Every transitive permutation representation of a finite group is the representation of the group in its action on the cosets of a particular subgroup of the group. The group has a certain rank for each of these representations. We first find almost all rank-3 and rank-4 transitive representations of the projective special linear group P SL(2, q) where q = pm and p is an odd prime. We also determine the rank of P SL (2, p) in terms of p on the cosets of particular given subgroups. We then investigate the construction of rank-3 transitive and primitive extensions of a simple group, such that the extension group formed is also simple. In the latter context we present a new, group theoretic construction of the famous Hoffman-Singleton graph as a rank-3 graph. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2015 / FAU Electronic Theses and Dissertations Collection

No contexto da teoria da relatividade geral de Einstein, se estudam espaço-tempos dinâmicos do tipo buraco negro em um ambiente cosmológico, em particular, uma generalização de massa variável do espaço-tempo de McVittie. São apresentados alguns espaço-tempos resultantes de limites da solução de McVittie generalizada. Se discutem as definições padrão de buraco negro e horizonte de eventos assim como as dificuldades de aplicá-las em situações dinâmicas, outras definições para horizontes são exploradas. É usado o conceito de horizonte aparente para localizar buracos negros e horizontes cosmológicos. Soluções para a busca dos horizontes aparentes são encontradas nas geometrias de Schwarzschild-de Sitter, McVittie e McVittie generalizado. / Black hole-like spacetimes in a cosmological background are studied within the Einsteins general relativity theory framework, in particular a mass varying generalization of the McVitties spacetime. We exhibit some of the resulting spacetimes as limit cases of the generalized McVittie solution. We discuss the standard definition of black hole and event horizon, and we address the difficulties in aplying it in dynamical situations, another definitions for horizons are explored. The apparent horizon concept is used to locate black holes and cosmological horizons. Solutions for apparent horizons in Schwarzschild-de Sitter, McVittie, and generalized McVittie geometries are shown.

Upper to lower delta plain fluvial sand bodies, sealed by delta plain mudstones, form important hydrocarbon reservoir targets. Modelling complex geobodies in the subsurface is challenging, with a significant degree of uncertainty on dimensions, distribution and connectivity. Studies of modern and ancient paralic systems have produced a myriad of nomenclature and hierarchy schemes for classifying fluvial architectural elements; often lacking clearly-defined terminology. These are largely based on outcrop data where lateral and vertical relationships of bounding scour surfaces can be assessed in detail. Many of these key defining criteria are difficult to recognise or cannot be obtained from typical 3D seismic reflection data at reservoir depths greater than or equal to 2 km subsurface. This research provides a detailed statistical analysis of the Triassic fluvio-deltaic Mungaroo Formation on the North West Shelf of Australia, which is one of the most important gas plays in the world. A multidisciplinary approach addresses the challenge of characterising the reservoir by utilising an integrated dataset of 830 m of conventional core, wireline logs from 21 wells (penetrating up to 1.4 km of the upper Mungaroo Fm) and a 3D seismic volume covering approximately 10,000 km2. Using seismic attribute analysis and frequency decomposition, constrained by well and core data, the planform geobody geometries and dimensions of a variety of architectural elements at different scales of observation are extracted. The results produce a statistically significant geobody database comprising over 27,000 measurements made from more than 6,000 sample points. Three classes of geobodies are identified and interpreted to represent fluvial channel belts and channel belt complexes of varying scales. Fluvial geobody dimensions and geomorphology vary spatially and temporally and the inferred controls on reservoir distribution and architecture are discussed. Results document periods of regression and transgression, interpreted in relation to potential allocyclic and autocyclic controls on the evolution of the depositional system. Statistical analysis of width-to-thickness dimensions and key metrics, such as sinuosity, provided a well-constrained and valuable dataset that augments, and has been compared to, existing published datasets. Uncertainty in interpretation caused by data resolution is addressed; something recognised in many other studies of paralic systems. Given the data distribution, type and resolution, geobodies have possible interpretations as either incised valleys or amalgamated channel belts, with implications for developing predictive models of the system. This study offers the first published, statistically significant dataset for the Mungaroo Formation. It builds upon previous regional work, offering a detailed analysis of this continental scale paralic system and provides insight into the controls and mechanisms that influenced its spatial and temporal evolution. Focusing on improved understanding of geobody distribution and origin, the statistical parameters generated provide a robust dataset that can be used for 3D static reservoir models of analogue systems. Thus, helping to constrain potential geobody dimensions and reduce the uncertainties associated with modelling.

