No description available.

The linear and weakly non-linear limits of two-dimensional gravity waves in an incompressible, inviscid and stably stratified atmosphere are studied. The linear results indicate the growth of waves propagating upward leading to the breakdown of the linear theory. The three-wave resonant interaction theory indicates an energy cascade from a vertically propagating wave (primary wave) to waves having smaller absolute values of Doppler shifted frequency ((OMEGA)). When the non-dimensional parameter / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / is in the range "1 to about 0.8" (N being the Brunt-Vaisala frequency), the energy of the primary wave is transferred to bands of small amplitude waves. The triads in these bands include a member with the same vertical group velocity as the primary wave while other triads contain a member with larger vertical group velocity. The band widths approach zero as the primary wave amplitude is reduced. The analysis suggests that the three-wave resonant interactions should be replaced by a higher order approximation in this limit.

No description available.

No description available.

Gravity datasets from two geothermal areas in Iceland, an Iceland-wide gravity dataset, and marine gravity data from the Reykjanes Ridge at 58˚N, which can be seen as the submarine extension of the Icelandic accretionary system, have been studied in this thesis. Results of previous local earthquake seismic tomography studies of the shallow crustal structure of two spreading segments in Iceland have been used, in conjunction with gravity observations, to assess the fidelity of the tomographic method and further refine the description of the crustal structure for these areas. This was accomplished by predicting the component of the observed gravity field which may be produced by the tomographically imaged bodies and in the process attempting to explain any residual anomalies. Results showed additional shallow structure inferred from gravity observation and suggested that local earthquake seismic tomography can 'overlook' some geological structure. The Icelandic gravity field was separated into long and short wavelength components which were attributed to mantle plume and crustal effects, respectively. Physical parameters were attributed to the sources of these anomalies where possible. Results showed that a simple cylinder model (radius -100 km) of anomalous mantle density (~ - 35 kg m(^-3)) could explain the large scale gravity field over Iceland. Shallow density variations in the top 1 km of the crust appeared to be mainly responsible for smaller scale gravity anomalies. A simple Bouguer slab model suggests that the crust may be ~7 km thicker beneath Iceland compared to neighbouring oceanic areas, consistent with an underplating mechanism for crustal accretion in Iceland. Gravity data were acquired on a cruise over the Reykjanes Ridge in the North Atlantic. The marine gravity data were reduced systematically to a residual anomaly and showed that there was the possibility of crustal thinning associated with a bathymetric offset which was interpreted as a second order discontinuity. The form of the residual gravity was similar to other discontinuities of this order on the Mid-Atlantic Ridge, although not of the same amplitude.

No description available.

We develop a new approach to classical gravity starting from Mach's principles and the idea that the local shape of spatial configurations is fundamental. This new theory, shape dynamics, is equivalent to general relativity but differs in an important respect: shape dynamics is a theory of dynamic conformal 3-geometry, not a theory of spacetime. Equivalence is achieved by trading foliation invariance for local conformal invariance (up to a global scale). After the trading, what is left is a gauge theory invariant under 3d diffeomorphisms and conformal transformations that preserve the volume of space. There is one non-local global Hamiltonian that generates the dynamics. Thus, shape dynamics is a formulation of gravity that is free of the local problem of time. In addition, the symmetry principle is simpler than that of general relativity because the local constraints are linear. Therefore, shape dynamics provides a novel new starting point for quantum gravity. Furthermore, the conformal invariance provides an ideal setting for studying the relationship between gravity and boundary conformal field theories. The procedure for the trading of symmetries was inspired by a technique called best matching. We explain best matching and its relation to Mach's principles. The key features of best matching are illustrated through finite dimensional toy models. A general picture is then established where relational theories are treated as gauge theories on configuration space. Shape dynamics is then constructed by applying best matching to conformal geometry. We then study shape dynamics in more detail by computing its Hamiltonian perturbatively and establishing a connection with conformal field theory.

In this thesis I present a mathematical tool for understanding the spin networks that arise from the study of the loop states of quantum gravity. The spin networks that arise in quantum gravity possess more information than the original spin networks of Penrose: they are embedded within a manifold and thus possess topological information. There are limited tools available for the study of this information. To remedy this I introduce a slightly modi ed mathematical object - Braided Ribbon Networks - and demonstrate that they can be related to spin networks in a consistent manner which preserves the di eomorphism invariant character of the loop states of quantum gravity. Given a consistent de nition of Braided Ribbon Networks I then relate them back to previous trinion based versions of Braided Ribbon Networks. Next, I introduce a consistent evolution for these networks based upon the duality of these networks to simplicial complexes. From here I demonstrate that there exists an invariant of this evolution and smooth deformations of the networks, which captures some of the topological information of the networks. The principle result of this program is presented next: that the invariants of the Braided Ribbon Networks can be transferred over to the original spin network states of loop quantum gravity. From here we represent other advances in the study of braided ribbon networks, accompanied by comments of their context given the consistent framework developed earlier including: the meaning of isolatable substructures, the particular structure of the capped three braids in trivalent braided ribbon networks and their application towards emergent particle physics, and the implications of the existence of microlocal topological structures in spin networks. Lastly we describe the current state of research in braided ribbon networks, the implications of this study on quantum gravity as a whole and future directions of research in the area.

Gauge/gravity duality is an important tool for learning about strongly coupled gauge theories. This thesis explores a set of examples of this duality in which the field theories have SU(2|4) supersymmetry and discrete sets of vacuum solutions. Specifically, we use the duality to propose Lagrangian definitions of type IIA Little String Theory on S⁵ as double-scaling limits of the Plane-Wave Matrix Model, maximally supersymmetric Yang-Mills theory on R x S² and N=4 supersymmetric Yang-Mills theory on R×S³/Zk. We find the supergravity solutions dual to generic vacua of the Plane-Wave Matrix Model and maximally supersymmetric Yang-Mills theory on R×S². We use the supergravity duals to calculate new instanton amplitudes for the Plane-Wave Matrix Model at strong coupling. Finally, we study a natural coarse-graining of the vacua, and find that the associated geometries are singular. We define an entropy functional that vanishes for regular geometries, is non-zero for singular geometries, and is maximized by the thermal state.

Copy of author's previously published article inserted. / Bibliography: p. 239-253. / xxx, 253, [42] p. : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis is concerned with the determination of gravity wave characteristics using operational radiosondes. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1996?