Hui Yuen Yung. / Thesis submitted in: August 1998. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 70-73). / Text in English; abstract also in Chinese. / Hui Yuen Yung. / Acknowledgements --- p.vi / Abstract --- p.vii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Second harmonic generation --- p.5 / Chapter 2.1 --- Introduction --- p.5 / Chapter 2.2 --- Maxwell's equations in dielectric media --- p.6 / Chapter 2.3 --- Second harmonic generation --- p.7 / Chapter 2.4 --- Phase matching --- p.8 / Chapter 2.5 --- Quasi phase matching --- p.10 / Chapter 2.6 --- Inversion symmetry --- p.11 / Chapter 3 --- Third order nonlinear optical processes in optical fibers --- p.14 / Chapter 3.1 --- Introduction --- p.14 / Chapter 3.2 --- Optical fibers --- p.15 / Chapter 3.3 --- Third order interaction between waves of same frequency --- p.16 / Chapter 3.4 --- Third order interaction between waves of different frequencies --- p.19 / Chapter 4 --- Multiphoton ionization interference effect --- p.23 / Chapter 4.1 --- Historical development --- p.23 / Chapter 4.2 --- Multiphoton ionization interference effect --- p.26 / Chapter 4.3 --- Periodic ionization --- p.27 / Chapter 4.4 --- Periodic electric field --- p.28 / Chapter 4.5 --- Physical interpretation --- p.29 / Chapter 5 --- Experimental setup --- p.32 / Chapter 5.1 --- Introduction --- p.32 / Chapter 5.2 --- Laser system --- p.32 / Chapter 5.3 --- Optical fibers --- p.33 / Chapter 5.4 --- Coupling light into fibers --- p.34 / Chapter 5.5 --- Detection system --- p.36 / Chapter 5.6 --- Optical layout --- p.36 / Chapter 6 --- Second harmonic generation in optical fibers --- p.40 / Chapter 6.1 --- Introduction --- p.40 / Chapter 6.2 --- Self-preparation in optical fibers --- p.41 / Chapter 6.3 --- Polarization dependence --- p.42 / Chapter 6.4 --- Seeding optical fibers --- p.42 / Chapter 6.5 --- Seeding by varying green light intensity --- p.45 / Chapter 6.6 --- Square dependence of second harmonic generation in optical fibers --- p.46 / Chapter 7 --- Erasure of x(2) grating in optical fibers --- p.56 / Chapter 7.1 --- Introduction --- p.56 / Chapter 7.2 --- Experiment --- p.58 / Chapter 7.3 --- Results --- p.59 / Chapter 7.3.1 --- Erasure by different propagating mode --- p.59 / Chapter 7.3.2 --- Erasure in germanium-doped fiber --- p.60 / Chapter 7.3.3 --- Erasure in erbium-doped fiber --- p.61 / Chapter 7.4 --- Discussion --- p.61 / Chapter 8 --- Conclusion --- p.68 / Chapter 8.1 --- Summary of our work --- p.68 / Chapter 8.2 --- Outlook --- p.69 / Chapter 8.2.1 --- Multiphoton ionization in polymer --- p.69 / Chapter 8.2.2 --- Erasure by blue light --- p.69 / Bibliography --- p.70

Asymptotic properties of solutions of the linear dispersion equation ut = uxxx in R × R+, and its (2k + 1)th-order generalisations are studied. General Hermitian spectral theory and asymptotic behaviour of its kernel, for the rescaled operator B = D3 + 1 3 yDy + 1 3 I, is developed, where a complete set of bi-orthonormal pair of eigenfunctions, {ψβ}, {ψ∗β }, are found. The results apply to the construction of VSS (very singular solutions) of the semilinear equation with absorption ut = uxxx − |u|p−1u in R × R+, where p > 1, which serves as a basic model for various applications, including the classic KdV area. Finally, the nonlinear dispersion equations such as ut = (|u|nu)xxx in R × R+, and ut = (|u|nu)xxx − |u|p−1u in R × R+, where n > 0, are studied and their “nonlinear eigenfunctions” are constructed. The basic tools include numerical methods and “homotopy-deformation” approaches, where the limits n → 0 and n → +∞ turn out to be fruitful. Local existence and uniqueness is proved and some bounds on the highly oscillatory tail are found. These odd-order models were not treated in existing mathematical literature, from the proposed point of view.

