A nonlinear stability analysis of a liquid sheet moving in an incompressible gas medium at rest subject to sinuous disturbances is presented. The first, second and third order governing equations have been derived along with appropriate initial and boundary conditions which describe the characteristics of the fundamental mode, and the first and second harmonics. It is found that the thinning of the sheet is caused by the growth of harmonic waves, and subsequent liquid sheet rupture occurs at every half wavelength interval. The amplitude growth rates of the disturbances are calculated at the dominant wavenumber for different initial amplitudes and are then compared with the predictions from the linear theory. The analysis also allows the determination of the breakup time and breakup length, and the effect of the flow parameters on the breakup time is also investigated. The present experimental study on the liquid sheet breakup explores the growth of liquid sheet instabilities and subsequent spray formation. Flow visualization reveals different flow regimes. Liquid sheet surface displacements, wavelengths and breakup lengths are measured using a photographic technique, and the drop sizes and velocities are measured simultaneously by the Phase Doppler Particle Analyzer (PDPA). The result of acoustic excitation for different regimes of liquid disintegration shows that for certain frequencies resonance and enhanced instability occur. However, in the spray regime where a fine spray is formed, although visually there are some effects of acoustic excitation on the wave development, the Phase Doppler Particle Analyzer (PDPA) measurements show no noticeable effect on the drop sizes and velocities. The theoretical predictions are compared with the experimental results for dominant wavelength and growth rate of the unstable waves on the liquid sheet surface. / Graduate

M.Ing. / Previous studies on the four-pulse dynamic compensator showed the existence of a stable limit cycle in the compensating current. Attempts were made to eliminate this limit cycle by placing a small signal active filter in the feedback path of the system, as it influenced the efficiency of the compensator. The efficiency of the active filter depends, on system parameters such as the impedance of the supply network and the load. Thus the small signal active filter eliminated the limit cycle only conditionally. A control method referred to as error modulation, was developed in order to eliminate the limit cycle unconditionally. According to this method the amplitude of the error is used to determine the modulation depth. Results showed that this method completely eliminates the limit cycle. In order to analyse this method analytically, a dual-input describing function for the altered non-linearity was derived. It was possible, by using the describing function, to explain the stability of the system with error modulation. Tests on the system revealed a poor dynamic response. The undamped nature of the system decreased the efficiency of the system. Damping was introduced to the system in such a way, that losses were kept at a minimum, while the dynamic response of the system improved. It has also been experienced that the losses in the system tends to use all the stored energy in the inductor. Previous attempts to stabilise the amount of stored energy in the inductor,did not succeed. 'n Control system using feedback was thus developed to stabilise the energy in the inductor, and the dynamic compensator losses are drawn from the supply.

