Thesis (Ph.D.)--Lehigh University, 2009. / Adviser: James D. Gunton.

<p> Sonnets and Psalm investigates the relationships between the sacred nature of Psalm 91 and the secular nature of two sonnets, William Shakespeare's Sonnet 73 and Henry Howard, Earl of Surrey's Sonnet 8. <i> Sonnets and Psalm</i> exploits a dynamic that arises from the juxtaposition of disparate musical universes, choral and instrumental, and the unique and, at times, ineffable aesthetic qualities that emerge as a result of the intentional ordering of musical language and block structures. In a five movement form the listener is guided from vocal events painted on orchestral palettes, to solely instrumental movements, and back again. While the movements can stand independently of each other, there are ponderous transformations of material within and throughout the piece that create a thread that functions as a consistent generative unifying element. A recurrent utilization of motive, color, register, pitch-specific sonorities and gesture, enhances the unity of the work while exploiting the contradistinctive nature of each movement. Relational aspects of hidden and transformed materials from the Psalm and the sonnets (including the Mosaic movements) that are present throughout create a forward and back-relating dynamic. There is a programmatic element at work as well that in itself is a statement: after the sonnets and the mosaics, the listener is finally presented with the Psalm, a conclusion.</p>

Twist grain boundaries, which are widely observed in block copolymer samples of lamellar phases, have been investigated through both direct numerical solution and multiple scale analysis of a coarse-grained mesoscopic model equation. We show that the twist boundary profile can be well described by a pair of Ginzburg-Landau equations (amplitude equations) characterizing the slow evolution of the lamellae. The stability of the grain boundary configuration has been examined, and our results show that the boundary width, albeit varying with twist angle, is of order epsilon-1/4 , with epsilon the measure of the distance to the order-disorder threshold. We also study the motion of twist grain boundaries subjected to slow transverse modulations of lamellae, and obtain both analytically and numerically the traveling velocity of the boundary as well as its dependence on modulation wavenumber.

<p> There is an interest in producing accurate and reliable computer simulations to predict the dynamic behavior of heterogeneous materials and to use these simulations to gain further insight into experimental results. In so doing, a more complete understanding of the multiple-length scales involved in heterogeneous material compaction can be obtained. Mesoscale computer simulations of dynamically shocked materials have proven to be a beneficial resource in unraveling data not observed in planar shock impact experiments, such as stress and temperature interactions between grains. </p><p> The modeled mono-dispersed geometry of particles, the densities of each material, equations of state, material properties and many other factors affect the simulated outcomes. By studying and analyzing these variables, many of which highlight the difference between experimental and simulated results, there manifests additional insight into the shock dynamics of the different heterogeneous granular materials. The heterogeneous materials in this study were created both by a "shake and pack" method, where individual grains were randomly seeded into the computational domain and grown until the grains matched the experimental volume fraction and average diameter. </p><p> Three planar shock experiments were utilized to validate simulation models and parameters: 1. Brake pad powder compaction at Marquette University, 2. Dry sand experiments at Georgia Tech, and 3. Release of dry sand at Cambridge University. Planar shock impact experiments were simulated using two different hydrocode packages: CTH and iSALE. Validated models are then used to setup future dry, water, and possible ice saturated sand release experiments. Particle velocity and stress traces obtained from the computer simulations were compared to VISAR, PDV, and Manganin gage measurements obtained from experiments. The results from simulations are compared to experiments and discussed in this document.</p>

