In this thesis, we consider two models from physics, which are characterized by the interplay of thermodynamical and fluid mechanical phenomena: demixing (spinodal decomposition) and Rayleigh--Bénard convection. In both models, we investigate the dependencies of certain intrinsic quantities on the system parameters. The first model describes a thermodynamically driven demixing process of a binary viscous fluid. During the evolution, the two components of the mixture separate into two domains of the different equilibrium volume fractions. One observes a clear tendency: Larger domains grow at the expense of smaller ones, and thus, the average domain sizes increases --- a phenomenon called coarsening. It turns out that two mechanisms are relevant for the coarsening process. At an early stage of the evolution, material transport is essentially mediated by diffusion; at a later stage, when the typical domain size exceeds a certain value, due to the viscosity of the mixture, a fluid flow sets in and becomes the relevant transport mechanism. In both regimes, the growth rates of the typical domain size obey certain power laws. In this thesis, we rigorously establish one-sided bounds on these growth rates via a priori estimates. The second model, Rayleigh--Bénard convection, describes the behavior of a fluid between two rigid horizontal plates that is heated from below and cooled from above. There are two competing heat transfer mechanisms in the system: On the one hand, thermodynamics favors a state in which temperature variations are locally minimized. Thus, in our model, the thermodynamical equilibrium state is realized by a temperature with a linearly decreasing profile, corresponding to pure conduction. On the other hand, due to differences in the densities of hot and cold fluid parcels, buoyancy forces act on the fluid. This results in an upward motion of hot parcels and a downward motion of cold parcels. We study the dependence of the average upward heat flux, measured in the so-called Nusselt number, on the temperature forcing encoded by the container height. It turns out that the efficiency of the heat transport is independent of the height of the container, and thus, the Nusselt number is a constant function of height. Using a priori estimates, we prove an upper bound on the Nusselt number that displays this dependency --- up to logarithmic errors. Further investigations on the flow pattern in Rayleigh--Bénard convection show a clear separation of length scales: Along the horizontal top and bottom plates one observes thin boundary layers in which heat is essentially conducted, whereas the large bulk is characterized by a convective heat flow. We give first rigorous results in favor of linear temperature profiles in the boundary layers, which indicate that heat is indeed essentially conducted close to the boundaries.:1 Introduction 2 Coarsening rates in binary viscous fluids 2.1 Background from physics 2.2 Background from mathematics 2.3 The model 2.4 The gradient flow structure 2.5 Heuristics 2.6 Numerical simulations 2.7 Main results 2.8 Preliminaries 2.9 Proof of upper bounds on coarsening rates 2.10 Appendix: Well-posedness and regularity of solutions 3 Scaling of the Nusselt number 3.1 Background from physics 3.2 The model and the Nusselt number 3.3 Heuristics 3.4 Main results 3.5 Scaling law in the linear regime 3.6 Preliminaries and review 3.7 Upper bound using the background field method 3.8 Upper bound using the maximum principle 3.9 Appendix: Some elementary estimates 4 The laminar boundary layer 4.1 Background, model, and motivation 4.2 Main results 4.3 Preparation: Bounds on the velocity field 4.4 On the energy distribution 4.5 Bounds on the second order derivatives of the temperature field 4.6 Bounds on the third order derivatives of the temperature field