O escopo deste mestrado é de se familiarizar com a chamada {\\it correspondência AdS/CFT}, que tem sido um dos mais importantes desenvolvimentos na física teórica nas últimas décadas. De acordo com essa correspondência, deformações das geometrias do lado da gravidade (ou lado \"AdS\") devem ser mapeadas para operadores das teorias de calibre duais (ou lado \"CFT\"). Em particular, nos temos estado interessados em explorar uma entrada particular no dicionário AdS/CFT, a relação entre os operadores 1/2 BPS em ${\\cal N}=4$ super Yang-Mills, e as chamadas {\\it geometrias bubbling} no lado da gravidade. A fim de fazer isso, apresentamos primeiramente as noções de ${\\cal N}=4$ SYM e soluções de Supergravidade. Portanto, podemos expor mais claramente o sentido da correspondência AdS /CFT, e depois mostrar a derivação das geometrias 1/2 BPS duais a estados 1/2 BPS em ${\\cal N}=4$ SYM como um exemplo. / The scope of this Master program was to get acquainted with the so-called {\\it AdS/CFT correspondence}, which has been one of the most important developments in theoretical physics in the last decades. According to this correspondence, deformations of the geometries in the gravity side (or \"AdS\" side) must be mapped to states of the dual gauge theories (or \"CFT\" side). In particular, we have been interested in exploring a particular entry in the AdS/CFT dictionary, namely, the relation between 1/2 BPS operators in ${\\cal N}=4$ super Yang-Mills, and the so-called {\\it bubbling geometries} on the gravity side. In order to do that, we first present the notions of N=4 SYM and Supergravity solutions. In this way, we can expose the statement of the AdS/CFT correspondence, and later show the derivation of 1/2 BPS geometries dual to 1/2 BPS states in N=4 SYM as an example of this one.

Charged particle chaos and its collective effects in different magnetic geometries are investigated in a sequence of various numerical experiments. The fields generated by the particles as a result of interaction with the background electric and magnetic fields is not accounted for in the simulation. An X-line is first used to describe the geometry of the magnetotail prior to magnetic reconnection and a study of the behavior of charged particles is done from a microscopic viewpoint. Another important geometry in the magnetotail prior to substorm onset is Bifurcated Current Sheet. The same analysis is done for this configuration. The existence of at least one positive Lyapunov exponent shows that the motion of the particles is chaotic. By using statistical mechanics, the macroscopic properties of this chaotic motion are studied. Due to particles being charged, an electric field (perpendicular to the magnetic field in weak magnetic field region) accelerates the particles on average. Finite average velocity in the direction of electric field gives rise to an effective resistivity even in a collisionless regime such as solar corona and the magnetotail. Starting from initial velocities that are chosen randomly from a uniform distribution, the evolution of these distributions tends to a Maxwellian by the end of the simulation that is somewhat analogous to collisions in a Lorentz gas model. The effective resistivity due to such collisions is estimated. Ohmic heating is found to occur as a result of such an effective resistivity. Such collisions due to collective particle effects are essentially a different mechanism from classical collision notion. These experiments are done for two types of ions found in the plasma sheet prior to substorm onset, viz., protons and oxygen ions. Observational evidence of oxygen ions in the central plasma sheet, which flow out along open field lines from the ionosphere, were also simulated in the same manner. Oxygen ions have been found to influence the bifurcation of the current sheet and are also important in reconnection and other nonohmic instabilities, such as Kelvin Helmholtz instability, due to their mass. It is found that acceleration in X-line scales with the mass of ion species and the resistivity remains constant for different electric field strengths. In a Bifurcated Current Sheet, the acceleration scales with the square of mass of ion species and the resistivity scales with the electric field. Also, the overall resistivity values found in a Bifurcated Current Sheet are an order of magnitude lower than that found in an X-line.

