Ng, Chi Kong. / "May 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 175-187). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Wang Jin. / "September 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 93-105). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

This thesis investigates two thematic lines of research, both underpinned by non-Markovian system-reservoir interactions in quantum optics. The overarching focus is on modelling the open system dynamics in a non-perturbative fashion, broadly on - though not restricted to - instances when the environment is structured. A theory is developed by means of enlarging the open system over environmental degrees of freedom to include memory effects in its dynamics. This is achieved using an established technique that involves mapping a bosonic environment onto a 1D chain of harmonic oscillators. Within this setting, we apply a Heisenberg equation-of-motion approach to derive an exact set coupled differential equations for the open system and a single auxiliary oscillator of the chain. The combined equations are shown to have their interpretation rooted in a quantum Markov stochastic process. Including the auxiliary chain oscillator as part of the original system then enables us to obtain an exact master equation for the enlarged system, avoiding any need for the Born-Markov approximations. Our method is valid for a dissipative two-state system, with cases of multiple excitations and added driving discussed. Separately, we apply the framework of quantum Darwinism to an atom-cavity system, and, subsequently, to a more general multiple-environment model. In both cases, the time-dependent spread of correlations between the open system and fractions of the environment is analysed during the course of the decoherence process. The degree to which information is redundant across different fractions is checked to infer the emergence of classicality. In the second case, we go further and present a decomposition of information in terms of its quantum and classical correlations. A quantitative measure of redundancy is also studied with regard to its ability to witness non-Markovian behaviour. Besides fundamental interest, our results have application to quantum information processing and quantum technologies, keeping in mind the potential beneficial use of non-Markovian effects in reservoir engineering.

The objective of this thesis is to develop the quantum theory of the motional degrees of freedom of a charged particle in a Penning trap. The theory is treated within the formalism of quantum optics, and explores the use of dressed-atom methods by exploiting the threefold SU(N) algebraic structure of the problem. The quantum form of the experimental techniques of sideband coupling and driving to the ultra-elliptical regime are examined in this context, and resulting future applications considered. Interpretation of the quantum dynamics of the separate x and y motions of an electron is discussed, motivated by the desire to modify the trapping potential without changing the basic experimental configuration. A detailed discussion of operator methods which exploit the algebraic structure of the problem is given. This results in a clearer understanding of the physical manifestations of a range of unitary transformations upon a general three-dimensional system, and a novel interpretation of the mapping between canonical angular momentum components of isotropic and anisotropic trapping systems. The results highly promote future use of these methods in Penning trap theory, detailing a robust formulation of unitary operations which can be used to prepare the quantum state of a charged particle. The majority of the results can be applied to any Penning trap, but the theory is based throughout upon the “Geonium Chip" trap at Sussex; the scalability and planar design of this trap promotes it as natural candidate in experimental quantum optics and Gaussian quantum information studies. The work in this thesis aims to provide framework for such future applications.

