Liquid droplet breakup and dynamics is a phenomena of immense practical importance in a wide variety of applications in science and engineering. Albeit, researchers have been studying this problem for over six decades, the fundamental physics governing droplet deformation and fragmentation is still unknown, not to mention the formulation and development of generalized correlations to predict droplet dynamics. The presence of disparate length and time scales, along with the complex unsteady physics, makes this a formidable problem, theoretically, experimentally and computationally. One of the important applications of interest and the motivation for the current research is a liquid fueled propulsion device, such as diesel, gas turbine or rocket engine. Droplet vaporization and ensuing combustion is accelerated if the droplet size is smaller, which makes any process leading to a reduction in drop size of prime importance in the combustion system design. This thesis is an attempt to address several unanswered questions currently confronting the spray community. Unanswered questions include identification and prediction of breakup modes at varying operating conditions, quantitative description of fundamental processes underlying droplet breakup and generalized correlations for child droplet size distributions and drag coefficient associated with the deformation and fragmentation of Newtonian and non-Newtonian fluids. The present work is aimed at answering the above questions by investigating the detailed flowfield and structure dynamics of liquid droplet breakup process and extracting essential physics governing this complex multiphase phenomena. High-fidelity direct numerical simulations are conducted using a volume-of-fluid (VOF) interface capturing methodology. To isolate the hydrodynamic mechanisms dictating droplet breakup phenomena, evaporation and compressibility are neglected, and numerical studies are performed for incompressible fluids at isothermal conditions. For Newtonian fluids, four different mechanisms are identified- oscillatory, bag, multimode and shear breakup modes. Various events during the deformation and fragmentation process are quantitatively identified and correlations are developed to predict the breakup mechanisms and droplet size distributions for a broad range of operating conditions. It was found that for We > 300 and Oh < 0.1 for rho_l/rho_g = 8.29, the child droplet size distributions can be modeled by a log-normal distribution. A correlation to predict the sauter mean diameter, d32, is also developed, given by d32 / D = 8We^-0.72 / Cd. Temporal evolution of momentum balance and droplet structure are also used to calculate the drag coefficient at each time step from first principles. Results show that the drag coefficient first increases to a maximum as the droplet frontal area increases and then decreases at the initiation of breakup. The drag coefficient reaches a steady value at the end of droplet lifetime, corresponding to the momentum retained by the droplet. A correlation to predict the time-mean drag coefficient given by, Cd / Cd,0 = 2We-^0.175, is developed, which indicates that the time averaged drag coefficient decreases with Weber number. The motivation to study non-Newtonian liquid droplet breakup stems from the various advantages gelled propellants offer as compared to traditional liquid or solid propellants in combustion systems, particularly in rocket engines. It was found that the breakup behavior of pseudoplastic, non-Newtonian liquids is drastically different as compared to Newtonian droplets. Several flow features commonly exhibited by non-Newtonian fluids are observed during the breakup process. The breakup initiates with the formation of beads-in-a-string due to the non-Newtonian nature of the fluid under consideration. This is followed by rapid rotation of the droplet with the appearance of helical instability and liquid budges, which forms the sites for primary and satellite droplet shedding. Child droplet size distribution are also examined and it is found that a Gaussian curve universally characterizes the droplets produced during non-Newtonian droplet breakup process. To put all things in perspective, the objectives of the thesis were two folds: (1) elucidate breakup physics for Newtonian and non-Newtonian liquid droplet deformation and breakup, and (2) develop correlations which can be used in an Eulerian-Lagrangian framework to study large-scale engineering problems. It is hoped that this research contributed to droplet breakup and dynamics literature by providing a more thorough and quantitative understanding of the breakup phenomena of liquid droplets and furnished models which can be used in future research endeavors.

The spatial and temporal structure of the flow, vorticity and stress over equilibrium orbital-scale sand ripples are investigated at turbulence-resolving scales with a wide-band coherent Doppler profiler (MFDop) in an oscillating tray apparatus. The oscillation period and horizontal excursion were 10 s and 0.5 m. Velocity profiles were acquired with 3 mm vertical resolution and at a 42 Hz sampling rate. Ripple wavelength and amplitude were 25 cm and 2.2 cm. The MFDop measurements are used to investigate the development of the lee vortex as a function of phase, and the co-evolution of turbulent kinetic energy, Reynolds stress and turbulence production. Shear stress is determined from the vertically-integrated vorticity equation and using the double-averaging approach. Friction factors obtained from the two methods are comparable and range from 0.1 to 0.2.

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.

In this thesis, Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) codes for one and two-dimensional discretised Euler equations are developed. The construction and application of the FV-WENO scheme and codes will be described. Also the effects of the grid coefficients as well as the effect of the Gaussian Quadrature on the solution have been tested and discussed. WENO schemes are high order accurate schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the high approximation level, where a convex combination of all the candidate stencils is used with certain weights. Those weights are used to eliminate the stencils, which contain discontinuity. WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures. The applications tested in this thesis are the Diverging Nozzle, Shock Vortex Interaction, Supersonic Channel Flow, Flow over Bump, and supersonic Staggered Wedge Cascade. The numerical solutions for the diverging nozzle and the supersonic channel flow are compared with the analytical solutions. The results for the shock vortex interaction are compared with the Roe scheme results. The results for the bump flow and the supersonic staggered cascade are compared with results from literature.