Esta pesquisa parte do pressuposto de que a Internet é um dispositivo sociotécnico não apenas indissociável do espaço geográfico, mas primordialmente tecido a partir das relações espaciais que o animam e que dele derivam. Estas relações espaciais e sociotécnicas produzem o incessante efeito de reconfiguração da geografia da Internet, enquanto espaço em movimento. O argumento desta tese é a de que a espacialidade da Internet define-se a partir de três dimensões complementares, a saber: uma dimensão de conectividade, responsável pela constituição do espaço reticular; uma dimensão lógica/informacional, a partir da qual o espaço virtual (ciberespaço) ganha forma; e uma dimensão normativa, encarregada da regulação da produção e usos da Internet. Argumentamos ainda que as relações e expressões espaciais que se formam no processo de configuração dessas dimensões possuem naturezas distintas, de acordo com o lócus de onde se originam os sujeitos, bem como de acordo com o projeto político de Internet que estes promovem e idealizam. O espaço da Internet define-se, desse modo, a partir de geometrias de poder que promovem políticas espaciais verticais ou hierárquicas de um lado e políticas espaciais horizontais ou distribuídas de outro. Considerando os argumentos supracitados, a hipótese central que aportamos é a de que a fricção entre as verticalidades e as horizontalidades socioespaciais, que se desenvolvem no processo de apropriação da aqui apresentada tridimensionalidade da Internet, despertam as territorialidades dos diversos setores da sociedade, dentre as quais as políticas espaciais horizontais promovidas intencionalmente pela sociedade civil possuem relevância no constante refazer das geometrias de poder da Internet. Para testar essa hipótese, empregamos quatro abordagens metodológicas: a análise de documentos e arquivos históricos relacionados ao desenvolvimento das redes digitais; pesquisa on-line para coleta de dados sobre organizações relacionadas ao nosso escopo; trabalho de campo em eventos voltados para a discussão e desenvolvimento de políticas para a Internet; entrevistas com integrantes de organizações civis que promovem ações de normatização, gestão, contestação e apropriação da Internet. Os resultados da pesquisa revelam uma densa presença de organizações civis em cada uma das dimensões investigadas, associada a uma capacidade de articulação entre entidades com habilidades e competências distintas para a construção de uma agenda comum e maior capacidade de incidência. / This research is based on the assumption that the Internet is a sociotechnical device not only inseparable from geographical space, but primarily woven from the spatial relations that animate and derive from it. These spatial and sociotechnical relations produce the incessant effect of reconfiguration of the geography of the Internet, as space in movement. The argument of this thesis is that the spatiality of the Internet is defined from three complementary dimensions, namely: a connectivity dimension, responsible for the constitution of the reticular space; a logical / informational dimension, from which the virtual space (cyberspace) takes shape; and a normative dimension, in charge of the regulation of the production and uses of the Internet. We also argue that the socio-spatial relationships that form in the process of configuring these dimensions have different natures according to the locus from which the actors originate, as well as according to the Internet political project that they promote and idealize. The Internet space is thus defined from power geometries that promote vertical or hierarchical spatial policies on the one hand and horizontal or distributed spatial policies on the other. Considering the aforementioned arguments, the central hypothesis we present is that the friction between the verticalities and the socio-spatial horizontalities that develop in the process of appropriation of the presented three-dimensionality of the Internet, awaken the territorialities of the various sectors of society, among which horizontalities intentionally promoted by civil society have relevance in the constant reconfiguration of the power geometries of the Internet. To test this hypothesis, we used four methodological approaches: the analysis of historical documents and archives related to the development of digital networks; search online for data collection on organizations related to our scope; fieldwork on events aimed at the discussion and development of policies for the Internet; interviews with members of civil organizations that promote standardization, management, contestation and appropriation of the Internet. The results of the research reveal a dense presence of civil organizations in each of the investigated dimensions, associated with a capacity of articulation between entities with distinct abilities and competences for the construction of a common agenda and greater capacity of incidence.