Severe stenosis may cause critical flow conditions related to artery collapse, plaque cap rupture which leads directly to stroke and heart attack. In this paper, a nonlinear viscoelastic model and a numerical method are introduced to study dynamic behaviors of the tube wall and viscous flow through a viscoelastic tube with a stenosis simulating blood flow in human carotid arteries. The Mooney-Rivlin material model is used to derive a nonlinear viscoelastic thin-wall model for the stenotic viscoelastic tube wall. The mechanical parameters in the Mooney-Rivlin model are calculated from experimental measurements. Incompressible Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation are used as the governing equation for the fluid flow. Interactions between fluid flow and the viscoelastic axisymmetric tube wall are handled by an incremental boundary iteration method. A Generalized Finite Differences Method (GFD) is used to solve the fluid model. The Fourth-Order Runge-Kutta method is used to deal with the viscoelastic wall model where the viscoelastic parameter is adjusted to match experimental measurements. Our result shows that viscoelasticity of tube wall causes considerable phase lag between the tube radius and input pressure. Severe stenosis causes cyclic pressure changes at the throat of the stenosis, cyclic tube compression and expansions, and shear stress change directions in the region just distal to stenosis under unsteady conditions. Results from our nonlinear viscoelastic wall model are compared with results from previous elastic wall model and experimental data. Clear improvements of our viscoelastic model over previous elastic model were found in simulating the phase lag between the pressure and wall motion as observed in experiments. Numerical solutions are compared with both stationary and dynamic experimental results. Mooney-Rivlin model with proper parameters fits the non-linear experimental stress-strain relationship of wall very well. The phase lags of tube wall motion, flow rate variations with respect to the imposed pulsating pressure are simulated well by choosing the viscoelastic parameter properly. Agreement between numerical results and experimental results is improved over the previous elastic model.

This thesis examines the nonlinear behaviour of thermoacoustic systems by using approaches from the field of nonlinear dynamics. The underlying behaviour of a nonlinear system is determined by two things: first, by the type and form of the attractors in phase space, and second, by the mechanism that the system transitions from one attractor to another. For a thermoacoustic system, both of these things must be understood in order to define a safe operating region in parameter space, where no high-amplitude oscillations exist. Triggering in thermoacoustics is examined in a simple model of a horizontal Rijke tube. A triggering mechanism is presented whereby the system transitions from a stable fixed point to a stable limit cycle, via an unstable limit cycle. The practical stability of the Rijke tube was investigated when the system is forced by stochastic noise. Low levels of noise result in triggering much before the linear stability limit. Stochastic stability maps are introduced to visualise the practical stability of a thermoacoustic system. The triggering mechanism and stochastic dependence of the Rijke tube match extremely well with results from an experimental combustor. The most common attractors in thermoacoustic systems are fixed points and limit cycles. In order to define the nonlinear behaviour of a thermoacoustic system, it is therefore important to find the regions of parameter space where limit cycles exist. Two methods of finding limit cycles in large thermoacoustic sytems are presented: matrix-free continuation methods and gradient methods. Continuation methods find limit cycles numerically in the time domain, with no additional assumptions other than those used to form the governing equations. Once the limit cycles are found, these continuation methods track them as the operating condition of the system changes. Most continuation methods are impractical for finding limit cycles in large thermoacoustic systems because the methods require too much computational time and memory. In the literature, there are therefore only a few applications of continuation methods to thermoacoustics, all with low-order models. Matrix-free shooting methods efficiently calculate the limit cycles of dissipative systems and have been demonstrated recently in fluid dynamics, but are as yet unused in thermoacoustics. These matrix-free methods are shown to converge quickly to limit cycles by implicitly using a 'reduced order model' property. This is because the methods preferentially use the influential bulk motions of the system, whilst ignoring the features that are quickly dissipated in time. The matrix-free methods are demonstrated on a model of a ducted 2D diffusion flame, and the safe