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Transport of sediment in coastal regions directly impacts mine countermeasure operations and naval construction efforts. Wave induced shear stress in the surf zone is responsible for entraining sediment particles into suspension within the combined wave and current boundary layer, where momentum is imparted through highly nonlinear processes. Therefore, a detailed understanding of sediment flux processes in the surf zone is essential to accurately model net sediment transport. This study examines the use of acoustic backscatter inversion as a means of measuring sediment concentration profiles. Measurements of sediment concentration and velocity profiles were made by a high frequency Doppler velocity profiler deployed on Blackâ s Beach during the Nearshore Canyon Experiment, NCEX. Profiles of sediment flux were compared with hourly mean current measurements from a cross-shore/long-shore array of PUV sensors and two-dimensional planner images of the morphological evolution provided by a three camera Argus video suite. Observations from a seven day period containing the development and evolution of a weak rip channel demonstrated that acoustic backscatter inversion techniques, when calibrated with in situ sediment samples, provide high spatial and temporal resolution estimates of sediment concentration and fluxes into the thin wave boundary layer. These sediment transport measurements were correlated with observed mean currents and rip channel evolution, and show a strong morphological response to the sediment flux.

Optically pumped semiconductor vertical external cavity surface emitting lasers (VECSEL) were first demonstrated in the mid 1990's. Due to the unique design properties of extended cavity lasers VECSELs have been able to provide tunable, high-output powers while maintaining excellent beam quality. These features offer a wide range of possible applications in areas such as medicine, spectroscopy, defense, imaging, communications and entertainment. Nowadays, newly developed VECSELs, cover the spectral regions from red (600 nm) to around 5 µm. By taking the advantage of the open cavity design, the emission can be further expanded to UV or THz regions by the means of intracavity nonlinear frequency generation. The objective of this dissertation is to investigate and extend the capabilities of high-power VECSELs by utilizing novel nonlinear conversion techniques. Optically pumped VECSELs based on GaAs semiconductor heterostructures have been demonstrated to provide exceptionally high output powers covering the 900 to 1200 nm spectral region with diffraction limited beam quality. The free space cavity design allows for access to the high intracavity circulating powers where high efficiency nonlinear frequency conversions and wavelength tuning can be obtained. As an introduction, this dissertation consists of a brief history of the development of VECSELs as well as wafer design, chip fabrication and resonator cavity design for optimal frequency conversion. Specifically, the different types of laser cavities such as: linear cavity, V-shaped cavity and patented T-shaped cavity are described, since their optimization is crucial for transverse mode quality, stability, tunability and efficient frequency conversion. All types of nonlinear conversions such as second harmonic, sum frequency and difference frequency generation are discussed in extensive detail. The theoretical simulation and the development of the high-power, tunable blue and green VECSEL by the means of type I second harmonic generation in a V- cavity is presented. Tens of watts of output power for both blue and green wavelengths prove the viability for VECSELs to replace the other types of lasers currently used for applications in laser light shows, for Ti:Sapphire pumping, and for medical applications such as laser skin resurfacing. The novel, recently patented, two-chip T-cavity configuration allowing for spatial overlap of two, separate VECSEL cavities is described in detail. This type of setup is further used to demonstrate type II sum frequency generation to green with multi-watt output, and the full potential of the T-cavity is utilized by achieving type II difference frequency generation to the mid-IR spectral region. The tunable output around 5.4 µm with over 10 mW power is showcased. In the same manner the first attempts to generate THz radiation are discussed. Finally, a slightly modified T-cavity VECSEL is used to reach the UV spectral regions thanks to type I fourth harmonic generation. Over 100 mW at around 265 nm is obtained in a setup which utilizes no stabilization techniques. The dissertation demonstrates the flexibility of the VECSEL in achieving broad spectral coverage and thus its potential for a wide range of applications.

