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

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

The Eleventh Circuit\u27s First Decade Contribution to the Law of the Nation, 1981-1991

Likewise, the task of commentary is difficult. The period covered here-the first decade of the Eleventh Circuit-represents, quite literally and figuratively, the formative era of the court. Indeed, the volume of decisions and their variety are qualities that ought to humble, if not intimidate, most commentators. Justice Holmes once observed that a common law court could be expected to replicate the entire corpus juris in the space of a single generation. The Eleventh Circuit did this consciously between 1981 and 1991. In Bonner v. City of Prichard, the inaugural en banc court held that the new court-just cleaved from the former Fifth Circuit-would deem itself bound by the precedents of the old court. Of course, any transfused precedent of the Fifth Circuit or any subsequent decision of the new Eleventh Circuit is subject to reconsideration by the en banc court