The purpose of this research is to characterize the response of an airfoil with an oscillatory morphing, Macro-fiber composite (MFC) trailing edge. Correlation of the airfoil lift with the oscillatory input is presented. Modal analysis of the test airfoil and apparatus is used to determine the frequency response function. The effects of static MFC inputs on the FRF are presented and compared to the unactuated airfoil. The transfer function is then used to determine the lift component due to cambering and extract the inertial components from oscillating airfoil. Finally, empirical wind tunnel data is modeled and used to simulate the deflection of airfoil surfaces during dynamic testing conditions. This research serves to combine modal analysis, empirical modeling, and aerodynamic testing of MFC driven, oscillating lift to formulate a model of a dynamic, loaded morphing airfoil. / Master of Science

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Neste trabalho, estudamos as consequências causadas em um condensado de Bose-Einstein de átomos de 87Rb quando sujeito a uma excitação oscilatória externa. Para a produção do condensado utilizamos técnicas de resfriamento atômico, como o resfriamento a laser e o resfriamento evaporativo, em átomos aprisionados em uma armadilha magnética harmônica. A excitação externa é produzida através de um campo magnético quadrupolar oscilatório que é sobreposto ao campo de aprisionamento. Para uma forma fixa dessa excitação, observamos que podemos excitar modos coletivos de oscilação na amostra de condensado, em especial analisamos os modos breathing, dipolar, quadrupolar e o scissor mode. Durante o movimento dipolar do condensado na armadilha magnética, identificamos que há um escoamento contrapropagante do condensado em relação à nuvem térmica que o permeia. Esse escoamento é analisado como um movimento de dois fluidos, onde o condensado desempenha o papel de um superfluido e a nuvem térmica o de um fluido normal. Irregularidades na superfície do condensado são observadas e seus comprimentos característicos crescem na região dos pontos de retorno do movimento dipolar do condensado. Nesses pontos, a forma das irregularidades sugerem estar relacionadas com o processo de geração de vórtices na amostra superfluida. Com base nestas análises, determinamos o valor da velocidade relativa dos fluidos e qual deve ser, tipicamente, o valor da velocidade relativa crítica para que as irregularidades se tornam maiores, possibilitando a geração de vórtices. As análises apresentadas neste trabalho são dedicadas a entender os mecanismos que possibilitaram, em nosso sistema, a observação de vórtices, turbulência quântica e a granulação do condensado, em 2009. / In this work we have studied the effects caused by an external oscillatory excitation in a Bose-Einstein condensate of 87Rb. The condensate is produced through by atomic laser cooling techniques, as laser cooling and evaporative cooling, for trapped atoms in a harmonic magnetic trap. The external excitation is generated by an oscillating magnetic quadrupole field superimposed to the trapping field. For a fixed type of excitation, we observe that collective modes of oscillation are excited in the condensate sample, particularly we analyze the dipole mode, quadrupole and scissor mode. During the motion of the condensate in dipolar mode inside the magnetic trap, we have identified a counterflow, i. e. a relative motion between the condensate and the thermal cloud. This flow is analyzed as a two fluids motion, where the condensate plays the role of a superfluid and the thermal cloud a normal fluid. Irregularities on the condensate surface are observed and their characteristic lengths grow in the turning point regions of this dipolar motion. At these points, the shape of this irregularities seems to be related to the vortices generation process in a superfluid sample. Based on this analysis, we determine the velocity of the counterflow and the critical velocity for the irregularities to become larger, allowing the generation of vortices. The analyses presented in this work are dedicated to understand the mechanisms that allowed in our system the observation of vortices, quantum turbulence and the condensate granulation, in 2009.

