The fundamental limits of electronic systems in communication networks motivated scholars to think of an alternative approach to overcome problems such as demand for wider bandwidths and heat dissipation. All-optical signal processing is demonstrated as a potential solution. A major improvement in cost and speed of networking systems is expected through replacing microelectronics by photonic chips. However, the variety of operations essential to perform all-optical signal processing cannot be handled by a single material platform yet. Several III-V semiconductors, such as AlGaAs, have demonstrated potentials for photonic integration; nevertheless, there is still lack of data in literature on nonlinear optical properties of these materials. In this thesis, we extend the quest to evaluate more candidates from this class of semiconductors. Moreover, we are aiming for demonstrating the potentials of various III-V compounds for nonlinear photonics on-a-chip. In this thesis, we propose several optical waveguide designs based on quaternary III-V semiconductors AlGaAsSb and InGaAsP. We present modal analysis for waveguide designs and show that effective mode area much less than 1 $\mu m^{2}$ can be obtained. We also report specific waveguide designs that display zero-dispersion points at the specific wavelength ranges of interest. The designed waveguides are thus expected to demonstrate efficient nonlinear optical interactions. Next step is the fabrication of these devices with the goal to experimentally assess their nonlinear optical performance. The fabrication process of InGaAsP/InP strip-loaded waveguide is briefly reviewed. Following that, we report on the first, to the best of our knowledge, demonstration of third-order nonlinear optical interactions in InGaAsP/InP strip-loaded waveguides. We have performed self-phase modulation, nonlinear absorption measurements, and four-wave mixing experiments at the telecom wavelength range. The nonlinear phase shift up to 2.5 $\pi$ has been observed. Following that, we use Monte-Carlo method for design optimization and tolerance analysis of a multi-step lateral taper Spot-Size Converter in indium phosphide. An exemplary four-step lateral taper design featuring 0.35 dB coupling loss at optimal alignment of a standard single-mode fiber, $>$7 $\mu m$ 1-dB displacement tolerance in any direction of in a facet plane, and a great stability against manufacturing variances demonstrated.

This dissertation introduces the Explicit Reference Governor: a simple and systematic add-on control unit that provides constraint handling capabilities to any pre-stabilized nonlinear system by suitably manipulating its applied reference. The main innovation of the proposed framework is that constraint satisfaction is ensured without having to solve implicit equations. As a result, the Explicit Reference Governor is particularly well suited for applications with limited computational capabilities. The basic idea behind the scheme consists in manipulating the derivative of the applied reference so that, at any given time instant, the currently applied reference will not cause a violation of constraints anytime in the future. The theory behind the proposed framework is presented in general terms and is then detailed to provide specific design strategies. Possible extensions to ensure robustness are also proposed. In addition to introducing the general theory of the Explicit Reference Governor, the dissertation illustrates its step-by-step implementation on Unmanned Aerial Vehicles. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

