 2.2 --- Spectral density --- p.8 / Chapter 2.3 --- Linear response --- p.11 / Chapter 2.4 --- Signal-to-noise ratio (SNR) --- p.13 / Chapter 2.5 --- Stochastic energy --- p.14 / Chapter 3 --- Perturbation due to a sinusoidal signal --- p.16 / Chapter 3.1 --- Presence of an external sinusoidal forcing --- p.16 / Chapter 3.1.1 --- PDF and linear reponse --- p.16 / Chapter 3.1.2 --- Phase lag --- p.19 / Chapter 3.1.3 --- SNR --- p.19 / Chapter 3.1.4 --- Stochastic energy --- p.23 / Chapter 3.2 --- Presence of a sinusoidally time-varying diffusion coefficient --- p.23 / Chapter 4 --- Perturbation due to a rectangular signal --- p.26 / Chapter 4.1 --- Linear response to a rectangular pulse --- p.26 / Chapter 4.2 --- Perturbation due to a periodic rectangular signal --- p.28 / Chapter 4.2.1 --- Linear response --- p.29 / Chapter 4.2.2 --- SNR --- p.31 / Chapter 4.2.3 --- Stochastic energy --- p.33 / Chapter 4.3 --- Comparison with the response to a sinusoidal driving force --- p.35 / Chapter 5 --- The Effects of Colored Noise on the Stationary Probability Distribution --- p.38 / Chapter 5.1 --- Formulation of a general colored noises-driven system --- p.39 / Chapter 5.2 --- Approximation schemes for a colored noise --- p.42 / Chapter 5.2.1 --- Decoupling approximation --- p.42 / Chapter 5.2.2 --- UCNA --- p.45 / Chapter 5.2.3 --- Small r approximation . --- p.46 / Chapter 5.2.4 --- Presence of an additive noise: g(x) = 1 --- p.47 / Chapter 5.2.5 --- Presence of a multiplicative noise: g(x) = x --- p.52 / Chapter 5.3 --- Approximation scheme for two colored noises --- p.53 / Chapter 5.3.1 --- Presence of two additive noises --- p.55 / Chapter 5.3.2 --- Presence of an additive noise and a multiplicative noise --- p.55 / Chapter 5.4 --- Unimodal-bimodal transitions --- p.61 / Chapter 6 --- A stochastic genetic regulatory transcription model with colored noises --- p.68 / Chapter 6.1 --- Biological background --- p.69 / Chapter 6.2 --- Effect of a single noise --- p.72 / Chapter 6.3 --- Effects of two noises --- p.75 / Chapter 6.4 --- Biological implications of colored noises in the model --- p.81 / Chapter 7 --- Conclusions --- p.82 / Bibliography --- p.85 / Chapter A --- Mittag-Leffler function --- p.90 / Chapter B --- H-function (Fox function) --- p.92 / Chapter C --- Operator algebra --- p.94 / Chapter D --- Mean first passage time --- p.97
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_325774 |
| Date | January 2006 |
| Contributors | Yim, Man Yi., 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, vi, 98 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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