<p> We study quantum theory as an example of entropic inference. Our goal is to remove conceptual difficulties that arise in quantum mechanics. Since probability is a common feature of quantum theory and of any inference problem, we briefly introduce probability theory and the entropic methods to update probabilities when new information becomes available. Nelson's stochastic mechanics and Caticha's derivation of quantum theory are discussed in the subsequent chapters. </p><p> Our first goal is to understand momentum and angular momentum within an entropic dynamics framework and to derive the corresponding uncertainty relations. In this framework momentum is an epistemic concept &ndash; it is not an attribute of the particle but of the probability distributions. We also show that the Heisenberg's uncertainty relation is an osmotic effect. Next we explore the entropic analog of angular momentum. Just like linear momentum, angular momentum is also expressed in purely informational terms. </p><p> We then extend entropic dynamics to curved spaces. An important new feature is that the displacement of a particle does not transform like a vector. It involves second order terms that account for the effects of curvature . This leads to a modified Schr&ouml;dinger equation for curved spaces that also take into account the curvature effects. We also derive Schrodinger equation for a charged particle interacting with external electromagnetic field on general Riemannian manifolds. </p><p> Finally we develop the entropic dynamics of a particle of spin 1/2. The particle is modeled as a rigid point rotator interacting with an external EM field. The configuration space of such a rotator is <i>R</i>³ &times; <i>S</i>³ (<i>S</i>³ is the 3-sphere). The model describes the regular representation of <i>SU</i>(2) which includes all the irreducible representations (spin 0, 1/2, 1, 3/2,...) including spin 1/2.</p>

<p> It is shown that at sufficiently large radii dark energy modifies the behavior of (a) bound orbits around a galaxy, and (b) virialized gas in a cluster of galaxies. In (a), there exists a maximum circular orbit beyond which periodic motion is no longer possible, and the evolution of orbits near critical binding is analytically calculable using an adiabatic invariant integral. The finding may have application to wide galaxy pairs. In (b), dark energy necessitates the use of the generalized Virial Theorem to describe gas at the outskirts of a cluster. As a result, gas at a radius of 4 Mpc or above will readily escape. A simple model indicates that this mechanism can lead to mass loss via an outflow.</p>

<p> Cohorts of 48 entering biological science majors was recruited in the fall of 2007 and again in 2008 and 2009 for the Interdisciplinary Science Experience (ISE). These ISE students enrolled in their own sections of standard courses of physics, chemistry, and biology. In these courses average ISE student out-performed their non-cohort peers by up to a full letter grade. A qualitative analysis of ISE student interviews illuminates the student experience and shows how the ISE students perceived themselves to be different than their non-cohort peers. Quantitative modeling of student performance shows that higher grades are correlated with multiple factors. These factors includes admissions characteristics such as high school GPA, and SAT scores, as well as demographic information. These trends support and elaborate on the selection narratives told by participants. Additionally the quantitative model found that higher student performance is predicted by structural aspects of the ISE program, specifically the timing of course, enrolling as a freshmen in many of their courses, and the sequencing of physics and chemistry courses. There is a statistically significant benefit to student performance in general and organic chemistry courses associated with completing the first quarter of the Physics for Bio-Science majors prior to enrollment. Further the combination of quantitative and qualitative data suggest that there is a epistemological transfer of problem solving skills and outlook from the physics to the chemistry courses.</p>

<p> Earthquakes are among the most devastating natural events faced by society. In 2011, just two events, the magnitude 6.3 earthquake in Christcurch New Zealand on February 22, and the magnitude 9.0 T&omacr;hoku earthquake off the coast of Japan on March 11, caused a combined total of $226 billion in economic losses. Over the last decade, 791,721 deaths were caused by earthquakes. Yet, despite their impact, our ability to accurately predict when earthquakes will occur is limited. This is due, in large part, to the fact that the fault systems that produce earthquakes are non-linear. The result being that very small differences in the systems now result in very big differences in the future, making forecasting difficult. In spite of this, there are patterns that exist in earthquake data. These patterns are often in the form of frequency-magnitude scaling relations that relate the number of smaller events observed to the number of larger events observed. In many cases these scaling relations show consistent behavior over a wide range of scales. This consistency forms the basis of most forecasting techniques. However, the utility of these scaling relations is limited by the size of the earthquake catalogs which, especially in the case of large events, are fairly small and limited to a few 100 years of events.</p><p> In this dissertation I discuss three areas of earthquake science. The first is an overview of scaling behavior in a variety of complex systems, both models and natural systems. The focus of this area is to understand how this scaling behavior breaks down. The second is a description of the development and testing of an earthquake simulator called Virtual California designed to extend the observed catalog of earthquakes in California. This simulator uses novel techniques borrowed from statistical physics to enable the modeling of large fault systems over long periods of time. The third is an evaluation of existing earthquake forecasts, which focuses on the Regional Earthquake Likelihood Models (RELM) test: the first competitive test of earthquake forecasts in California.</p>

