Jacobi Elliptic Functions and the Complete Solution to the Bead on the Hoop Problem

Jacobi elliptic functions are flexible functions that appear in a variety of problems in physics and engineering. We introduce and describe important features of these functions and present a physical example from classical mechanics where they appear: a bead on a spinning hoop. We determine the complete analytical solution for the motion of a bead on the driven hoop for arbitrary initial conditions and parameter values.Comment: Accepted for publication in American Journal of Physics. 9 pages, 6 figure

Thermal stress analysis of ceramic gas-path seal components for aircraft turbines

Stress and temperature distributions were evaluated numerically for a blade-tip seal system proposed for gas turbine applications. The seal consists of an abradable ceramic layer on metallic backing with intermediate layers between the ceramic layer and metal substrate. The most severe stresses in the seal, as far as failure is concerned, are tensile stresses at the top of the ceramic layer and shear and normal stresses at the layer interfaces. All these stresses reach their maximum values during the deceleration phase of a test engine cycle. A parametric study was carried out to evaluate the influence of various design parameters on these critical stress values. The influences of material properties and geometric parameters of the ceramic, intermediate, and backing layers were investigated. After the parametric study was completed, a seal system was designed which incorporated materials with beneficial elastic and thermal properties in each layer of the seal. An analysis of the proposed seal design shows an appreciable decrease in the magnitude of the maximum critical stresses over those obtained with earlier configurations

Cascading Proximity Effects in Rotating Magnetizations

We demonstrate two effects that occur in all diffusive superconducting-magnetic heterostructures with rotating magnetization: the reappearance of singlet $|0,0>$ correlations deep in the magnetic material and a cascade of $s=1$, $m=0, \pm 1$ components (in the two spin-$1/2$ basis $|s,m>$). We do so by examining the order parameter and Josephson current through a multilayer with five mutually perpendicular ferromagnets. The properties of the middle layer determine whether the current is due to $m=0$ or $m\neq 0$ contributions. We conclude that so-called long- and short-range components are present across a proximity system with rotating magnetization.Comment: 5 pages, 4 figure

What Matters Most? A Survey of Accomplished Middle-Level Educators\u27 Beliefs and Values about Literacy

Ninety teachers working in award-winning middle schools responded to a survey that explored, quantitatively and qualitatively, how they (1) defined themselves as teachers of literacy, (2) viewed multiliteracies in adolescents\u27 lives, and (3) valued these literacies in the classroom. Mean scores indicated that Basic Literacies (e.g., comprehension, word identification, fluency, writing) were rated more favorably than New Literacies (e.g., media, Internet, critical, out of school). Strong qualitative support existed for literacy instruction in all disciplines, but interpretations varied. The most positive agreement centered on every teacher being a teacher of literacy. Little support existed for developing students\u27 out-of-school literacies in schools. Such findings have strong implications for altering curricular emphases and merging teacher practice with adolescents\u27 needs and interests