A micromachined magnetic field sensing system capable of measuring the direction of the Earths magnetic field has been fabricated, measured, and characterized. The system is composed of a micromachined silicon resonator combined with a permanent magnet, excitation and sensing coils, and a magnetic feedback loop. Electromagnetic excitation of the mechanical resonator enables it to operate with very low power consumption and low excitation voltage. The interaction between an external magnetic field surrounding the sensor and the permanent magnet generates a rotating torque on the silicon resonator disc, changing the effective stiffness of the beams and therefore the resonant frequency of the sensor. MEMS-based mechanically-resonant sensors, in which the sensor resonant frequency shifts in response to the measurand, are widely utilized. Such sensors are typically operated in their linear resonant regime. However, substantial improvements in resonant sensor performance can be obtained by designing the sensors to operate far into their nonlinear regime. This effect is illustrated through the use of a magnetically-torqued, rotationally-resonant MEMS platform. Platform structural parameters such as beam width and number of beams are parametrically varied subject to the constraint of constant small-deflection resonant frequency. Nonlinear performance improvement characterization is performed both analytically as well as with Finite Element Method (FEM) simulation, and confirmed with measurement results. These nonlinearity based sensitivity enhancement mechanisms are utilized in the device design. The complete magnetic sensing system consumes less than 200 microwatts of power in continuous operation, and is capable of sensing the direction of the Earths magnetic field. Such low power consumption levels enable continuous magnetic field sensing for portable electronics and potentially wristwatch applications, thereby enabling personal navigation and motion sensing functionalities. A total system power consumption of 138W and a resonator actuation voltage of 4mVpp from the 1.2V power supply have been demonstrated with capability of measuring the direction of the Earths magnetic field. Sensitivities of 0.009, 0.086, and 0.196 [mHz/(Hz and #903;degree)] for the Earths magnetic field were measured for 3, 4, and 6 beam structures, respectively.

Many phenomena associated with nonlinear optics are produced by the light-matter interaction in liquid crystals. Nematic liquid crystals possess the properties of the birefringence and that refractive indexes of nematic liquid crystal vary with temperature. As a light beam propagates in liquid crystals, the light beam experiences changes of refractive indexes because the optical field reorientates molecules or the optical intensity changes the temperature of liquid crystal. Then, some interesting phenomena of optical nonlinearity produce in liquid crystals. This study investigates mainly the nonlinear behaviors in nematic liquid crystals. By etching ITO glasses to control distribution of electric field, we discuss applications in photo-electric field. These works are described as follows: First, a low voltage was applied to a planar nematic liquid crystal cell; the director field can be reoriented using a low intensity. Then, the self-focusing effect produces due to a variation of refractive indexes. The light beam in nematic liquid crystal forms a spatial soliton by producing the effect of the self-focusing to balance the diffraction. Additionally, we study the interaction between solitons. One soliton creates a potential well of refractive index, anther one will be attracted in the potential well. As the separated distance between two solitons and the pumping angle are appropriate, two solitons propagate in the form of spiral. Second, we study the behavior of light in a periodic refractive index medium. The director field of the nematic liquid crystal (NLC) is reorientated in a grating¡Vlike indium-tin-oxide electrode cell by applying a controllable-voltage. The variation of refractive index with voltage varied 0v to 10v was observed by a conoscopic method. Numerical simulations have reproduced the main features of the gradient distribution of refractive index in the waveguide. Several phenomena of a polarized laser beam that propagated in the waveguide with different incident angles and positions have observed by a CCD camera, including solitons, undulate beam, the total internal reflection and beam coupling. Third, at the temperature close to nematic-isotropic phase transition temperature, the variation of refractive index in the liquid crystal becomes obvious to the change of temperature. And, a laser beam can easily reorientate molecules. We changed beam intensity in liquid crystal cell, different nonlinear phenomena were observed. Besides, A combined microscopic and conoscopic technique was used in experiments as a convenient way to analyze the optical nonlinearity that is associated with the molecular configuration of nematic liquid crystal.

