Neste trabalho, analisamos o modelo de gravitação dilatônica proposto por Callan, Giddings, Harvey e Strominger (modelo de CGHS). Aplicamos a teoria de vínculos ao modelo e mostramos que só existem vínculos de primeira classe. Em seguida ap0licamos a técnica de BRST-BFV para quantizar a teoria. Mostramos que os fantasmas na função de partição estão desacoplados dos campos e podem ser integrados. Utilizamos uma transformação canônica para escrever os vínculos na forma quadrática, que facilita a quantização da teoria. Para completar a quantização usamos o procedimento de Dirac para obter a álgebra dos vínculos expressa na forma do tensor momento-energia. Existe uma anomalia na álgebra que é apropriadamente eliminada quando adicionamos um termo de improvement à ação. Finalmente usamos o procedimento de Dirac para obter soluções para a função de onda. Isto prova que a teoria de CGHS em duas dimensões é perfeitamente quantizável. / We analyse a theory of gravitation in two dimensions using the hamiltonian formalism. For this purpose we use the CGHS model in the conformal gauge. The theory of constraints shows that we have only first-class constraints. After that, we apply the BRST-BFV technique to quantize the theory. We show that the ghosts in the partition function are decoupled from the fields. Then we integrate the ghosts in the partition function. By a suitable canonical transformation we write the constraints in a quadratic form which facilitates the quantization of the theory. To complete the quantization we use the Dirac procedure to obtain the constraints algebra expressed in the energy-momentum tensor form. There is an anomaly in the algebra which can be suitably eliminated by the addition of an improvement term in the action. Finally we use the Dirac procedure tro obtain solutions for the wave function. This proves that the CGHS theory in two dimensions is quantizable.

Gravity waves are ubiquitous at the surface of the ocean and play a key role in the coupled ocean-atmosphere system. These wind generated waves, for which gravity provides the restoring force, influence the kinematics and dynamics of the upper ocean and lower atmosphere. Their breaking injects turbulence into the upper ocean, generates bubble plumes and sea-spray thus transferring energy, momentum, heat and mass between the atmosphere and the ocean. In the anthropocene, with CO2 driving the warming trend and the ocean acting as the main carbon sink, it is imperative to understand the complex physical controls of air-sea gas transfer. Large uncertainties still remain under high wind speed conditions where wave breaking processes are dominant. This dissertation seeks to shed light onto the dependence of wave breaking and air-sea gas transfer on environmental parameters. It further explores process based models of air-sea gas transfer that explicitly account for the breaking related processes. Air entraining breaking waves are easily detectable as bright features on the ocean surface composed of foam and subsurface bubble plumes. These features, termed whitecaps, arise at wind speed as as low as 3 m s−1 . The whitecap coverage (W) has been recognized as a useful proxy for quantifying wave breaking related processes. It can be determined from shipboard, air-borne and satellite remote sensing. W is most commonly parameterized as a function of wind speed, but previous parameterizations display over three orders of magnitude scatter. Concurrent wave field and flux measurements acquired during the Southern Ocean Gas Exchange (SO GasEx) and the High Wind Gas exchange Study (HiWinGS) projects permitted evaluation of the dependence of W on wind speed, wave age, wave steepness, mean square slope, as well as on wave-wind and breaking Reynolds numbers. W was determined from over 600 high frequency visible imagery recordings of 20 minutes each. Wave statistics were computed from in situ and remotely sensed data as well as from a WAVEWATCH-III® hind cast. The first ship-borne estimates of W under sustained wind speeds (U10N ) of 25 m s−1 were obtained during HiWinGS. These measurements suggest that W levels off at high wind speed, not exceeding 10% when averaged over 20 minutes. Combining wind speed and wave height in the form of the wave-wind Reynolds number resulted in closely agreeing models for both datasets, individually and combined. These are also in good agreement with two previous studies. When expressing W in terms of wave field statistics only or wave age, larger scatter is observed and/or there is little agreement between SO GasEx, HiWinGS, and previously published data. The wind–speed-only parameterizations deduced from the SO GasEx and HiWinGS datasets agree closely and capture more of the observed W variability than Reynolds number parameterizations. However, these wind-speed-only models do not agree as well with previous studies than the wind-wave Reynolds numbers. The ability to quantify air-sea gas transfer hinges on parameterizations of the gas transfer velocity k. k represents physical mass transfer mechanisms and is usually parameterized as a non-linear function of wind forcing. Previous eddy-covariance measurements and models based on the global radio carbon inventory led to diverging parameterizations with both cubic and quadratic wind speed dependence. At wind speeds above 10 m s−1 these parameterizations differ considerably and measurements display large scatter. In an attempt to reduce uncertainties in k, explored empirical parameterizations that incorporate both wind speed and sea state dependence via breaking and wave-wind Reynolds numbers, were explored. Analysis of concurrent eddy covariance gas transfer and measured wave field statistics supplemented by wave model hindcasts shows for the first time that wave-related Reynold numbers collapse four open ocean datasets that have a wind speed dependence of CO2 transfer velocity ranging from lower than quadratic to cubic. Wave-related Reynolds number and wind speed show comparable performance for parametrizing DMS which, because of its higher solubility, is less affected by bubble-mediated exchange associated with wave breaking. While single parameter models may be readily used in climate studies, their application is gas specific and may be limited to select environments. Physically based parameterizations that incorporate multiple forcing factors allow to model the gas transfer of gases with differing solubility for a wide range of environmental conditions. Existing mechanistic models were tested and a novel framework to model gas transfer in the open ocean in the presence of breaking waves is put forward. This analysis allowed to update NOAA’s Coupled OceanAtmosphere Response Experiment Gas transfer algorithm (COAREG) and exposed limitation of other existing physically based parameterizations. The newly proposed mechanistic model incorporates both the turbulence and bubble mediated transfer. It is based on various statistics determined from the breaking crest length distribution (Λ(c)). Λ(c) was obtained by tracking the advancing front of breaking waves in the high frequency videos taken during HiWinGS. Testing the mechanistic model with the HiWinGS dataset shows promising results for both CO2 and DMS, though it does not perform better than COAREG. Uncertainties remain in the quantification of bubble cloud which are at the core of the formulation of the bubble mediated transfer and additional field measurements are necessary to characterize bubble plume properties in the open ocean.

