On two theorems for flat, affine group schemes over a discrete valuation ring

We include short and elementary proofs of two theorems characterizing reductive group schemes over a discrete valuation ring, in a slightly more general context.Comment: 10 pages. To appear in C. E. J.

Electromagnetic waves in a Josephson junction in a thin film

We consider a one-dimensional Josephson junction in a superconducting film with the thickness that is much less than the London penetration depth. We treat an electromagnetic wave propagating along this tunnel contact. We show that the electrodynamics of a Josephson junction in a thin film is nonlocal if the wave length is less than the Pearl penetration depth. We find the integro-differential equation determining the phase difference between the two superconductors forming the tunnel contact. We use this equation to calculate the dispersion relation for an electromagnetic wave propagating along the Josephson junction. We find that the frequency of this wave is proportional to the square root of the wave vector if the wave length is less than the Pearl penetration depth.Comment: 12 pages, a figure is included as a uuencodeded postscript file, ReVTe

Modular Lie algebras and the Gelfand-Kirillov conjecture

Let g be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero. We show that if the Gelfand-Kirillov conjecture holds for g, then g has type A_n, C_n or G_2.Comment: 20 page

Chern-Simons Solitons, Toda Theories and the Chiral Model

The two-dimensional self-dual Chern--Simons equations are equivalent to the conditions for static, zero-energy solutions of the $(2+1)$-dimensional gauged nonlinear Schr\"odinger equation with Chern--Simons matter-gauge dynamics. In this paper we classify all finite charge $SU(N)$ solutions by first transforming the self-dual Chern--Simons equations into the two-dimensional chiral model (or harmonic map) equations, and then using the Uhlenbeck--Wood classification of harmonic maps into the unitary groups. This construction also leads to a new relationship between the $SU(N)$ Toda and $SU(N)$ chiral model solutions

Modeling the influence of snow cover on low Arctic net ecosystem exchange

The Arctic net ecosystem exchange (NEE) of CO2 between the land surface and the atmosphere is influenced by the timing of snow onset and melt. The objective of this study was to examine whether uncertainty in model estimates of NEE could be reduced by representing the influence of snow on NEE using remote sensing observations of snow cover area (SCA). Observations of NEE and time-lapse images of SCA were collected over four locations at a low Arctic site (Daring Lake, NWT) in May-June 2010. Analysis of these observations indicated that SCA influences NEE, and that good agreement exists between SCA derived from time-lapse images, Landsat and MODIS. MODIS SCA was therefore incorporated into the vegetation photosynthesis respiration model (VPRM). VPRM was calibrated using observations collected in 2005 at Daring Lake. Estimates of NEE were then generated over Daring Lake and Ivotuk, Alaska (2004-2007) using VPRM formulations with and without explicit representations of the influence of SCA on respiration and/or photosynthesis. Model performance was assessed by comparing VPRM output against unfilled eddy covariance observations from Daring Lake and Ivotuk (2004-2007). The uncertainty in VPRM estimates of NEE was reduced when respiration was estimated as a function of air temperature when SCA ≤ 50% and as a function of soil temperature when SCA > 50%

High quantum efficiency photon-number-resolving detector for photonic on-chip information processing

We demonstrate a high-efficiency, photon-number resolving transition edge sensor, integrated on an optical silica waveguide structure. The detector consists of three individual absorber/sensor devices providing a total system detection efficiency of up to 93% for single photons at a wavelength of 1551.9 nm. This new design enables high fidelity detection of quantum information processes in on-chip platforms

Optimization of the Strength-Fracture Toughness Relation in Particulate-Reinforced Aluminum Composites via Control of the Matrix Microstructure