For reliable service, a power system must remain stable and capable of withstanding a wide range of disturbances especially for the large interconnected systems. In the last decade and a half and in particular after the famous blackout in N.Y. U.S.A. 1965, considerable research effort has gone in to the stability investigation of power systems. To deal with the requirements of real power systems, various stabilizing control techniques were being developed over the last decade. Conventional control engineering approaches are unable to effectively deal with system complexity, nonlinearities, parameters variations and uncertainties. This dissertation presents a non-linear control technique which relies on prediction of the large power system behaviour. One example of a large modern power system formed by interconnecting the power systems of various states is the South-Eastern Australian power network made up of the power systems of Queensland, New South Wales, Victoria and South Australia. The Model Predictive Control (MPC) for the total power system has been shown to be successful in addressing many large scale nonlinear control problems. However, for application to the high order problems of power systems and given the fast control response required, total MPC is still expensive and is structured for centralized control. This thesis develops a MPC algorithm to control the field currents of generators incorporating them in a decentralized overall control scheme. MPC decisions are based on optimizing the control action in accordance with the predictions of an identified power system model so that the desired response is obtained. Energy Function based design provides good control for direct influence items such as SVC (Static Var Compensators), FACTS (Flexible AC Transmission System) or series compensators and can be used to define the desired flux for generator. The approach in this thesis is to use the design flux for best system control as a reference for MPC. Given even a simple model of the relation between input control signal and the resulting machine flux, the MPC can be used to find the control sequence which will start the correct tracking. The continual recalculation of short time optimal control and then using only the initial control value provides a form of feedback control for the system in the desired tracking task but in a manner which retains the nonlinearity of the model.

Quantum information science has shown that computers which exploit the quantum nature of particles, namely quantum computers, can outperform contemporary computers in some computational tasks. The fundamental building blocks of a quantum computer are quantum logical gates and quantum bits (qubits). Previous research has shown that the optical approach to quantum computing is promising. However, linear optical quantum computing (LOQC) schemes require a huge amount of resource, which makes large scale LOQC impractical, and hence there have been renewed interests in nonlinear optical quantum computing schemes, where less resource is required. The performance of these quantum gates depends on the properties of the nonlinear media. However, requirements on some of the properties for high performance quantum gates are not fully known. This thesis intends to bridge this gap of knowledge and examines the necessary conditions on several types optical nonlinearities that are common in two-qubit quantum gates schemes. These types of nonlinearities are, namely two-photon absorption, $\chi^{(2)}$ nonlinearity and $\chi^{(3)}$ cross-Kerr nonlinearity. The two-photon absorption based quantum Zeno gate is modeled in this thesis. It is shown that for practical absorbers, the photon loss significantly lowers the quantum fidelity of the Zeno gate. Nevertheless, this thesis proposes to use the Zeno gate for fusing optical cluster states. With the best theoretical estimate of single photon loss in the absorbers, the Zeno gate can outperform linear optical schemes. This thesis also proposes to embed the Zeno gate in the teleportation-type of two-qubit gate, namely GC-Zeno gate, such that the success rate of the gate can be traded off for higher gate fidelity. The effect of some mode matching error and detector inefficiency on the GC-Zeno gate are also considered here. It is shown that the photon loss requirement as well as the mode matching requirement are both stringent for having a fault tolerant GC-Zeno gate. This thesis models some of the properties of a $\chi^{(3)}$ optical medium and explores how they affect the fidelity of the cross-Kerr nonlinearity based quantum gate. This thesis shows that for a cross-Kerr medium with fast time response but negligible wave dispersion, the medium would induce spectral entanglement between the input photons and this significantly lowers the fidelity of the quantum gate. Nevertheless, when the dispersion has a stronger effect than the time response, and if phase noise is negligible, it is possible to achieve a quantum gate with high fidelity. However, the noise is actually significant, and this thesis suggests that spectral filtering can be applied to prohibit the occurrence of the noise. The requirements on employing optical $\chi^{(2)}$ nonlinearity for quantum computing are also examined. This study models the spectral effects of a $\chi^{(2)}$ medium on its efficiency. It is shown in this thesis that since the Hamiltonian of the medium does not commute at different times, the unitary operation should be modeled by a Dyson series, which leads to undesired spectral entanglement that lowers the efficiency of the medium. However, in the case of periodical poling, the unitary operation can be modeled by a Taylor series, where under some phase matching conditions, the medium can have a high efficiency. Furthermore, this thesis proposes a Bell measurement scheme and a quantum gate scheme based on $\chi^{(2)}$ nonlinearity that can always outperform linear optics even when the nonlinearity strength is weak. In the case of sufficiently strong nonlinearity, a quantum gate with high success rate can be achieved. In summary, this thesis models some of the properties of two-photon absorbers, $\chi^{(2)}$ nonlinearity and $\chi^{(3)}$ nonlinearity, and shows that it is possible to achieve the conditions required for high performance quantum gates, however these conditions are experimentally challenging to meet.