operating region is calculated as a function of the Peclet number and the heat release parameter. Both subcritical and supercritical Hopf bifurcations are found. Physical information about the flame-acoustic interaction is found from the limit cycles and Floquet modes. Invariant subspace preconditioning, higher order prediction techniques, and multiple shooting techniques are all shown to reduce the time required to generate bifurcation surfaces. Two types of shooting are compared, and two types of matrix-free evaluation are compared. The matrix-free methods are also demonstrated on a model of a ducted axisymmetric premixed flame, using a kinematic G-equation solver. The methods find limit cycles, period-2 limit cycles, fold bifurcations, period-doubling bifurcations and Neimark-Sacker bifurcations as a function of two parameters: the location of the flame in the duct, and the aspect ratio of the steady flame. The model is seen to display rich nonlinear behaviour and regions of multistability are found. Gradient methods can also efficiently calculate the limit cycles of large systems. A scalar cost function is defined that describes the proximity of a state to a limit cycle. The gradient of the cost function is used in an optimisation routine to iteratively converge to a limit cycle (or fixed point). The gradient of the cost function is found with a forwards-backwards process: first, the direct equations are marched forwards in time, second, the adjoint equations are marched backwards in time. The adjoint equations are derived by partially differentiating the direct governing equations. The gradient method is demonstrated on a model of a horizontal Rijke tube. This thesis describes novel nonlinear analysis techniques that can be applied to coupled systems with both advanced acoustic models and advanced flame models. The techniques can characterise the rich nonlinear behaviour of thermoacoustic models with a level of detail that was not previously possible.

Les réseaux de neurones artificiels constituent des systèmes alternatifs pour effectuer des calculs complexes, ainsi que pour contribuer à l'étude des systèmes neuronaux biologiques. Ils sont capables de résoudre des problèmes complexes, tel que la prédiction de signaux chaotiques, avec des performances à l'état de l'art. Cependant, la compréhension du fonctionnement des réseaux de neurones dans la résolution de problèmes comme la prédiction reste vague ; l'analogie avec une boîte-noire est souvent employée. En combinant la théorie des systèmes dynamiques non linéaires avec celle de l'apprentissage automatique (Machine Learning), nous avons développé un nouveau concept décrivant à la fois le fonctionnement des réseaux neuronaux ainsi que les mécanismes à l'œuvre dans leurs capacités de prédiction. Grâce à ce concept, nous avons pu imaginer un processeur neuronal hybride composé d'un réseaux de neurones et d'une mémoire externe. Nous avons également identifié les mécanismes basés sur la synchronisation spatio-temporelle avec lesquels des réseaux neuronaux aléatoires récurrents peuvent effectivement fonctionner, au-delà de leurs états de point fixe habituellement utilisés. Cette synchronisation a entre autre pour effet de réduire l'impact de la dynamique régulière spontanée sur la performance du système. Enfin, nous avons construit physiquement un réseau récurrent à retard dans un montage électro-optique basé sur le système dynamique d'Ikeda. Celui-ci a dans un premier temps été étudié dans le contexte de la dynamique non-linéaire afin d'en explorer certaines propriétés, puis nous l'avons utilisé pour implémenter un processeur neuromorphique dédié à la prédiction de signaux chaotiques. / Artificial neural networks are systems prominently used in computation and investigations of biological neural systems. They provide state-of-the-art performance in challenging problems like the prediction of chaotic signals. Yet, the understanding of how neural networks actually solve problems like prediction remains vague; the black-box analogy is often employed. Merging nonlinear dynamical systems theory with machine learning, we develop a new concept which describes neural networks and prediction within the same framework. Taking profit of the obtained insight, we a-priori design a hybrid computer, which extends a neural network by an external memory. Furthermore, we identify mechanisms based on spatio-temporal synchronization with which random recurrent neural networks operated beyond their fixed point could reduce the negative impact of regular spontaneous dynamics on their computational performance. Finally, we build a recurrent delay network in an electro-optical setup inspired by the Ikeda system, which at first is investigated in a nonlinear dynamics framework. We then implement a neuromorphic processor dedicated to a prediction task.

Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO. / Vita. / Bibliography: p. 232-237. / by W. Michael Bowles. / Sc.D.