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[pt] Nessa tese é analisada a dinâmica dos modos de lasers aleatórios à fibra com feedback distribuído. Um rigoroso estudo é feito sobre o mecanismo de feedback distribuído, i.e., o espalhamento Rayleigh, que é um dos principais elementos contribuindo para emissão laser. É desenvolvido um modelo teórico para previsão do retro espalhamento Rayleigh de luz coerente, o qual é baseado na ordem de médio alcance da sílica, e na tensão residual de fibras ópticas. As previsões do modelo são comparadas com resultados experimentais, levando a conclusão de que o retro espalhamento Rayleigh em fibras ópticas é um processo ergódigo nos domínios do tempo e da frequência óptica. O modelo mostrou-se eficaz na previsão das flutuações de intensidade do retro espalhamento Rayleigh de luz coerente, e foi utilizado para explicar a emissão de luz laser numa nova configuração de laser aleatório à fibra, que faz uso de um amplificador óptico a semicondutor (SOA) como meio de ganho. É demostrado que operação monomodo só é possível em emissão pulsada e com bombeio próximo ao limiar laser, enquanto operação multimodo é dominante para bombeio acima do limiar. Resultados experimentais indicam que potência dos modos é limitada pela competição entre modos por ganho. A operação em regime pulsado é atribuída a um efeito de cintilação da luz Rayleigh retro espalhada, que equivale a um fenômeno de chaveamento de perdas (Q-switching) aleatório na cavidade. O tempo de vida dos modos é ~ 1 ms e larguras de linha estreitas, no intervalo entre 4 e 7 kHz, foram obtidas experimentalmente. Lasers aleatórios à fibra com ganho Brillouin também foram analisados, mostrando semelhante dinâmica dos modos. Entretanto, por conta da estreita banda espectral do ganho Brillouin a competição entre modos não limitou a potência dos modos, a qual foi observada ser limitada por luz Stokes proveniente do espalhamento Brillouin de segunda ordem. Por último, experimentos com modulação de fase intra-cavidade foram avaliados, e mostraram que emissão laser pode ser controlada a partir da supressão da condição de fase ou ganho. / [en] In this thesis, it is provided a thorough analysis of mode dynamics of random distributed feedback fiber lasers. A rigorous investigation is proposed for the feedback mechanism, Rayleigh backscattering, which plays a key role in laser action. Based on the intermediate range order of silica glasses, and on residual stress of optical fibers, a theoretical model was built to predict intensity fluctuations of Rayleigh backscattered coherent light. Model predictions were compared to experimental results, strongly supporting the conclusion that Rayleigh backscattering in single mode fibers is an ergodic process exhibiting ergodicity in the time-frequency sense so that the model can be used to predict the statistical behavior of backscattered intensity fading. The model was used to explain laser action in a novel configuration of random fiber laser, with a semiconductor optical amplifier (SOA) employed as the gain medium. It is here demonstrated that single-mode operation is only possible in pulsed regime at SOA driving currents close to the threshold, whereas multimode regime dominates under higher currents. Experimental results indicate that the mode power is limited by mode competition, which is observed under high SOA currents. Pulsed regime is shown to be due to randomly driven Q-switching induced by a scintillation effect in the Rayleigh backscattered light, which effectively translates as a time-varying cavity loss. Mode lifetimes of ∼1 ms and narrow linewidths ranging from 4 to 7 kHz were experimentally obtained. Brillouin-based random fiber lasers were also analyzed, showing similar mode dynamics, but due to the much narrower gain spectral width, mode competition did not limit the mode power, which was rather limited by the second order Brillouin-Stokes light. Last, intra-cavity phase-modulation experiments showed that laser action can be efficiently controlled by breaking either phase or gain conditions.

[pt] Este estudo apresenta um método computacional para modelar campos eletromagnéticos em guias de onda retangulares curvados com seção transversal uniforme, usando o método variacional de Rayleigh-Ritz. Potenciais aplicações desta pesquisa em engenharia incluem o projeto de alimentadores para antenas, conversores de modais na faixa de micro-ondas, filtros, entre outros. Embora vários modelos tenham sido propostos para resolver este problema, as técnicas numéricas convencionais baseadas em elementos finitos, diferenças finitas e volumes finitos requerem altos custos computacionais. Para superar esses problemas, foi desenvolvida uma formulação variacional para resolver as equações de Maxwell em um sistema de coordenadas toroidal local, por meio de um novo funcional introduzido neste trabalho. O funcional foi adaptado para domínios uniformemente curvados com seção transversal arbitrária, e investigações analíticas foram conduzidas para confirmar suas características estacionárias. O formalismo Rayleigh-Ritz foi utilizado para converter o funcional em um problema equivalente de autovalores e autovetores, usando uma expansão em harmônicas retangulares de um guia de onda reto como funções de base para modelar um guia de onda retangular curvo. Um algoritmo numérico foi desenvolvido em Matlab para validar nosso modelo, e os resultados foram comparados com soluções perturbacionais e numéricas de referência, demonstrando alta precisão e menor custo computacional. / [en] This study presents a computational method for modeling electromagnetic fields in curved rectangular waveguides with uniform cross-section, using the variational Rayleigh-Ritz method. The potential applications of this research in engineering include the design of feeders for antennas, microwave mode converter devices, filters, among others. While various models have been proposed to solve this problem, conventional numerical techniques based on finite elements, finite differences, and finite volumes require high computational costs. To overcome these issues, a variational formulation for solving Maxwell s equations in a local toroidal coordinate system was developed via a novel functional introduced in this work. The functional was adapted to handle uniformly bend domains with arbitrary cross-section, and analytical investigations were conducted to confirm its stationary characteristics. The Rayleigh-Ritz formalism was employed to convert the functional into an equivalent problem of eigenvalues and eigenvectors using an expansion in terms of rectangular harmonics of a straight waveguide as basis functions for modeling a bend rectangular waveguide. A numerical algorithm was developed in Matlab to validate our model, and the results were compared against reference perturbational and numerical solutions, demonstrating high accuracy and lower computational costs.