La rupture des matériaux quasi-fragiles, tels que les céramiques ou les bétons, peut être représentée schématiquement par la succession des étapes de nucléation et de coalescence de micro-fissures. Modéliser ce processus de rupture est un enjeu particulièrement important lorsque l'on s'intéresse à la résistance des structures en béton, en particulier à la prédiction de la perméabilité des structures endommagées. La démarche choisie est une vision multi-échelle où le comportement global est caractérisé par la mécanique de la rupture, et le comportement local représenté par la méthode des éléments discrets. Le modèle représente la fissuration par des grandeurs généralisées, qui seront définies dans le cadre de la mécanique de la rupture. Afin de prendre en compte l’aspect non linéaire de la fissuration dans les matériaux quasi-fragiles, la cinématique usuelle de la mécanique de la rupture est enrichie par l’ajout de degrés de libertés supplémentaires chargés de représenter la part non linéaire du champ de vitesse. L'évolution du comportement est alors condensé par l'évolution de facteurs d'intensité. Le modèle proposé permet de prédire le comportement lors de chargements de mode mixte I+II proportionnel et non-proportionnel. Enfin, une campagne d'essais visant à caractériser le comportement en fissuration du mortier à été réalisée. Les résultats obtenus montrent un rôle important de la fissuration par fatigue. La méthode de changement d'échelle a également été appliquée sur les champs de vitesse en pointe de fissure, confirmant la représentation du comportement en pointe de fissure par une cinématique enrichie. / Fracture in quasi-brittle materials, such as ceramics or concrete, can be represented schematically by series of events of nucleation and coalescence of micro-cracks. Modeling this process is an important challenge for the reliability and life prediction of concrete structures, in particular the prediction of the permeability of damaged structures. A multi-scale approach is proposed. The global behavior is modeled within the fracture mechanics framework and the local behavior is modeled by the discrete element method. An approach was developed to condense the non linear behavior of the mortar. A model reduction technic is used to extract the relevant information from the discrete elements method. To do so, the velocity field is partitioned into mode I, II, linear and non-linear components, each component being characterized by an intensity factor and a fixed spatial distribution. The response of the material is hence condensed in the evolution of the intensity factors, used as non-local variables. A model was also proposed to predict the behavior of the crack for proportional and non-proportional mixed mode I+II loadings. An experimental campaign was finally conducted to characterize the fatigue and fracture behavior of mortar. The results show that fatigue crack growth can be of significant  importance. The experimental velocity field determined, in the crack tip region, by DIC, were analyzed using the same technic as that used for analyzing the fields obtained by the discrete element method showing consistent results.

M.Sc. / There have been an extensive study on solutions of differential equations modeling physical phenomena that blows up in finite time. The blow-up time often represents an important change in the properties of such models and hence it is very important to compute it as accurate as possible. In this work, an adaptive in time numerical method for computing blow-up solutions for nonlinear ODEs is introduced. The method is named implicit midpoint-implicit Euler method (IMIE) and is based on the implicit Euler and the implicit midpoint method. The method is used to compute blow-up time for different examples of ODEs, PDEs and VIDEs. The PDEs studied are reaction-diffusion equations whereby the method of lines is first used to discretize the equation in space to obtain a system of ODEs. Quadrature rules are used to approximate the integral in the VIDE to get a system of ODEs. The IMIE method is then used then to solve the system of ODEs. The results are compared to results obtained by the PECEIE method and Matlab solvers ode45 and ode15s. The results show that the IMIE method gives better results than the PECE-IE and ode15s and compares quite remarkably with the 4th order ode45 yet it is of order 1 with order 2 superconvergence at the mesh points.

The control of flotation circuits is a complicated problem, since flotation circuits are nonlinear multivariable processes with a significant degree of interaction between the variables. Isolated PID controllers usually do not perform adequately. The application of a nonlinear model predictive algorithm based on second order Volterra models was investigated. Volterra series models are a higher order extension of linear impulse response models. The nonlinear model predictive control algorithm can also be seen as a linear model predictive controller with higher order correction terms. A dynamic model of a flotation circuit based on the governing continuity equations was developed. The responses obtained represented the qualitative relationships between the model inputs and the controlled variables. This model exhibited strong nonlinearities, including asymmetrical responses to symmetrical inputs and gain sign changes. This dynamic model was treated as the plant to be identified and from which second order Volterra models were obtained. Full Volterra models required excessively large data sets, but significant reductions in the size of the required data set could be achieved if some of the second order coefficients were constrained to zero. These "pruned" Volterra models represented the plant dynamics significantly better than linear models. In particular, these second order Volterra models were able to model asymmetrical responses including gain sign changes. A special case of "pruned" second order Volterra models are diagonal second order models, where all the off-diagonal coefficients (hij where i ≠ j) are constrained to zero. These models required less data than pruned Volterra models containing off-diagonal coefficients, but were less accurate. The performance of nonlinear model predictive controllers based on a pruned second order and diagonal second order Volterra models was evaluated. The performance of these controllers was also compared to the performance obtained with a first order (linear) Volterra model. All three controllers gave equivalent results for large manipulated variable weights. However, when the controllers were tuned more aggressively, results obtained from the three controllers differed considerably. The pruned nonlinear controller performed well even when tuned aggressively while the performance of the linear controller deteriorated. For the case of disturbance rejection, the linear controller performed slightly better than the nonlinear controllers. / Dissertation (MEng (Control Engineering))--University of Pretoria, 2006. / Chemical Engineering / unrestricted