Vita. / Digitized by Kansas Correctional Industries

<div>In this dissertation I present three essays. The overarching theme of these projects is how price-discriminating sellers endogenously modify their pricing schemes in the face of regulatory interventions. The application I have in mind when writing the papers is that of a food retailer deciding menu characteristics, such as price and quantity, in the context of a given food policy environment. The particular policies I consider are portion cap rules and taxes, both designed by the policy-maker to reduce the consumption of certain foods and ingredients. My approach diverges from studies focusing on buyers' reactions to paternalistic food policies by placing the seller at the center of the analysis. I use models of nonlinear pricing to derive hypotheses, which I test in controlled laboratory experiments. In the first two essays I explore the economic impacts of taxes and portion cap rules when single-product sellers serve privately informed buyers. In the third, I examine the economic effects of portion cap rules when two-product sellers serve buyers with private preferences. </div><div><br></div><div>In the first essay, collective work with Dr. Joseph Balagtas and Dr. Steven Wu, I compare the impacts of taxes and portion control rules on profit and consumer surplus. I model the pricing problem of a single-product seller serving two types of privately-informed customers. I aim to answer the following questions: i) what effects do taxes have on portion sizes, buyer surplus, and seller's expected profit; ii) how does the tax affect the seller's ability to screen the market, and iii) how the effects of taxes and portion cap rules compare. I find that under a tax regime, all package sizes are smaller; high willingness to pay buyers see a reduction in their surplus, and the retailer's expected profit is unambiguously diminished. Both policy instruments curb consumption. In contrast with tax regimes, however, cap rules leave buyer surplus unaffected. These outcomes suggest that portion control rules might be a preferred over tax regimes as methods to regulate consumption of calorie-dense and low-nutrient foods traded in settings where retailers engage in second-degree price discrimination.</div><div><br></div><div>In the second paper, also joint work with Dr. Joseph Balagtas and Dr. Steven Wu, I report a controlled laboratory experiment designed to test the results of my first essay. In this project, human subjects take on the role of sellers and are free to decide their pricing strategies, including number of ``packages'', their price and their quantity. We vary the policy environment across treatments,and these include: unregulated baseline, cap rule, and specific tax. My principal goal is to test the theoretical outcomes of the first essay and find which regulation is associated with a smaller negative impact on consumers' economic surplus in the laboratory. My main finding is that the cap does not impact buyers' information rents regardless of the seller's segmentation scheme; while the effect of the tax is contingent on the seller's strategy and is neutral at best.</div><div><br></div><div><br></div><div>In the last essay, I study the economic impacts resulting from enforcing a maximum-quantity limit on one of the two products offered by a seller facing demand from privately-informed heterogeneous buyers. Specifically, I look at impacts on: i) consumption of the regulated component, ii) purchases of the unregulated item, and iii) consumer surplus. Hypotheses derived from a bi-dimensional nonlinear pricing predict reductions in consumption of the target component, changes in consumption of the unregulated product by some buyers, and mixed impacts on consumer surplus. Data from a laboratory experiment corroborates the predictions regarding consumption of the regulated good; however, no significant changes in consumption of the unregulated product are found, surprisingly a subset of buyers are better-off after the cap rule while no buyer type is worse-off. The results have implications for food policy discussions around portion cap rules, where the assumption that these regulations negatively impact consumers' well-being largely drives public debate. </div>