ITC/USA 2008 Conference Proceedings / The Forty-Fourth Annual International Telemetering Conference and Technical Exhibition / October 27-30, 2008 / Town and Country Resort & Convention Center, San Diego, California / Although multiple-input multiple-output (MIMO) systems have become increasingly popular, the existence of real time results to compare with those predicted by theory is still surprisingly limited. In this work the hardware description of a MIMO wireless communication system using orthogonal space time block codes (OSTBC) is discussed for two antennas at both the transmitter and receiver. A numerical example for a frequency flat time correlated channel is given to show the impact of channel estimation.

A method for numerical simulation of train induced track vibration and wave propagation in subgrade has been proposed. The method uses a mass to simulate the bogie of a train and considers the effect of rail roughness. For this method, rail roughness is considered as a randomly generated signal and a filter is used to block the undesired components. The method predicts the particle velocity around the track and can be applied to many kinds of railroad trackbeds including traditional ballast trackbed and modern Hot mix asphalt (HMA) trackbed. Results from ballast and HMA trackbeds are compared and effects of HMA layer on damping track vibration and dissipating wave propagation are presented. To verify the credibility of the method, in-track measurements were also conducted. Site measurements included performing geophysical tests such as spectral analysis of surface wave test and seismic refraction test to determine the subsurface conditions at the test site. Ballast and HMA samples were tested in the laboratory by resonant column test to obtain the material properties. Particle velocities were measured and analyzed in the frequency domain. Results from in-track tests confirm the applicability of the numerical method. The findings and conclusions are summarized and future research topics are suggested.

La détermination expérimentale des composantes du tenseur d'hyper-polarisabilité est essentielle au développement de nouvelles molécules possédant des propriétés d'optique non-linéaire. La diffusion harmonique de la lumière (DHL) correspond à un phénomène de diffusion non linéaire de la lumière pour laquelle les molécules considérées sont dans une solution isotrope. Du fait des fluctuations d'orientations et de positions des molécules, seules six observables, où invariants orientationnels, sont mesurables par DHL. Afin de déterminer expérimentalement ces six observables, nous avons mis au point un polarimètre à lame de phase tournantes fonctionnant avec une source laser impulsionnelle accordable en longueur d'onde et dédié au mesures de diffusion harmonique de la lumière. Nous avons dans un premier temps optimisé l'architecture du montage polarimétrique en nous appuyant sur la réduction du nombre de conditionnement de la matrice d'appareil, réduisant par la même les erreurs statistiques. Puis nous avons étalonné le montage au moyen d'un échantillon référence dédié à la conversion de longueur d'onde, afin de réduire les erreurs systématiques. Enfin, nous avons réalisé des mesures de diffusion harmonique de la lumière sur deux molécules connues, le DR1 et le Cristal Violet.

