To investigate the generation of mesoscale gravity waves from upper-tropospheric jet-front systems, five different life cycles of baroclinic waves are simulated with a high-resolution mesoscale model (MM5 with 10-km grid spacing). The baroclinicity (and the growth rates) of the baroclinic waves differs significantly among these five experiments as a result of using different tropospheric static stability and tropopause geometry for the initial two-dimensional baroclinic jet. After a short initial adjustment, the baroclinic waves in each experiment grow nearly linearly for as long as five days before the final nonlinear growth stage. Vertically propagating mesoscale gravity waves are generated universally in the exit region of the upper-tropospheric jet streaks near the tropopause level at the later stage of quasi-linear growth and the early stage of nonlinear growth of baroclinic waves. The synoptic environments of gravity waves are consistent with previous studies of typical mesoscale gravity waves. The low-stratospheric gravity waves generated from the upper-level jet streak in these experiments have a horizontal wavelength of 75-175 km and an intrinsic frequency 3-10 times of the Coriolis parameter. The intrinsic frequency of these gravity waves appears to be directly correlated with the growth rate and the strength of the baroclinic waves. In general, the faster the growth rate of the baroclinic waves, the higher the intrinsic frequency of the gravity waves. Similar frequencies of the gravity waves are found in experiments with smaller quasi-linear growth rates of baroclinic waves but with significantly different initial tropospheric static stability and tropopause geometry. The residuals of the nonlinear balance equation are used to assess the flow imbalance. It is also suggested that growth of imbalance is directly related to the growth rate of baroclinic waves and thus the frequency of primary gravity waves of interest. Diagnosis of flow imbalance suggests that balance adjustment, as a generalization of geostrophic adjustment, may be responsible for the generation of the gravity waves in the upper-tropospheric jet-front systems.

Two different works in mathematical physics are presented: A construction of conformal infinity in null and spatial directions is constructed for the Rainbow-flat space-time corresponding to doubly special relativity. From this construction a definition of asymptotic DSRness is put forward which is com- patible with the correspondence principle of Rainbow gravity. Furthermore a result equating asymptotically flat space-times with asymptotically DSR spacetimes is presented. An overview of microlocality in braided ribbon networks is presented. Follow- ing this, a series of definitions are presented to explore the concept of microlocality and the topology of ribbon networks. Isolated substructure of ribbon networks are introduced, and a theorem is proven that allows them to be relocated. This is fol- lowed by a demonstration of microlocal translations. Additionally, an investigation into macrolocality and the implications of invariants in braided ribbon networks are presented.

In this thesis some equilibrium and non-equilibrium statistical methods are implied on two different versions of non-perturbative quantum gravity. Firstly, we report a novel statistical mechanics in which a class of evolutionary maps act on trivalent spin network in randomly chosen initial states and give rise to Self-organized Criticality. The result of continuously applying these maps indicate an expansion in the space-time area associated. Secondly, a previously unknown statistical mechanics in quantum gravity is introduced in the framework of two dimensional Causal Dynamical Triangulations. This provides us a useful and new tools to understand this quantum gravity in terms of effective spins. This study reveals a correspondence between the statistics of Anti-ferromagnetic systems and Causal Dynamical quantum gravity. More importantly, it provides a basis for studying anti-ferromagnetic systems in a background independent way. Thirdly, two novel properties of area operator in Loop Quantum Gravity are reported: 1) the generic degeneracy and 2) the ladder symmetry. These were not known previously for years. The first one indicates that corresponding to any eigenvalue of area operator in loop quantum gravity there exists a finite number of degenerate eigenstates. This degeneracy is shown to be one way for the explanation of black hole entropy in a microscopic way. More importantly, we reproduce Bekenstein-Hawking entropy of black hole by comparing the minimal energy of a decaying frequency from a loop quantum black hole and the extracted energy from a perturbed black hole in the highly damping mode. This consistency reveals a treasure model for describing a black hole in loop quantum gravity that does nor suffer from the restrictions of an isolated horizon. The second property indicates there exists a ladder symmetry unexpectedly in the complete spectrum of area eigenvalues. This symmetry suggests the eigenvalues of area could be classified into different evenly spaced subsets, each called a `generation.' All generations are evenly spaced; but the gap between the levels in any every generation is unique. One application of the two new properties of area operator have been considered here for introducing a generalized picture of horizon whose area cells are not restricted to the subset considered in quantum isolated horizon theory. Instead, the area cells accepts values from the complete spectrum. Such horizon in the presence of all elements of diffeomorphism group contains a number of degrees of freedom independently from the bulk freedom whose logarithm scales with the horizon area. Note that this is not the case in quantum isolated horizon when the complete elements of diffeomorphism applies. Finally, we use a simple statistical method in which no pre-assumption is made for the essence of the energy quanta radiated from the hole. We derive the effects of the black hole horizon fluctuations and reveal a new phenomenon called "quantum amplification effects" affecting black hole radiation. This effect causes unexpectedly a few un-blended radiance modes manifested in spectrum as discrete brightest lines. The frequency of these modes scales with the mass of black hole. This modification to Hawking's radiation indicates a window at which loop quantum gravity can be observationally tested at least for primordial black holes.