The main goal of this thesis is a contribution to the classification of all incidence geometries of rank two on which some group PSL(2,q), q a prime power, acts flag-transitively. Actually we require that the action be RWPRI (residually weakly primitive) and (2T)1 (doubly transitive on every residue of rank one). In fact our definition of RWPRI requires the geometry to be firm (each residue of rank one has at least two elements) and RC (residually connected). The main goal is achieved in this thesis. It is stated in our "Main Theorem". The proof of this theorem requires more than 60pages. Quite surprisingly, our proof in the direction of the main goal uses essentially the classification of all subgroups of PSL(2,q), a famous result provided in Dickson’s book "Linear groups: With an exposition of the Galois field theory", section 260, in which the group is called Linear Fractional Group LF(n, pn). Our proof requires to work with all ordered pairs of subgroups up to conjugacy. The restrictions such as RWPRI and (2T)1 allow for a complete analysis. The geometries obtained in our "Main Theorem" are bipartite graphs; and also locally 2-arc-transitive graphs in the sense of Giudici, Li and Cheryl Praeger. These graphs are interesting in their own right because of the numerous connections they have with other fields of mathematics.

Which tensor fields G on a smooth manifold M can serve as a spacetime structure? In the first part of this thesis, it is found that only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry predictive, interpretable and quantizable matter dynamics. The obvious dependence of this characterization of admissible tensorial spacetime geometries on specific matter is not a weakness, but rather presents an insight: it was Maxwell theory that justified Einstein to promote Lorentzian manifolds to the status of a spacetime geometry. Any matter that does not mimick the structure of Maxwell theory, will force us to choose another geometry on which the matter dynamics of interest are predictive, interpretable and quantizable. These three physical conditions on matter impose three corresponding algebraic conditions on the totally symmetric contravariant coefficient tensor field P that determines the principal symbol of the matter field equations in terms of the geometric tensor G: the tensor field P must be hyperbolic, time-orientable and energy-distinguishing. Remarkably, these physically necessary conditions on the geometry are mathematically already sufficient to realize all kinematical constructions familiar from Lorentzian geometry, for precisely the same structural reasons. This we were able to show employing a subtle interplay of convex analysis, the theory of partial differential equations and real algebraic geometry. In the second part of this thesis, we then explore general properties of any hyperbolic, time-orientable and energy-distinguishing tensorial geometry. Physically most important are the construction of freely falling non-rotating laboratories, the appearance of admissible modified dispersion relations to particular observers, and the identification of a mechanism that explains why massive particles that are faster than some massless particles can radiate off energy until they are slower than all massless particles in any hyperbolic, time-orientable and energy-distinguishing geometry. In the third part of the thesis, we explore how tensorial spacetime geometries fare when one wants to quantize particles and fields on them. This study is motivated, in part, in order to provide the tools to calculate the rate at which superluminal particles radiate off energy to become infraluminal, as explained above. Remarkably, it is again the three geometric conditions of hyperbolicity, time-orientability and energy-distinguishability that allow the quantization of general linear electrodynamics on an area metric spacetime and the quantization of massive point particles obeying any admissible dispersion relation. We explore the issue of field equations of all possible derivative order in rather systematic fashion, and prove a practically most useful theorem that determines Dirac algebras allowing the reduction of derivative orders. The final part of the thesis presents the sketch of a truly remarkable result that was obtained building on the work of the present thesis. Particularly based on the subtle duality maps between momenta and velocities in general tensorial spacetimes, it could be shown that gravitational dynamics for hyperbolic, time-orientable and energy distinguishable geometries need not be postulated, but the formidable physical