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ABSTRACT Title of dissertation: *Weakly* Compressible Navier-Stokes Approximation of Gas Dynamics

"... This dissertation addresses mathematical issues regarding weakly compressible approximations of gas dynamics that arise both in fluid dynamical and in kinetic settings. These approximations are derived in regimes in which (1) transport coeffi-cients (viscosity and thermal conductivity) are small and ..."

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and (

*2*) the gas is near an abso-lute equilibrium — a spatially uniform, stationary state. When we consider regimes in which both the transport scales and Re vanish, we derive the*weakly*compressible Stokes approximation — a linear system. When we consider regimes in which the transport scales vanish###
POLISH ACADEMY OF SCIENCES WARSZAWA 19** REFINED *ALGEBRAIC* QUANTIZATION: SYSTEMS WITH A SINGLE CONSTRAINT

, 1999

"... Abstract. This paper explores in some detail a recent proposal (the Rieffel induction/refined algebraic quantization scheme) for the quantization of constrained gauge systems. Below, the focus is on systems with a single constraint and, in this context, on the uniqueness of the construction. While i ..."

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Abstract. This paper explores in some detail a recent proposal (the Rieffel induction/refined

*algebraic*quantization scheme) for the quantization of constrained gauge systems. Below, the focus is on systems with a single constraint and, in this context, on the uniqueness of the construction. While### new algorithm to compute fusion coecients By

"... This is a proceedings article reviewing a recent combinatorial construction of the bsu(n)k WZNW fusion ring by C. Stroppel and the author. It contains one novel aspect: the explicit derivation of an algorithm for the computation of fusion coecients dierent from the Kac-Walton formula. The discussion ..."

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This is a proceedings article reviewing a recent combinatorial construction of the bsu(n)k WZNW fusion ring by

*C*. Stroppel and the author. It contains one novel aspect: the explicit derivation of an algorithm for the computation of fusion coecients dierent from the Kac-Walton formula### unknown title

"... A short review on the derivation of the nonlinear quantum Boltzmann equations ..."

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A short review on the derivation of the nonlinear quantum Boltzmann equations

### Nuclear Physics B Proceedings Supplement – preprint (2014) 1–42 Nuclear Physics B Proceedings Supplement Universal Aspects of QCD-like TheoriesI

"... In these lectures I review some basic examples of how the concepts of universality and scaling can be used to study aspects of the chiral and the deconfinement transition, if not in QCD directly but in QCD-like theories. As an example for flavor dynamics I discuss a quark-hadron model to describe th ..."

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the phase diagram of two-color QCD with the functional renormalization group. Universal aspects of deconfinement are illustrated mainly in the

*2*+ 1 dimensional SU(N) gauge theories with second order transition where many exact results from spin models can be exploited.### q 1999 American Meteorological Society Eddy Formation and Interaction in a Baroclinic Frontal Geostrophic Model*

, 1998

"... The authors investigate the behavior of buoyancy-driven coastal currents in a series of numerical experiments based on a two-layer frontal geostrophic model. The model focuses on baroclinic instability, allows for finite amplitude variations in the upper-layer thickness, and includes a topographic b ..."

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The authors investigate the behavior of buoyancy-driven coastal currents in a series of numerical experiments based on a two-layer frontal geostrophic model. The model focuses on baroclinic instability, allows for finite amplitude variations in the upper-layer thickness, and includes a topographic background vorticity gradient. Simulations of isolated fronts demonstrate meandering of the frontal outcropping, filamentation, and the de-velopment of both warm core and cold core eddies. Eddies can merge with each other, separate, or be reabsorbed into the current. Despite the assumption of only two layers, it is found that growth rates and length scales of the emergent features are in agreement with results of studies based on more sophisticated primitive equation models. It is determined that the cross-front topographic slope has a significant effect on the instability. In particular, a bottom that slopes in the same sense as the fluid interface hinders the growth of perturbations. Simulations with two outcroppings (i.e., coupled fronts) are also described. The authors found that such currents break up into distinct vortices that propagate very little but exhibit merging and splitting, behavior consistent with previous numerical studies involving similar models as well as laboratory experiments. Finally, an analytical nonlinear wave-packet stability theory for a marginally unstable flow with a simple linearly varying height profile is presented. The authors show that the unstable modes can saturate as solitons. 1.

### COSMOLOGICAL MODELS OF MODIFIED GRAVITY

, 2013

"... The recent discovery of dark energy has prompted an investigation of ways in which the accelerated expansion of the universe can be realized. In this dissertation, we present two separate projects related to dark energy. The first project analyzes a class of braneworld models in which multiple brane ..."

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The recent discovery of dark energy has prompted an investigation of ways in which the accelerated expansion of the universe can be realized. In this dissertation, we present two separate projects

*related*to dark energy. The first project analyzes a class of braneworld models in which multiple### Abstract Cosmological Black Holes as Models of Cosmological Inhomogeneities

, 2006

"... Since cosmological black holes modify the density and pressure of the surrounding universe, and introduce heat conduction, they produce simple models of cosmologi-cal inhomogeneities that can be used to study the eect of inhomogeneities on the universe's expansion. In this thesis, new cosmologi ..."

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Since cosmological black holes modify the density and pressure of the surrounding universe, and introduce heat conduction, they produce simple models of cosmologi-cal inhomogeneities that can be used to study the eect of inhomogeneities on the universe's expansion. In this thesis, new cosmological black hole solutions are ob-tained by generalizing the expanding Kerr-Schild cosmological black holes to obtain the charged case, by performing a Kerr-Schild transformation of the Einstein-de Sitter universe (instead of a closed universe) to obtain non-expanding Kerr-Schild cosmo-logical black holes in asymptotically-
at universes, and by performing a conformal transformation on isotropic black hole spacetimes to obtain isotropic cosmological black hole spacetimes. The latter approach is found to produce cosmological black holes with energy-momentum tensors that are physical throughout spacetime, unlike previous solutions for cosmological black holes, which violate the energy conditions in some region of spacetime. In addition, it is demonstrated that radiation-dominated and matter-dominated Einstein-de Sitter universes can be directly matched across a hypersurface of constant time, and this is used to generate the rst solutions for primordial black holes that evolve from being in radiation-dominated background universes to matter-dominated background universes. Finally, the Weyl curvature, volume expansion, velocity eld, shear, and acceleration are calculated for the cos-ii mological black holes. Since the non-isotropic black holes introduce shear, according to Raychaudhuri's equation they will tend to decrease the volume expansion of the universe. Unlike several studies that have suggested the relativistic backreaction of inhomogeneities would lead to an accelerating expansion of the universe, it is con-cluded that shear should be the most likely in
uence of inhomogeneities, so they should most likely decrease the universe's expansion. iii