In type II noncommutative geometry, the geometry on a C∗-algebra A is given by an unbounded Breuer–Fredholm module (ρ,N,D) over A. Here ρ:A→N is a ∗-homomorphism from A to the semi-finite von Neumann algebra N⊂B(H), and D is an unbounded Breuer–Fredholm operator affiliated with N that satisfies certain axioms. Each Breuer–Fredholm module assigns an index to a given element in the K-theory of A. The Breuer–Fredholm index provides a real-valued pairing between the K-homology and the K-theory of A. When N=B(H), a construction of Jaffe-Lesniewski-Osterwalder associates to the module (ρ,N,D) a cocycle in the entire cyclic cohomology group of A for D is theta-summable. The JLO character and the K-theory character intertwine the K-theoretical pairing with the pairing of entire cyclic theory. If (ρ,N,F) is a finitely summable bounded Breuer–Fredholm module, Benameur-Fack defined a cocycle generalizing the Connes's cocycle for bounded Fredholm modules. On the other hand, given a finitely-summable unbounded Breuer–Fredholm module, there is a canonically associated bounded Breuer–Fredholm module. The first main result of this thesis extends the JLO theory to Breuer–Fredholm modules (possibly N does not equal B(H)) in the graded case, and proves that the JLO cocycle and Connes cocycle define the same class in the entire cyclic cohomology of A. This extends a result of Connes-Moscovici for Fredholm modules. An example of an unbounded Breuer–Fredholm module is given by the noncommutative space of G-connections due to Aastrup-Grimstrup-Nest. In their original work, the authors limit their construction to the case that the group G=U(1) or G=SU(2). Another main result of the thesis extends AGN’s construction to any connected compact Lie group G; and generalizes by considering connections defined on sequences of graphs, using limits of spectral triples. Our construction makes it possible to equip the module (ρ,N,D) with a Z_2-grading. The last part of this thesis studies the JLO character of the Breuer–Fredholm module of AGN. The definition of this Breuer–Fredholm module depends on a divergent sequence. A concrete condition on possible perturbations of the sequence ensuring that the resulting JLO class remains invariant is established. The condition implies a certain functoriality of AGN’s construction.

To recover oil remaining in petroleum reservoirs after waterflooding, the gravitationally stable mode of gas injection is recognized as a promising tertiary oil recovery process. Understanding the phenomena occurring over the course of the gravity-assisted inert gas injection (GAIGI) process is thus important. Extensive studies on both secondary and tertiary modes of gravity drainage have shown promising results in recovering oil from homogeneous water-wet glass bead packs, sand packs, and sandstone cores, respectively. However, it is not realistic to anticipate similar flow mechanisms and recovery results in all types of reservoirs because the natural hydrocarbon reservoirs are all heterogeneous in terms of their permeability, porosity, and wettability. Such heterogeneities cause irregular displacement patterns, and nonuniform fluid distribution. The impact of heterogeneity of the porous media on the GAIGI process has not been fully addressed in the experimental studies carried out to date; therefore, this thesis aims to fill in the gap of knowledge on this area. The impact of reservoir wettability and pore structure heterogeneities at the macroscopic scale on the recovery efficiency of the GAIGI process was investigated through a systematic experimental study for tertiary recovery of waterflood residual oil. To obtain heterogeneous (in terms of wettability) packings, isolated inclusions of oil-wet consolidated glass beads were embedded in a continuum of unconsolidated water-wet glass beads. Similarly, the heterogeneous porous media exhibiting permeability heterogeneity consisted of large-pore-size isolated regions randomly distributed in a small-pore-size continuum. Upon waterflooding, significantly higher waterflood residual oil saturation was established in both cases of heterogeneous media in comparison to water-wet homogeneous porous media. The amount of waterflood residual oil varied linearly with the volume fraction of heterogeneities in the packings. Experimental results obtained from tertiary gravity drainage experiments demonstrated that the continuity of water-wet portions of the heterogeneous porous media facilitates the residual oil recovery through the film flow mechanism, provided that the oil spreading coefficient is positive. In addition, owing to the high waterflood residual oil content of the heterogeneous media tested, the oil bank formation occurred earlier and grew faster than that in homogeneous media, resulting in a higher oil recovery factor. However, the favorable wettability conditions in both the homogeneous and heterogeneous porous media exhibiting permeability heterogeneity resulted in slightly lower reduced residual oil saturation after the GAIGI process compared to that in the heterogeneous media with wettability heterogeneity under the same condition of withdrawal rate. In addition, the oil recovery factor at gas breakthrough was found to be inversely related to the production rate due to the functionality of gravity and viscous forces over the course of gravity drainage. These two forces were combined into a dimensionless form, defined as the gravity number (Ngv=Kogg/oVpg). It was discovered that there is a correlation between the oil recovery factor at gas breakthrough and the gravity number for both the heterogeneous and homogeneous media. The correlation of recovery factor at gas breakthrough versus the gravity number in heterogeneous media followed a similar trend as that found for homogeneous water-wet porous media. However, at a given gravity number, the recovery factor in heterogeneous media was greater than that in the homogeneous media. This implies that heterogeneous media will be better target reservoirs for applying the GAIGI process compared to the homogeneous reservoirs.