Les phénomènes observés dans le comportement élastique non linéaire des roches et des bétons sont reconnus pour être étroitement reliés à leur microstructure. La signature non linéaire de ces matériaux est complexe avec notamment une perte temporaire des propriétés élastiques en sollicitation dynamique ainsi que des phénomènes d’hystérésis et de relaxation lente. Depuis les années 90, de nombreuses études académiques et industrielles ont démontré l’intérêt de l’acoustique non linéaire pour la caractérisation non-destructive avec des indicateurs dont la sensibilité à l’endommagement est décuplée par rapport à ceux utilisés jusqu’alors. Cependant, les effets tridimensionnels associés aux couplages éventuels des phénomènes non linéaires sont généralement négligés dans ces études, ce qui limite l’obtention de paramètres quantitatifs, pouvant même mener à des conclusions erronées. Dans ce contexte, ces travaux de thèse s’attachent à développer une approche théorique tridimensionnelle unifiée, adaptée de l’acousto-élasticité. Le premier chapitre, introduit le support bibliographique de ces travaux. Le deuxième chapitre expose un modèle de relaxation tridimensionnel, couplé aux coefficients élastiques d’ordre trois. Il est validé expérimentalement sur du mortier et du grès. Il est démontré que la perte temporaire des propriétés élastiques en sollicitation dynamique est un phénomène anisotrope induit. Le troisième chapitre, applique le modèle à la résonance non linéaire. Le quatrième chapitre introduit le modèle à la prospection non linéaire in situ. Les perspectives de ces travaux sont vastes, couvrant des domaines fondamentaux ou plus pratiques (contrôle non destructif). / The phenomena observed in the nonlinear elastic behavior of rocks and concretes are known to be closely related to their microstructure. The nonlinear signature of those materials is complex with temporary loss of elastic properties under dynamic loading as well as hysteresis and slow relaxation phenomena. Since the 1990s, numerous academic and industrial studies have demonstrated the value of nonlinear acoustics for non-destructive characterization with indicators whose sensitivities to damage is tenfold compared to those used up to now. However, the three-dimensional effects associated with the possible coupling of nonlinear phenomena are generally neglected in these studies, which limits the obtaining of quantitative parameters, which may even lead to erroneous conclusions. In this context, these theses work aims to develop a unified three-dimensional theoretical approach, adapted from the acousto-elasticity. The first chapter introduces the bibliographic support of this work. The second chapter presents a three-dimensional relaxation model coupled to the three-order elastic coefficients. It is validated experimentally on mortar and sandstone. It is shown that the temporary loss of elastic properties under dynamic loading is an induced anisotropic phenomenon.The third chapter applies the model to nonlinear resonance experiment. The forth chapter introduces the model to in situ nonlinear prospecting. The perspectives of this work are broad, covering fundamental domains (non-linear elasticity) or more practical (non-destructive testing and passive monitoring of buildings).

