A stand-alone genetic algorithm (GA) and an surrogate-based optimization (SBO) combined with a GA were compared for accuracy and performance. Comparisons took place using the Ackley Function and Rastrigin's Function, two functions with multiple local maxima and minima that could cause problems for more traditional optimization methods, such as a gradient-based method. The GA and SBO with GA were applied to the functions through a fortran interface and it was found that the SBO could use the same number of function evaluations as the GA and achieve at least 5 orders of magnitude greater accuracy through the use of surrogate evaluations. The two optimization methods were used in conjunction with computational fluid dy- namics (CFD) analysis to optimize the shape of a bumpy airfoil section. Results of opti- mization showed that the use of an SBO can save up to 553 hours of CPU time on 196 cores when compared to the GA through the use of surrogate evaluations. Results also show the SBO can achieve greater accuracy than the GA in a shorter amount of time, and the SBO can reduce the negative effects of noise in the simulation data while the GA cannot.

Current research in experimental and computational fluid dynamics is focused in the area of flow control. Flow control devices are usually classified as either passive or active. Plasma actuators are active flow control devices that require input from an external power source. Current efforts have modeled the effects of plasma actuators as a body force near the electrode. The research presented herein focuses on modeling the fluid-plasma interaction seen in dielectric barrier discharge plasma actuators as a body force vector in the region above the embedded electrode using computational fluid dynamics (CFD). This body force is modeled as the product of the gradient of the potential due to the electric field and the net charge density. In a passive flow control study, two-dimensional simulations using CFD are done with a smooth and bumpy Eppler 398 airfoil with laminar, transition, and turbulent models in an effort to improve the understanding of the flow over bumpy airfoils and to quantify the advantages or disadvantages of the bumps.

Let M be a possibly non compact smooth manifold. We study genericity in the C^k topology (3<=k<=+infty) of nondegeneracy properties of semi-Riemannian geodesic flows on M. Namely, we prove a new version of the Bumpy Metric Theorem for a such M and also genericity of metrics that do not possess any degenerate geodesics satisfying suitable endpoints conditions. This extends results of Biliotti, Javaloyes and Piccione for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P of MxM that satisfies an admissibility condition. Immediate consequences are generic non conjugacy between two points and non focality between a point and a submanifold (or also between two submanifolds). / Seja M uma variedade suave possivelmente não compacta. Estuda-se a genericidade na topologia C^k (3<=k<=+infty) de propriedades de não degenerescência de fluxos geodésicos semi-Riemannianos em M. A saber, provase uma nova versão do Teorema de Métricas Bumpy para uma tal M e também a genericidade de métricas que não possuem geodésicas degeneradas cujos pontos finais satisfazem certas condições. Isso estende resultados anteriores de Biliotti, Javaloyes and Piccione para geodésicas com extremos fixos para o caso onde os extremos variam em uma subvariedade compacta P de M ×M que satisfaz uma condição de admissibilidade. Consequências imediatas são genericidade de não conjugação entre dois pontos e não focalidade entre um ponto e uma subvariedade (ou também entre duas subvariedades).

In this thesis we prove the genericity of the set of metrics on a manifold with boundary M^{n+1}, such that all free boundary constant mean curvature (CMC) embeddings \\varphi: \\Sigma^n \\to M^{n+1}, being \\Sigma a manifold with boundary, are non-degenerate (Bumpy Metrics), (Theorem 2.4.1). We also give sufficient conditions to obtain a free boundary CMC deformation of a CMC inmersion (Theorems 3.2.1 and 3.2.2), and a stability criterion for this type of immersions (Theorem 3.3.3 and Corollary 3.3.5). In addition, given a one-parametric family, {\\varphi _t : \\Sigma \\to M} , of free boundary CMC immersions, we give criteria for the existence of smooth bifurcated branches of free boundary CMC immersions for the family {\\varphi_t}, via the implicit function theorem when the kernel of the Jacobi operator J is non-trivial, (Theorems 4.2.3 and 4.3.2), and we study stability and instability problems for hypersurfaces in this bifurcated branches (Theorems 5.3.1 and 5.3.3). / Nesta tese, provamos a genericidade do conjunto de métricas em uma variedade com fronteira M^{n+1}, de modo que todos os mergulhos de curvatura média constante (CMC) e fronteira livre \\varphi : \\Sigma^n \\to M^{n+1}, sendo \\Sigma uma variedade com fronteira, sejam não-degenerados (Métricas Bumpy), (Teorema 2.4.1). Nós também fornecemos condições suficientes para obter uma deformação CMC e fronteira livre de uma imersão CMC (Teoremas 3.2.1 and 3.2.2), e um critério de estabilidade para este tipo de imersões (Teorema 3.3.3 and Corolario 3.3.5). Além disso, dada uma família 1-paramétrica, {\\varphi _t : \\Sigma \\to M} , de imersões de CMC e fronteira livre, damos os critérios para a existência de ramos de bifurcação suaves de imersões CMC e fronteira livre para a familia {\\varphi_t}, por meio de o teorema da função implícita quando o kernel do operador Jacobi J é não-trivial, (Teoremas 4.2.3 and 4.3.2), e estudamos o problema da estabilidade e instabilidade para hipersuperfícies em naqueles ramos de bifurcação (Teoremas 5.3.1 and 5.3.3).