problem of their construction can be reduced to a mere mathematical task: the solution of a system of homogeneous linear partial differential equations. This far-reaching physical result on modified gravity theories is a direct, but difficult to derive, outcome of the findings in the present thesis. Throughout the thesis, the abstract theory is illustrated through instructive examples. / Welche Tensorfelder G auf einer glatten Mannigfaltigkeit M können eine Raumzeit-Geometrie beschreiben? Im ersten Teil dieser Dissertation wird es gezeigt, dass nur stark eingeschränkte Klassen von Tensorfeldern eine Raumzeit-Geometrie darstellen können, nämlich Tensorfelder, die eine prädiktive, interpretierbare und quantisierbare Dynamik für Materiefelder ermöglichen. Die offensichtliche Abhängigkeit dieser Charakterisierung erlaubter tensorieller Raumzeiten von einer spezifischen Materiefelder-Dynamik ist keine Schwäche der Theorie, sondern ist letztlich genau das Prinzip, das die üblicherweise betrachteten Lorentzschen Mannigfaltigkeiten auszeichnet: diese stellen die metrische Geometrie dar, welche die Maxwellsche Elektrodynamik prädiktiv, interpretierbar und quantisierbar macht. Materiefeld-Dynamiken, welche die kausale Struktur von Maxwell-Elektrodynamik nicht respektieren, zwingen uns, eine andere Geometrie auszuwählen, auf der die Materiefelder-Dynamik aber immer noch prädiktiv, interpretierbar und quantisierbar sein muss. Diesen drei Voraussetzungen an die Materie entsprechen drei algebraische Voraussetzungen an das total symmetrische kontravariante Tensorfeld P, welches das Prinzipalpolynom der Materiefeldgleichungen (ausgedrückt durch das grundlegende Tensorfeld G) bestimmt: das Tensorfeld P muss hyperbolisch, zeitorientierbar und energie-differenzierend sein. Diese drei notwendigen Bedingungen an die Geometrie genügen, um alle aus der Lorentzschen Geometrie bekannten kinematischen Konstruktionen zu realisieren. Dies zeigen wir im ersten Teil der vorliegenden Arbeit unter Verwendung eines teilweise recht subtilen Wechselspiels zwischen konvexer Analysis, der Theorie partieller Differentialgleichungen und reeller algebraischer Geometrie. Im zweiten Teil dieser Dissertation erforschen wir allgemeine Eigenschaften aller solcher hyperbolischen, zeit-orientierbaren und energie-differenzierenden Geometrien. Physikalisch wichtig sind der Aufbau von frei fallenden und nicht rotierenden Laboratorien, das Auftreten modifizierter Energie-Impuls-Beziehungen und die Identifizierung eines Mechanismus, der erklärt, warum massive Teilchen, die sich schneller als einige masselosse Teilchen bewegen, Energie abstrahlen können, aber nur bis sie sich langsamer als alle masselossen Teilchen bewegen. Im dritten Teil der Dissertation ergründen wir die Quantisierung von Teilchen und Feldern auf tensoriellen Raumzeit-Geometrien, die die obigen physikalischen Bedingungen erfüllen. Eine wichtige Motivation dieser Untersuchung ist es, Techniken zur Berechnung der Zerfallsrate von Teilchen zu berechnen, die sich schneller als langsame masselose Teilchen bewegen. Wir finden, dass es wiederum die drei zuvor im klassischen Kontext identifizierten Voraussetzungen (der Hyperbolizität, Zeit-Orientierbarkeit und Energie-Differenzierbarkeit) sind, welche die Quantisierung allgemeiner linearer Elektrodynamik auf einer flächenmetrischen Raumzeit und die Quantizierung massiver Teilchen, die eine physikalische Energie-Impuls-Beziehung respektieren, erlauben. Wir erkunden auch systematisch, wie man Feldgleichungen aller Ableitungsordnungen generieren kann und beweisen einen Satz, der verallgemeinerte Dirac-Algebren bestimmt und die damit Reduzierung des Ableitungsgrades einer physikalischen Materiefeldgleichung ermöglicht. Der letzte Teil der vorliegenden Schrift skizziert ein bemerkenswertes Ergebnis, das mit den in dieser Dissertation dargestellten Techniken erzielt wurde. Insbesondere aufgrund der hier identifizierten dualen Abbildungen zwischen Teilchenimpulsen und -geschwindigkeiten auf allgemeinen tensoriellen Raumzeiten war es möglich zu zeigen, dass man die Gravitationsdynamik für hyperbolische, zeit-orientierbare und energie-differenzierende Geometrien nicht postulieren muss, sondern dass sich das Problem ihrer Konstruktion auf eine rein mathematische Aufgabe reduziert: die Lösung eines homogenen linearen Differentialgleichungssystems. Dieses weitreichende Ergebnis über modifizierte Gravitationstheorien ist eine direkte (aber schwer herzuleitende) Folgerung der Forschungsergebnisse dieser Dissertation. Die abstrakte Theorie dieser Doktorarbeit wird durch mehrere instruktive Beispiele illustriert.