在適當的條件下，正向入射激光束令GaAs量子阱微腔產生方向的不穩定性，並生成橫向光學圖案。方向不穩定性的形成是由於極化子，即光子及量子阱激子的強非線性耦合的本徵態，在微腔內散射的結果。電腦模擬顯示，通過一個非常弱的控制激光束，橫向光學圖案可以從一個方向切換到另一個。它可以作為一個全光學開關，而全光開關可有效地改善計算機的性能。 / 本論文先介紹GaAs量子阱微腔的理論及其數值模擬，以顯示GaAs量子阱微腔能夠產生光學圖案和全光學開關。然而，透過複雜的模擬數據去理解其規律及原理實在太困難。為此，我們發展一個低維的群種競爭模型，以理解這些現象。 / 為了分析群種競爭模型，我們應用了一些數學工具，如Gröbner bases 和廣義判式，以減少計算模型的相圖所需的電腦負荷。此外，我們也利用了突變理論來分類和解釋所有相圖中的相界。這個人口競爭模型使我們對不同物理系統中的圖案生成現象有一個全面的定性理解。 / 在本論文的最後一部分，我們研究量子阱雙微腔，即兩個耦合的微腔，而每個微腔中間也有一個量子阱。透過傳輸矩陣的方法，我們獲得了雙微腔的色散關係，並與實驗結果作比較。我們預期沿著這個研究方向在未來能夠加快實現全光開關。 / Under favorable conditions, laser beams incident normally to a GaAs quantumwell microcavity develop directional instabilities and generate transverse patterns in the far field. The directional instabilities are driven by scattering among polaritons inside the microcavity, where the polaritons are the eigenstates of strong linear coupling between the cavity photons and the excitons inside the quantum-well. It has been predicted that the transverse pattern can be switched from one to another by the use of a very weak control beam. It can serve as an all-optical switching, which can potentially be used to improve computers’ performance. / In this thesis, the theory of the GaAs quantum-well microcavity is first introduced and numerical results showing the formation of patterns and the all-optical switching scheme are presented. However, understanding the patterns and their dynamics through numerical simulations turns out to be very complicated. To this end, we derive a low-dimensional population-competition model for the interpretation of these behaviors. / To facilitate the analysis the population-competition model, we apply mathematical tools such as the Gröbner basis and the generalized discriminant to reduce the computational load in finding the ‘phase diagrams’ of the populationcompetition model. Besides, we also make use of the catastrophe theory to classify and explain all the phase boundaries in the phase diagrams. This population-competition model enables us to acquire an overall qualitative picture of pattern formation in various physical systems. / In the last part of this thesis, we use the transfer-matrix method to study the polariton spectrum of a quantum-well double-microcavity, which is two coupled optical cavities each containing a quantum well, and compare the spectrum with the experimental results. We expect our efforts along this direction could expedite realization of all-optical switching in the future. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Tse, Yuen Chi = 分析橫向光學圖案的低維群種競爭模型 / 謝沅志. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 112-119). / Abstracts also in Chinese. / Tse, Yuen Chi = Fen xi heng xiang guang xue tu an de di wei qun zhong jing zheng mo xing / Xie Yuanzhi. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Optical computation and all-optical switching --- p.3 / Chapter 1.2 --- Nonlinear optics and low-intensity ultra-fast all-optical switching of transverse optical pattern --- p.4 / Chapter 1.3 --- Pattern formation and amplitude equation formalism --- p.6 / Chapter 1.4 --- Semiconductor quantum-well double-microcavity and transfermatrix method --- p.9 / Chapter 2 --- Semiconductor quantum-well microcavity --- p.10 / Chapter 2.1 --- Physical configuration and theroy --- p.10 / Chapter 2.2 --- Simplified models --- p.19 / Chapter 2.3 --- Directional instability and the effect of anisotropy in model PCO-Q --- p.25 / Chapter 2.4 --- Effect of control beam and all-optical switching in PCO-Q --- p.30 / Chapter 2.5 --- Simulation results of model PCO-L, a model without quadratic dependence --- p.33 / Chapter 3 --- Population-competition model --- p.37 / Chapter 3.1 --- Derivation of PC model --- p.37 / Chapter 3.1.1 --- Approximation from the simulation results --- p.38 / Chapter 3.1.2 --- Adiabatic approximation for the field equations --- p.39 / Chapter 3.1.3 --- Revised dynamical equations --- p.40 / Chapter 3.1.4 --- Taylor expansion approximation about phase locking --- p.42 / Chapter 3.1.5 --- Comparison with the simulation results --- p.45 / Chapter 3.1.6 --- Modelling of the control beam --- p.47 / Chapter 3.1.7 --- Reduction in the number of parameters --- p.47 / Chapter 3.2 --- Physical meaning of the simplified PC model --- p.49 / Chapter 3.3 --- Comparison with amplitude equations formalism and others competition models --- p.49 / Chapter 4 --- Mathematical tools --- p.52 / Chapter 4.1 --- Steady states and linear stability analysis --- p.52 / Chapter 4.2 --- Gröbner basis --- p.54 / Chapter 4.3 --- Generalized discriminant --- p.55 / Chapter 4.4 --- Algorithm for conditions for qualitative changes --- p.56 / Chapter 4.5 --- Reduction in computational power --- p.57 / Chapter 4.6 --- Elementary catastrophe theory --- p.58 / Chapter 5 --- Population-competition model analysis --- p.66 / Chapter 5.1 --- Symmetric model L without source term --- p.67 / Chapter 5.2 --- Symmetric model Q without source term --- p.70 / Chapter 5.3 --- Asymmetric model L and Q without source term --- p.74 / Chapter 5.4 --- Symmetric models L and Q with control beam S₂ --- p.80 / Chapter 5.5 --- Asymmetric Model L and Q with control beam S₂ --- p.81 / Chapter 6 --- Semiconductor quantum-well double-microcavity --- p.91 / Chapter 6.1 --- Motivation --- p.91 / Chapter 6.2 --- Transfer-matrix method inside dielectrics --- p.94 / Chapter 6.3 --- Transfer-matrix method across QW --- p.97 / Chapter 6.4 --- Analysis of the QWDM through transfer-matrix method --- p.98 / Chapter 7 --- Conclusion and Outlook --- p.105 / Chapter 7.1 --- Conclusion --- p.105 / Chapter 7.2 --- Outlook --- p.107 / Chapter 7.2.1 --- Extension of the PC model --- p.107 / Chapter 7.2.2 --- Extension of the transfer-matrix method to nonlinear analysis --- p.109 / Bibliography --- p.112 / Chapter A --- Dispersion relations inside QWM --- p.120 / Chapter B --- Analysis on the steady states with and without off-axis instability --- p.122 / Chapter B.1 --- Steady states of E₀ and p₀ --- p.122 / Chapter B.2 --- Analysis on the steady states without off-axis instability --- p.123 / Chapter B.3 --- The effects of instability on E₀ and p₀ --- p.124 / Chapter C --- Analytical derivation of the phase diagram asymmetry versus quadratic terms (δβ1 vs γ) without control beam (S₂ = 0) --- p.127 / Chapter D --- Verification of the elliptic umbilic (D₋₄) singularity --- p.129