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 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

In recent years, neuromorphic architectures have been an increasingly effective tool used to solve big data problems. Hardware neural networks have not been able to fully exploit the power efficient properties of the neural paradigm, however, due to limitations in standard CMOS. One of the largest challenges is the quadratic scaling of the synapses in a neural network. There has been some work in using post CMOS technology as synapses to overcome this limitation, but systems to date have not been scalable due to the design of their neurons. This dissertation aims to design and build scalable neural network architectures that can use emerging resistive memory technology as synapses. Using analog computing techniques to build networks is promising, especially due to the development of dense, CMOS compatible analog resistive memories. Building functional analog networks in advanced technology nodes, however, is challenging due to the relatively poor performance of analog components in these nodes. This work explores oscillatory neural networks (ONNs), which use phase as the analog state variable instead of voltage or current, reducing the number of traditional analog components required and making the networks better-suited for advanced nodes. This thesis develops additional ONN theory with regard to hardware networks, since previous work did not consider the effect of transmission delay on network dynamics. Transmission delay is proven to cause desynchronization in unmodified ONNs, and the theoretical analysis suggests ways to build networks which do synchronize. Conclusions from the theoretical development are used to build a PLL-based ONN in hardware. The PLL-based ONN is more energy efficient than comparable systems implemented in digital CMOS, although the neuron area is somewhat larger. The measurement of the PLL-based ONN also reveals additional poorly-studied facets of ONN dynamics. Using the knowledge gained from the PLL-based ONN, a larger, PLL-free ONN is built in the same technology. Removing the PLL in each neuron reduces the power and area consumption without sacrificing any functionality.This dissertation demonstrates that ONNs are well-suited to take advantage of emerging resistive memory technology to build efficient hardware neural networks.

Thermoacoustic devices are a group of systems that make use of the thermoacoustic effect to achieve an energy conversion between thermal and acoustic energy. The thermoacoustic effect occurs when a solid boundary is introduced into an acoustic field, and a non-zero net heat transportation takes place while the net mass transfer remains null. Thermoacoustic technologies are gaining an increasing research interest because of their potential applications for building alternative prime movers or heat pumps which do not use working fluids causing environmental damage and require very little maintenance due to their lack of moving part. However, the operation of this type of system is yet to be fully understood: fluid flow and heat transfer processes within the system components such as thermoacoustic stacks and heat exchangers still require a lot of attention. The performance of the system working with relatively low amplitude acoustic wave can be predicted by the linear thermoacoustic theory, which is already well developed. However, a high amplitude acoustic wave is usually required in order to achieve high power density or high power output. Unfortunately, the performance of such systems can be seriously degraded due to nonlinear effects, such as turbulence, minor loss or high proportion of harmonics. The lack of understanding of these effects impedes the design and construction of high efficiency systems. The work described in this thesis is focused on the study of flow phenomena taking place around parallel plate stack placed in a standing wave thermoacoustic resonator, by using advanced flow diagnostics techniques such as particle image velocimetry (PIV) and hot wire anemometry (HWA). In order to carry out the experimental study, a standing wave thermoacoustic device working at relatively low frequency of 13.1Hz was designed, commissioned and tested. The frequency response of this device was carefully investigated and compared with the analytical results using linear acoustic equations and a linear model of the loudspeaker. A further comparison with the analytical results obtained with the modelling tool DeltaEC (Design Environment for Low-amplitude Thermoacoustic Energy Conversion) was also presented. The resonator was driven from low to large pressure amplitudes with drive ratios up to 10%. A good agreement is obtained for small amplitudes, but the discrepancies become larger when the driving amplitude is increased. The analysis reveals that the large discrepancy at high amplitude can be attributed to minor losses. Following the above preliminary work, a more comprehensive study of the flow field around parallel-plate stacks was conducted by means of PIV and HWA. It was shown that the flow around the two studied parallel-plate stacks exhibits rather complicated flow features when the amplitude of the acoustic oscillation varies. Symmetrical and asymmetrical vortex shedding phenomena are observed and two distinct modes of generating 'vortex streets' are identified. It shown that a velocity related parameter such as the Reynolds number, defined on the plate thickness and the velocity amplitude at the entrance to the stack, and a geometrical parameter are not sufficient to define the flow characteristics in this type of flow problem. It is also proposed to introduce an extra frequency related parameter such as the Keulegan-Carpenter number (KC) and to carry out a similarity analysis in order to understand better the physics behind the flow phenomena and their controlling parameters. Typical ensemble-averaged velocity fields are used in the analysis above. However, the detailed flow features obtained from the ensemble averaged flow fields and the instantaneous flow fields could be different in a substantial way. The flow behaviour, its kinematics, dynamics and scales of turbulence, therefore are further investigated by using the classical Reynolds decomposition to separate the instantaneous velocity fields into ensemble-averaged mean velocity fields and fluctuations in a set of predetermined phases within an oscillation cycle. The mean velocity field and the fluctuation intensity distributions are investigated over the acoustic oscillation cycle. By using fast Fourier transform (FFT) spatial filtering techniques, the velocity fluctuation is further divided into large- and small-scale fluctuations, and their physical significance is discussed. The physics behind the flow phenomena are further studied by carrying out an analysis of the wake flow during the ejection part of the flow cycle, where either closed re-circulating vortices or alternating vortex shedding can be observed. A similarity analysis of the governing Navier-Stokes equations is then undertaken in order to derive the similarity criteria governing the wake flow behaviour. Similarity numbers including two types of Reynolds number, the KC number and a non-dimensional stack configuration parameter are considered. The influence of these parameters on the flow behaviour is discussed by investigating the experimental data obtained, along with additional data from literature.

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.

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