In type II noncommutative geometry, the geometry on a C∗-algebra A is given by an unbounded Breuer–Fredholm module (ρ,N,D) over A. Here ρ:A→N is a ∗-homomorphism from A to the semi-finite von Neumann algebra N⊂B(H), and D is an unbounded Breuer–Fredholm operator affiliated with N that satisfies certain axioms. Each Breuer–Fredholm module assigns an index to a given element in the K-theory of A. The Breuer–Fredholm index provides a real-valued pairing between the K-homology and the K-theory of A. When N=B(H), a construction of Jaffe-Lesniewski-Osterwalder associates to the module (ρ,N,D) a cocycle in the entire cyclic cohomology group of A for D is theta-summable. The JLO character and the K-theory character intertwine the K-theoretical pairing with the pairing of entire cyclic theory. If (ρ,N,F) is a finitely summable bounded Breuer–Fredholm module, Benameur-Fack defined a cocycle generalizing the Connes's cocycle for bounded Fredholm modules. On the other hand, given a finitely-summable unbounded Breuer–Fredholm module, there is a canonically associated bounded Breuer–Fredholm module. The first main result of this thesis extends the JLO theory to Breuer–Fredholm modules (possibly N does not equal B(H)) in the graded case, and proves that the JLO cocycle and Connes cocycle define the same class in the entire cyclic cohomology of A. This extends a result of Connes-Moscovici for Fredholm modules. An example of an unbounded Breuer–Fredholm module is given by the noncommutative space of G-connections due to Aastrup-Grimstrup-Nest. In their original work, the authors limit their construction to the case that the group G=U(1) or G=SU(2). Another main result of the thesis extends AGN’s construction to any connected compact Lie group G; and generalizes by considering connections defined on sequences of graphs, using limits of spectral triples. Our construction makes it possible to equip the module (ρ,N,D) with a Z_2-grading. The last part of this thesis studies the JLO character of the Breuer–Fredholm module of AGN. The definition of this Breuer–Fredholm module depends on a divergent sequence. A concrete condition on possible perturbations of the sequence ensuring that the resulting JLO class remains invariant is established. The condition implies a certain functoriality of AGN’s construction.

