Asymptotics of Clebsch-Gordan Coefficients

Asymptotic expressions for Clebsch-Gordan coefficients are derived from an exact integral representation. Both the classically allowed and forbidden regions are analyzed. Higher-order approximations are calculated. These give, for example, six digit accuracy when the quantum numbers are in the hundreds.Comment: 30 pages, two figures. New Appendix added. Accepted for publication in the Journal of Mathematical Physic

History of Nazareth United Methodist Church, Westminster, SC

Narrative history of Nazareth United Methodist Church from the 1890s to 1971, including list of members, ministers, memorials, the budget for 1972, significant events, and officers for 1972.https://digitalcommons.wofford.edu/methodistbooks/1010/thumbnail.jp

Two 120-Meter-Tall Meteorological Towers in Central Iowa: A Statistical Overview of Wind Turbine Influence

Tower data from two towers in Central Iowa are used to study tower biases and to observe if there is a wind turbine influence. Using statistical analysis to identify if there is a clear observation of one tower warmer or colder at levels based on conditions of the wind turbine influence. By highlighting outliers of large temperature gradients between the towers, this can identify how the meteorological towers respond to the passages of large frontal passages and other synoptic conditions. Evidence in some cases of turbine influence includes warming of a layer at night, correspondingly a cooling during the day. Unmixed/Undisturbed regions of the wind field show little difference of temperature between the towers

Demonstration of superluminal effects in an absorptionless, non-reflective system

We present an experimental and theoretical study of a simple, passive system consisting of a birefringent, two-dimensional photonic crystal and a polarizer in series, and show that superluminal dispersive effects can arise even though no incident radiation is absorbed or reflected. We demonstrate that a vector formulation of the Kramers-Kronig dispersion relations facilitates an understanding of these counter-intuitive effects.Comment: 6 pages, 3 figures, accepted on Physical Review Letter

Combustion Stability Characteristics of the Project Morpheus Liquid Oxygen/Liquid Methane Main Engine

The Project Morpheus liquid oxygen (LOX) / liquid methane rocket engines demonstrated acousticcoupled combustion instabilities during sealevel groundbased testing at the NASA Johnson Space Center (JSC) and Stennis Space Center (SSC). Highamplitude, 1T, 1R, 1T1R (and higher order) modes appear to be triggered by injector conditions. The instability occurred during the Morpheusspecific engine ignition/start sequence, and did demonstrate the capability to propagate into mainstage. However, the instability was never observed to initiate during mainstage, even at low power levels. The Morpheus main engine is a JSCdesigned ~5,000 lbfthrust, 4:1 throttling, pressurefed cryogenic engine using an impinging element injector design. Two different engine designs, named HD4 and HD5, and two different builds of the HD4 engine all demonstrated similar instability characteristics. Through the analysis of more than 200 hot fire tests on the Morpheus vehicle and SSC test stand, a relationship between ignition stability and injector/chamber pressure was developed. The instability has the distinct characteristic of initiating at high relative injection pressure drop (dP) at low chamber pressure (Pc); i.e., instabilities initiated at high dP/Pc at low Pc during the start sequence. The high dP/Pc during start results during the injector /chamber chillin, and is enhanced by hydraulic flip in the injector orifice elements. Because of the fixed mixture ratio of the existing engine design (the main valves share a common actuator), it is not currently possible to determine if LOX or methane injector dP/Pc were individual contributors (i.e., LOX and methane dP/Pc typically trend in the same direction within a given test). The instability demonstrated initiation characteristic of starting at or shortly after methane injector chillin. Colder methane (e.g., subcooled) at the injector inlet prior to engine start was much more likely to result in an instability. A secondary effect of LOX subcooling was also possibly observed; greater LOX sub cooling improved stability. Some tests demonstrated a lowamplitude 1L1T instability prior to LOX injector chillin. The Morpheus main engine also demonstrated chug instabilities during some engine shutdown sequences on the flight vehicle and SSC test stand. The chug instability was also infrequently observed during the startup sequence. The chug instabilities predictably initiated at low dP/Pc at low Pc. The chug instabilities were always selflimiting; startup chug instabilities terminated during throttleup and shutdown chug instabilities decayed by shutdown termination

Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen

A systematic semiclassical expansion of the hydrogen problem about the classical Kepler problem is shown to yield remarkably accurate results. Ad hoc changes of the centrifugal term, such as the standard Langer modification where the factor l(l+1) is replaced by (l+1/2)^2, are avoided. The semiclassical energy levels are shown to be exact to first order in $\hbar$ with all higher order contributions vanishing. The wave functions and dipole matrix elements are also discussed.Comment: 5 pages, to appear in Phys. Rev.

Thyroid Lymphoma as a Cause of Dysphagia and Dyspnea in a Patient without Palpable Nodules or Goiter

Tumors originating in the neck are well-known causes of progressive dysphagia and dyspnea (including stridor), and thyroid lymphoma is an uncommon example. Physical examination provides an important first step in the evaluation of such complaints, as tumors large enough to produce such symptoms are typically considered to be palpable, if not able to be seen grossly. In this case presentation, the authors describe a nonsubsternal thyroid lymphoma measuring 3 × 4 cm at its largest diameter, producing dysphagia and leading to respiratory emergency, that was entirely nonpalpable to physical exam even after confirmation of its presence by computed tomography