A sismologia estelar oferece uma oportunidade única de sondar as propriedades internas das estrelas através do estudo de oscilações estelares. Essas oscilações são dependentes diretamente da física da cavidade onde são formadas. No entanto, a rotação da estrela introduz um eixo de simetria e levanta a degenerescência nas frequências, dificultando assim, a sua identificação. O objetivo deste trabalho foi estudar a dependência das frequências de oscilação estelar com a velocidade de rotação para modelos de massas intermediárias ao longo da sequência principal. Este estudo foi realizado através da modelagem de estrelas com uma grande variedade de massas e velocidades de rotação (2-8 Msol, 20-100km/s) com os códigos CESAM/FILOU. O comportamento do splitting rotacional e de sua assimetria nos modos g2, g1, p1 e p2 mostrou uma dependência com outros parâmetros físicos, além da rotação. A assimetria apresenta variações interessantes levando a um método de diagnóstico de evolução: quando vários modos são observados, as assimetrias levam a uma determinação precisa da fase evolutiva da estrela. Modelos representativos para a estrela HD50844 foram comparados com os dados observacionais. A falta da identificação dos modos (l,m) e o grande número de frequências não permite obter-se resultados precisos. / Asteroseismology provides a unique opportunity to probe the inner properties of stars through the study of stellar oscillations. These oscillations depend on the physics of the cavity where they are formed. However, the stellar rotation introduces an axis of symmetry and lifts the degeneracy of the frequencies, thus hindering the identification. The goal of this work was to study the dependence of the oscillation frequency on the stellar rotation velocities for models of intermediate mass along the main sequence. This study was performed through the modeling of stars with a wide range of masses and rotational velocities (2-8 Msun, 20-100km/s) with the codes CESAM/FILOU. The behavior of the rotational \\textit and its asymmetry for the modes g2, g1, p1 and p2 showed a dependence on other physical parameters, as well as rotation. The asymmetry presents interesting variations leading to a diagnostic method of evolution: when multiple modes are observed, the asymmetries lead to a precise determination of the evolution phase of the star. Representative models for the star HD50844 were compared with the observational data. The lack of identification of the modes (l,m) and the large number of frequencies does not allow to obtain accurate results.

La perception explicite du temps écoulé (la durée, l'ordre temporel¿) et les jugements implicites des dynamiques de notre environnement (percevoir le mouvement, la parole) nécessitent l'extraction des relations temporelles entre événements sensoriels. Alors que le temps physique est communément évalué en rapport à un référentiel externe (celui de l'horloge), le cerveau lui n'a pas accès à ce référentiel. Dans cette thèse, nous émettons l'hypothèse que le cerveau génère son propre référentiel temporel à partir des dynamiques neurales. Combinant la magnétoencéphalographie (MEG) aux données psychophysiques, les présents travaux suggèrent que les oscillations corticales sont impliquées dans l'encodage du temps perçu. Une première étude montre que la phase des oscillations corticales basse-fréquences peut encoder l'ordre temporel perçu entre événements sensoriels s'il y a entrainement neural, i.e. si l'activité cérébrale suit les régularités temporelles de la stimulation. L'implication des oscillations cérébrales en l'absence d'entrainement est testée dans une seconde expérience. Les résultats d'une troisième expérience suggèrent que l'entrainement neural n'a d'influence sur le traitement temporel des informations multisensorielles qu'à basse fréquence (1-2 Hz). Un dernier chapitre aborde le rôle de l'entrainement neural dans l'encodage des dynamiques du signal acoustique pour la perception de la parole. En conclusion, cette thèse suggère que le cerveau est capable de suivre la structure temporelle du monde extérieur, et que cet ajustement permet la construction d'un référentiel temporel interne pour la perception explicite et implicite du temps. / The timing of sensory events is a crucial perceptual feature, which affects both explicit judgments of time (e.g. duration, temporal order) and implicit temporal perception (e.g. movement, speech). Yet, while the relative external timing between events is commonly evaluated with a clock in physics, the brain does not have access to this external reference. In this dissertation, we tested the hypothesis that the brain should recover the temporal information of the environment from its own dynamics. Using magnetoencephalography (MEG) combined with psychophysics, the experimental work suggests the involvement of cortical oscillations in the encoding of timing for perception. In the first part of this dissertation, we established that the phase of low-frequency cortical oscillations could encode the explicit timing of events in the context of entrainment, i.e. if neural activity follows the temporal regularities of the stimulation. The implications of brain oscillations for the encoding of timing in the absence of external temporal regularities were investigated in a second experiment. Results from a third experiment suggest that entrainment does only influence audiovisual temporal processing when bound to low-frequency dynamics in the delta range (1-2 Hz). In the last part of the dissertation, we tested whether oscillations in sensory cortex could also ‘tag’ the timing of acoustical features for speech perception. Overall, this thesis provides evidence that the brain is able to tune its timing to match the temporal structure of the environment, and that such tuning may be crucial to build up internal temporal reference frames for explicit and implicit timing perception.

