This work investigates how black holes can be described in terms of different definitions of horizons. Global definitions in terms of event horizons and Killing horizons are contrasted with local definitions in terms of trapping horizons and dynamical horizons. The discussion is framed in the context of the laws of black hole thermodynamics.

This work investigates how black holes can be described in terms of different definitions of horizons. Global definitions in terms of event horizons and Killing horizons are contrasted with local definitions in terms of trapping horizons and dynamical horizons. The discussion is framed in the context of the laws of black hole thermodynamics.

Basal reinforcement, where high tensile geogrids are employed beneath structures, is becoming an increasingly accepted construction technique along the eastern coast of southern Africa. The presence of compressible, soft, thin and shallow clay horizons usually associated with complex estuarine or lagoonal deposits are a major consideration when using basal reinforcement as a founding technique. Basal reinforcement involves the use of high tensile strength geogrids beneath a structure to form a reinforced sand foundation. Deformation behaviour under loading is an important component of stability analysis of earth structures. If reinforcement is used, the mechanisms become altered. Geotechnical centrifuge modelling is a unique physical modelling technique, as it allows replication of in situ stresses, which is most important because soil behaviour is a function of stress. This is achieved by placing the model at the end of the centrifuge arm, and subjecting it to an increased gravitational field, which creates the correct stress distribution in the model. Centrifuge modelling provides an appropriate technique to observe the behaviour of compressible, soft, thin and shallow clay horizons when basal reinforcement is utilized. An appropriate centrifuge model was constructed and compared the behaviour of the clay horizon under unreinforced and reinforced conditions. Reinforcement configurations were adjusted to observe the influence of additional geogrid layers, and extension of the width of the reinforcement. It was found that deformation behaviour is distinctly different between unreinforced and reinforced tests. Vertical deformation in the unreinforced test localised to the region directly beneath the platform, with little lateral disturbance to the clay horizon beyond the platform edge. As such, the sand directly beneath the platform acts as a deeper rigid platform. The deformation behaviour of the clay horizon changes with the inclusion of reinforcement. When reinforcement is included a wider portion of clay is deformed. The lateral width of this deformation zone is controlled by the width of the reinforcement, as the applied load is spread. A ‘wide-slab’ effect is evident with an increase in the geogrid width, as the tensioned membrane-effect is mobilised to increase the capacity of the reinforced foundation sand. This results in a wider portion of the clay deforming. Addition of geogrid reinforcement to the sand foundation under a wide platform load enhances deformation of the clay, but has the advantage of an increased load-bearing capacity of the system. Furthermore, the addition of multiple layers of reinforcement contributes to this increase in load-bearing capacity. Additionally, increasing the installation width of the reinforcement contributes to an increased vertical load-bearing capacity. However, this resultant increase is only mobilised after a certain amount of vertical displacement. This is likely due to the reinforcement requiring a certain amount of vertical displacement to mobilise tension in order to support the applied load. The behaviour of a thin compressible clay horizon changes with the inclusion of reinforcement under a wide platform load. The deformation behaviour of the clay is increased by additional layers of reinforcement as well as an increase in the width of the reinforcement. However, the increase in deformation comes at the benefit of an increased vertical load-bearing capacity of the reinforced foundation sand. / Dissertation (MSc)--University of Pretoria, 2014. / gm2014 / Geology / unrestricted

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.

Les recherches menées ont pour objectif de dresser un bilan, le plus exhaustif possible, sur la céramique gallo-romaine de la partie occidentale de la province de Lyonnaise définie par les territoires des civitates des Vénètes, des Coriosolites, des Osismes et des Riédons. Cette synthèse régionale à d'abord consisté en l'élaboration d'un catalogue de formes, puis d'une approche typo-chronologique. Ce premier corpus est constitué de 792 formes qui se répartissent en 20 grandes catégories techniques et fonctionnelles. Un système de classement ouvert a été employé afin de pouvoir être complété en fonction des nouvelles découvertes. L'analyse de 34 assemblages de céramique issus de 21 sites a permis de définir huit horizons chronologiques couvrant la période de la seconde moitié du Ier s. av. J.-C. jusqu'aux premières décennies du IVe s. ap. J.-C. Ces horizons offrent un premier aperçu de l'évolution des céramiques consommées et des stratégies d'approvisionnement au cours de cette période. / The research aim to take stock, as exhaustive as possible, on the Gallo-Roman ceramic of the western part of Lyonnaise province defined by the territories of the civitates of the Veneti, of Coriosolite, of Osismii and Redones. This regional summary presents the development of a catalogue of forms and a typo chronological approach. This first corpus is composed of 792 forms divided into 20 major technical and functional categories. An open ranking system was used in order to make additions according to new discoveries. The analysis of 34 pottery assemblages from 21 sites defined eight horizons from the second half of the 1st century BC until the first decades of the 4th century AD. They offer a first look of the evolution of consumed ceramics and supplying strategies during this period.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