Quantum information science has shown that computers which exploit the quantum nature of particles, namely quantum computers, can outperform contemporary computers in some computational tasks. The fundamental building blocks of a quantum computer are quantum logical gates and quantum bits (qubits). Previous research has shown that the optical approach to quantum computing is promising. However, linear optical quantum computing (LOQC) schemes require a huge amount of resource, which makes large scale LOQC impractical, and hence there have been renewed interests in nonlinear optical quantum computing schemes, where less resource is required. The performance of these quantum gates depends on the properties of the nonlinear media. However, requirements on some of the properties for high performance quantum gates are not fully known. This thesis intends to bridge this gap of knowledge and examines the necessary conditions on several types optical nonlinearities that are common in two-qubit quantum gates schemes. These types of nonlinearities are, namely two-photon absorption, $\chi^{(2)}$ nonlinearity and $\chi^{(3)}$ cross-Kerr nonlinearity. The two-photon absorption based quantum Zeno gate is modeled in this thesis. It is shown that for practical absorbers, the photon loss significantly lowers the quantum fidelity of the Zeno gate. Nevertheless, this thesis proposes to use the Zeno gate for fusing optical cluster states. With the best theoretical estimate of single photon loss in the absorbers, the Zeno gate can outperform linear optical schemes. This thesis also proposes to embed the Zeno gate in the teleportation-type of two-qubit gate, namely GC-Zeno gate, such that the success rate of the gate can be traded off for higher gate fidelity. The effect of some mode matching error and detector inefficiency on the GC-Zeno gate are also considered here. It is shown that the photon loss requirement as well as the mode matching requirement are both stringent for having a fault tolerant GC-Zeno gate. This thesis models some of the properties of a $\chi^{(3)}$ optical medium and explores how they affect the fidelity of the cross-Kerr nonlinearity based quantum gate. This thesis shows that for a cross-Kerr medium with fast time response but negligible wave dispersion, the medium would induce spectral entanglement between the input photons and this significantly lowers the fidelity of the quantum gate. Nevertheless, when the dispersion has a stronger effect than the time response, and if phase noise is negligible, it is possible to achieve a quantum gate with high fidelity. However, the noise is actually significant, and this thesis suggests that spectral filtering can be applied to prohibit the occurrence of the noise. The requirements on employing optical $\chi^{(2)}$ nonlinearity for quantum computing are also examined. This study models the spectral effects of a $\chi^{(2)}$ medium on its efficiency. It is shown in this thesis that since the Hamiltonian of the medium does not commute at different times, the unitary operation should be modeled by a Dyson series, which leads to undesired spectral entanglement that lowers the efficiency of the medium. However, in the case of periodical poling, the unitary operation can be modeled by a Taylor series, where under some phase matching conditions, the medium can have a high efficiency. Furthermore, this thesis proposes a Bell measurement scheme and a quantum gate scheme based on $\chi^{(2)}$ nonlinearity that can always outperform linear optics even when the nonlinearity strength is weak. In the case of sufficiently strong nonlinearity, a quantum gate with high success rate can be achieved. In summary, this thesis models some of the properties of two-photon absorbers, $\chi^{(2)}$ nonlinearity and $\chi^{(3)}$ nonlinearity, and shows that it is possible to achieve the conditions required for high performance quantum gates, however these conditions are experimentally challenging to meet.