In this thesis we prove the genericity of the set of metrics on a manifold with boundary M^{n+1}, such that all free boundary constant mean curvature (CMC) embeddings \\varphi: \\Sigma^n \\to M^{n+1}, being \\Sigma a manifold with boundary, are non-degenerate (Bumpy Metrics), (Theorem 2.4.1). We also give sufficient conditions to obtain a free boundary CMC deformation of a CMC inmersion (Theorems 3.2.1 and 3.2.2), and a stability criterion for this type of immersions (Theorem 3.3.3 and Corollary 3.3.5). In addition, given a one-parametric family, {\\varphi _t : \\Sigma \\to M} , of free boundary CMC immersions, we give criteria for the existence of smooth bifurcated branches of free boundary CMC immersions for the family {\\varphi_t}, via the implicit function theorem when the kernel of the Jacobi operator J is non-trivial, (Theorems 4.2.3 and 4.3.2), and we study stability and instability problems for hypersurfaces in this bifurcated branches (Theorems 5.3.1 and 5.3.3). / Nesta tese, provamos a genericidade do conjunto de métricas em uma variedade com fronteira M^{n+1}, de modo que todos os mergulhos de curvatura média constante (CMC) e fronteira livre \\varphi : \\Sigma^n \\to M^{n+1}, sendo \\Sigma uma variedade com fronteira, sejam não-degenerados (Métricas Bumpy), (Teorema 2.4.1). Nós também fornecemos condições suficientes para obter uma deformação CMC e fronteira livre de uma imersão CMC (Teoremas 3.2.1 and 3.2.2), e um critério de estabilidade para este tipo de imersões (Teorema 3.3.3 and Corolario 3.3.5). Além disso, dada uma família 1-paramétrica, {\\varphi _t : \\Sigma \\to M} , de imersões de CMC e fronteira livre, damos os critérios para a existência de ramos de bifurcação suaves de imersões CMC e fronteira livre para a familia {\\varphi_t}, por meio de o teorema da função implícita quando o kernel do operador Jacobi J é não-trivial, (Teoremas 4.2.3 and 4.3.2), e estudamos o problema da estabilidade e instabilidade para hipersuperfícies em naqueles ramos de bifurcação (Teoremas 5.3.1 and 5.3.3).

Let M be a possibly non compact smooth manifold. We study genericity in the C^k topology (3<=k<=+infty) of nondegeneracy properties of semi-Riemannian geodesic flows on M. Namely, we prove a new version of the Bumpy Metric Theorem for a such M and also genericity of metrics that do not possess any degenerate geodesics satisfying suitable endpoints conditions. This extends results of Biliotti, Javaloyes and Piccione for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P of MxM that satisfies an admissibility condition. Immediate consequences are generic non conjugacy between two points and non focality between a point and a submanifold (or also between two submanifolds). / Seja M uma variedade suave possivelmente não compacta. Estuda-se a genericidade na topologia C^k (3<=k<=+infty) de propriedades de não degenerescência de fluxos geodésicos semi-Riemannianos em M. A saber, provase uma nova versão do Teorema de Métricas Bumpy para uma tal M e também a genericidade de métricas que não possuem geodésicas degeneradas cujos pontos finais satisfazem certas condições. Isso estende resultados anteriores de Biliotti, Javaloyes and Piccione para geodésicas com extremos fixos para o caso onde os extremos variam em uma subvariedade compacta P de M ×M que satisfaz uma condição de admissibilidade. Consequências imediatas são genericidade de não conjugação entre dois pontos e não focalidade entre um ponto e uma subvariedade (ou também entre duas subvariedades).