A quantização geométrica e um método desenvolvido para prover uma construção geométrica que relacione a mecânica clássica com a quântica. O primeiro passo consiste em apresentar uma forma simplética, \'omega\'!, sobre uma variedade simplética, M, como a forma curvatura da conexão abla de um brado linear, L, sobre M. As funções sobre M operam como seções de L. Mas o espaço de todas as seções é grande demais. Queremos considerar seções constantes em certa direção, com respeito a derivada covariante dada por abla, e para isso precisamos o conceito de polarizações, essas seções são chamadas de seções polarizadas. Para obter uma estrutura de espaco de Hilbert nestas seções, precisamos de certos objetos chamados de meias densidades. Além disso, também temos um empareamento sesquilinear entre seções de polarizações diferentes. Neste trabalho, primeiramente consideraremos o empareamento para seções polarizadas adaptadas a polarizações reais não transversais, como método para obter aplicações integrais entre estes espaços de Hilbert que em combinação com a convolução do par grupóide M x \' M BARRA\', pode definir um produto integral de funções definidas na variedade simplética. Este produto, no caso do plano euclidiano e do plano de Bieliavsky, coincide com produto de Weyl integral e o produto de Bieliavsky, respectivamente. Jáa no caso do plano hiperbólico, este tipo de polarizações reais não são transversais nem são não transversais, dessa forma, escolhemos o empareamento entre uma polarização real e uma polarização holomorfa do par grupóide, as quais são transversais, para obter um produto integral no plano hiperbólico, que no caso do plano euclidiano e o produto de Weyl / The geometric quantization is a method developed to provide a geometrical construction relating classical to quantum mechanics. The first step consists of realizing the symplectic form, \'omega\', on a symplectic manifold, M, as the curvature form of a line bundle, L, over M. The functions on M then operate as sections of L. However, the space of all sections of L is too large. One wants to consider sections which are constant in certain directions (polarized sections) and for that one needs to introduce the concept of a polarization. To get a Hilbert space structure on the polarized sections, one needs to consider objects known as half densities. In this work, first we consider a sesquilinear pairing between objects associated to certain different polarizations, which are nontransverse real polarizations, to obtain integral applications between their associated Hilbert spaces, and to use the convolution of the pair groupoid M x \' M BARRA\' to obtain an integral product of functions on M. In the euclidian plane case, we recover the integral Weyl product and, in the Bieliavsky plane case, we obtain the Bieliavsky product. On the other hand, for the hyperbolic plane, such real polarizations are neither transverse nor nontransverse, so we use the pairing between a real polarization and a holomorphic polarization, which are transverse polarizations on the pair groupoid, to obtain an integral product of functions on the hyperbolic plane. This same procedure, in the euclidian plane case, also produces the integral Weyl product

Continuous flow reaction using micro-reactors is a valued technology due to its excellent mass and heat transfer performance, reduced reactor volume, handling capacity of hazardous reactions, and many other process intensifications. These intensifications opportunities interest the fine chemicals, pharmaceuticals producers and other multiphase reaction users who currently use batch processes or already use continuous flow. In this thesis, elements of passive and active mixing are investigated for the application of immiscible liquid-liquid systems. In the first study, the effects of geometrical arrangements of a residence time between mixing units on the interphase mass transfer rates are evaluated with four different immiscible liquid-liquid systems. A presentation of an algorithm for the optimal selection of a reactor and its operating conditions is given in order to enable easy and improved use of one’s micro-reactor. In the second study, the impact of a secondary pulse flow on interphase mass transfer is investigated. A coil without internal baffles is used as the oscillatory-flow coil reactor with a continuous active mixing source. The best application for the reactor is determined using a comparison to other complementary continuous flow platforms in the toolbox approach. The novel advancements presented here will help lead new molecular discoveries and connect the laboratory science scale to the process engineering production scale.