Dans cette thèse, nous faisons l'analyse des conditions d'existence du phénomène de supratransmission non linéaire dans deux modèles différents: un système de Klein-Gordon de cinquième ordre modifié et un système de sine-Gordon modifié. Les modèles modifiés considérés ici sont ceux avec couplage mixte, le couplage linéaire pur étant associé à un couplage non linéaire. En particulier, nous quantifions numériquement l'influence du coefficient de couplage non linéaire sur l'amplitude de seuil qui déclenche le phénomène de supratransmission non-linéaire. Notre résultat principal montre que, dans les deux modèles, lorsque le coefficient de couplage non linéaire augmente, l'amplitude de seuil déclenchant le phénomène de supratransmission non linéaire diminue. / In this thesis, we analyze the conditions of existence of the phenomenon of nonlinear supratransmission in two different models: a modified fifth-order Klein-Gordon system and a modified sine-Gordon system. The modified models considered here are those with mixed coupling, the pure linear coupling being associated with a nonlinear coupling. In particular, we quantify numerically the influence of the non-linear coupling coefficient on the threshold amplitude which triggers the phenomenon of non-linear supratransmission. Our main result shows that in both models, when the nonlinear coupling coefficient increases, the threshold amplitude triggering the phenomenon of nonlinear supratransmission decreases.

abstract: The focus of this dissertation is first on understanding the difficulties involved in constructing reduced order models of structures that exhibit a strong nonlinearity/strongly nonlinear events such as snap-through, buckling (local or global), mode switching, symmetry breaking. Next, based on this understanding, it is desired to modify/extend the current Nonlinear Reduced Order Modeling (NLROM) methodology, basis selection and/or identification methodology, to obtain reliable reduced order models of these structures. Focusing on these goals, the work carried out addressed more specifically the following issues: i) optimization of the basis to capture at best the response in the smallest number of modes, ii) improved identification of the reduced order model stiffness coefficients, iii) detection of strongly nonlinear events using NLROM. For the first issue, an approach was proposed to rotate a limited number of linear modes to become more dominant in the response of the structure. This step was achieved through a proper orthogonal decomposition of the projection on these linear modes of a series of representative nonlinear displacements. This rotation does not expand the modal space but renders that part of the basis more efficient, the identification of stiffness coefficients more reliable, and the selection of dual modes more compact. In fact, a separate approach was also proposed for an independent optimization of the duals. Regarding the second issue, two tuning approaches of the stiffness coefficients were proposed to improve the identification of a limited set of critical coefficients based on independent response data of the structure. Both approaches led to a significant improvement of the static prediction for the clamped-clamped curved beam model. Extensive validations of the NLROMs based on the above novel approaches was carried out by comparisons with full finite element response data. The third issue, the detection of nonlinear events, was finally addressed by building connections between the eigenvalues of the finite element software (Nastran here) and NLROM tangent stiffness matrices and the occurrence of the ‘events’ which is further extended to the assessment of the accuracy with which the NLROM captures the full finite element behavior after the event has occurred. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2020

