Direct Scattering for the Benjamin-Ono Equation with Rational Initial Data

We compute the scattering data of the Benjamin-Ono equation for arbitrary rational initial conditions with simple poles. Specifically, we obtain explicit formulas for the Jost solutions and eigenfunctions of the associated spectral problem, yielding an Evans function for the eigenvalues and formulas for the phase constants and reflection coefficient.Comment: 16 Pages, 2 Figure

Increasing Returns to Education and Progress towards a College Degree

Returns to college have increased, but graduation rates have changed relatively little. Modifying a human capital model of college enrollment to endogenize time-to-graduation, we predict that higher returns to education will both speed graduation and increase enrollment. Some of those new entrants may, however, take longer to graduate. Using the 1989 and 1995 Beginning Postsecondary Studies, we employ a multinomial logit to model the association between individual and family characteristics, and five-year college outcomes: graduation, continued enrollment, and non-enrollment. Between cohort differences arise either because the characteristics of those entering college are different or because the relations between characteristics and outcomes have changed. We utilize a Oaxaca-Blinder style decomposition to distinguish between these two alternatives, attributing differences in characteristics to newly attracted students and differences in the relations between characteristics and outcomes to historically attracted students behaving differently. It is changes in behavior that explain the increased progress we observe.Higher Education, Graduation Rates, Persistence

Reported Progress under the Student Right-to-Know Act: How Reliable is It?

The Student Right-to-Know Act requires colleges to provide institution-specific information on graduation rates for students initially enrolling full-time in the fall term. Not all students enroll in that fashion, especially at two-year institutions. We use data on degree-seeking students from the 1996/2001 Beginning Post-Secondary Survey to identify students for whom statistics are and are not reportable under the Act and to track their progress. Results indicate the published progress rates are substantially higher than the progress rates for the non-reportable populations, whether students enter a two-year or a four-year institution. While progress rates for the two samples are significantly correlated within four-year institutions, they are not within two-year institutions. For those beginning at two-year institutions, the progress rates reported under the Student Right-to-Know Act are indicative of neither their absolute nor their relative (cross-institution) probability of success. Policy makers and prospective students will not make efficient decisions without better information.Efficiency, Resource Allocation, Graduation

Three Stratified Fluid Models: Benjamin-Ono, Tidal Resonance, and Quasi-Geostrophy.

In this dissertation, we study three models arising in stratified fluid dynamics: the Benjamin-Ono equation, a two-layer tidal model, and the quasi-geostrophic equations. First, we compute the scattering data of the Benjamin-Ono equation for arbitrary rational initial conditions with simple poles, under mild restrictions. For this class of initial conditions, we are able to obtain explicit formulas for the Jost solutions and eigenfunctions of the associated spectral problem, yielding an Evans function for the eigenvalues and formulas for the phase constants and reflection coefficient. We proceed to use these exact formulas to deduce precise asymptotics for the reflection coefficient, the location of the eigenvalues and their density, and the asymptotic dependence of the phase constant on the eigenvalue. Second, we present a simplified analytical tidal model that demonstrates the influence of stratification on both large- and small-scale surface tidal elevations in a qualitatively similar manner as in previous global realistic-domain numerical simulations. Our analytical results demonstrate the potential for the presence of stratification and changes to stratification to alter the large-scale (barotropic) tide. We find that changes in stratification may change large-scale tidal elevations at the same order as small-scale tidal elevations if there is significant bottom topography and the damping acts primarily on the bottom layer. Third, we investigate the influence of bottom friction on quasi-geostrophic turbulence dynamics in a multi-level forced-dissipated model that includes buoyancy advection at the boundaries. Motivated by earlier studies of two-layer quasi-geostrophic turbulence, we study the influence of bottom friction on the horizontal scales and vertical structure of eddy kinetic energy with the aid of a ‘surface-aware’ modal decomposition.PhDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/116662/1/wreagan_1.pd