A volume-filtered Large-Eddy Simulation (LES) of oscillatory flow over a rippled mobile bed is conducted using an Euler-Lagrange approach. As in unsteady marine flows over sedimentary beds, the experimental data, referenced in this work for validation, shows quasi-steady state ripples in the sand bed under oscillatory flow. This work approximately reproduces this configuration with a sinusoidal pressure gradient driven flow and a sinusoidally rippled bed of particles. The LES equations, which are volume-filtered to account for the effect of the particles, are solved on an Eulerian grid, and the particles are tracked in a Lagrangian framework. In the Discrete Particle Method (DPM) used in this work, the particle collisions are handled by a soft-sphere model, and the liquid and solid phases are coupled through volume fraction and momentum exchange terms. Comparison of the numerical results to the experimental data show that the LES-DPM is capable of capturing the mesoscale features of the flow. The large scale shedding of vortices from the ripple peaks are observed in both datasets, which is reflected in the good quantitative agreement between the wall-normal flow statistics, and good qualitative agreement in ripple shape evolution. Additionally, the numerical data provides three insights into the complex interaction between the three-dimensional flow dynamics and bed morphology: (1) there is no observable distinction between reptating and saltating particle velocities, angular velocities or observed Shields parameters; (2) the potential motion of the mobile bed may create issues in the estimation of the bed shear stress used in classical models; and, (3) a helical pairing of vortices is observed, heretofore not known to have to have been identified in this type of flow configuration.

In the present study, a fifth-order weighted essentially non-oscillatory (WENO) scheme was built for solving the surface-capturing level-set equation. Combined with the level-set equation, the three-dimensional Reynolds averaged Navier-Stokes (RANS) equations were employed for the prediction of nonlinear wave-interaction and wave-breaking phenomena over sloping beaches. In the level-set finite-analytic Navier-Stokes (FANS) method, the free surface is represented by the zero level-set function, and the flows are modeled as immiscible air-water two phase flows. The Navier-Stokes equations for air-water two phase flows are formulated in a moving curvilinear coordinate system and discretized by a 12-point finite-analytical scheme using the finite-analytic method on a multi-block over-set grid system. The Pressure Implicit with Splitting of Operators / Semi-Implicit Method for Pressure-Linked Equation Revised (PISO/SIMPLER) algorithm was used to determine the coupled velocity and pressure fields. The evolution of the level-set method was solved using the third-order total variation diminishing (TVD) Runge-Kutta method and fifth-order WENO scheme. The accuracy was confirmed by solving the Zalesak's problem. Two major subjects are discussed in the present study. First, to identify the WENO scheme as a more accurate scheme than the essentially non-oscillatory scheme (ENO), the characteristics of a nonlinear monochromatic wave were studied systematically and comparisons of wave profiles using the two schemes were conducted. To eliminate other factors that might produce wave profile fluctuation, different damping functions and grid densities were studied. To damp the reflection waves efficiently, we compared five damping functions. The free-surface elevation data collected from gauges distributed evenly in a numerical wave tank are analyzed to demonstrate the damping effect of the beach. Second, as a surface-tracking numerical method built on curvilinear coordinates, the level-set RANS model was tested for nonlinear bichromatic wave trains and breaking waves on a sloping beach with a complex free surface. As the wave breaks, the velocity of the fluid flow surface became more complex. Numerical modeling was performed to simulate the two-phase flow velocity and its corresponding surface and evolution when the wave passed over different sloping beaches. The breaking wave test showed that it is an efficient technique for accurately capturing the breaking wave free surface. To predict the breaking points, different wave heights and beach slopes are simulated. The results show that the dependency of wave shape and breaking characteristics to wave height and beach slope match the results provided by experiments.

In the study of the Degasperis-Procesi dierential equation, an eigenvalue problem called the cubic string occurs. This is a third order generalization of the second order problem describing the eigenmodes of a vibrating string. In this thesis we study the eigenfunctions of the cubic string for discrete and continuous mass distributions, using the theory of total positivity, via a combinatorial approach with planar networks.