Predicting the evolution of turbulent gravity currents is of great interest in many areas of geophysics and engineering, in particular due to their impact on the environment. In most practical applications in river, coastal and ocean engineering, gravity currents propagate over loose surfaces containing large scale bedforms (e.g., dunes). In others, arrays of obstacles (e.g., ribs) are often used as protective measures on hilly terrains to stop or slow down gravity currents in the form of powder-snow avalanches. To predict the capacity of a turbulent gravity current propagating over a loose bed to entrain, carry, and deposit sediment requires a detailed understanding of its structure and the role played by the large-scale instabilities present in the flow. The present study uses high-resolution Large Eddy Simulation to study the physics of high Reynolds number compositional Boussinesq gravity currents with large and small volume of release in lock-exchange configurations and their dynamic effects on various obstacles (e.g., bedforms, flow retarding obstacles, submerged dams that are used to control sediment deposition in reservoirs). The study shows that gravity currents propagating over large-scale roughness elements reach a turbulent drag-dominated regime in which the front velocity decays proportional to t-1/2, similar to the case of gravity currents propagating within a porous medium. Though the establishment of a regime in which the flow evolution is mainly determined by the balance between the turbulent drag and the buoyancy force driving the flow was expected, the fact that the law of decay of the front velocity with time is identical for gravity currents propagating over roughness elements and in a porous medium of uniform porosity is not obvious. The simulations provide detailed information on the temporal evolutions of the front velocity, energy balance, sediment entrainment capacity and the flow instabilities, and of the distributions of the density, velocity, local dissipation rate and bed shear stresses at different stages of the propagation of the gravity current. The study investigates of the effect of the shape and relative size of the obstacles, with respect to the current height, on the structure of the current and on the differences with the simpler, but much more widely studied case of a gravity current propagating over a flat smooth surface. For example, the simulation results are used to explain why gravity currents propagating over dunes have a much larger capacity to entrain sediment than gravity currents propagating over ribs of the same height and with similar spacing. The accurate estimation of impact of gravity current on the structures over its path is very important from engineering point of view since many submerged cables over the ocean bottom or submerged dams in reservoirs are under the risk of such impacts. The simulations of gravity currents propagating past arrays of ribs or isolated dams are used to estimate the characteristic times and magnitudes of the hydrodynamic impact forces on these obstacles. This information is crucial for the proper design of these structures. The study shows the critical role played by flow disturbances (e.g., backward propagating hydraulic jumps) that form as a result of the interaction between the current and the large-scale obstacles. Finally, the study investigates scale effects between the Reynolds numbers at which most experimental investigations of gravity currents are conducted and Reynolds numbers at field scale.

