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Quantum field theory (QFT) in curved spacetime treats a gravitational field as a classical background upon which quantum corrections may be computed. When couplings are assumed to be small, it is traditionally believed that perturbation theory yields trustworthy predictions about interacting quantum fields in such settings — this work asserts that this is not always the case. It is argued that perturbative predictions about evolution for very long times near a horizon are subject to problems of secular growth — ie. powers of small couplings come systematically together with growing functions of time. Such growth signals a breakdown of na ̈ıve perturbative calculations of late-time behaviour, regardless of how small ambient curvatures might be. Evidence is built that such breakdowns should be generic for gravitational fields, particularly those containing horizons. This work makes use of the Rindler horizon in flat Minkowski space to demonstrate an explicit example of such perturbative breakdown. A loop correction involving an IR/UV interplay is shown to result in a two-point correlation function which exhibits secular growth. This result is shown to parallel a breakdown occurring in finite temperature QFT, where problems of secular growth are known to occur. The problematic correction is then resummed, allowing for trustworthy late-time inferences. We conclude by discussing how this calculation may be relevant for predictions near black hole horizons. / Thesis / Master of Science (MSc) / Perturbation theory is an approximation technique widely used in the study of quantum field theory (QFT). In this work it is argued that the predictions of per- turbation theory can fail when used on a QFT living in a spacetime that contains an event horizon. This work focuses on perturbative breakdowns that occur after long lengths of time have passed, providing an explicit example in the simplest possible spacetime with an event horizon: Rindler space. It is argued that this breakdown may occur in more complicated settings.

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Earth and Planetary Sciences. / Microfiche copy available in Archives and Science. / Vita. / Bibliography : leaves 108-110. / Ph.D.

This work will explore the musical ideas and philosophy discussed by George Russell in his book “The Lydian Chromatic Concept of Tonal Organization” (2001). Through the lens of a performing musician, improviser and composer/arranger, it will explore how the ideas of unity (vertical) and duality (horizontal), interact with each other through Tonal Gravity, and how they can be practically implemented as tools used to expand the scope of vertical (harmonic) consciousness and individual expression. Through my studies of the LCC, I have composed new music, in addition to contextualizing familiar jazz repertoire, in new and refreshing ways. Russell describes the Lydian Chromatic scale and its eleven member scales, as well as three different coexistent levels of Tonal Gravity in his River Trip analogy (Vertical, Horizontal and Supra-Vertical), which together opens up both ingoing and outgoing tonal resources. I have been exploring ways of integrating these elements in my expression. George Russell’s 50 years of work on The Concept was explicitly made to inspire future innovators to develop “[…] intellectual brilliance, intuitive perception, emotional fire, and spiritual depth.” (Russell, 2001, p. 98). Studying the Concept has helped me find my own expression more believable. By avoiding mechanical playing and rather developing my ears and fluency on the instrument, it allows for harmonic color and expression to be felt and created, instead of prepared licks and patterns. / <p><strong>For my exam concert I chose to play my own compositions in a quartet with the following contributing musicians:</strong></p><p>Trumpet and compositions - Øyvind Solheim</p><p>Piano - Rasmus Mannervik</p><p>Double bass - Anton Berndts</p><p>Drums - Richard Andersson Rasheed</p><p>The concert took place at the Royal College of Music in Stockholm on the 26th of March 2024. The set list consisted of six pieces, some of which had seamless transitions in-between each other. Since we had rehearsed with an open approach, we went in to the performance with the same attitude of playing something new.</p><p><strong>Repertoire (with timestamps from the recording)</strong></p><p>1. [00:00:40 – 00:05:40] October March - Øyvind Solheim</p><p>2. [00:06:35 – 00:15:40] Reaching - Øyvind Solheim</p><p>3. [00:16:30 – 00:25:40] Acrimony - Øyvind Solheim</p><p>4. [00:25:40 – 00:36:32] Wheelez - Øyvind Solheim</p><p>5. [00:38:02 – 00:47:40] Acending, Decending - Øyvind Solheim</p><p>6. [00:49:29 – 00:58:47] Lam-ent - Øyvind Solheim</p>

