The stable braid group and the determinant of the Burau representation

This article gives certain fibre bundles associated to the braid groups which are obtained from a translation as well as conjugation on the complex plane. The local coefficient systems on the level of homology for these bundles are given in terms of the determinant of the Burau representation. De Concini, Procesi, and Salvetti [Topology 40 (2001) 739--751] considered the cohomology of the n-th braid group B_n with local coefficients obtained from the determinant of the Burau representation, H^*(B_n;Q[t^{+/-1}]). They show that these cohomology groups are given in terms of cyclotomic fields. This article gives the homology of the stable braid group with local coefficients obtained from the determinant of the Burau representation. The main result is an isomorphism H_*(B_infty; F[t^{+/-1}])-->H_*(Omega^2S^3; F) for any field F where Omega^2S^3 denotes the double loop space of the 3-connected cover of the 3-sphere. The methods are to translate the structure of H_*(B_n;F[t^{+/-1}]) to one concerning the structure of the homology of certain function spaces where the answer is computed.Comment: This is the version published by Geometry & Topology Monographs on 29 January 200

The Detailed Chemical Abundance Patterns of M31 Globular Clusters

We present detailed chemical abundances for $>$20 elements in $\sim$30 globular clusters in M31. These results have been obtained using high resolution ($\lambda/\Delta\lambda\sim$24,000) spectra of their integrated light and analyzed using our original method. The globular clusters have galactocentric radii between 2.5 kpc and 117 kpc, and therefore provide abundance patterns for different phases of galaxy formation recorded in the inner and outer halo of M31. We find that the clusters in our survey have a range in metallicity of $-2.2<$[Fe/H]$<-0.11$. The inner halo clusters cover this full range, while the outer halo globular clusters at R$>$20 kpc have a small range in abundance of [Fe/H]$=-1.6 \pm 0.10$. We also measure abundances of alpha, r- and s-process elements. These results constitute the first abundance pattern constraints for old populations in M31 that are comparable to those known for the Milky Way halo.Comment: XII International Symposium on Nuclei in the Cosmos August 5-12, 2012 Cairns, Australia. To appear in Proceedings of Scienc

Large Magnetic Fields and Motions of OH Masers in W75 N

We report on a second epoch of VLBA observations of the 1665 and 1667 MHz OH masers in the massive star-forming region W75 N. We find evidence to confirm the existence of very strong (~40 mG) magnetic fields near source VLA 2. The masers near VLA 2 are dynamically distinct and include a very bright spot apparently moving at 50 km/s relative to those around VLA 1. This fast-moving spot may be an example of a rare class of OH masers seen in outflows in star-forming regions. Due to the variability of these masers and the rapidity of their motions, tracking these motions will require multiple observations over a significantly shorter time baseline than obtained here. Proper motions of the masers near VLA 1 are more suggestive of streaming along magnetized shocks rather than Keplerian rotation in a disk. The motions of the easternmost cluster of masers in W75 N (B) may be tracing slow expansion around an unseen exciting source.Comment: 7 pages including 4 figures (2 color) & 3 tables, to appear in Ap

Diffractive energy spreading and its semiclassical limit

We consider driven systems where the driving induces jumps in energy space: (1) particles pulsed by a step potential; (2) particles in a box with a moving wall; (3) particles in a ring driven by an electro-motive-force. In all these cases the route towards quantum-classical correspondence is highly non-trivial. Some insight is gained by observing that the dynamics in energy space, where $n$ is the level index, is essentially the same as that of Bloch electrons in a tight binding model, where $n$ is the site index. The mean level spacing is like a constant electric field and the driving induces long range hopping 1/(n-m).Comment: 19 pages, 11 figs, published version with some improved figure

Study of transition temperatures in superconductors Final report, 11 Mar. 1968 - 10 Mar. 1970

Thermodynamic and electrical properties of niobium stannide and other superconductor