Combustion instabilities are a significant problem in combustion systems, particularly in Low NOx Gas Turbine combustors. These instabilities result in large-scale pressure oscillations in the combustor, leading to degraded combustor performance, shortened lifetime, and catastrophic combustor failure. The objective of this research was to develop a practical adaptive active control system that, coupled with an appropriate actuator, is capable of controlling the combustor pressure oscillations without a priori knowledge of the combustor design, operating conditions or instability characteristics. The adaptive controller utilizes an observer that determines the frequencies, phases and amplitudes of the dominant modes of the oscillations in real time. The research included development and testing of the adaptive controller on several combustors and on an unstable acoustic feedback system in order to analyze its performance. The research also included investigations of combustor controllability and combustor stability margin, which are critical issues for practical implementation of an active control system on an industrial combustor. The results of this research are directly applicable to a variety of combustors and can be implemented on full-scale industrial combustion systems.

An almost universal instability in high pressure plasmas is the Neoclassical Tearing Mode (NTM). NTMs are driven by local perturbations in the current density and result in magnetic island like deformations of the magnetic topology. They can be stabilized by compensating the current perturbations with local electron cyclotron resonance heating (ECRH) or with non-inductive current drive (ECCD). The modified Rutherford equation describes the nonlinear evolution of tearing modes as determined by various contributions to the local current density pertubation. An extensive investigation of the two terms representing the stabilizing effects from ECRH and ECCD have been made resulting in accurate description of both terms. The results of this model can now be compared to the experimental observations. For this purpose, an extensive data set exists from the past experiments on tearing mode stabilization by ECRH and ECCD on TEXTOR. The properly benchmarked model can then be used to predict the effectiveness of ECRH and ECCD for NTM stabilization on International Thermonuclear Experimental Reactor (ITER). In addition, a number of predictions on the effects of ECRH and ECCD on the growth of the NTM have been made on the basis of crude approximations to the ECRH and ECCD tems in the modified Rutherford equation. These predictions can now be checked against the more accurate expressions obtained.

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<p>In this thesis we apply linear feedback control to spatially evolving flows in order to minimize disturbance growth. The dynamics is assumed to be described by the linearized Navier--Stokes equations. Actuators and sensor are designed and a Kalman filtering technique is used to reconstruct the unknown flow state from noisy measurements. This reconstructed flow state is used to determine the control feedback which is applied to the Navier--Stokes equations through properly designed actuators. Since the control and estimation gains are obtained through an optimization process, and the Navier--Stokes equations typically forms a very high-dimensional system when discretized there is an interest in reducing the complexity of the equations. One possible approach is to perform Fourier decomposition along (almost) homogeneous spatial directions and another is by constructing a reduced order model by Galerkin projection on a suitable set of vectors. The first strategy is used to control the evolution of a range of instabilities in the classical family of Falkner--Skan--Cooke flows whereas the second is applied to a more complex cavity type of geometry.</p>

This thesis discusses two patterning techniques: Step and Flash Imprint Lithography, a nanoimprint technique, and patterning thin films utilizing electrohydrodynamic instabilities. Step and Flash Imprint Lithography, SFIL, is promising alternative approach to photolithography. SFIL replicates the relief pattern of a template in a photocurable liquid that has been dispensed on a substrate. The pattern is then crosslinked when the photocurable liquid is exposed to UV light through the template. In order to study the volume change in the created features upon exposure, a stochastic mesoscale model was formulated. This model allows the study of the possibility of defects forming, from under cured etch barrier, or particle contamination of the template. The results showed large defects should not occur regularly until the minimum feature size is below 3 nanometers. The mesoscale model proved to computationally intensive to simulate features of engineering interest. A base multiscale model was formulated to simulate the effects of the densification of the photocurable liquid as well as the effects of the polymerization on the feature integrity. The multiscale model combines a continuum model (compressible Mooney-Rivlin) coupled to the mesoscale code using the Arlequin method. The multiscale model lays the framework that may be adapted to the study of other SFIL processes like template release. Patterning thin films utilizing electrohydrodynamic instabilities allows for the creation of periodic arrays of pillar like features. These pillars form due to the electric field destabilizing the thin film. Prior work has focused on utilizing polymeric films heated above their glass transition temperatures. In order to decrease the process time in the pillar formation process, work was done to study photocurable systems. The systems which proved favorable to the pillar creation process were the thiol-ene system as well as the maleimide systems. Further work was done on controlling the packing and ordering of the formed pillar arrays by using patterned templates. The result of these studies is that control was only able to be achieved to the third generation of pillars formed due to the inability to fully control the gap over the entire active area. / text