An Zhong. / "November 30, 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. [167]-173). / 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.

by Yuen Chung Man. / Bibliography: leaves 47-48 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1985

Seet Wah Cheong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 78-81). / Acknowledgement --- p.i / Abstract --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Perturbation approach and Effective Medium Approximation --- p.6 / Chapter 2.1 --- Perturbation method of calculating local fields --- p.6 / Chapter 2.1.1 --- Formalism --- p.7 / Chapter 2.1.2 --- Results of the perturbation calculations of potentials --- p.10 / Chapter 2.2 --- Effective Medium Approximation (EMA) --- p.13 / Chapter 2.2.1 --- Self-consistency conditions --- p.14 / Chapter 2.2.2 --- Results from the self-consistency conditions --- p.14 / Chapter 2.2.3 --- A simplified version of EMA --- p.16 / Chapter 2.3 --- Conclusion --- p.19 / Chapter 3 --- Dilute limit : Enhancement due to surface plasmon resonance --- p.20 / Chapter 3.1 --- Formalism --- p.21 / Chapter 3.2 --- Models and results --- p.25 / Chapter 3.2.1 --- Nonlinear spherical metallic inclusion --- p.25 / Chapter 3.2.2 --- Shell model with nonlinear core --- p.26 / Chapter 3.2.3 --- Shell model with nonlinear shell --- p.28 / Chapter 3.3 --- Conclusion --- p.30 / Chapter 4 --- Numerical calculations of electric potential --- p.32 / Chapter 4.1 --- Formalism --- p.33 / Chapter 4.2 --- Results --- p.41 / Chapter 4.3 --- Symbolic simulations --- p.43 / Chapter 4.3.1 --- Formalism --- p.43 / Chapter 4.3.2 --- Results --- p.45 / Chapter 4.4 --- Conclusion --- p.45 / Chapter 5 --- Local field enhancement in nonlinear composites of multiply coated spherical inclusion --- p.46 / Chapter 5.1 --- Formalism --- p.47 / Chapter 5.2 --- Single spherical inclusion --- p.49 / Chapter 5.3 --- Single shell particle inclusion --- p.50 / Chapter 5.4 --- Nonlinear problem --- p.50 / Chapter 5.5 --- Core field in the single sphere --- p.52 / Chapter 5.6 --- Summary --- p.55 / Chapter 6 --- Optical transition and random resistor network --- p.57 / Chapter 6.1 --- Formalism --- p.58 / Chapter 6.1.1 --- Model --- p.58 / Chapter 6.1.2 --- Solution of the model --- p.60 / Chapter 6.1.3 --- EMA --- p.61 / Chapter 6.1.4 --- Optical transition --- p.62 / Chapter 6.1.5 --- Scaling functions --- p.63 / Chapter 6.2 --- Random resistor network simulation --- p.64 / Chapter 6.2.1 --- One sample frequency dependence --- p.64 / Chapter 6.2.2 --- Sample averages --- p.66 / Chapter 6.3 --- Nonlinear EMA calculations of optical transition --- p.67 / Chapter 6.4 --- Symbolic calculation of conductivities in small h expansion --- p.69 / Chapter 6.4.1 --- Formalism --- p.69 / Chapter 6.4.2 --- Finite size scaling and exponents --- p.71 / Chapter 6.4.3 --- Scaling Function expansion coefficients --- p.74 / Appendix Estimation of surface plasmon resonance frequency --- p.76 / Chapter A.1 --- Single nonlinear metallic sphere --- p.76 / Chapter A.2 --- "Single metallic shell, nonlinear core model" --- p.77 / Bibliography --- p.78 / Figure Caption --- p.82 / List of Tables --- p.91

