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In this work we explore the collider prospects for the asymptotic safety scenario being realized as a quantum theory of gravity. Testing gravity at colliders becomes a real possibility in the case of extra dimensional models, or with additional physics leading to a fundamental scale of gravity significantly lower than the Planck mass. We present several approximations for the full non-perturbative renormalization group running, and show how these can be implemented at the level of the graviton wave-function renormalization. The issue of scale identi fication of the physical process with the renormalization group scale k is clarified and several different choices are compared. The various approximations are resolved and shown in most cases to generate scheme independent results. On the phenomenological side, we investigate two separate observables. First, at tree-level we present results on LHC di-muon production due to asymptotically safe gravitons. By including fixed point scaling Kaluza- Klein modes, the predicted signal is enhanced and simultaneously problems associated with the breakdown of perturbative unitarity are reduced. At the one-loop level, we outline our calculation for the contribution to electro-weak precision observables originating from asymptotically safe gravity. New bounds are derived which show different behaviour as a function of the number of extra dimensions compared with previous effective field theory results. Finally, we comment on possible further directions for exploring the frontier of collider physics and quantum gravity.

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In this dissertation, we consider a generalization of the historically significant problem posed in 1850 by Reverend Thomas Kirkman which asked whether it was possible for 15 schoolgirls to walk in lines of three to school for seven days so that no two of them appear in the same line on multiple days. This puzzle spawned the study of what we now call resolvable pairwise balanced designs, which balance pair coverage of points within blocks while also demanding that the blocks can be grouped in such a way that each group partitions the point-set. Our generalization aims to relax this condition slightly, so that each group of blocks balances point-wise coverage but each point occurs in each group σ times (instead of just once). We call these objects thickly-resolvable designs. Here we show that the necessary divisibility conditions for the existence of thickly-resolvable designs are also sufficient when the size of the point set is large enough. A few variations of this problem are considered as well. / Graduate

When two fluid drops come close enough together to touch, surface tension quickly pulls the drops together into one larger drop. This is an example of a singular fluid flow, as the topology of the interface changes at the moment of contact. Similarly, when a pair of bubbles touch, the surface topology changes and a singular flow begins. Since the stress from surface tension depends on the surface curvature, these singularities are often characterised by divergent fluid velocities. Experimental observation or numerical simulation of these flows is therefore difficult due to the high velocities and small lengthscales. In this thesis, I will find multi-scale theoretical solutions for the singular flows during the initial stages of the coalescence of bubbles and drops, solving for the velocity field in the fluid and the rate of coalescence. Each solution has several lengthscales, and on each lengthscale, we must solve some form of the Navier--Stokes equations. I will employ a variety of analytical and numerical techniques to solve for the flow on each scale. These asymptotic solutions are valid at early times; future numerical simulations of the subsequent flow could be initialised with these solutions, rather than the actual singularity. In the course of solving for these singular flows, I will also describe the solution for the motion of a stretched fluid edge, the retraction of a narrow fluid wedge, the capillary flow around a parabola, and the effect of a time-dependent force on a fluid half-space. These fundamental flows have applications outside of coalescence, which I will outline throughout the thesis.

Thesis (M.S.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (February 6, 2007) Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

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