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This thesis is concerned with the modelling of miscible fluid flow through porous media, with the intended application being the displacement of oil from a reservoir by a solvent with which the oil is miscible. The primary difficulty that we encounter with such modelling is the existence of a fingering instability that arises from the viscosity and the density differences between the oil and solvent. We take as our basic model the Peaceman model, which we derive from first principles as the combination of Darcy’s law with the mass transport of solvent by advection and hydrodynamic dispersion. In the oil industry, advection is usually dominant, so that the Péclet number, Pe, is large. We begin by neglecting the effect of density differences between the two fluids and concentrate only on the viscous fingering instability. A stability analysis and numerical simulations are used to show that the wavelength of the instability is proportional to Pe^−1/2, and hence that a large number of fingers will be formed. We next apply homogenisation theory to investigate the evolution of the average concentration of solvent when the mean flow is one-dimensional, and discuss the rationale behind the Koval model. We then attempt to explain why the mixing zone in which fingering is present grows at the observed rate, which is different from that predicted by a naive version of the Koval model. We associate the shocks that appear in our homogenised model with the tips and roots of the fingers, the tip-regions being modelled by Saffman-Taylor finger solutions. We then extend our model to consider flow through porous media that are heterogeneous at the macroscopic scale, and where the mean flow is not one dimensional. We compare our model with that of Todd & Longstaff and also models for immiscible flow through porous media. Finally, we extend our work to consider miscible displacements in which both density and viscosity differences between the two fluids are relevant.

This thesis deals with the works of Philip Meadows Taylor, nineteenth-century British administrator and author of six novels on Indian themes. His works, published between 1839 and 1878, belong to the little researched early period of Anglo-Indian literature when popular fiction reflected the confidence and beliefs of British rule in India. Meadows Taylor worked in India as a political agent in various parts of Hyderabad from 1824 until his early retirement in 1860. His work, his close friendships with Indians, and his marriage to an Eurasian woman exposed him to various aspects of Indian life closed to many of his British contemporaries in India. This is reflected in his novels, of which the best known is his first, Confessions of a Thug, published in 1839. Subsequent works include Tippoo Sultaun: A Tale of the Mysore War (1841), Tara (1863), Ralph Darnell (1865), Seeta (1873), and A Noble Queen (1878). All these works present Indian scenery and Indian customs vividly and sympathetically, and are characterised by unusually liberal views on such things as interracial marriage, race relations and Indian religious practices; views at odds with those of many of his contemporaries. This thesis examines Meadows Taylor's works, and the connection between his portrayal of British conceptions of India and its people and the historical development of British rule in India. Ultimately Taylor's works illustrate his view that underneath the surface differences of race and religious creed lies a common human experience shared by both East and West, a view which differentiates him from other nineteenth-century writers on India. Other unusual thematic concerns include his use of Victorian concepts of domesticity in Indian settings, his presentation of strongly idealised Indian characters, and his frequent use as subject matter of "pre-colonial" Indian history.

This dissertation explores theologies of suffering through engagement with five theologians from across fifteen centuries of the Christian tradition: Gregory the Great, Julian of Norwich, Jeremy Taylor, C.S. Lewis and Ivone Gebara. It uses a typological method to examine the types of responses that are advocated by each theologian, and the relation of their responses to five theological touchstones: Humanity, Sin and Evil; God’s Providence; Salvation; Christ; and Eternal Life. The Introductory Chapter provides an exploration of the definitions and etymologies of suffering and grief; a description of the typological method; an examination of notable relevant literature; and an introduction to the five thinkers. Chapter One is an examination of the life and writings of the 6th century pope Gregory the Great, with particular focus on The Book of the Pastoral Rule and Moralia. Gregory understands suffering to be a discipline sent by God to the faithful. Chapter Two is an examination of the life and Revelations text of the 13th century English mystic Julian of Norwich, who focuses on the reward God desires to give those who suffer. Chapter Three is an examination of the life and writings of 17th century Anglican bishop Jeremy Taylor, with particular focus on Holy Living and Holy Dying. Taylor places an emphasis on the lifelong practice of faithfulness in preparation for death. Chapter Four is an examination of the life and writings of 20th century Anglican theologian and author C. S. Lewis, with particular attention to The Problem of Pain, The Chronicles of Narnia, A Grief Observed, and Letters to Malcom. Lewis offers the example of one who is willing to engage with the depth of his grief and to question God on his road to acceptance. Chapter Five is an examination of the life and writings of contemporary Brazilian, feminist and liberation theologian Ivone Gebara, with particular focus on her book Out of the Depths and her engagement with Latin American author Isabel Allende. Gebara questions traditional understandings of suffering, as well as when suffering is to be accepted and when suffering is unjust and should be combated. The Concluding Chapter constructs a contemporary theology of suffering drawing on the insights and wrestling with the challenges raised by the varying perspectives of the five theologians. The goal is to provide a hopeful and nuanced way of thinking theologically about suffering for contemporary Christians. The contemporary theology affirms the importance of the call, found in Gebara, to combat unjust suffering through acts of love and mercy, while also affirming that acceptance of the reality of endemic suffering, found in all five theologians, can provide one with opportunities to grow spiritually, live more faithfully and to experience the blessings in the midst of suffering that are a foretaste of heavenly bliss.