NonLinear Principal Component Analysis (NLPCA) using three-hidden-layer feed-forward neural networks can produce solutions that over-fit the data and are non-unique. These problems have been dealt with by subjective methods during the network training. This study shows that these problems are intrinsic due to the three-hidden-layer architecture. A simplified two-hidden-layer feed-forward neural network that has no encoding layer and no bottleneck and output biases is proposed. This new, compact NLPCA model alleviates these problems without employing the subjective methods and is called quasi-objective. The compact NLPCA is applied to the zonal winds observed at seven pressure levels between 10 and 70 hPa in the equatorial stratosphere to represent the Quasi-Biennial Oscillation (QBO) and investigate its variability and structure. The two nonlinear principal components of the dataset offer a clear picture of the QBO. In particular, their structure shows that the QBO phase consists of a predominant 28.4-month cycle that is modulated by an 11-year cycle and a longer-period cycle. The significant difference in variability of the winds between cold and warm seasons and the tendency for a seasonal synchronization of the QBO phases are well captured. The one-dimensional NLPCA approximation of the dataset provides a better representation of the QBO than the classical principal component analysis and a better description of the asymmetry of the QBO between westerly and easterly shear zones and between their transitions. The compact NLPCA is then applied to the Arctic Oscillation (AO) index and aforementioned zonal winds to investigate the relationship of the AO with the QBO. The NLPCA of the AO index and zonal-winds dataset shows clearly that, of covariation of the two oscillations, the phase defined by the two nonlinear principal components progresses with a predominant 28.4-month periodicity, plus the 11-year and longer-period modulations. Large positive values of the AO index occur when westerlies prevail near the middle and upper levels of the equatorial stratosphere. Large negative values of the AO index arise when easterlies occupy over half the layer of the equatorial stratosphere. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

Polarization mode dispersion (PMD) is stochastic in nature and continues evolving in an unpredictable manner according to the changing environment. Nonlinear birefringence in multichannel systems alters the polarization states of the bits, so that they vary from one bit to the next in a way that is difficult to predict. These are the two major signal-impairment effects that are inherent in optical fibre transmission links which can seriously degrade network performance. It is therefore extremely challenging to compensate for both linear and nonlinear birefringence in multichannel systems. The purpose of this thesis is to investigate the interaction between PMD and nonlinear induced birefringence in a fibre with consideration of mode coupling. A sound knowledge of this interaction is necessary in designing a linear and nonlinear polarization mode dispersion compensator for WDM systems, as was successfully carried out in this study. The investigation shows that the effect of nonlinear birefringence alone depolarizes the signal, while in high PMD links where polarization mode coupling is high, the nonlinear birefringence effect couples with second-order PMD such that it may reduce the penalty and improve the signal DOP. Further investigation shows that when nonlinear birefringence becomes significant, asymmetry arises between the two principal axes of the fibre, such that it is only one axis which experiences the effect of nonlinear birefringence. It is found out that along this vii axis, there exists a critical point in pump power where the nonlinear birefringence cancels PMD in the link and improves the signal. An adaptive compensator to cancel PMD and nonlinear birefringence was designed based on feedforward DOP-monitoring signal. The compensator was tested both at laboratory level and on the Telkom buried fibre link and found to be functioning as intended. It was able to adaptively track and compensate PMD in the link in less than a second. The compensator was able to cancel PMD in the link up to a maximum of 30 ps. The compensator improved the DOP of the worst signal by more than 100 percent.

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This thesis deals with a set of overlapping problems in finance and econometrics which involve nonlinearities and dynamics: nonlinear co-integration, asset pricing dynamics and nonparametric derivative asset pricing.

Coherent anti-Stokes Raman scattering microscopy is a versatile technique for label-free imaging and spectroscopy of systems of biophysical interest. Due to the coherent nature of the generated signals, CARS images and spectra can often be difficult to interpret. In this thesis, we document how distortions and enhancements can be produced in CARS hyperspectroscopy as a result of the instrument, geometrical optical effects, or unique molecular states, and discuss how these effects may be suppressed or exploited in various CARS applications.