Song Liang = 向列液晶中激光束感应的取向重联非线性光学效应和取向性光折变光栅形成 / 宋亮. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references. / Text in English; abstracts in English and Chinese. / Song Liang = Xiang lie ye jing zhong ji guang shu gan ying de qu xiang zhong lian fei xian xing guang xue xiao ying he qu xiang xing guang zhe bian guang zha xing cheng / Song Liang. / Abstract --- p.i / 论文摘要 --- p.iii / Acknowledgement --- p.iv / Contents --- p.v / Chapter Chapter 1 --- Introduction --- p.1 / References --- p.5 / Chapter Chapter 2 --- Brief review of liquid crystals and nonlinear optics of liquid crystals --- p.9 / Chapter 2.1 --- Brief review of liquid crystals --- p.9 / Chapter 2.1.1 --- General description --- p.9 / Chapter 2.1.2 --- Types of liquid crystals --- p.11 / Chapter 2.1.3 --- Order parameter --- p.14 / Chapter 2.1.4 --- Liquid crystal alignment --- p.14 / Chapter 2.1.5 --- Continuum theory of liquid crystals --- p.16 / Chapter 2.2 --- Nonlinear optics of liquid crystals --- p.20 / Chapter 2.2.1 --- Basic mechanism of nonlinear optics --- p.20 / Chapter 2.2.2 --- Self-phase modulation --- p.23 / Chapter 2.2.3 --- Orientational photorefractive effects --- p.29 / Chapter 2.3 --- Sample preparation --- p.34 / Chapter 2.4 --- Conclusion --- p.37 / References --- p.39 / Chapter Chapter 3 --- Domain formation in homeotropic nematic liquid crystal cell --- p.42 / Chapter 3.1 --- Introduction --- p.42 / Chapter 3.2 --- Domain formation under applied dc and ac electric fields --- p.44 / Chapter 3.3 --- Light scattering of domains under applied dc and ac electric fields --- p.49 / Chapter 3.4 --- Conclusion --- p.53 / References --- p.54 / Chapter Chapter 4 --- Laser induced self-phase modulation and effects of applied electric field --- p.56 / Chapter 4.1 --- Introduction --- p.56 / Chapter 4.2 --- Self-phase modulation without applied electric field --- p.58 / Chapter 4.2.1 --- Experimental setup --- p.58 / Chapter 4.2.2 --- Experimental results and discussions --- p.59 / Chapter 4.3 --- Effects of applied electric field --- p.67 / Chapter 4.3.1 --- Effects of applied dc electric field --- p.67 / Chapter 4.3.2 --- Effects of applied ac electric field --- p.72 / Chapter 4.4 --- Conclusion --- p.75 / References --- p.77 / Chapter Chapter 5 --- Orientational photorefractive grating in nematic liquid crystals --- p.80 / Chapter 5.1 --- Introduction --- p.80 / Chapter 5.2 --- Orientational photorefractive grating under dc electric field --- p.82 / Chapter 5.2.1 --- Experimental setup --- p.82 / Chapter 5.2.2 --- Experimental results and discussion --- p.84 / Chapter 5.3 --- Orientational photorefractive grating under ac electric field --- p.90 / Chapter 5.3.1 --- Raman-Nath grating --- p.90 / Chapter 5.3.2 --- Quasi-Bragg grating --- p.96 / Chapter 5.4 --- Conclusion --- p.98 / References --- p.100 / Chapter Chapter 6 --- Summary and future outlook --- p.103 / List of Publications and Conference Presentations --- p.107