1In this dissertation we work out in detail a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, and propose how to compare in detail the physics of this sector with that of loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. To impose the symmetry at the quantum level, on both the connection and its conjugate momentum, the method used necessarily has similiarities to the Gupta-Bleuler method of quantizing the electromagnetic field. Lastly, a strategy for embedding states of loop quantum cosmology into this new homogeneous isotropic sector, and using this embedding to compare the physics, is presented. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

The spin-foam is a covariant path-integral style approaching to the quantization of the gravity. There exist several spin-foam models of which the most successful one is the Engle-Pereira-Rovelli-Levine/Freidel-Krasnov (EPRL-FK) model. Using the EPRLFK model people are able to calculate the transition amplitude and the n-point functions of 4D geometry (both Euclidean and Lorentzian) surrounding by a given triangulated 3D geometry. The semi-classical limit of the EPRL-FK amplitude reproduces discrete classical gravity under certain assumptions, which shows that the EPRLFK model can be understood as UV completion of general relativity. On the other hand, it is very hard to dene a continuum limit and couple a cosmological constant to the EPRL-FK model. In this dissertation, we addressed the problems about continuum limit and coupling a cosmological constant to the EPRL-FK model. Followed by chapter one as a brief introduction of the loop quantum gravity and EPRL-FK model, chapter two introduces our work about demonstrating (for the first time) that smooth curved spacetime geometries satisfying Einstein equation can emerge from discrete spin-foam models under an appropriate low energy limit, which corresponds to a semi-classical continuum limit of spin-foam models. In chapter three, we bring in the cosmological constant into the spin-foam model by coupling the SL(2, C) Chern-Simons action with the EPRL action, and find that the quantum simplicity constraint is realized as the 2d surface defect in SL(2, C)Chern-Simons theory in the construction of spin-foam amplitudes. In chapter four, we present a way to describe the twisted geometry with cosmological constant whose corresponding quantum states can forms the Hilbert space of the loop quantum gravity with cosmological constant. In chapter five, we introduced a new definition of the graviton propagator, and calculate its semi-classical limit in the contents of spin-foam model with the cosmological constant. Finally the chapter six will be a outlook for my future work. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

We experimentally investigate the phenomena of large jet rebound, a mode of fluid transfer following oblique jet impacts on hydrophobic substrates. We initially seek to describe the jet rebound regimes in tests conducted in the weightless environment of a drop tower. A parametric study reveals the dependence of the flow structure on the relevant dimensionless groups such as Reynolds number and Weber number defined on the velocity component perpendicular to the substrate. We show that significantly larger diameter jets behave similarly as much smaller jets demonstrated during previous terrestrial investigations is some parameter ranges while the flow is fundamentally different in others. Level-set numerical predictions are provided for comparisons where practicable. Simple models are developed predicting landing geometry and the onset of instability that are found to yield good agreement with experiments and simulations. Improving our understanding of such jet rebound opens avenues for unique transport capabilities.

The diffeomorphism field is introduced to the physics literature in [1] where it arises as a background field coupled to Polyakov’s quantum gravity in two dimensions, where Einstein’s gravity is trivial. Moreover, it is seen in many ways as the gravitational analog of the Yang-Mills field. This raises the question of whether the diffeomorphism field exists in higher dimensions, playing an essential role in gravity either by supplementing Einstein’s theory or by modifying it. With this motivation, several distinct theories governing the dynamics of the diffeomorphism field have been constructed and developed by mimicking the construction of the Yang-Mills theory from the Kac-Moody algebra. This analogy, however, is not perfect and there are many subtleties and difficulties encountered. This thesis constitutes a further development. The previously proposed theories are carefully examined; certain subtleties and problems in them have been discovered and made apparent. Some of these problems have been solved, and for others possible routes to follow have been laid down. Finally, other geometric approaches than the ones followed before are investigated.