<p> QPOs (Quasi-Periodic Oscillations) are time oscillations that appear in the light curve of observational data in x-ray bands. They are of mysterious origin although they are believed to be a result of the intense gravity around neutron stars and black holes and emit x-rays from accretion disks. I investigate a derived ratio between two periods has been found in the QPO data. The two periods, which appear as peaks in the power density spectrum have been found to be in a 3:2 ratio and can possibly distinguish theoretical models. In the work presented here, two physical approaches are developed that can explain the integer resonance ratio. One is a cusp layer model, which is based on a boundary layer model that uses the physical conditions at opposite sides of said layer to explore the magnitude of the vertical versus radial epicyclic frequencies and confirm the anticipated scales of the observed frequencies. It also happens to recreate a 3:2 resonance ratio for the Keplerian angular frequencies at the ISCO, taken as the preferred radius for the boundary layer model. </p><p> A toy model was recreated and utilized to emulate the Alfven radius due to the accretion disk's innate magnetic field and explore how it serves as a disruption radius and impacts the accretion of mass and the effective inner edge of the disk. The simulations show that there is no significance deviation from the ISCO as an effective inner edge for the accretion disk due to the magnetospheric influence of the disk alone. </p><p> I also invoke a parameter to handle the coupling between the vertical and radial epicyclical frequencies and relate it to the pressure within the disk. I show the coupling is strongest at the equatorial plane where pressure is at its maximum value. </p><p> A model I utilize is a relativistic resonance model, combined with a helioseismological approach to explore the pulsation of the inner edge of the accretion disk that imparts the resonance of the accreting matter moving along the Kerr space-time orbits. The helioseismological model gives a characteristic frequency for small perturbations in the stellar matter within the atmosphere of a star. The diskoseismological model extends that principle to material within an accretion disk. I take it to the same extent that the QPO frequencies are due to small perturbations along the marginally stable circular orbit, in the vertical and radial directions and use it as a probe into the inner disk and what information it yields. The inner disk edge, per the model, is treated as a vibrating surface that yields the radial and vertical epicyclic frequencies as characteristic features of the vibration. The epicyclical frequencies found using the physical parameters of the model within the cusp layer inside the disk could explain the physical context of the phenomenon responsible for the creation of the QPOs. An approach within the diskoseismological model uses the cylindrical reference frame of a disk in terms of the distribution of mass in combination with the strong gravity of the central object and the Keplerian velocity and sonic speed to yield a natural resonance ratio of 3/2 as well. </p><p> The model can be used as a diagnostic tool to explore the physical phenomena of the material orbits and the disk itself. Most importantly, the model can be used to determine and constrain the ratio of spin to mass of the compact object itself. It yields new information as previously undetermined by any earlier model; the adiabatic index at a specific radius within the accretion disk, which serves to lend insight into the innate phenomena of accretion disks at large. It establishes what were previously unknown information, such as the mass density distribution at a specific radius and outward, the radius of influence in terms of the sonic radius, the accretion rate, and the temperature distribution at the same radius for the accretion disk, as all are dependent on the adiabatic index. In all previous literature, the adiabatic index is taken as an assumptive estimate, and the models build on that assumed value of the adiabatic index. This model allows us to obtain an actual value of the adiabatic index at the ISCO and use it as an establishing feature to refine models on for more physically realistic observations.</p>

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. / Source: Dissertation Abstracts International, Volume: 68-11, Section: B, page: 7409. Adviser: Alfred Hubler. Includes bibliographical references (leaves 77-83) Available on microfilm from Pro Quest Information and Learning.