在實際分析數據的時候,我們經常遇到二元時間序列數據。在許多情況下，由於普通線性二元時間序列模型未必足以說明較複雜的社會和自然現象，許多分析家認為，多元非線性時間序列模型可以提供一個可行的解決方案。在許多不同類型的多元非線性時間序列中，一個重要的類別是二元門限自回歸（BTAR）模型。BTAR 模型可以充分捕到時間序列數據中的極限週期跳躍現象及振幅頻率。Tsay (1998) [37] 提出了多元的門限型的非線性檢驗。然而，這種檢驗對被異常點污染了的時間序列數據的表現不太令人滿意。為了糾正Tsay (1998) [37]檢驗的缺點，我們提出一個穩健的檢驗程序。本論文的重點是二元時間序列數據。重新加權二元最小消平方法被採用從而推出一個穩健的門限型非線性檢驗。亦得出該檢驗的統計量在原假設下的漸近分怖。透過模擬實驗,找出提出的檢驗的性能，並且與根據最小消平方法建立的Tsay (1998) [37]的檢驗作出比較，我們也會提供實際的數據例子給予說明。 / Bivariate time series data are frequently encountered in practical situations. In many cases, since ordinary linear bivariate time series models may not be sufficient to de-scribe complex social and natural phenomena, many analysts believe that vector non-linear time series models could provide a viable solution. Among many different types of vector non-linear time series processes, an important class is the bivariate threshold autoregressive (BTAR) model. BTAR model can be employed to capture limit cycles, jump phenomenon and amplitude-frequency in the time series data. A test for threshold-type non-linearity in a vector time series was proposed by Tsay (1998) [38]. However, this test does not perform satisfactorily if the data are contaminated by outliers. To remedy the drawback of the Tsay' s (1998) [38] test, we propose a robust testing procedure. The focus of this thesis is on bivariate time series data. The reweighted bivariate least trimmed squares method is adopted to derive a robust test for threshold-type non-linearity. The asymptotic null distribution of the proposed test statistic is dervied. Simulation studies are conducted to investigate the performance of the proposed test and to compare it with the least squares method based on the Tsay's (1998) [38] test. Numerical examples are provided for illustrative purposes. / Detailed summary in vernacular field only. / Chow, Wai Kit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 40-44). / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Linear Time Series Models and Their Applications --- p.1 / Chapter 1.2 --- Non-linear Time Series Models and Their Applications --- p.3 / Chapter 1.3 --- Threshold Autoregressive Model (TAR) and the Self-exciting Threshold Autoregressive Model (SETAR) --- p.4 / Chapter 1.4 --- Outliers in Univariate Time Series --- p.5 / Chapter 1.5 --- Bivariate Autoregressive Model (BAR) --- p.6 / Chapter 1.6 --- Bivariate Threshold Autoregressive Model (BTAR) --- p.7 / Chapter 1.7 --- Outliers in Bivariate Time Series --- p.8 / Chapter 1.8 --- Objectives of the Thesis --- p.9 / Chapter 1.9 --- Organisation of the Thesis --- p.10 / Chapter 2 --- The Proposed Test --- p.11 / Chapter 2.1 --- Tsay's Test --- p.11 / Chapter 2.2 --- Reweighted Multivariate Least Trimmed Squares Method --- p.14 / Chapter 2.3 --- The Proposed Test --- p.18 / Chapter 3 --- Simulation Study --- p.24 / Chapter 3.1 --- Under the Null Hypothesis --- p.24 / Chapter 3.2 --- Under the Alternative Hypothesis --- p.26 / Chapter 3.3 --- The Choice of γ and δ --- p.28 / Chapter 4 --- Examples --- p.31 / Chapter 4.1 --- Simulated Data --- p.31 / Chapter 4.2 --- Gas-Furnace Data --- p.33 / Chapter 4.3 --- Blowfly Data --- p.35 / Chapter 5 --- Conclusions and Further Research --- p.38 / Bibliography --- p.40