We analyze a finite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to find an inventory policy and a pricing strategy maximizing expected profit over the finite horizon. We show that when the demand model is additive, the profit-to-go functions are k-concave and hence an (s,S,p) policy is optimal. In such a policy, the period inventory is managed based on the classical (s,S) policy and price is determined based on the inventory position at the beginning of each period. For more general demand functions, i.e., multiplicative plus additive functions, we demonstrate that the profit-to-go function is not necessarily k-concave and an (s,S,p) policy is not necessarily optimal. We introduce a new concept, the symmetric k-concave functions and apply it to provide a characterization of the optimal policy. / Singapore-MIT Alliance (SMA)

[pt] A visualização de horizontes sísmicos constitui uma importante área de conhecimento amplamente aplicada na prospecção de hidrocarbonetos pela indústria do petróleo. Diferentes técnicas são atualmente empregadas na apresentação destas superfícies, sendo usualmente utilizadas as soluções baseadas na geração de malhas poligonais, que se beneficiam da otimização das placas gráficas atuais no desenho de triiângulos. Este trabalho faz uma avaliação do uso da renderização baseada em pontos, no lugar de polígonos, para a visualização de horizontes sísmicos. Para isso as técnicas de cada etapa do processo são avaliadas, levando-se em conta a natureza específica dos dados de interpretação de horizontes em volumes sísmicos e o resultado final esperado para a visualização deste tipo de dados. O algoritmo utilizado baseia-se no método conhecido como Surface Splatting para a renderização dos pontos originais, sendo estudados a estruturação apropriada para os dados a serem visualizados, a técnica para obtenção de normais, a abordagem adequada para o cálculo da iluminação e mecanismos adicionais necessários ao processo. Resultados da aplicação do método em dados reais são, ao final do trabalho, analisados e comparados à renderização tradicional para os horizontes avaliados. / [en] Seismic horizon visualization stands as an important knowledge area used to support exploration on the oil industry. Different techniques currently employed to render this kind of surfaces are usually based on polygonal meshes generation, which benefits from graphics boards optimization on drawing triangles. This work is an evaluation of Point Based rendering techniques to replace polygonal approaches in seismic horizons visualization. To do so, this study revisits each stage of the seismic visualization process. The algorithm adopted here is based on the Surface Splatting with the EWA filter. This work also presents a study on normal evaluation and data structures to store points and normal. Special care is taken in shading techniques. The implementation yielded results that are used to support the evaluation of the Point Based Techniques on real 3D Seismic data. Traditional triangle based rendering is also presented to compare results.

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On the moon and other airless bodies, ballistically emplaced ejecta transitions from a thinning, continuous inner deposit to become discontinuous beyond approximately one crater radius from the crater rim and can further break into discrete rays and secondary craters. In contrast, on Mars, ejecta often form continuous, distinct, and sometimes thick deposits that transition to a low ridge or escarpment that may be circular or lobate. The Martian ejecta type has been variously termed pancake, rampart, lobate, or layered, and in this work we refer to it as abrupt termini ejecta (ATE). Two main formation mechanisms have been proposed, one requiring interaction of the ejecta with the atmosphere and the other mobilization of near-surface volatiles. ATE morphologies are also unambiguously seen on Ganymede, Europa, Dione, and Tethys, but they are not as common as on Mars. We have identified up to 38 craters on Charon that show signs of ATE, including possible distal ramparts and lobate margins. These ejecta show morphologic and morphometric similarities with other moons in the solar system, which are a subset of the properties observed on Mars. From comparison of these ejecta on Charon and other solar system bodies, we find the strongest support for subsurface volatile mobilization and ejecta fluidization as the main formation mechanism for the ATE, at least on airless, icy worlds. This conclusion comes from the bodies on which they are found, an apparent preference for certain terrains, and the observation that craters with ATE can be near to similarly sized craters that only have gradational ejecta.