Two different works in mathematical physics are presented: A construction of conformal infinity in null and spatial directions is constructed for the Rainbow-flat space-time corresponding to doubly special relativity. From this construction a definition of asymptotic DSRness is put forward which is com- patible with the correspondence principle of Rainbow gravity. Furthermore a result equating asymptotically flat space-times with asymptotically DSR spacetimes is presented. An overview of microlocality in braided ribbon networks is presented. Follow- ing this, a series of definitions are presented to explore the concept of microlocality and the topology of ribbon networks. Isolated substructure of ribbon networks are introduced, and a theorem is proven that allows them to be relocated. This is fol- lowed by a demonstration of microlocal translations. Additionally, an investigation into macrolocality and the implications of invariants in braided ribbon networks are presented.

In this thesis some equilibrium and non-equilibrium statistical methods are implied on two different versions of non-perturbative quantum gravity. Firstly, we report a novel statistical mechanics in which a class of evolutionary maps act on trivalent spin network in randomly chosen initial states and give rise to Self-organized Criticality. The result of continuously applying these maps indicate an expansion in the space-time area associated. Secondly, a previously unknown statistical mechanics in quantum gravity is introduced in the framework of two dimensional Causal Dynamical Triangulations. This provides us a useful and new tools to understand this quantum gravity in terms of effective spins. This study reveals a correspondence between the statistics of Anti-ferromagnetic systems and Causal Dynamical quantum gravity. More importantly, it provides a basis for studying anti-ferromagnetic systems in a background independent way. Thirdly, two novel properties of area operator in Loop Quantum Gravity are reported: 1) the generic degeneracy and 2) the ladder symmetry. These were not known previously for years. The first one indicates that corresponding to any eigenvalue of area operator in loop quantum gravity there exists a finite number of degenerate eigenstates. This degeneracy is shown to be one way for the explanation of black hole entropy in a microscopic way. More importantly, we reproduce Bekenstein-Hawking entropy of black hole by comparing the minimal energy of a decaying frequency from a loop quantum black hole and the extracted energy from a perturbed black hole in the highly damping mode. This consistency reveals a treasure model for describing a black hole in loop quantum gravity that does nor suffer from the restrictions of an isolated horizon. The second property indicates there exists a ladder symmetry unexpectedly in the complete spectrum of area eigenvalues. This symmetry suggests the eigenvalues of area could be classified into different evenly spaced subsets, each called a `generation.' All generations are evenly spaced; but the gap between the levels in any every generation is unique. One application of the two new properties of area operator have been considered here for introducing a generalized picture of horizon whose area cells are not restricted to the subset considered in quantum isolated horizon theory. Instead, the area cells accepts values from the complete spectrum. Such horizon in the presence of all elements of diffeomorphism group contains a number of degrees of freedom independently from the bulk freedom whose logarithm scales with the horizon area. Note that this is not the case in quantum isolated horizon when the complete elements of diffeomorphism applies. Finally, we use a simple statistical method in which no pre-assumption is made for the essence of the energy quanta radiated from the hole. We derive the effects of the black hole horizon fluctuations and reveal a new phenomenon called "quantum amplification effects" affecting black hole radiation. This effect causes unexpectedly a few un-blended radiance modes manifested in spectrum as discrete brightest lines. The frequency of these modes scales with the mass of black hole. This modification to Hawking's radiation indicates a window at which loop quantum gravity can be observationally tested at least for primordial black holes.

We construct a 4d Lorentzian spin foam model capable of describing both spacelike and timelike surfaces. To do so we use a coherent state approach inspired by the Riemannian FK model. Using the coherent state method we reproduce the results of the EPRL model for Euclidean tetrahedra and extend the model to include Lorentzian tetrahedra. The coherent states of spacelike/timelike triangles are found to correspond to elements of the discrete/continuous series of SU(1,1). It is found that the area spectrum of both spacelike and timelike surfaces is quantized. A path integral for the quantum theory is defined as a product of vertex amplitudes. The states corresponding to timelike triangles are constructed in a basis diagonalised with respect to a noncompact generator. A derivation of the matrix elements of the generators of SL(2,C) in this basis is provided.