Yuen, Kin Pong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 93-95). / Yuen, Kin Pong. / Contents --- p.i / Abstract --- p.iv / Acknowledgement --- p.v / List of Figures --- p.vi / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Optically Bistable Behavior --- p.5 / Chapter 2.1 --- Bistable behavior of two component composites --- p.5 / Chapter 2.1.1 --- Formalism --- p.6 / Chapter 2.1.2 --- Results and Discussion --- p.7 / Chapter 2.1.3 --- Stability analysis --- p.9 / Chapter 2.2 --- Bistable behavior of three component composites: Nonlinear dielec- tric core embedded in a metallic shell --- p.11 / Chapter 2.2.1 --- Spectral representation of the local field --- p.11 / Chapter 2.2.2 --- The onset of bistable behavior --- p.20 / Chapter 2.2.3 --- The extinction coefficient and reflectance at normal incidence --- p.24 / Chapter 2.2.4 --- Discussion and Conclusion --- p.28 / Chapter 2.3 --- Bistable behavior of three component composites: Metallic core em- bedded in a nonlinear dielectric shell --- p.30 / Chapter 2.3.1 --- Linear response of spherical inclusions and concentric spheres --- p.31 / Chapter 2.3.2 --- Onset of bistable behavior --- p.35 / Chapter 2.3.3 --- Results and Discussion --- p.41 / Chapter 2.4 --- Possible development of the spectral representation --- p.44 / Chapter Chapter 3. --- Optical Repsonse of a Nonlinear Composite Film --- p.45 / Chapter 3.1 --- Enhanced nonlinear response of coated spheres --- p.46 / Chapter 3.2 --- Solution of nonlinear wave equation --- p.48 / Chapter 3.3 --- Results and Discussion --- p.49 / Chapter 3.4 --- Conclusion --- p.52 / Chapter 3.5 --- Transfer matrix formalism for transmittance: Possible control over the size of a photonic band gap --- p.52 / Chapter 3.5.1 --- Transfer matrix method --- p.54 / Chapter Chapter 4. --- Bounds and Estimates for Nonlinear Composites --- p.59 / Chapter 4.1 --- Linear response of spherical inclusions --- p.60 / Chapter 4.2 --- Strongly nonlinear response of spherical inclusions --- p.61 / Chapter 4.3 --- Linear response of concentric spheres --- p.64 / Chapter 4.4 --- Strongly nonlinear response of concentric spheres --- p.66 / Chapter 4.5 --- Some exactly solvable cases --- p.68 / Chapter 4.6 --- Concentric spheres with nonlinear shell embedded in a linear dielec- tric host --- p.71 / Chapter 4.7 --- Discussion and Conclusion --- p.73 / Chapter 4.8 --- Small contrast expansion --- p.75 / Chapter 4.9 --- Hashin-Shtrikman microgeometry --- p.78 / Chapter 4.10 --- Exact bounds for linear composites --- p.79 / Chapter 4.11 --- Variational approach for Hashin-Shtrikman microstructure --- p.82 / Chapter 4.12 --- Improved variational approach --- p.85 / Chapter 4.13 --- Discussion and Conclusion --- p.87 / Appendix A. Derivation of the Energy Functional --- p.88 / Chapter A.1 --- The energy functional --- p.88 / Chapter A.2 --- Effect of higher order terms to the energy functional --- p.91 / Bibliography --- p.93

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaves 170-173. / by Daniel Ocone. / Ph.D.

The development of compact and low-cost coherent sources in visible and infrared wavelength range can provide indispensible tools for a variety of scientific, technological and industrial applications. Great progress over the last years in material science, crystal growth and semiconductor material processing in combination with recent advances in some of the more traditional technologies, in particular nonlinear frequency conversion and parametric sources, have led to the realisation of a new generation of laser sources. Furthermore, the advent of a new generation of quasi-phase-matched, waveguided and semiconductor nonlinear materials together with novel semiconductor lasers have led to the development of new frequency conversion and parametric sources with previously unattainable performance capabilities. The research described in this thesis relates to the development and characterisation of novel semiconductor based laser sources tunable in the broad spectral ranges which are unattainable for conventional lasers due to a lack of suitable laser gain materials. In the first part of the thesis the subject matter is concerned with the direct emission from laser devices. In particular, a broadly tunable InGaAs/InP strained multi-quantum well external cavity diode laser, operating in the spectral range of 1494 nm – 1667 nm with a maximum CW output power in excess of 81 mW and side-mode suppression ratio higher than 50 dB is demonstrated. This represents the highest output power and side-mode suppression ratio ever to be generated in this spectral region. A record broadly tunable high-power external cavity InAs/GaAs quantum-dot diode laser with a tuning range of 202 nm (1122 nm - 1324 nm), a maximum output power of 480 mW and a side-mode suppression ratio greater than 45 dB, is also demonstrated. This represents a promising achievement for the development of a high-power fast swept tunable laser and compact nonlinear frequency generation schemes for the green-yellow-orange-red spectral range. The second part of the thesis relates to induced nonlinear processes, focusing on frequency doubling and optical parametric oscillation. In particular, an all-room-temperature CW second harmonic generation at 612.9 nm and 591.5 nm in periodically poled potassium titanyl phosphate waveguides pumped by a broadly-tunable quantum-dot external cavity diode laser with a conversion efficiency of 10.5% and 7.9%, respectively, is demonstrated. For the first time, a green-to-red tunable laser source with tunability of over 60 nm (567.7 nm – 629.1 nm) based on frequency doubling in a single periodically poled potassium titanyl phosphate waveguide pumped by a single broadly-tunable quantum dot laser is demonstrated. These results are an important step towards a compact tunable coherent visible light source, operating at room temperature. The possibility of nonlinear frequency conversion in orientation-patterned GaAs waveguides is also investigated. The technology of low-loss periodically poled GaAs waveguided crystals is developed and such crystals are fabricated. Second harmonic generation at 1621 nm in low-loss periodically poled GaAs waveguide is demonstrated. An optical parametric oscillator system used as the pump source for GaAs devices and based on the periodically poled 5 mol% MgO-doped Congruent Lithium Niobate crystal, generating light in the wavelength range between 1430 nm and 4157 nm, is presented. The obtained results show a great promise for realisation of efficient quasi-phase-matched optical parametric oscillator devices based on orientation-patterned GaAs waveguides, which enables the extending generated wavelength up to 16 µm.