<p>The nonlinear interaction between light and atoms is an extensive field of study with a broad range of applications in quantum information science and condensed matter physics. Nonlinear optical phenomena occurring in cold atoms are particularly interesting because such slowly moving atoms can spatially organize into density gratings, which allows for studies involving optical interactions with structured materials. In this thesis, I describe a novel nonlinear optical effect that arises when cold atoms spatially bunch in an optical lattice. I show that employing this spatial atomic bunching provides access to a unique physical regime with reduced thresholds for nonlinear optical processes and enhanced material properties. Using this method, I observe the nonlinear optical phenomenon of transverse optical pattern formation at record-low powers. These transverse optical patterns are generated by a wave- mixing process that is mediated by the cold atomic vapor. The optical patterns are highly multimode and induce rich non-equilibrium atomic dynamics. In particular, I find that there exists a synergistic interplay between the generated optical pat- terns and the atoms, wherein the scattered fields help the atoms to self-organize into new, multimode structures that are not externally imposed on the atomic sample. These self-organized structures in turn enhance the power in the optical patterns. I provide the first detailed investigation of the motional dynamics of atoms that have self-organized in a multimode geometry. I also show that the transverse optical patterns induce Sisyphus cooling in all three spatial dimensions, which is the first observation of spontaneous three-dimensional cooling. My experiment represents a unique means by which to study nonlinear optics and non-equilibrium dynamics at ultra-low required powers.</p> / Dissertation

This thesis is focused on the dynamics and control of nonlinear engineering systems. A developed approach is applied to three specific problems: suppression of torsional vibrations occurring in a drill-string, lateral vibrations on an unbalanced rotor and vibrational energy extraction from rotating pendulum systems. The first problem deals with drill-string torsional vibrations while drilling, which is conducted in the experimental drilling rig developed at University of Aberdeen. A realistic model of the experimental setup is then constructed, taking into account the dynamics of the drill-string and top motor. Physical parameters of the experimental drilling rig are estimated in order to calibrate the model to ensure the correspondence of the research results to the experimental conditions. Consequently, a control method is introduced to suppress torsional and stick-slip oscillations exhibited in the experimental drilling rig. The experimental and numerical results considering delay of the actuator are shown to be in close agreement, including the success of the controller in significantly reducing the vibrations. In the second problem a soft impact oscillator approach is used to study the dynamics of the asymmetric Jeffcott rotor. A realistic model of the experimental setup is developed, taking into account an asymmetric physical configuration in rotor part as well as snubber rig. Several experimental bifurcation diagrams are conducted with different conditions in range around the grazing point. Experimental and numerical results based on the proposed model are compared and shown to be in close agreement. The last problem relates to initiating and maintaining the rotational motion of a parametric pendulum as an energy harvesting system. Several possible control methods to initiate and maintain the rotational motion of a harmonically-excited pendulum are proposed and then verified experimentally. The time-delayed feedback method is shown to maintain quite well the rotational motion of a sinusoidally excited parametric pendulum, even in the presence of noise. A control method for the wave-excited pendulum system is then suggested and tested in order to increase the probability of its rotational motion. This proposed control method succeeds in significantly raising the probability of rotational motion of the wave-excited pendulum.