The article of record as published may be found at http://dx.doi.org/10.1007/s11661-998-0119-9The evolution of the microstructure and mechanical properties of a 17.5 vol. pct SiC particulatereinforced aluminum alloy 6092-matrix composite has been studied as a function of postfabrication processing and heat treatment. It is demonstrated that, by the control of particulate distribution, matrix grain, and substructure and of the matrix precipitate state, the strength-toughness combination in the composite can be optimized over a wide range of properties, without resorting to unstable, underaged (UA) matrix microstructures, which are usually deemed necessary to produce a higher fracture toughness than that displayed in the peak-aged condition. Further, it is demonstrated that, following an appropriate combination of thermomechanical processing and unconventional heat treatment, the composite may possess better stiffness, strength, and fracture toughness than a similar unreinforced alloy. In the high- and low-strength matrix microstructural conditions, the matrix grain and substructure were found to play a substantial role in determining fracture properties. However, in the intermediate- strength regime, properties appeared to be optimizable by the utilization of heat treatments only. These observations are rationalized on the basis of current understanding of the grain size dependence of fracture toughness and the detailed microstructural features resulting from thermomechanical treatments.United States Army Research OfficeArmy Research LabratoryUnited States Air Force Office of Scientific ResearchWright Materials LabratoryDWA Composite

High-efficiency Bragg grating enhanced on-chip photon-number-resolving detectors

The recent trend towards integration of quantum optics experiments has produced a demand for on-chip single photon detectors with high quantum efficiencies. In previous work we demonstrated integrated photon number resolving detectors for use at telecommunications wavelengths [1], here we outline developments of this design which have enabled improvements in the quantum efficiency, permitting an on-chip detection efficiency of 92% to be obtained in the device of Fig. 1. ..

Pb0.4Bi1.6Sr2Ca1Cu2O8+xPb_{0.4}Bi_{1.6}Sr_{2}Ca_{1}Cu_{2}O_{8+x} and Oxygen Stoichiometry: Structure, Resistivity, Fermi Surface Topology and Normal State Properties

$Pb_{0.4}Bi_{1.6}Sr_2CaCu_2O_{8+x}$ ($Bi(Pb)-$2212) single crystal samples were studied using transmission electron microscopy (TEM), $ab-$plane ($\rho_{ab}$) and $c-$axis ($\rho_c$) resistivity, and high resolution angle-resolved ultraviolet photoemission spectroscopy (ARUPS). TEM reveals that the modulation in the $b-$axis for $Pb(0.4)-$doped $Bi(Pb)-$2212 is dominantly of $Pb-$type that is not sensitive to the oxygen content of the system, and the system clearly shows a structure of orthorhombic symmetry. Oxygen annealed samples exhibit a much lower $c-$axis resistivity and a resistivity minimum at $80-130$K. He-annealed samples exhibit a much higher $c-$axis resistivity and $d\rho_c/dT<0$ behavior below 300K. The Fermi surface (FS) of oxygen annealed $Bi(Pb)-$2212 mapped out by ARUPS has a pocket in the FS around the $\bar{M}$ point and exhibits orthorhombic symmetry. There are flat, parallel sections of the FS, about 60\% of the maximum possible along $k_x = k_y$, and about 30\% along $k_x = - k_y$. The wavevectors connecting the flat sections are about $0.72(\pi, \pi)$ along $k_x = k_y$, and about $0.80(\pi, \pi)$ along $k_x = - k_y$, rather than $(\pi,\pi)$. The symmetry of the near-Fermi-energy dispersing states in the normal state changes between oxygen-annealed and He-annealed samples.Comment: APS_REVTEX 3.0, 49 pages, including 11 figures, available upon request. Submitted to Phys. Rev. B

Circumstellar interaction in supernovae in dense environments - an observational perspective

In a supernova explosion, the ejecta interacting with the surrounding circumstellar medium (CSM) give rise to variety of radiation. Since CSM is created from the mass lost from the progenitor star, it carries footprints of the late time evolution of the star. This is one of the unique ways to get a handle on the nature of the progenitor star system. Here, I will focus mainly on the supernovae (SNe) exploding in dense environments, a.k.a. Type IIn SNe. Radio and X-ray emission from this class of SNe have revealed important modifications in their radiation properties, due to the presence of high density CSM. Forward shock dominance of the X-ray emission, internal free-free absorption of the radio emission, episodic or non-steady mass loss rate, asymmetry in the explosion seem to be common properties of this class of SNe.Comment: Fixed minor typos. 31 pages, 9 figures, accepted for publication in Space Science Reviews. Chapter in International Space Science Institute (ISSI) Book on "Supernovae" to be published in Space Science Reviews by Springe