Reshetikhin's Formula for the Jones Polynomial of a Link: Feynman diagrams and Milnor's Linking Numbers

We use Feynman diagrams to prove a formula for the Jones polynomial of a link derived recently by N.~Reshetikhin. This formula presents the colored Jones polynomial as an integral over the coadjoint orbits corresponding to the representations assigned to the link components. The large $k$ limit of the integral can be calculated with the help of the stationary phase approximation. The Feynman rules allow us to express the phase in terms of integrals over the manifold and the link components. Its stationary points correspond to flat connections in the link complement. We conjecture a relation between the dominant part of the phase and Milnor's linking numbers. We check it explicitly for the triple and quartic numbers by comparing their expression through the Massey product with Feynman diagram integrals.Comment: 33 pages, 11 figure

Spray coating apparatus having a rotatable workpiece holder

A spray coating apparatus is provided for rotating a workpiece relative to a spray station to obtain a uniform coating of the workpiece. In a typical example, the workpiece comprises a ceramic tile which is to be coated with a ceramic coating and the tile is to be used as a reusable component of the thermal protection system for a space shuttle. The apparatus for rotating the workpiece includes a base support having a first rotatable stage for rotation in the horizontal plane and a second rotatable stage for rotation in a second plane inclined at an angle, such as 45 degrees, to the horizontal plane and the workpiece is supported on this second stage. Thus the workpiece is rotatable in both of two planes of rotation

Very High Energy Gamma Rays from Supernova Remnants and Constraints on the Galactic Interstellar Radiation Field

The large-scale Galactic interstellar radiation field (ISRF) is the result of stellar emission and dust re-processing of starlight. Where the energy density of the ISRF is high (e.g., the Galactic Centre), the dominant gamma-ray emission in individual supernova remnants (SNRs), such as G0.9+0.1, may come from inverse Compton (IC) scattering of the ISRF. Several models of the ISRF exist. The most recent one, which has been calculated by us, predicts a significantly higher ISRF than the well-used model of Mathis, Mezger, and Panagia. However,comparison with data is limited to local observations. Based on our current estimate of the ISRF we predict the gamma-ray emission in the SNRs G0.9+0.1 and RXJ1713, and pair-production absorption features above 20 TeV in the spectra of G0.9+0.1, J1713-381, and J1634-472. We discuss how GLAST, along with current and future very high energy instruments, may be able to provide upper bounds on the large-scale ISRF.Comment: To appear in the proceedings of the 1st GLAST Symposiu

Sensitivity of Building Loss Estimates to Major Uncertain Variables

This paper examines the question of which sources of uncertainty most strongly affect the repair cost of a building in a future earthquake. Uncertainties examined here include spectral acceleration, ground-motion details, mass, damping, structural force-deformation behavior, building-component fragility, contractor costs, and the contractor's overhead and profit. We measure the variation (or swing) of the repair cost when each basic input variable except one is taken at its median value, and the remaining variable is taken at its 10th and at its 90th percentile. We perform this study using a 1960s highrise nonductile reinforced-concrete moment-frame building. Repair costs are estimated using the assembly-based vulnerability (ABV) method. We find that the top three contributors to uncertainty are assembly capacity (the structural response at which a component exceeds some damage state), shaking intensity (measured here in terms of damped elastic spectral acceleration, Sa), and details of the ground motion with a given Sa

Inverse Compton scattering on solar photons, heliospheric modulation, and neutrino astrophysics

We study the inverse Compton scattering of solar photons by Galactic cosmic-ray electrons. We show that the gamma-ray emission from this process is substantial with the maximum flux in the direction of the Sun; the angular distribution of the emission is broad. This previously-neglected foreground should be taken into account in studies of the diffuse Galactic and extragalactic gamma-ray emission. Furthermore, observations by GLAST can be used to monitor the heliosphere and determine the electron spectrum as a function of position from distances as large as Saturn's orbit to close proximity of the Sun, thus enabling unique studies of solar modulation. This paves the way for the determination of other Galactic cosmic-ray species, primarily protons, near the solar surface which will lead to accurate predictions of gamma rays from pp-interactions in the solar atmosphere. These albedo gamma rays will be observable by GLAST, allowing the study of deep atmospheric layers, magnetic field(s), and cosmic-ray cascade development. The latter is necessary to calculate the neutrino flux from pp-interactions at higher energies (>1 TeV). Although this flux is small, it is a "guaranteed flux" in contrast to other astrophysical sources of neutrinos, and may be detectable by km^3 neutrino telescopes of the near future, such as IceCube. Since the solar core is opaque for very high-energy neutrinos, directly studying the mass distribution of the solar core may thus be possible.Comment: 4 pages, 4 figures, emulateapj.cls, final version; published in ApJ Letters, added an erratum; conclusions unchange

Giant Electron-hole Charging Energy Asymmetry in Ultra-short Carbon Nanotubes

Making full usage of bipolar transport in single-wall carbon nanotube (SWCNT) transistors could permit the development of two-in-one quantum devices with ultra-short channels. We report on clean $\sim$10 to 100 nm long suspended SWCNT transistors which display a large electron-hole transport asymmetry. The devices consist of naked SWCNT channels contacted with sections of SWCNT-under-annealed-gold. The annealed gold acts as an n-doping top gate which creates nm-sharp barriers at the junctions between the contacts and naked channel. These tunnel barriers define a single quantum dot (QD) whose charging energies to add an electron or a hole are vastly different ($e-h$ charging energy asymmetry). We parameterize the $e-h$ transport asymmetry by the ratio of the hole and electron charging energies $\eta_{e-h}$. We show that this asymmetry is maximized for short channels and small band gap SWCNTs. In a small band gap SWCNT device, we demonstrate the fabrication of a two-in-one quantum device acting as a QD for holes, and a much longer quantum bus for electrons. In a 14 nm long channel, $\eta_{e-h}$ reaches up to 2.6 for a device with a band gap of 270 meV. This strong $e-h$ transport asymmetry survives even at room temperature