This research presents the results of two interrelated sets of experiments examining the dynamics of plumes and fountains in two-layer and continuously stratified environments. The first study examines the evolution of an axisymmetric turbulent fountain in a two-layer stratified environment. Interacting with the interface, the fountain is observed to exhibit three regimes of flow. It may penetrate the interface but nonetheless return to the source where it spreads as a radially propagating gravity current; the return flow may be trapped at the interface where it spreads as a radially propagating intrusion or it may do both. These regimes have been classified using empirically determined regime parameters which govern the relative initial momentum of the fountain and the relative density difference of the fountain and the ambient fluid. The maximum vertical distance travelled by the fountain in a two-layer fluid has been theoretically determined by extending the theory developed for fountains in a homogeneous environment. The theory compares favourably with experimental measurements. We have also developed a theory to analyse the initial speeds of the resulting radial currents. We found that the currents exhibited two different regimes of flow. The second study presents experimental results of the generation of internal gravity waves by a turbulent buoyant plume impinging upon the interface between a uniform density layer of fluid and a linearly stratified layer. The wave field is observed and its properties measured non-intrusively using axisymmetric Schlieren. In particular, we determine the fraction of the energy flux associated with the plume at the neutral buoyancy level that is extracted by the waves. On average, this was found to be approximately 4 per cent. Within the limits of the experimental parameters, the maximum vertical displacement amplitude of waves were found to depend linearly upon the maximum penetration height of the plume beyond the neutral level. The frequency of the waves was found to lie in a narrow range relative to the buoyancy frequency. The results are used to interpret the generation of waves in the atmosphere by convective storms impinging upon the tropopause via the mechanical oscillator effect. / Applied Mathematics

In this thesis we present work done in an analysis of models of brane induced gravity. These are higher dimensional generalizations of Einstein's General relativity where our universe is considered as a brane in a higher dimensional bulk and where the gravitational dynamics on the brane is enhanced. This provides a modification of gravity on the brane as compared to ordinary general relativity, primarily at very large distances. These models are therefore very interesting for adressing the cosmological constant problem. Even though the basic setup is natural to consider from the perspective of effective field theory and also follow from certain string theoretical considerations, the models have been plagued by inconsistencies in the form of unstable modes. In particular, a ghostlike and tachyonic scalar mode appears already at the linear level in a perturbative treatment. In order to gain a deeper insight into the nature of these consistency problems we have revisited the models, performing a more extensive analysis of the generic models than has previously been done. We have worked entirely in a gauge invariant formalism in order not to be obscured by gauge issues. We have also incorporated an effective thickness of the brane in our analysis and performed an explicit analysis of the effect of contributions from the extrinsic geometry. Although our analysis has been carried out at the linear level in a perturbative treatment we are able to get a deeper understanding of the unstable mode and illuminate some of the difficulties of these models that would likely persist even in a full nonlinear analysis.

The purpose of this research is to develop a systematic methodology for the innovative design of Gravity Single Site IC Test Handler. First, basic characteristics of Gravity Single Site IC Test Handler are deduced. Next, all possible variants of function structure are synthesized by using the functional analysis method. Next, a system of kinematic notation is used to generate the principle solutions of each function in a functional structure and all possible design concepts of Gravity Single Site IC Test Handler are created. Then, promising design concepts are evaluated by using the decision matrix method. Finally, feasible design concepts of Gravity Single Site IC Test Handler are provided, and then optimum Gravity Single Site IC Test Handler can be synthesized by using the theory of kinematic design. Based on the foreging, four innovative design conceps of Gravity Single Site IC Test Handler are created step by step. The results of this work are of benefit to the development and innovative design for new Gravity Single Site IC Test Handler¡C