La technique de la génération de second harmonique (SHG) a été employée pour étudier la réponse non linéaire des assemblées de nano particules métalliques aux interfaces liquides. Les nanoparticules ont d'abord été caractérisées en utilisant la génération de second harmonique incohérente, également nommée diffusion hyper Rayleigh. L'étude de particules d'or et d'argent, nanosphères et des nanobâtonnets, ont permis de mettre en évidence l'influence de la couche protectrice de surfactants sur l'hyperpolarisabilité quadratique de ces particules. Ces particules ont ensuite été placées à l'interface air/eau dans une cuve de Langmuir afin d'étudier le rôle des interactions entre les particules sur la réponse optique linéaire et non linéaire. Celle-ci a révélé dans ces films formés à l'interface la présence de couplages forts entre les particules lors de la compression de la surface. Cela conduit à une transition dans le film une fois que la distance entre les particules passe en dessous d'une distance critique. Ces études ont été complétées par des expériences réalisées à l'interface liquide/liquide et sur une électrode de carbone vitreux pour examiner plus en détail le rôle de la rugosité à l'échelle nanométrique dans l'exaltation de la réponse non linéaire SHG

Traditional methods of imaging the Earth’s subsurface using seismic waves require an identifiable, impulsive source of seismic energy, for example an earthquake or explosive source. Naturally occurring, ambient seismic waves form an ever-present source of energy that is conventionally regarded as unusable since it is not impulsive. As such it is generally removed from seismic data and subsequent analysis. A new method known as seismic interferometry can be used to extract useful information about the Earth’s subsurface from the ambient noise wavefield. Consequently, seismic interferometry is an important new tool for exploring areas which are otherwise seismically quiet, such as the British Isles in which there are relatively few strong earthquakes. One of the possible applications of seismic interferometry is the ambient noise tomography method (ANT). ANT is a way of using interferometry to image subsurface seismic velocity variations using seismic (surface) waves extracted from the background ambient vibrations of the Earth. To date, ANT has been used to successfully image the Earth’s crust and upper-mantle on regional and continental scales in many locations and has the power to resolve major geological features such as sedimentary basins and igneous and metamorphic cores. In this thesis I provide a review of seismic interferometry and ANT and apply these methods to image the subsurface of north-west Scotland and the British Isles. I show that the seismic interferometry method works well within the British Isles and illustrate the usefulness of the method in seismically quiet areas by presenting the first surface wave group velocity maps of the Scottish Highlands and across the British Isles using only ambient seismic noise. In the Scottish Highlands, these maps show low velocity anomalies in sedimentary basins such as the Moray Firth and high velocity anomalies in igneous and metamorphic centres such as the Lewisian complex. They also suggest that the Moho shallows from south to north across Scotland, which agrees with previous geophysical studies in the region. Rayleigh wave velocity maps from ambient seismic noise across the British Isles for the upper and mid-crust show low velocities in sedimentary basins such as the Midland Valley, the Irish Sea and the Wessex Basin. High velocity anomalies occur predominantly in areas of igneous and metamorphic rock such as the Scottish Highlands, the Southern Uplands, North-West Wales and Cornwall. In the lower crust/upper mantle, the Rayleigh wave maps show higher velocities in the west and lower velocities in the east, suggesting that the Moho shallows generally from east to west across Britain. The extent of the region of higher velocity correlates well with the locations of British earthquakes, agreeing with previous studies that suggest British seismicity might be influenced by a mantle upwelling beneath the west of the British Isles. Until the work described in Chapter 6 of this thesis was undertaken in 2009, seismic interferometry was concerned with cross-correlating recordings at two receivers due to a surrounding boundary of sources, then stacking the cross-correlations to construct the inter-receiver Green’s function. A key element of seismic wave propagation is that of source-receiver reciprocity i.e. the same wavefield will be recorded if its source and receiver locations and component orientations are reversed. By taking the reciprocal of its usual form, in this thesis I show that the impulsive-source form of interferometry can also be used in the opposite sense: to turn any energy source into a virtual sensor. This new method is demonstrated by turning earthquakes in Alaska and south-west USA into virtual seismometers located beneath the Earth’s surface.

Approved for public release, distribution is unlimited / Ensign, United States Navy