Energies of knot diagrams

We introduce and begin the study of new knot energies defined on knot diagrams. Physically, they model the internal energy of thin metallic solid tori squeezed between two parallel planes. Thus the knots considered can perform the second and third Reidemeister moves, but not the first one. The energy functionals considered are the sum of two terms, the uniformization term (which tends to make the curvature of the knot uniform) and the resistance term (which, in particular, forbids crossing changes). We define an infinite family of uniformization functionals, depending on an arbitrary smooth function $f$ and study the simplest nontrivial case $f(x)=x^2$, obtaining neat normal forms (corresponding to minima of the functional) by making use of the Gauss representation of immersed curves, of the phase space of the pendulum, and of elliptic functions

A Chandra Study of the Effects of a Major Merger on the Structure of Abell 2319

We present an analysis of a Chandra observation of the massive, nearby galaxy cluster Abell 2319. A sharp surface brightness discontinuity--suggested by previous, lower angular resolution X-ray imaging--is clearly visible in the ACIS image. This roughly 300kpc feature suggests that a major merger is taking place with a significant velocity component perpendicular to the line of sight. The cluster emission-weighted mean temperature is 11.8+/-0.6kev, somewhat higher than previous temperature measurements. The Chandra temperature map of A2319 reveals substructure resembling that anticipated based on hydrodynamic simulations of cluster mergers. The merger feature shows a pressure change across the surface brightness discontinuity by a factor of <=2.5. The higher density side of the front has a lower temperature, suggesting the presence of a cold front similar to those in many other merging clusters. The velocity of the front is roughly sonic. We compare bulk properties of the ICM and galaxies in A2319 to the same properties in a large sample of clusters as a way of gauging the effects of the major merger. Interestingly, by comparing A2319 to a sample of 44 clusters studied with the ROSAT PSPC we find that the X-ray luminosity, isophotal size, and ICM mass are consistent with the expected values for a cluster of its temperature; in addition, the K-band galaxy light is consistent with the light--temperature scaling relation derived from a sample of about 100 clusters studied with 2MASS. Together, these results indicate either that the merger in A2319 has not been effective at altering the bulk properties of the cluster, or that there are large but correlated displacements in these quantities.Comment: 11 pages, 8 figures, ApJ Submitte

Auger decay, Spin-exchange, and their connection to Bose-Einstein condensation of excitons in Cu_2O

In view of the recent experiments of O'Hara, et al. on excitons in Cu_2O, we examine the interconversion between the angular-momentum triplet-state excitons and the angular-momentum singlet-state excitons by a spin-exchange process which has been overlooked in the past. We estimate the rate of this particle-conserving mechanism and find a substantially higher value than the Auger process considered so far. Based on this idea, we give a possible explanation of the recent experimental observations, and make certain predictions, with the most important being that the singlet-state excitons in Cu_2O is a very serious candidate for exhibiting the phenomenon of Bose-Einstein condensation.Comment: 4 pages, RevTex, 1 ps figur

Pure Gas of Optically Trapped Molecules Created from Fermionic Atoms

We report on the production of a pure sample of up to 3x10^5 optically trapped molecules from a Fermi gas of 6Li atoms. The dimers are formed by three-body recombination near a Feshbach resonance. For purification a Stern-Gerlach selection technique is used that efficiently removes all trapped atoms from the atom-molecule mixture. The behavior of the purified molecular sample shows a striking dependence on the applied magnetic field. For very weakly bound molecules near the Feshbach resonance, the gas exhibits a remarkable stability with respect to collisional decay.Comment: 4 pages, 5 figure

The infant with bilateral skull fractures: diagnostic considerations in consultation with a child abuse pediatrician

Bilateral skull fractures in infancy may result from accidental or abusive injury. Consultation with a child abuse pediatrician may assist with determining the likelihood of accident or abuse. Diagnostic considerations for the infant with bilateral skull fractures are reviewed, including single impact, double impact, and compression mechanisms of injury, as well as the possibility of accessory sutures as skull fracture mimics. Illustrative cases exemplify the evaluative process, including obtaining a detailed history, assessing for the presence or absence of additional physical or radiographic signs of injury, screening for psychosoical risk, and obtaining three-dimensional reconstruction of CT bone images. An understanding of plausible mechanisms of injury that can result in bilateral skull fractures in infancy can assist with making an accurate determination of likelihood of accident or abuse

Efficient and robust initialization of a qubit register with fermionic atoms

We show that fermionic atoms have crucial advantages over bosonic atoms in terms of loading in optical lattices for use as a possible quantum computation device. After analyzing the change in the level structure of a non-uniform confining potential as a periodic potential is superimposed to it, we show how this structure combined with the Pauli principle and fermion degeneracy can be exploited to create unit occupancy of the lattice sites with very high efficiency.Comment: 4 pages, 3 figure