yes / The accurate prediction of the dilution and motion of the produced denser water (e.g. discharge of concentrated brine generated during solution mining and desalination) is of importance for environmental protection. Boundary conditions and ambient stratification can significantly affect the dilution and motion of gravity currents. In this study, a multiphase model is applied to simulate the gravity current descending a slope into a linearly stratified ambient. The k- turbulence model is used to better simulate the near bed motion. The mathematical model, initial and boundary conditions and the details of the numerical scheme are described. The time-dependent evolution of the gravity current, the flow thickness and the velocity and density field are simulated for a range of flow parameters. Simulations show that the Kelvin–Helmholtz billows are generated at the top of trailing fluid by the interfacial velocity shear. The K-H type instability becomes weaker with the slope distance from the source due to the decrease of the interfacial velocity shear along slope. The ambient stratification restricts and decreases the current head velocity as it descends slope, which differs from the situation in homogenous ambient while the head velocity remains an approximately steady state. Motion of the descending flow into the stratified ambient has two stages: initial acceleration and deceleration at later stage based on the balance of inertial, buoyancy and friction forces. When the descending current approaches the initial neutral position at later stage, it separates from the slope and spreads horizontally into environment. The simulated results, such as vertical velocity and density profiles and front positions, agree well with the measurements, indicating that the mathematical model can be successfully applied to simulate the effect of the boundary condition and ambient stratification on the dilution and propagation of gravity currents. / UK EPSRC

Over 700 km of industry seismic reflection data in the central Appalachians were reprocessed using both conventional and newly developed processing schemes. A new processing sequence, called dip projection, is introduced. The technique projects crooked-line processed CMPs onto a straight line oriented in the general dip direction for the area. The new stacked sections more closely approximate a dip line and hence are more migration-friendly and interpretable than the crooked-line stacks. Methods of determining the lateral continuity of subsurface density contrasts were also applied to gravity data from the study area. Known collectively as potential field attributes, the analytic signal, the tilt angle, and the gradient of the tilt angle (the potential field wavenumber ) proved valuable in the analysis of the gravity data. Comparison of reflection seismic data from the southern and central Appalachians revealed a dichotomy of seismic reflectivity from east to west. A highly reflective crust beneath the Piedmont in both the central and southern Appalachians contrasts with a general lack of reflectivity beneath the Blue Ridge and Valley and Ridge provinces where coherent reflections are restricted to the upper 3-4 seconds of the data. This difference in reflectivity is interpreted as a fundamental difference in the location and orientation of preexisting zones of weakness between the different crustal regions with respect to the tectonic events affecting the Appalachians since the early Paleozoic. The combination of the results of new methods of seismic and potential fields processing with deep well and geologic information allowed the lateral continuity of two major structures in the central Appalachians to be examined. The Blue Ridge in Virginia was found to overly a duplex of Cambrian-Ordovician carbonates formed in response to stresses during the Alleghanian Orogeny. A large thrust sheet of similar carbonate rocks was interpreted beneath the Nittany Anticlinorium in West Virginia. To the south in Virginia, this thrust sheet is replaced by imbrication of the carbonate package. The change in structural style may be related to the existence of a lateral ramp or it may reflect the overall change in structural style from the central to southern Appalachians. / Ph. D.

The purpose of the project herein described was to determine the acceleration due to gravity for the locale of Blacksburg, Virginia., to five significant figures. As far as the author has been able to determine, there has never been a formal determination of “g” made for this area. Supporting this prime purpose was the fact that the equipment required for this experiment, i .e. a secondary standard of length, a recording system, and several portable photocell relay circuits, and the vacuum tank, would be useful to the department in the future. / Master of Science