by Kang Xiaosong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 44-47). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- Preliminary Analysis --- p.11 / Chapter 3 --- Liapunov-Schmidt Reduction --- p.16 / Chapter 4 --- A Maximizing Procedure --- p.27 / Chapter 5 --- Proof of Theorem 1.1 --- p.30 / Chapter 6 --- Proof of Theorem 1.2 --- p.33 / Chapter 7 --- Concluding Remarks --- p.42

by Tso Man Kit. / Thesis submitted in: December 2001. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 58-61). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Preliminary analysis --- p.14 / Chapter 3 --- Liapunov-Schmidt reduction --- p.23 / Chapter 4 --- A minimizing procedure --- p.36 / Chapter 5 --- Proof of theorem 11 --- p.40 / Chapter 6 --- Proof of theorem 12 --- p.43 / Chapter 7 --- Proof of theorem 13 --- p.55 / Bibliography --- p.58

The identification of the dynamic characteristics of nonlinear systems is of increasing interest in the field of modal testing. In this work an investigation has been carried out into the force-state mapping approach to identification of nonlinear systems proposed by Masri and Caughey. They originally suggested a nonparametric identification technique based on curve fitting the restoring force in terms of the velocity and displacement using two dimensional Chebyshev polynomials. It has been shown that the use of Chebyshev polynomials is unnecessarily restrictive and that a simpler approach based on ordinary polynomials and special functions provides a simpler, faster and more accurate identification for polynomial and nonpolynomial types of nonlinearity. This simpler approach has allowed the iterative identification technique for multi-degree of freedom systems to be simplified and a direct identification approach, which is not subject to bias errors, has been suggested. A new procedure for identifying both the type and location of nonlinear elements in lumped parameter systems has been developed and has yielded encouraging results. The practical implementation of the force-state mapping technique required the force, acceleration, velocity and displacement signals to be available at the same instants of time for each measurement station. In order to minimise the instrumentation required, only the force and acceleration are measured and the remaining signals are estimated by integrating the acceleration. The integration problem has been investigated using several approaches both in the frequency and time domains. An analysis of the sensitivity of the estimated parameters with respect to any amplitude and phase measurement errors has been carried out for single-d.o.f. linear systems. Estimates are shown to be extremely sensitive to phase errors for lightly damped structures. The estimation of the mass or generalised mass and modal matrices required for the identification of single or multi-d.o.f. nonlinear systems respectively, has also been investigated. Initial estimates were obtained using a linear multi-point force appropriation method, normally used for the excitation of normal modes. These estimates were then refined using a new technique based on studying the sensitivity of the mass with respect to the estimated system parameters obtained using a nonlinear model. This sensitivity approach seemed promising since accurate results were obtained. It was also shown that accurate estimates for the modal matrix were not essential for carrying out a force-state mapping identification. Finally, the technique has been applied experimentally to the identification of a cantilevered T-beam structure with stiffness and damping nonlinearity. The cases of two well separated and then two fairly close modes were considered. Reasonable agreement between the behaviour of the nonlinear mathematical model and the structure was achieved considering inaccuracies in the measurement set-up. Conclusions have been drawn and some ideas for future work presented.