An expansive panel of well exposed (periglacial) strata of the Upper Kaza Group permitted a detailed study of the stratal architecture of proximal basin floor deposits in the Neoproterozoic Windermere turbidite system. Detailed stratigraphic and petrographic analyses identified six lithofacies: poorly-sorted, clast-rich mudstone (F1), thin-bedded siltstone and mudstone (F2), thick-bedded, massive sandstone (F3), medium-scale, cross-stratified sandstone (F4), mudstone-clast breccia (F5), and medium-bedded turbidites (F6). The spatial distribution of these facies identify five architectural elements: heterolithic feeder channel deposits (FA1), thin-bedded intralobe turbidites (FA2), terminal splay deposits (FA3), distributary channel deposits (FA4), and isolated scours (FA5). FA 1-4 are genetically related and form the basic building blocks of large-scale basin floor depositional lobes. FA 5, which is isolated to the stratigraphic top of the study area, is interpreted to have formed in a base-of-slope setting, and its superposition on FA 1-4 suggests the long-term progradation of the Windermere turbidite system.

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In the first part of this thesis we discuss classes of new exact NUT-charged solutions in four dimensions and higher, while in the remainder of the thesis we make a study of their properties and their possible applications. <br /><br /> Specifically, in four dimensions we construct new families of axisymmetric vacuum solutions using a solution-generating technique based on the hidden <em>SL</em>(2,R) symmetry of the effective action. In particular, using the Schwarzschild solution as a seed we obtain the Zipoy-Voorhees generalisation of the Taub-NUT solution and of the Eguchi-Hanson soliton. Using the <em>C</em>-metric as a seed, we obtain and study the accelerating versions of all the above solutions. In higher dimensions we present new classes of NUT-charged spaces, generalizing the previously known even-dimensional solutions to odd and even dimensions, as well as to spaces with multiple NUT-parameters. We also find the most general form of the odd-dimensional Eguchi-Hanson solitons. We use such solutions to investigate the thermodynamic properties of NUT-charged spaces in (A)dS backgrounds. These have been shown to yield counter-examples to some of the conjectures advanced in the still elusive dS/CFT paradigm (such as the maximal mass conjecture and Bousso's entropic N-bound). One important application of NUT-charged spaces is to construct higher dimensional generalizations of Kaluza-Klein magnetic monopoles, generalizing the known 5-dimensional Kaluza-Klein soliton. Another interesting application involves a study of time-dependent higher-dimensional bubbles-of-nothing generated from NUT-charged solutions. We use them to test the AdS/CFT conjecture as well as to generate, by using stringy Hopf-dualities, new interesting time-dependent solutions in string theory. Finally, we construct and study new NUT-charged solutions in higher-dimensional Einstein-Maxwell theories, generalizing the known Reissner-Nordström solutions.

We study a proposed statistical explanation for the Bekenstein-Hawking entropy of a black hole in which entropy arises quantum-mechanically as a result of entanglement. Arguments for the identification of black hole entropy with entanglement entropy are reviewed in the framework of quantum field theory, emphasizing the role of renormalization and the need for a physical short-distance cutoff. Our main novel contribution is a calculation of entanglement entropy in loop quantum gravity. The kinematical Hilbert space and spin network states are introduced, and the entanglement entropy of these states is calculated using methods from quantum information theory. The entanglement entropy is compared with the density of states previously computed for isolated horizons in loop quantum gravity, and the two are found to agree up to a topological term. We investigate a conjecture due to Sorkin that the entanglement entropy must be a monotonically increasing function of time under the assumption of causality. For a system described by a finite-dimensional Hilbert space, the conjecture is found to be trivial, and for a system described by an infinite-dimensional Hilbert space a counterexample is provided. For quantum states with Euclidean symmetry, the area scaling of the entanglement entropy is shown to be equivalent to the strong additivity condition on the entropy. The strong additivity condition is naturally interpreted in information-theoretic terms as a continuous analog of the Markov property for a classical random variable. We explicitly construct states of a quantum field theory on the one-dimensional real line in which the area law is exactly satisfied.