Charged particle chaos and its collective effects in different magnetic geometries are investigated in a sequence of various numerical experiments. The fields generated by the particles as a result of interaction with the background electric and magnetic fields is not accounted for in the simulation. An X-line is first used to describe the geometry of the magnetotail prior to magnetic reconnection and a study of the behavior of charged particles is done from a microscopic viewpoint. Another important geometry in the magnetotail prior to substorm onset is Bifurcated Current Sheet. The same analysis is done for this configuration. The existence of at least one positive Lyapunov exponent shows that the motion of the particles is chaotic. By using statistical mechanics, the macroscopic properties of this chaotic motion are studied. Due to particles being charged, an electric field (perpendicular to the magnetic field in weak magnetic field region) accelerates the particles on average. Finite average velocity in the direction of electric field gives rise to an effective resistivity even in a collisionless regime such as solar corona and the magnetotail. Starting from initial velocities that are chosen randomly from a uniform distribution, the evolution of these distributions tends to a Maxwellian by the end of the simulation that is somewhat analogous to collisions in a Lorentz gas model. The effective resistivity due to such collisions is estimated. Ohmic heating is found to occur as a result of such an effective resistivity. Such collisions due to collective particle effects are essentially a different mechanism from classical collision notion. These experiments are done for two types of ions found in the plasma sheet prior to substorm onset, viz., protons and oxygen ions. Observational evidence of oxygen ions in the central plasma sheet, which flow out along open field lines from the ionosphere, were also simulated in the same manner. Oxygen ions have been found to influence the bifurcation of the current sheet and are also important in reconnection and other nonohmic instabilities, such as Kelvin Helmholtz instability, due to their mass. It is found that acceleration in X-line scales with the mass of ion species and the resistivity remains constant for different electric field strengths. In a Bifurcated Current Sheet, the acceleration scales with the square of mass of ion species and the resistivity scales with the electric field. Also, the overall resistivity values found in a Bifurcated Current Sheet are an order of magnitude lower than that found in an X-line.

The discovery of new geometries in the 19th century and the departure from an absolute to a relative understanding of space-time, together with the invention of higher dimensions have caused a shift towards the idealization of space. This new type of ideal space was called hyperspace. The counter-intuitive quality of hyperspace has opened up new formal possibilities and representation techniques in art and architecture. In a similar manner, with the introduction of computers, the virtual and immaterial quality of cyberspace has offered new design techniques and forms to architecture. Algorithmic design tools and the use of surface as the primary architectural element in cyberspace have caused a shift in the conception of space together with the way it is perceived. Taking its departure point from physical space, this thesis investigates the upper and lower dimensions of space in order to understand and analyze the current conception of architectural space in the virtual realm. Three types of spatial qualities are investigated in detail: the ideal characteristic of hyperspace, the visual medium of cyberspace and the algorithmic formation of hypospace.