Understanding the impact of jet noise and other high-amplitude sound sources can be improved by quantifying the nonlinearity in a signal with a single-microphone measurement. An ensemble-averaged, frequency-domain version of the generalized Burgers equation has been used to derive a quantitative expression for the change in spectral levels (in decibels) over distance due to geometric spreading, thermoviscous absorption, and nonlinearity, respectively. The nonlinearity indicator, called νN , is based on the quadspectral Morfey-Howell indicator, which has been used in the past to characterize nonlinearity in noise waveforms. Unlike the Morfey-Howell indicator, the νN indicator has direct physical significance, giving a change in decibels per meter of the sound pressure level spectrum specifically due to nonlinearity. However, a detailed characterization of the expected behavior and potential issues for the nonlinearity indicator has been lacking. The quadspectral nonlinearity indicator is first calculated for well-known solutions to several basic acoustical scenarios to determine its expected behavior in both the near field and far field. Next, the accuracy of νN is examined as a function of measurement parameters such as sampling frequency, signal bandwidth, scattering, and noise. Recommendations for conducting experiments are given based on the findings. Finally, the indicator is calculated for model-scale and military jet noise waveforms. These tests reveal the utility and accuracy of the νN indicator for characterizing broadband noise; the indicator gives frequency-dependent information about the waveform from a single-point measurement.

In this thesis, we present a sensor model comprised of a geometrically nonlinear beam coupled with a nonlinear viscoelastic Pasternak foundation via a distributed system of compliant elements. The governing equations of the system are obtained. By posing an inverse problem, the model is used to simulate the estimation of coupled substrates' material (constitutive) parameters. In the inverse problem, beam deformations are considered as measured parameters, and therefore an eventual hardware implementation would require measurements of these quantities. Different case studies are simulated to assess the robustness and applicability of this sensor model.

The presence of various impairments in fiber channel has forced researchers to uncover solutions to minimize those effects. With the advancement of technology, optical solutions were finally easier to implement in the system. To this day, optical compensation methods are still found to be as the best way to minimize fiber impairments. With the development of digital signal processing (DSP) and FIR techniques, coherent detection with digital signal processing (DSP) is developed, analyzed theoretically and numerically and experimentally demonstrated in long-haul high speed fiber‐optic transmission system. The use of DSP in conjunction with coherent detection unleashes the benefits of coherent detection which rely on the preservation of full information of the transmitted field. These benefits include high receiver sensitivity, the ability to achieve high spectral‐efficiency and the use of advanced modulation formats. The local oscillator (LO) of coherent receiver alleviates the need for hardware phase‐locking and polarization tracking, which can now be achieved in the digital domain. The computational complexity previously associated with coherent detection is hence significantly diminished and coherent detection is once again considered a feasible detection alternative. In this thesis, an optical fiber communication scheme using the coherent detection method is simulated. Firstly, at the beginning of each chapter, we introduce the various compensation methods for certain optical fiber impairments which is developed by the pioneers. However, such technique does introduce enormous complexity to the system, in addition to a large cost. For that reason, the main focus had to shift to an alternative method. DSP techniques has enabled simple techniques to mitigate various impairments in fiber-optical systems. In this thesis, the background knowledge about the structure of fiber-optical transmission system is provided. After the mathematical analysis of the various impairments (laser noise, chromatic dispersion, polarization mode dispersion and nonlinearity) in fiber-optical links, the compensation methods by using DSP techniques are provided. By the methods of fourth-power carrier recovery algorithm and feedforward carrier recovery algorithm, the phase rotation in constellation due to laser noise is compensated in QPSK systems and QAM systems, respectively. The feedforward carrier recovery algorithm has a high tolerance for laser linewidth in high-order QAM system. As for PMD compensation, on the basis of adaptive equalizers in both time domain and frequency domain achiever by the pioneers, a novel LMS algorithm is proposed in this thesis. It has a fair comparative and steady computational complexity with the increase in the number of training blocks. The last part is the nonlinearity compensation. The DBP compensation is a popular method for nonlinearity compensation but its computational complexity is fair high (Shao J, Kumar S and Liang X., 2013). We adopt two kinds of fold-DBP which are distance-folded DBP and dispersion-folded DBP to compensate the joint impairments of chromatic dispersion and nonlinearity in dispersion-managed system. The distance-folded DBP works well in the full compensation dispersion-managed system but in the presence of RDPS, only the dispersion-folded DBP is efficient. / Thesis / Master of Applied Science (MASc)