This thesis studies matter emergent as topological excitations of quantum geometry in quantum gravity models. In these models, states are framed four-valent spin networks embedded in a topological three manifold, and the local evolution moves are dual Pachner moves. We first formulate our theory of embedded framed four-valent spin networks by proposing a new graphic calculus of these networks. With this graphic calculus, we study the equivalence classes and the evolution of these networks, and find what we call 3-strand braids, as topological excitations of embedded four-valent spin networks. Each 3-strand braid consists of two nodes that share three edges that may or may not be braided and twisted. The twists happen to be in units of 1/3. Under certain stability condition, some 3-strand braids are stable. Stable braids have rich dynamics encoded in our theory by dual Pachner moves. Firstly, all stable braids can propagate as induced by the expansion and contraction of other regions of their host spin network under evolution. Some braids can also propagate actively, in the sense that they can exchange places with substructures adjacent to them in the graph under the local evolution moves. Secondly, two adjacent braids may have a direct interaction: they merge under the evolution moves to form a new braid if one of them falls into a class called actively interacting braids. The reverse of a direct interaction may happen too, through which a braid decays to another braid by emitting an actively interacting braid. Thirdly, two neighboring braids may exchange a virtual actively interacting braid and become two different braids, in what is called an exchange interaction. Braid dynamics implies an analogue between actively interacting braids and bosons. We also invent a novel algebraic formalism for stable braids. With this new tool, we derive conservation laws from interactions of the braid excitations of spin networks. We show that actively interacting braids form a noncommutative algebra under direction interaction. Each actively interacting braid also behaves like a morphism on non-actively interacting braids. These findings reinforce the analogue between actively interacting braids and bosons. Another important discovery is that stable braids admit seven, and only seven, discrete transformations that uniquely correspond to analogues of C, P, T, and their products. Along with this finding, a braid's electric charge appears to be a function of a conserved quantity, effective twist, of the braids, and thus is quantized in units of 1/3. In addition, each $CPT$-multiplet of actively interacting braids has a unique, characteristic non-negative integer. Braid interactions turn out to be invariant under C, P, and T. Finally, we present an effective description, based on Feynman diagrams, of braid dynamics. This language manifests the analogue between actively interacting braids and bosons, as the topological conservation laws permit them to be singly created and destroyed and as exchanges of these excitations give rise to interactions between braids that are charged under the topological conservation rules. Additionally, we find a constraint on probability amplitudes of braid interactions. We discuss some subtleties, open issues, future directions, and work in progress at the end.

This thesis aims to investigate the trade intensity between the Baltic States and the Nordic countries over a period of 14 years. The bilateral exports of 42 European countries are explored with the focus on the Baltic-Nordic trade. Since many previous studies provided support for the strong relationship between the Baltic States and the Nordic countries, this thesis aims to explore this relationship over time. The Baltic States after their independence, shifted their trade to the Western economies, including Nordic countries. The results reveal that the magnitude of the trade intensity between these two regions have become more important and is higher than expected. Furthermore, it is accounted for commodities of different values traded between the Baltic States and the Nordic countries by introducing dummy variables. It has been shown that the value of commodities is not very important in the Baltic-Nordic trade and therefore there is no trend over time.

Despite interest in the influence of religion on economic activity by early economists like Adam Smith, modern economists have done little research on the subject. In light of the apparent religious fervour in many parts of the global economy, economists' seeming lack of interest in studying how religious cultures enhance or retard the globalization of economic activity is especially surprising. In general, trade theories have given less weight towards the reason for trade explanation on demand side. As a contrary to H-O theory Linder had proposed a theoretically sound and empirically consistent trade theory with a new claim for the reasons why countries trade on the demand side. To fill this gap, I use international survey data on religiosity for a broad panel of countries trading with US to investigate the effects of church attendance and religious beliefs on trade. The beliefs are, in turn, the principal output of the religion sector, and the believer alignment to a specific denomination measures the inputs to this sector. Hence, I used an extended gravity model of international trade to control for a variety of factors that determine trade, and I used two regression methods, OLS and WLS, to exploit the model to its fullest. I find that the sharing of same religious cultures by people in different countries has a significantly positive influence on bilateral trade, all other things being equal. These results accord with a perspective in which religious beliefs influence individual traits that enhance trade and economic performance in general. And my attempt to magnify religion as a means to trade is only a derivation of Linder’s overlapping demand theory.