Plasmonic structures with nanometer scale gaps provide localized field enhancement and allow for engineering of the optical response, which is well described by conventional classical models. For subnanometer scale gaps, quantum effects and nonlocal effects become important and classical electromagnetics fail to describe the plasmonic coupling response. Coupled plasmonic system of gold nanoparticles on top of thin gold film separated with self-assembled monolayers (SAMs) provides a convenient geometry to experimentally explore plasmonic features in subnanometer scale gaps. However, the surface roughness of the thin metal film can significantly influence the plasmonic coupling properties. In this dissertation, I suggest modifying the coupled nanoparticles-film structures by using ultraflat thin metal films. Using these structures, I investigated the far-field optical response for gap size variations by dark field scattering measurements. A red-shift of the plasmon resonance wavelength was observed by reducing the gap width. However, I did not observe the previously reported saturation trend of the resonance shift for subnanometer scale gaps. I attribute the difference to surface roughness effects in past works since as they were not present in my studies with ultraflat films. To study the near-field enhancement in subnanometer scale gaps, I used third harmonic generation as a method that is highly sensitive (as the third power) to the local field intensity. The onset of the quantum tunneling regime was determined for gap thicknesses of 0.51 nm, where there was a sudden drop in the third harmonic when the gap width decreases from 0.69 nm to 0.51 nm. The experimental observations were consistent with analytical calculations that applied the quantum-corrected model for SAM separating two gold regions. In comparison to the gap without SAMs in which the onset of the tunneling regime was reported at 0.31 nm, the onset of tunneling across the gap with SAM occurred for larger gaps. This was an expected outcome because the material in the gap reduced the barrier height to tunneling. Furthermore, I investigated the wavelength dependence of the third harmonic generation for the gold plasmonic system to determine the role of the interband transitions in the nonlinear response of gold. Past works reported a strong wavelength dependence of the nonlinear response of gold for the fundamental wavelength at about 550 nm, attributed to the interband transitions between the 5d to 6s-6p bands. However, the roles of the interband transitions and wavelength-dependent field enhancement in the nonlinear response of gold was not investigated. In this dissertation, results showed the third harmonic generation enhanced by an order of magnitude by the interband transition (as compared to the non-resonant case). In my research I also used an analytic model for the dielectric function of gold in which contributions of the interband transitions were considered. This model was also consistent with the experimental observations. / Graduate / 0752 / 0544 / Ghazal.hajisalem@gmail.com

Research considered investigates the optimal control problem which is constrained by a hyperbolic conservation law (HCL). We carried out a comparative study of the solutions of the optimal control problem subject to each one of the two di erent types of hyperbolic relaxation systems [64, 92]. The objective was to employ the adjoint-based optimization to minimize the cost functional of a matching type between the optimal solution and the target solution. Numerical tests were then carried out and promising results obtained. Finally, an extension was made to the adjoint-based optimization approach to apply second-order schemes for the optimal control problem in which also good numerical results were observed.

A dissertation submitted to the Faculty of Science School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg. April 27, 2013. / In a number of situations the derivative of the objective function of an optimization problem is not available. This thesis presents a novel algorithm for solving mixed integer programs when this is the case. The algorithm is the first developed for problems of this type which uses a trust region methodology. Three implementations of the algorithm are developed and deterministic proofs of convergence to local minima are provided for two of the implementations. In the development of the algorithm several other contributions are made. The derivative free algorithm requires the solution of several mixed integer quadratic programming subproblems and novel methods for solving nonconvex instances of these problems are developed in this thesis. Additionally, it is shown that the current definitions of local minima for mixed integer programs are deficient and a rigorous approach to developing possible definitions is proposed. Using this approach we propose a new definition which improves on those currently used in the literature. Other components of this thesis are an overview of derivative based mixed integer non-linear programming, extensive reviews of mixed integer quadratic programming and deterministic derivative free optimization and extensive computational results illustrating the effectiveness of the contributions mentioned in the previous paragraphs.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2015. / I would like to acknowledge a number of people who contributed towards the completion of this thesis. Firstly, I thank my supervisor Professor Montaz Ali for his patience, enthusiasm, guidance and teachings. The skills I have acquired during this process have infiltrated every aspect of my life. I remain forever grateful. Secondly, I would like to say a special thank you to Professor Jan Snyman for his assistance, which contributed immensely towards this thesis. I would also like to thank Professor Dominque Orban for his willingness to assist me for countless hours with the installation of CUTEr, as well as Professor Jose Mario Martinez for his email correspondence. A heartfelt thanks goes out to my family and friends at large, for their prayers, support and faith in me when I had little faith in myself. Thank you also to my colleagues who kept me sane and motivated, as well as all the support staff who played a pivotal roll in this process. Above all, I would like to thank God, without whom none of this would have been possible.

M.Sc., Faculty of Science, University of the Witwatersrand, 2011