We are interested in the onset of instability of the axisymmetric flow between two concentric spherical shells that differentially rotate about a common axis in the narrow-gap limit. The expected mode of instability takes the form of roughly square axisymmetric Taylor vortices which arise in the vicinity of the equator and are modulated on a latitudinal length scale large compared to the gap width but small compared to the shell radii. At the heart of the difficulties faced is the presence of phase mixing in the system, characterised by a non-zero frequency gradient at the equator and the tendency for vortices located off the equator to oscillate. This mechanism serves to enhance viscous dissipation in the fluid with the effect that the amplitude of any initial disturbance generated at onset is ultimately driven to zero. In this thesis we study a complex Ginzburg-Landau equation derived from the weakly nonlinear analysis of Harris, Bassom and Soward [D. Harris, A. P. Bassom, A. M. Soward, Global bifurcation to travelling waves with application to narrow gap spherical Couette flow, Physica D 177 (2003) p. 122-174] (referred to as HBS) to govern the amplitude modulation of Taylor vortex disturbances in the vicinity of the equator. This equation was developed in a regime that requires the angular velocities of the bounding spheres to be very close. When the spherical shells do not co-rotate, it has the remarkable property that the linearised form of the equation has no non-trivial neutral modes. Furthermore no steady solutions to the nonlinear equation have been found. Despite these challenges Bassom and Soward [A. P. Bassom, A. M. Soward, On finite amplitude subcritical instability in narrow-gap spherical Couette flow, J. Fluid Mech. 499 (2004) p. 277-314] (referred to as BS) identified solutions to the equation in the form of pulse-trains. These pulse-trains consist of oscillatory finite amplitude solutions expressed in terms of a single complex amplitude localised as a pulse about the origin. Each pulse oscillates at a frequency proportional to its distance from the equatorial plane and the whole pulse-train is modulated under an envelope and drifts away from the equator at a relatively slow speed. The survival of the pulse-train depends upon the nonlinear mutual-interaction of close neighbours; as the absence of steady solutions suggests, self-interaction is inadequate. Though we report new solutions to the HBS co-rotation model the primary focus in this work is the physically more interesting case when the shell velocities are far from close. More specifically we concentrate on the investigation of BS-style pulse-train solutions and, in the first part of this thesis, develop a generic framework for the identification and classification of pulse-train solutions. Motivated by relaxation oscillations identified by Cole [S. J. Cole, Nonlinear rapidly rotating spherical convection, Ph.D. thesis, University of Exeter (2004)] whilst studying the related problem of thermal convection in a rapidly rotating self-gravitating sphere, we extend the HBS equation in the second part of this work. A model system is developed which captures many of the essential features exhibited by Cole's, much more complicated, system of equations. We successfully reproduce relaxation oscillations in this extended HBS model and document the solution as it undergoes a series of interesting bifurcations.

<p>Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.</p><p>A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case. </p><p>In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state. </p><p>LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.</p> / Dissertation

One notes that Kant's philosophy became a part of Coleridge's thinking, and his devotion to its principle intensified through the years. Although Kant influenced Coleridge's aesthetics greatly, significant parallels between Kant's moral and ethical principles and Coleridge's religious doctrines are evidence of distinct influence. Particularly interesting are the views these two men had on the being and nature of God; on sin, salvation, and redemption; and on the various aspects of religion and faith.

It is the purpose of this study to determine if ego-involvement influences the performance of an individual in a learning situation.

In my artistic practice, I emphasize personal and pan-cultural anxieties regarding civilization and the environment as an impetus for work in sculpture, video, and drawing. By locating marginal microcosmic subject matter that tellingly exhibits macrocosmic global dread, I seek to capture and distill our overwhelming eco-socio-political anxiety into a portrait of a society at a point in its history when the specter of nameless impending disaster weighs pressingly on the collective psyche. This thesis is supplementary to my work of sculpture in the Graduate School of the Arts Thesis Exhibition at the Anderson Gallery opening on April 27th, 2007. The work was entitled Busted Butte Or the Evening Deadness in the West, and images of it are contained within the text. This document was created in Microsoft Word 2004.

Existing estimations of implicit inflation target are primarily based on the assumption of parameter stability over time horizon. This work relaxes this assumption and proposes alternative framework based on time-varying parameter model. We aim on behaviour of European Central Bank in order to compare its official proclamations of price stability levels with our implicit estimations. We will also examine how two pillar strategy of European Central Bank is practically used.