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An apparatus for producing atomic-gas Bose-Einstein condensates (BECs) of 87-Rb atoms is described. The apparatus produces 87-Rb BECs in a dual-chamber vacuumsystem that incorporates magnetic transport of trapped atoms from the magneto-optical trapping cell to the BEC production cell via the operation of a series of overlapping magnet coils. The design, construction, and operation of the apparatus are described in detail.The apparatus is used to study the creation of quantized vortices in BECs by the merging and interference of multiple trapped condensates. In this experiment, a single harmonic potential well is partitioned into three sections by an optical barrier,enabling the simultaneous formation of three independent, uncorrelated BECs. The BECs may either merge together during their growth, or, for high-energy barriers, the BECs can be merged together by barrier removal after their formation. Either process may instigate vortex formation in the resulting BEC, depending on the initially indeterminate relative phases of the condensates and the merging rate.

The research presented in this dissertation focuses on understanding the dynamics of waves and currents in the presence of wave breaking. The simplest approach, direct numerical simulation of the ocean dynamics, is computationally prohibitive--waves typically have periods of tens of seconds, while currents vary on times from hours to days. This work uses a multi-scale asymptotic theory for the waves and currents (Craik and Leibovich, 1976; McWilliams et al., 2004}, similar to Reynolds-averaged Navier-Stokes, in order to avoid resolving the wave field. The theory decomposes the total flow into the mean flow (current) and fluctuations (waves), then takes a moving time average of the total flow equations to determine the wave forcing on the current. The main challenge is extending this theory to include a physical model for dissipative wave effects, notably breaking, in terms of the wave age, wind speed, and bottom topography. Wave breaking is difficult to observe, model, and predict, because it is an unsteady, non-linear process that takes place over disparate scales in both space and time. In the open ocean, white-capping often covers less than 2% of the surface, yet still plays an important role in the flux of mass, momentum, heat, and chemicals between the atmosphere and ocean. The first part of this dissertation proposes a stochastic model for white-capping events, and examines the stability of the ensemble average of these events. Near the shore, the decreasing ocean depth causes waves to overturn and break. Over time, this drives currents that erode sediment from beaches and deposit it around coastal structures. These currents are often so strong that their effect on the wave field, and thus their own forcing, is significant. A detailed analysis of this phenomena makes up the second part of this dissertation.

Nous avons investigué, via les simulations de Monte Carlo, les propriétés non-perturbatives du modèle de Higgs abélien en 2+1 dimensions sans et avec le terme de Chern-Simons dans la phase de symétrie brisée, en termes de ses excitations topologiques: vortex et anti-vortex. Le but du présent travail est de rechercher les phases possibles du système dans ce secteur et d'étudier l'effet du terme de Chern-Simons sur le potentiel de confinement induit par les charges externes trouvé par Samuel. Nous avons formulé une description sur réseau du modèle effectif en utilisant une tesselation tétraédrique de l'espace tridimensionnel Euclidien pour générer des boucles de vortex fermées. En présence du terme de Chern-Simons, dans une configuration donnée, nous avons formulé et calculé le nombre d'enlacement entre les différentes boucles de vortex fermées. Nous avons analysé les propriétés du vide et calculé les valeurs moyennes de la boucle de Wilson, de la boucle de Polyakov à différentes températures et de la boucle de 't Hooft en présence du terme de Chern-Simons. En absence du terme de Chern-Simons, en variant la masse des boucles de vortex, nous avons trouvé deux phases distinctes dans le secteur de la symétrie brisée, la phase de Higgs habituelle et une autre phase caractérisée par l'apparition de boucles infinies. D'autre part, nous avons trouvé que la force entre les charges externes est écrantée correpondant à la loi périmètre pour la boucle de Wilson impliquant qu'il n'y a pas de confinement. Cependant, après la transition, nous avons trouvé qu'il existe toujours une portion de charges externes écrantée, mais qu'après une charge critique, l'énergie libre diverge. En présence du terme de Chern-Simons, et dans la limite de constante de couplage faible de Chern-Simons nous avons trouvé que les comportements de la boucle de Wilson et de la boucle de 't Hooft ne changent pas correspondants à une loi périmètre, impliquant qu'il n'y a pas de confinement. De plus, le terme de Chern-Simons ne contribue pas à la boucle de Wilson. / We investigate, via Monte Carlo simulations, non-perturbative properties of a 2+1 dimensional Abelian Higgs model without and with the Chern-Simons term in the symmetry broken phase in terms of its topological excitations: vortices and anti-vortices. The aim of the present work is to understand what phases exist for the system in that sector and the effect of the Chern-Simons term on the confining potential induced between external charges found by Samuel. We formulate a lattice description of the effective model starting from a tetrahedral tessellation of Euclidean three space to generate non-intersecting closed vortex loops. In the presence of the Chern-Simons term, for a given configuration, we formulate and compute the linking number between different closed vortex loops. We analyse properties of the vacuum and compute the expectation value of Wilson loop operator, Polyakov loop operator at different temperatures and the 't Hooft loop operator in the presence of the Chern-Simons term. In the absence of a Chern-Simons term, as we vary the mass of the vortex loops, we find two distinct phases in the symmetry broken sector, the usual Higgs phase and a novel phase which is heralded by the appearance of the so-called infinite loops. On the other hand, we find that the force between all external charges is screened, corresponding to a perimeter law for the Wilson loop implying no confinement. However, after the transition, we find that small external charges are still screened, but after a critical value of the external charge, free energy diverges. In the presence of Chern-Simons term, and in the limit where the coupling constant is low for Chern-Simons we find that the behavior of Wilson loop does not change: it is still a perimeter law, implying no confinement. Moreover, the Chern-Simons term does not contribute to the Wilson loop. 'tHooft loop behaves like a perimeter law too.