In this thesis we review the status of an approach to Quantum Gravity through lattice toy models, Quantum Graphity. In particular, we describe the two toy models introduced in the literature and describe with a certain level of details the results obtained so far. We emphasize the connection between Quantum Graphity and emergent gravity, and the relation with Variable Speed of Light theories.

To investigate the generation of mesoscale gravity waves from upper-tropospheric jet-front systems, five different life cycles of baroclinic waves are simulated with a high-resolution mesoscale model (MM5 with 10-km grid spacing). The baroclinicity (and the growth rates) of the baroclinic waves differs significantly among these five experiments as a result of using different tropospheric static stability and tropopause geometry for the initial two-dimensional baroclinic jet. After a short initial adjustment, the baroclinic waves in each experiment grow nearly linearly for as long as five days before the final nonlinear growth stage. Vertically propagating mesoscale gravity waves are generated universally in the exit region of the upper-tropospheric jet streaks near the tropopause level at the later stage of quasi-linear growth and the early stage of nonlinear growth of baroclinic waves. The synoptic environments of gravity waves are consistent with previous studies of typical mesoscale gravity waves. The low-stratospheric gravity waves generated from the upper-level jet streak in these experiments have a horizontal wavelength of 75-175 km and an intrinsic frequency 3-10 times of the Coriolis parameter. The intrinsic frequency of these gravity waves appears to be directly correlated with the growth rate and the strength of the baroclinic waves. In general, the faster the growth rate of the baroclinic waves, the higher the intrinsic frequency of the gravity waves. Similar frequencies of the gravity waves are found in experiments with smaller quasi-linear growth rates of baroclinic waves but with significantly different initial tropospheric static stability and tropopause geometry. The residuals of the nonlinear balance equation are used to assess the flow imbalance. It is also suggested that growth of imbalance is directly related to the growth rate of baroclinic waves and thus the frequency of primary gravity waves of interest. Diagnosis of flow imbalance suggests that balance adjustment, as a generalization of geostrophic adjustment, may be responsible for the generation of the gravity waves in the upper-tropospheric jet-front systems.

Multiphase and non-Darcy flow effects in hydraulically fractured gas wells reduce effective fracture conductivity. Typical proppant pack laboratory experiments are oriented in such a way such that phase segregation is not possible, which results in mixed flow. Tidwell and Parker (1996), however, showed that in proppant packs, gravity segregation occurs for simultaneous gas and liquid injection at laboratory scale (1500 cm2). Although the impact of gravity on flow in natural fractures has been described, previous work has not fully described the effect of gravity on multiphase non-Darcy flow in hydraulic fractures. In this work, reservoir simulation modeling was used to determine the extent and impact of gravity segregation in a hydraulic fracture at field scale. I found that by ignoring segregation, effective fracture conductivity can be underestimated by up to a factor of two. An analytical solution was developed for uniform flux of water and gas into the fracture. The solution for pressures and saturations in the fracture agrees well with reservoir simulation. Gravity segregation occurs in moderate-to-high conductivity fractures. Gravity segregation impacts effective fracture conductivity when gas and liquid are being produced at all water-gas ratios modeled above 2 Bbls per MMscf. More realistic, non-uniform-flux models were also run with the hydraulic fracture connected to a gas reservoir producing water. For constant-gas-rate production, differences in pressure drop between segregated cases and mixed flow cases range up to a factor of two. As the pressure gradient in the fracture increases above 1 to 2 psi/ft, the amount of segregation decreases. Segregation is also less for fracture half-length-to-height ratios less than or close to two. When there is less segregation, the difference in effective conductivity between the segregated and mixed flow cases is reduced. I also modeled the water injection and cleanup phases for a typical slickwater fracture treatment both with and without gravity effects and found that for cases with segregation, effective fracture conductivity is significantly higher than the conductivity when mixed flow occurs. Gravity segregation is commonly ignored in design and analysis of hydraulically fractured gas wells. This work shows that segregation is an important physical process and it affects effective fracture conductivity significantly. Hydraulic fracture treatments can be designed more effectively if effective fracture conductivity is known more accurately.

Thesis (Ph. D.)--University of Alberta, 2009. / Title from PDF file main screen (viewed on Nov. 27, 2009). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Department of Physics, University of Alberta." Includes bibliographical references.