Wang, Chongyu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 74-78). / Abstract also in Chinese. / Abstract --- p.1 / Abstract in Chinese --- p.3 / Acknowledgement --- p.4 / Contents --- p.5 / List of Tables --- p.7 / List of Figures --- p.8 / Chapter 1. --- Introduction --- p.9 / Chapter 2. --- Conventional Dynamic Programming --- p.15 / Chapter 2.1. --- Principle of optimality and decomposition --- p.15 / Chapter 2.2. --- Backward dynamic programming --- p.17 / Chapter 2.3. --- Forward dynamic programming --- p.20 / Chapter 2.4. --- Curse of dimensionality --- p.23 / Chapter 3. --- Surrogate Constraint Formulation --- p.26 / Chapter 3.1. --- Surrogate constraint formulation --- p.26 / Chapter 3.2. --- Singly constrained dynamic programming --- p.28 / Chapter 3.3. --- Surrogate dual search --- p.29 / Chapter 4. --- Distance Confined Path Algorithm --- p.34 / Chapter 4.1. --- Yen´ةs algorithm for the kth shortest path problem --- p.35 / Chapter 4.2. --- Application of Yen´ةs method to integer programming --- p.36 / Chapter 4.3. --- Distance confined path problem --- p.42 / Chapter 4.4. --- Application of distance confined path formulation to integer programming --- p.50 / Chapter 5. --- Convergent Surrogate Dual Search --- p.59 / Chapter 5.1. --- Algorithm for convergent surrogate dual search --- p.62 / Chapter 5.2. --- "Solution schemes for (Pμ{αk,αβ)) and f(x) = αk" --- p.63 / Chapter 5.3. --- Computational Results and Analysis --- p.68 / Chapter 6. --- Conclusions --- p.72 / Bibliography --- p.74

A hydraulically undersized control structure could result in water overtopping a dam or channel banks. To increase hydraulic capacity and reduce flooding risk, nonlinear spillways are frequently replacing linear weirs. This study investigates four subjects to further knowledge for two types of nonlinear weir, the piano key and labyrinth. Weir submergence is a condition when the downstream water level of a weir exceeds the weir crest elevation, and can influence the head-discharge relationship of the structure. The effects of submergence on laboratory-scale piano key weir head-discharge relationships were evaluated experimentally and compared to published submergence data for linear and labyrinth weirs. For relatively low levels of submergence, the piano key weir requires less upstream head relative to the labyrinth weir (<6%). This increase in efficiency was reversed at higher levels. Staged labyrinth weirs feature multiple weir segments with different crest elevations, which confine base flows and/or satisfy downstream discharge requirements. Head-discharge relationships for various laboratory-scale staged labyrinth weir configurations were established. The accuracy of a head-discharge predictive technique based upon superposition and traditional labyrinth weir empirical data was evaluated, and found to be generally within ±5%. The influence of linear, labyrinth, and staged labyrinth weir head-discharge characteristics on the outflow hydrograph behavior was evaluated by numerically routing various flood discharges through a fictitious reservoir; peak outflow, maximum water surface elevation, and required detention volume data are presented for each weir alternative. A staged labyrinth weir can be an effective alternative for decreasing the peak outflow hydrograph for frequent events, while increasing discharge for higher return period storm events. Approach flow perpendicular to the labyrinth weir centerline axis may not be possible in all situations. The head-discharge characteristics of a laboratory-scale labyrinth weir were evaluated with three different approach flow angles (0°, 15°, and 45°). For approach flow angles up to 15°, no measurable loss in discharge efficiency occurred. The discharge efficiency reduced as much as 11% for the 45° approach angle case. While all data presented are specific to the weir configurations and geometries tested, these data can be beneficial to the general understanding of nonlinear weirs.