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Vortex-induced vibrations of a pivoted circular cylinder and control of these vibrations were investigated experimentally. A novel experimental setup was employed to reproduce orbiting response observed in some engineering applications. An adaptive pendulum tuned-mass damper (TMD) was integrated with the cylindrical structure in order to control the vortex-induced vibrations. All experiments were performed at a constant Reynolds number of 2100 for a range of reduced velocities from 3.4 to 11.3 and damping ratios from 0.004 to 0.018. For the experiments involving TMD, the TMD mass ratio was 0.087 and the TMD damping ratios investigated were 0 and 0.24. The results of the experiments performed without the TMD show that, in the synchronization region, the frequencies of transverse and streamwise vibrations lock onto the natural frequency of the structure. The cylinder is observed to trace elliptic trajectories. A mathematical model is introduced to investigate the mechanism responsible for the occurrence of the observed elliptic trajectories and figure-8 type trajectories reported in previous laboratory investigations. The results show that the occurrence of either elliptic trajectories or figure-8 type trajectories is governed primarily by structural coupling between vibrations in streamwise and transverse directions. Four types of elliptic trajectories were identified. The results show that the occurrence of the different types of elliptic trajectories is linked to phase angle between the streamwise and transverse vibrations of the structure, which depends on structural coupling. The results of the experiments performed to investigate effectiveness of the TMD in controlling vortex-induced vibrations show that tuning the TMD natural frequency to the natural frequency of the structure decreases significantly the amplitudes of transverse and streamwise vibrations of the structure. Specifically, the transverse amplitudes of vibrations are decreased by a factor of ten and streamwise amplitudes of vibrations are decreased by a factor of three. The results show that, depending on the value of the TMD damping ratio, the frequency of transverse vibrations is either characterized by the natural frequency or by two frequencies: one higher and the other lower than the natural frequency of the structure, referred to as fundamental frequencies. Independent of TMD damping and tuning frequency ratios, the frequency of streamwise vibrations matches that of the transverse vibrations in the synchronization region, and the cylinder traces elliptic trajectories. The phase angle between the streamwise and transverse vibrations is nearly constant when the pendulum is restrained. However, with the TMD engaged and tuned to the natural frequency, the phase angle fluctuates significantly with time. A mathematical model was utilized to gain insight into the frequency response of the structure. The results of the modeling show that the frequency of transverse vibrations is characterized by the fundamental frequency or frequencies of the structure and the frequency of streamwise vibrations is characterized by the fundamental frequency or frequencies as well as the first harmonic of the fundamental frequency or frequencies of the structure.