Lee Sim Heung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references. / Abstracts in English and Chinese. / ABSTRACT --- p.i / ACKNOWLEGEMENT --- p.vi / LIST OF FIGURES --- p.xi / Chapter 1. --- INTRODUCTION --- p.1 / Chapter 1.1. --- New challenges in telecommunication --- p.2 / Chapter 1.2. --- Introduction to optical non-linearity and its impact to optical network --- p.3 / Chapter 1.3. --- Applications of optical nonlinearity --- p.5 / Chapter 1.3.1. --- Extinction ratio enhancement and wavelength conversion --- p.5 / Chapter 1.3.2. --- All optical ASK to DPSK converter --- p.6 / Chapter 1.3.3. --- All-optical RZ to NRZ format converter --- p.8 / Chapter 1.3.4. --- RF clock component enhancement for NRZ data --- p.10 / Chapter 1.3.5. --- Multi-wavelength converter with multi-channel broadcasting --- p.11 / Chapter 1.4. --- Overview --- p.12 / Chapter 2. --- PRINCIPLES AND THEORIES --- p.18 / Chapter 2.1. --- Optical nonlinearity --- p.19 / Chapter 2.2. --- Self-phase modulation (SPM) --- p.21 / Chapter 2.3. --- Cross-phase modulation (XPM) --- p.25 / Reference: --- p.28 / Chapter 3. --- EXTINCTION RATIO ENHANCEMENT AND WAVELENGTH CONVERSION USING CROSS-PHASE MODULATION IN A DISPERSION-SHIFTED FIBER --- p.29 / Chapter 3.1. --- Introduction --- p.30 / Chapter 3.2. --- Experimental details of extinction ratio enhancement --- p.31 / Chapter 3.3. --- Result and Discussions --- p.32 / Chapter 3.4. --- Conclusion --- p.36 / References: --- p.37 / Chapter 4. --- ALL-OPTICAL ASK TO DPSK FORMAT CONVERSION --- p.38 / Chapter 4.1. --- All Optical ASK to DPSK Format Conversion Using Cross-Phase Modulation in a Non-linear Fiber --- p.39 / Chapter 4.1.1. --- Introduction --- p.40 / Chapter 4.1.2. --- Experimental Details of ASK to DPSK format conversion by XPM in DSF --- p.42 / Chapter 4.1.3. --- Results and Discussion --- p.44 / Chapter 4.1.4. --- Experimental Details of ASK to DPSK format conversion by XPM in PCF --- p.47 / Chapter 4.1.5. --- Result and Discussion of XPM in PCF --- p.49 / Chapter 4.1.6. --- Comparison of DSF and PCF --- p.51 / References: --- p.54 / Chapter 4.2. --- All Optical ASK to ASK/DPSK Orthogonal Code Format Conversion Using Cross-Phase Modulation in a Dispersion-Shifted Fiber --- p.56 / Chapter 4.2.1. --- Introduction --- p.57 / Chapter 4.2.2. --- Experimental Details of ASK to ASK/DPSK format conversion --- p.58 / Chapter 4.2.3. --- Results and Discussion --- p.60 / Chapter 4.2.4. --- Conclusion --- p.63 / References: --- p.64 / Chapter 5. --- ALL-OPTICAL RZ TO NRZ FORMAT CONVERSION --- p.65 / Chapter 5.1. --- Introduction --- p.65 / Chapter 5.2. --- All-Optical RZ to NRZ Data Format Conversion Using Spectral Broadening Effect in a Dispersion-Shifted Fiber --- p.67 / Chapter 5.2.1. --- Principle of RZ-to-NRZ format conversion using SPM --- p.68 / Chapter 5.2.2. --- Experiment Details --- p.71 / Chapter 5.2.3. --- Results and Discussion --- p.72 / Chapter 5.2.4. --- Conclusion --- p.77 / Chapter 5.3. --- Spectral Filtering from a Cross-Phase Modulated Signal for RZ to NRZ Format and Wavelength Conversion --- p.78 / Chapter 5.3.1. --- Principle of RZ to NRZ format conversion by XPM --- p.79 / Chapter 5.3.2. --- Experiment --- p.81 / Chapter 5.3.3. --- Results and Discussion --- p.83 / Chapter 5.3.4. --- Conclusions --- p.87 / References: --- p.88 / Chapter 6. --- ALL-OPTICAL CLOCK COMPONENT EXTRACTION FROM NRZ DATA SIGNALS USING SELF-PHASE MODULATION IN A DISPERSION-SHIFTED FIBER --- p.90 / Chapter 6.1. --- Introduction --- p.91 / Chapter 6.2. --- Experimental Details --- p.92 / Chapter 6.3. --- Results and Discussion --- p.93 / Chapter 6.4. --- Conclusion --- p.96 / References: --- p.97 / Chapter 7. --- ALL-OPTICAL WAVELENGTH MULTICASTING USING SELF- PHASE MODULATION IN A NONLINEAR PHOTONIC CRYSTAL FIBER --- p.98 / Chapter 7.1. --- Introduction --- p.99 / Chapter 7.2. --- Simulation results --- p.100 / Chapter 7.3. --- Experimental Details --- p.103 / Chapter 7.4. --- Result and Discussion --- p.104 / Chapter 7.5. --- Conclusions --- p.109 / References: --- p.110 / Chapter 8. --- CONCLUSION AND FUTURE WORK --- p.111 / Chapter 8.1. --- Conclusion --- p.111 / Chapter 8.2. --- Possible Future Work --- p.114 / References: --- p.116 / APPENDIX --- p.117 / List of Publications --- p.117