The work in this thesis focuses primarily on equilibrium and stability properties of collisionless current sheet models, in particular of the force-free Harris sheet model. A detailed investigation is carried out into the properties of the distribution function found by Harrison and Neukirch (Physical Review Letters 102, 135003, 2009) for the force-free Harris sheet, which is so far the only known nonlinear force-free Vlasov-Maxwell equilibrium. Exact conditions on the parameters of the distribution function are found, which show when it can be single or multi-peaked in two of the velocity space directions. This is important because it may have implications for the stability of the equilibrium. One major aim of this thesis is to find new force-free equilibrium distribution functions. By using a new method which is different from that of Harrison and Neukirch, it is possible to find a complete family of distribution functions for the force-free Harris sheet, which includes the Harrison and Neukirch distribution function (Physical Review Letters 102, 135003, 2009). Each member of this family has a different dependence on the particle energy, although the dependence on the canonical momenta remains the same. Three detailed analytical examples are presented. Other possibilities for finding further collisionless force-free equilibrium distribution functions have been explored, but were unsuccessful. The first linear stability analysis of the Harrison and Neukirch equilibrium distribution function is then carried out, concentrating on macroscopic instabilities, and considering two-dimensional perturbations only. The analysis is based on the technique of integration over unperturbed orbits. Similarly to the Harris sheet case (Nuovo Cimento, 23:115, 1962), this is only possible by using approximations to the exact orbits, which are unknown. Furthermore, the approximations for the Harris sheet case cannot be used for the force-free Harris sheet, and so new techniques have to be developed in order to make analytical progress. Full analytical expressions for the perturbed current density are derived but, for the sake of simplicity, only the long wavelength limit is investigated. The dependence of the stability on various equilibrium parameters is investigated.

Astrophysical flows have an enormous dynamic range of relevant length scales. The physics occurring on the smallest scales often influences the physics of the largest scales, and vice versa. I present a detailed study of the multiscale and multidimensional behavior of three high-energy astrophysical flows: jet-driven supernovae, massive black hole accretion, and current-driven instabilities in gamma-ray burst external shocks. Both theory and observations of core-collapse supernovae indicate these events are not spherically-symmetric; however, the observations are often modeled assuming a spherically-symmetric explosion. I present an in-depth exploration of the effects of aspherical explosions on the observational characteristics of supernovae. This is accomplished in large part by high-resolution, multidimensional numerical simulations of jet-driven supernovae. The existence of supermassive black holes in the centers of most large galaxies is a well-established fact in observational astronomy. How such black holes came to be so massive, however, is not well established. In this work, I discuss the implications of radiative feedback and multidimensional behavior on black hole accretion. I show that the accretion rate is drastically reduced relative to the Eddington rate, making it unlikely that stellar mass black holes could grow to supermassive black holes in less than a Hubble time. Finally, I discuss a mechanism by which magnetic field strength could be enhanced behind a gamma-ray burst external shock. This mechanism relies on a current-driven instability that would cause reorganization of the pre-shock plasma into clumps. Once shocked, these clumps generate vorticity in the post-shock plasma and ultimately enhance the magnetic energy via a relativistic dynamo process. / text

The spinning process of hollow fiber membranes was investigated with regards to two fundamental phenomena: flow (shear and elongation) and phase separation. Quantitative analysis of phase separation kinetics of binary (polymer/solvent) and ternary (polymer/solvent/volatile co-solvent) polymer solution was carried out with a newly developed microfluidic device. The device enables visualization of in situ phase separation and structure formation in controlled vapor and liquid environments. Results from these studies indicated that there was a weak correlation between phase separation kinetics and macroscopic defect (macrovoid) formation. In addition, the effect of shear and elongation on membrane morphology was tested by performing fiber extrusion through microfluidic channels. It was found that the membrane morphology is dominated by different factors depending on the rate of deformation. At high shear rates typical of spinning processes, shear was found to induce macrovoid formation through normal stresses, while elongation suppressed macroscopic defect formation. Furthermore, draw resonance, one of the key instabilities that can occur during fiber spinning, was investigated. It was found that draw resonance occurs at aggressive elongation condition, and could be suppressed by enhanced phase separation kinetics. These results can be used as guidelines for predicting hollow fiber membrane spinnability.