The Effects of Storage Conditions and Time on Extracted Ignitable Liquids

In arson investigation, the presence of ignitable liquid is important in determining intent. In some cases, extracts of fire debris recovered from the scene must be stored for later analysis; though little is known about how to properly store extracted samples while upholding analytical integrity over time. Three petroleum distillates were selected as samples and extracted onto activated charcoal strips using a passive headspace method. Samples were transferred to a nylon fire debris bag or PTFE-lined glass vial. Once contained, samples were stored at room temperature or refrigerated for 3, 6, and 9 months then analyzed using gas chromatography mass spectrometry. Analysis was performed through compound identification according to ASTM protocol by utilizing the NIST Mass Spectral database. Comparisons were made between all variables noting any loss of compounds. This research indicates a limited difference in compound retention over time between nylon fire debris bag and PTFE-lined glass vial

Hydrological connectivity inferred from diatom transport through the riparian-stream system

Funding for this research was provided by the Luxembourg National Research Fund (FNR) in the framework of the BIGSTREAM (C09/SR/14), ECSTREAM (C12/SR/40/8854) and CAOS (INTER/DFG/11/01) projects. We are most grateful to the Administration des Services Techniques de l’Agriculture (ASTA) for providing meteorological data. We also acknowledge Delphine Collard for technical assistance in diatom sample treatment and preparation, François Barnich for the water chemistry analyses, and Jean-François Iffly, Christophe Hissler, Jérôme Juilleret, Laurent Gourdol and Julian Klaus for their constructive comments on the project and technical assistance in the field.Peer reviewedPublisher PD

The role of cerebral edema in ischemic cerebral neuropathy after cardiac arrest in dogs and monkeys and its treatment with hypertonic urea

1. 1. The value of hypertonic urea in forestalling the neurologic sequellae after cardiac arrest has been assessed in dogs and monkeys. Simulated cardiac arrest was produced with an inflow-outflow occlusion technique in which the blood supply to the heart was maintained during the period of complete cerebral ischemia. 2. 2. A number of factors increase the duration of cardiac arrest which can be tolerated without gross neurologic sequellae. These include the presence of an effective circulatory state before and after the arrest, the administration of 100 per cent oxygen before and after the test period, the use of an efficient respirator, and avoidance of premature efforts to promote spontaneous respirations postoperatively. 3. 3. Under optimum conditions almost all dogs and monkeys will recover completely after 12 minutes of simulated cardiac arrest. With longer occlusions, death and serious neurologic morbidity occur. 4. 4. Monkeys and dogs were subjected to simulated cardiac arrest for 14 minutes. Hypertonic urea did not materially decrease either the mortality rate or neurologic morbidity in either species, as compared to the recovery rate in controls, despite the fact that the urea-treated animals had demonstrably less brain swelling. 5. 5. From this it is concluded that cerebral edema is an overemphasized factor in the post-cardiac arrest syndrome, and that the principal deterrent to recovery is anoxic injury to the neurons which is not beneficially influenced by reduction of brain volume. © 1960

Modelling chemical abundance distributions for dwarf galaxies in the Local Group: the impact of turbulent metal diffusion

We investigate stellar metallicity distribution functions (MDFs), including Fe and ${\alpha}$-element abundances, in dwarf galaxies from the Feedback in Realistic Environments (FIRE) project. We examine both isolated dwarf galaxies and those that are satellites of a Milky Way-mass galaxy. In particular, we study the effects of including a sub-grid turbulent model for the diffusion of metals in gas. Simulations that include diffusion have narrower MDFs and abundance ratio distributions, because diffusion drives individual gas and star particles toward the average metallicity. This effect provides significantly better agreement with observed abundance distributions of dwarf galaxies in the Local Group, including the small intrinsic scatter in [${\alpha}$/Fe] vs. [Fe/H] (less than 0.1 dex). This small intrinsic scatter arises in our simulations because the interstellar medium (ISM) in dwarf galaxies is well-mixed at nearly all cosmic times, such that stars that form at a given time have similar abundances to within 0.1 dex. Thus, most of the scatter in abundances at z = 0 arises from redshift evolution and not from instantaneous scatter in the ISM. We find similar MDF widths and intrinsic scatter for satellite and isolated dwarf galaxies, which suggests that environmental effects play a minor role compared with internal chemical evolution in our simulations. Overall, with the inclusion of metal diffusion, our simulations reproduce abundance distribution widths of observed low-mass galaxies, enabling detailed studies of chemical evolution in galaxy formation.Comment: 19 pages, 13 figures, published in MNRA