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In this thesis I study compact objects described by the Manko-Novikov spacetime. The Manko- Novikov spacetime is an exact solution to the Einstein Field Equations that allows objects to be black hole-like, but with a multipole structure di erent from Kerr black holes. The aim of the research is to investigate whether we will observationally be able to tell these bumpy black holes, if they exist, apart from traditional Kerr black holes. I explore the geodesic motion of a test probe in the Manko-Novikov spacetime. I quantify the motion using Poincar e maps and rotation curves. The Manko-Novikov spacetime admits regions with regular motion as well as regions with chaotic motion. The occurrence of chaos is correlated with orbits for which the characteristic frequencies are resonant. The new result presented in this thesis is a global characterisation of where resonances and thus chaos are likely to occur for all orbits. These calculations are performed in the Kerr spacetime, from which I obtain that low order resonances occur within 20 Schwarzschild radii (or 40M) of the compact object with mass M. By the KAM theorem, the occurrence of chaos is therefore limited to this region for all small perturbations from Kerr. These resonant events will be measurable in the Galactic Centre using eLISA. This con nement of low order resonances indicates that the frequency values of orbits of radii well outside of 20 Schwarzschild radii can be approximated using canonical perturbation theory. / AFRIKAANSE OPSOMMING: In hierdie tesis word kompakte voorwerpe bestudeer soos omskryf deur die Manko-Novikov ruimtetyd. Die Manko-Novikov ruimtetyd is 'n eksakte oplossing van die Einstein Veldvergelykings. Die Manko-Novikov ruimtetyd formuleer gravitasiekolk-tipe voorwerpe waarvan die veelpool-struktuur afwyk van die tradisionele Kerr gravitasiekolk-struktuur. Die oogmerk van die navorsing is om vas te stel of ons met behulp van waarnemings hierdie bonkige gravitasiekolke van die tradisionele Kerr gravitasiekolke kan onderskei. Ek ondersoek die geodetiese beweging van 'n toetsmassa in die Manko-Novikov ruimtetyd. Die beweging word gekwanti seer met behulp van Poincar e afbeeldings en rotasiekrommes. In die Manko-Novikov ruimtetyd identi seer ek gebiede waarbinne re elmatige beweging voorkom asook gebiede waarbinne chaotiese bane voorkom. Die ontstaan van chaos word geassosieer met bane waarvan die fundamentele frekwensies resonant is. 'n Nuwe resultaat wat in hierdie tesis voorgehou word behels 'n globale karakterisering wat aandui waar resonansies en dus chaos na alle waarskynlikheid voorkom. Laasgenoemde berekeninge word vir die Kerr ruimtetyd uitgevoer. Hierdeur toon ek alle lae orde resonansies kom voor binne 20 Schwarzschild radii (of 40M) vanaf die kompakte voorwerp met mass M. Die KAM Stelling bepaal dan dat vir alle klein steurings toegepas op die Kerr ruimtetyd die voorkoms van chaos beperk sal wees tot bogenoemde gebied. Die resonansies binne hierdie gebied sal deur eLISA in die sentrum van die melkwegstelsel gemeet kan word. Hierdie beperking van lae orde resonansies tot 'n sekere afstand vanaf die kompakte voorwerp verseker dat die frekwensies van bane wat buite hierdie gebied val, akkuraat deur kanoniese steuringsteorie bepaal kan word.

UAV development and usage has increased dramatically in the last 15 years. In this time frame the potential has been realized for deployable UAVs to the extent that a new class of UAV was defined for these systems. Inflatable wing UAVs provide a unique solution for deployable UAVs because they are highly packable (some collapsing to 5-10% of their deployed volume) and have the potential for the incorporation of wing shaping. In this thesis, aerodynamic coefficients and aileron effectiveness were derived from the equations of motion of aircraft as necessary parameters for autonomous flight. A wind tunnel experiment was performed to determine the aerodynamic performance of a bumpy inflatable wing airfoil for comparison with the baseline smooth airfoil from which it was derived. Results showed that the bumpy airfoil has improved aerodynamics over the smooth airfoil at low-Re. The results were also used to create aerodynamic performance curves to supplement results of aerodynamic modeling with a smooth airfoil. A modeling process was then developed to calculate the aileron effectiveness of a wing shaping demonstrator aircraft. Successful autonomous flight tests were then performed with the demonstrator aircraft including in-flight aileron doublets to validate the predicted aileron effectiveness, which matched within 8%.