A computational and experimental study of the Richtmyer-Meshkov instability is presented here for an inclined interface perturbation. The computational work is composed of simulation studies of the inclined interface RMI performed using the Arbitrary Lagrange Eulerian (ALE) code called ARES. These simulations covered a wide range of Mach numbers (1.2 to 3.5), gas pairs (Atwood numbers 0.23to 0.95), inclination angles (30° to 85°), and explored various perturbation types (both inclined interface and sinusoidal). The computational work included the first parametric study of the inclined interface RMI. This study yielded the first scaling method for the inclined interface RMI mixing width growth rates. It was extended to explore the effect of perturbation linearity and identified that a sharp transition in growth regimes occurs for an initial perturbation inclination angle of 75° with angles below (above) this growing faster (slower). Finally a study of the effects of incident shock strength on the refracted shock wave perturbation decay rate is presented. This study examined how the perturbations induced on the transmitted shock front by the RMI decay with time and found that the decay rates follow a power law model, Alpha=Beta∗S^(Epsilon). When the coefficients from the power law decay model were plotted versus Mach number, a distinct transition region was found which is likely a result of the post-shock heavy gas velocity transitioning from the subsonic to supersonic range. The experimental portion of this work was conducted using the TAMUFMSTF, completed in May of 2012. This facility uses a variable inclination shock tube, with a modular construction design for incident shock strengths of up to Mach 3.0. It employs optical systems for measuring density and velocity fields simultaneously using the planar laser induced fluorescence and particle imaging velocimetry techniques. The design and construction of this facility is reviewed in detail in chapter 4 of this work. The initial experiments performed in the TAMUFMSTF provided the first known extensive experimental data for an inclined interface RMI. Planar laser Mie scattering images and velocity vectors were obtained for a N_(2)/CO_(2) interface at a 60° inclination angle and an incident shock strength of Mach 1.55. These images have been compared with simulations made using the ARES codes and have been shown to have some distinct differences. Some of these differences indicate that the initial conditions in the experiments deviate from the ideal planar interface. Other differences have revealed features which have not been resolved by the simulations due to resolution limitations.

In this thesis a model for saturated tearing mode islands is developed. The equations for the mode amplitudes are essentially those of R B White et al,after a pertubation expansion has been made. It is well known that these equations are not then analytic at the mode rational surface. In our model this problem is overcome when a suitable choice of the axisymmetric current density perturbation is added to the unperturbed equilibrium current density profile. The modelled axisymmetric current density perturbation flattens the unperturbed profile locally at the rational surface and is sufficient to induce an island. No modelling in the interior of the island is necessary. The axisymmetric perturbation has a free variable which adjusts the amount of local flattening. However, when the boundary conditions are taken into account, this free parameter is determined, and the problem becomes an eigenvalue problem. The boundary condition thus determines the amount of local flattening at the rational surface. The saturated island widths are determined using D.' (W) criterion. The model allows for non axsymmetric plasma surface in a simple way, requiring careful choice of D (W). The different criteria are compared to establish the validity of the use of such criteria for perturbed boundaries. In the cylindrical approximation, one or two modes may be included in the model. In the case of two modes, non-linear coupling via the current density profile is introduced. Toroidal coupling between modes can also be simply introduced. Two modes that are toroidally coupled are considered, but mode-mode coupling is ignored. The emphasis falls in large part on the boundary conditions. Various boundary conditions can be considered because distortion of the plasma surface can be fixed by wall effects, plasma rotation, external DC coil currents, plasma rotation with external coil currents, etc. Of particular interest is the case of toroidally coupled modes, coupled in turn to these external conditions as this is the first study of such a nature. Results flowing from the study include among others that: for the special case of circular boundaries the model agrees reasonably with the results of R B White et al. No significant difference was found between the D. I (W) criterion of P H Rutherford, which is valid for circular boundaries, and that of A H Reiman, which is also valid for perturbed boundaries, when the boundary is perturbed significantly. Toroidally coupled islands do not increase in size if the boundary condition of that particular mode is not changed. If a coil current of particular helicity is switched on, it will only affect the mode of that particular helicity. Toroidally induced sideband islands have approximately the same width as natural tearing islands when the size of the natural island is large. / Thesis (Ph.D.)-University of Natal, Durban, 1992.