Non-Perturbative Methods in Quantum Field Theory and Quantum Gravity

This thesis considers non-perturbative methods in quantum field theory with applications to gravity and cosmology. In particular, there are chapters on black hole holography, inflationary model building, and the conformal bootstrap.

Dinoflagellate Genomic Organization and Phylogenetic Marker Discovery Utilizing Deep Sequencing Data

Dinoflagellates possess large genomes in which most genes are present in many copies. This has made studies of their genomic organization and phylogenetics challenging. Recent advances in sequencing technology have made deep sequencing of dinoflagellate transcriptomes feasible. This dissertation investigates the genomic organization of dinoflagellates to better understand the challenges of assembling dinoflagellate transcriptomic and genomic data from short read sequencing methods, and develops new techniques that utilize deep sequencing data to identify orthologous genes across a diverse set of taxa. To better understand the genomic organization of dinoflagellates, a genomic cosmid clone of the tandemly repeated gene Alchohol Dehydrogenase (AHD) was sequenced and analyzed. The organization of this clone was found to be counter to prevailing hypotheses of genomic organization in dinoflagellates. Further, a new non-canonical splicing motif was described that could greatly improve the automated modeling and annotation of genomic data. A custom phylogenetic marker discovery pipeline, incorporating methods that leverage the statistical power of large data sets was written. A case study on Stramenopiles was undertaken to test the utility in resolving relationships between known groups as well as the phylogenetic affinity of seven unknown taxa. The pipeline generated a set of 373 genes useful as phylogenetic markers that successfully resolved relationships among the major groups of Stramenopiles, and placed all unknown taxa on the tree with strong bootstrap support. This pipeline was then used to discover 668 genes useful as phylogenetic markers in dinoflagellates. Phylogenetic analysis of 58 dinoflagellates, using this set of markers, produced a phylogeny with good support of all branches. The Suessiales were found to be sister to the Peridinales. The Prorocentrales formed a monophyletic group with the Dinophysiales that was sister to the Gonyaulacales. The Gymnodinales was found to be paraphyletic, forming three monophyletic groups. While this pipeline was used to find phylogenetic markers, it will likely also be useful for finding orthologs of interest for other purposes, for the discovery of horizontally transferred genes, and for the separation of sequences in metagenomic data sets.

INVESTIGATIONS INTO MECHANISMS UNDERLYING EXTREME WAVE FORMATIONS AND COMPUTATIONALLY INTENSIVE SIMULATIONS

Various mechanisms have been proposed to explain extreme waves or rogue waves in an oceanic environment including directional focusing, dispersive focusing, wave-current interaction, and nonlinear modulational instability. The Benjamin-Feir instability (nonlinear modulational instability), however, is considered to be one of the primary mechanisms for rogue-wave occurrence. The nonlinear Schrodinger equation is a well-established approximate model based on the same assumptions as required for the derivation of the Benjamin-Feir theory. Solutions of the nonlinear Schrodinger equation, including new rogue-wave type solutions are presented in the author's dissertation work. The solutions are obtained by using a predictive eigenvalue map based predictor-corrector procedure developed by the author. Features of the predictive map are explored and the influences of certain parameter variations are investigated. The solutions are rescaled to match the length scales of waves generated in a wave tank. Based on the information provided by the map and the details of physical scaling, a framework is developed that can serve as a basis for experimental investigations into a variety of extreme waves as well localizations in wave fields. To derive further fundamental insights into the complexity of extreme wave conditions, Smoothed Particle Hydrodynamics (SPH) simulations are carried out on an advanced Graphic Processing Unit (GPU) based parallel computational platform. Free surface gravity wave simulations have successfully characterized water-wave dispersion in the SPH model while demonstrating extreme energy focusing and wave growth in both linear and nonlinear regimes. A virtual wave tank is simulated wherein wave motions can be excited from either side. Focusing of several wave trains and isolated waves has been simulated. With properly chosen parameters, dispersion effects are observed causing a chirped wave train to focus and exhibit growth. By using the insights derived from the study of the nonlinear Schrodinger equation, modulational instability or self-focusing has been induced in a numerical wave tank and studied through several numerical simulations. Due to the inherent dissipative nature of SPH models, simulating persistent progressive waves can be problematic. This issue has been addressed and an observation-based solution has been provided. The efficacy of SPH in modeling wave focusing can be critical to further our understanding and predicting extreme wave phenomena through simulations. A deeper understanding of the mechanisms underlying extreme energy localization phenomena can help facilitate energy harnessing and serve as a basis to predict and mitigate the impact of energy focusing.