The orbit structure of Dynkin curves

Let G be a simple algebraic group over an algebraically closed field k; assume that Char k is zero or good for G. Let \cB be the variety of Borel subgroups of G and let e in Lie G be nilpotent. There is a natural action of the centralizer C_G(e) of e in G on the Springer fibre \cB_e = {B' in \cB | e in Lie B'} associated to e. In this paper we consider the case, where e lies in the subregular nilpotent orbit; in this case \cB_e is a Dynkin curve. We give a complete description of the C_G(e)-orbits in \cB_e. In particular, we classify the irreducible components of \cB_e on which C_G(e) acts with finitely many orbits. In an application we obtain a classification of all subregular orbital varieties admitting a finite number of B-orbits for B a fixed Borel subgroup of G.Comment: 12 pages, to appear in Math

Diagrammatic self-energy approximations and the total particle number

There is increasing interest in many-body perturbation theory as a practical tool for the calculation of ground-state properties. As a consequence, unambiguous sum rules such as the conservation of particle number under the influence of the Coulomb interaction have acquired an importance that did not exist for calculations of excited-state properties. In this paper we obtain a rigorous, simple relation whose fulfilment guarantees particle-number conservation in a given diagrammatic self-energy approximation. Hedin's G(0)W(0) approximation does not satisfy this relation and hence violates the particle-number sum rule. Very precise calculations for the homogeneous electron gas and a model inhomogeneous electron system allow the extent of the nonconservation to be estimated

Search for Global Dipole Enhancements in the HiRes-I Monocular Data above 10^{18.5} eV

Several proposed source models for Ultra-High Energy Cosmic Rays (UHECRs) consist of dipole distributions oriented towards major astrophysical landmarks such as the galactic center, M87, or Centaurus A. We use a comparison between real data and simulated data to show that the HiRes-I monocular data for energies above 10^{18.5} eV is, in fact, consistent with an isotropic source model. We then explore methods to quantify our sensitivity to dipole source models oriented towards the Galactic Center, M87, and Centaurus A.Comment: 17 pages, 31 figure

Observation of the Ankle and Evidence for a High-Energy Break in the Cosmic Ray Spectrum

We have measured the cosmic ray spectrum at energies above $10^{17}$ eV using the two air fluorescence detectors of the High Resolution Fly's Eye experiment operating in monocular mode. We describe the detector, PMT and atmospheric calibrations, and the analysis techniques for the two detectors. We fit the spectrum to models describing galactic and extragalactic sources. Our measured spectrum gives an observation of a feature known as the ``ankle'' near $3\times 10^{18}$ eV, and strong evidence for a suppression near $6\times 10^{19}$ eV.Comment: 14 pages, 9 figures. To appear in Physics Letters B. Accepted versio

A Measurement of Time-Averaged Aerosol Optical Depth using Air-Showers Observed in Stereo by HiRes

Air fluorescence measurements of cosmic ray energy must be corrected for attenuation of the atmosphere. In this paper we show that the air-showers themselves can yield a measurement of the aerosol attenuation in terms of optical depth, time-averaged over extended periods. Although the technique lacks statistical power to make the critical hourly measurements that only specialized active instruments can achieve, we note the technique does not depend on absolute calibration of the detector hardware, and requires no additional equipment beyond the fluorescence detectors that observe the air showers. This paper describes the technique, and presents results based on analysis of 1258 air-showers observed in stereo by the High Resolution Fly's Eye over a four year span.Comment: 7 pages, 3 figures, accepted for publication by Astroparticle Physics Journa

Air fluorescence measurements in the spectral range 300-420 nm using a 28.5 GeV electron beam

Measurements are reported of the yield and spectrum of fluorescence, excited by a 28.5 GeV electron beam, in air at a range of pressures of interest to ultra-high energy cosmic ray detectors. The wavelength range was 300 - 420 nm. System calibration has been performed using Rayleigh scattering of a nitrogen laser beam. In atmospheric pressure dry air at 304 K the yield is 20.8 +/- 1.6 photons per MeV.Comment: 29 pages, 10 figures. Submitted to Astroparticle Physic

Measurement of Pressure Dependent Fluorescence Yield of Air: Calibration Factor for UHECR Detectors

In a test experiment at the Final Focus Test Beam of the Stanford Linear Accelerator Center, the fluorescence yield of 28.5 GeV electrons in air and nitrogen was measured. The measured photon yields between 300 and 400 nm at 1 atm and 29 deg C are Y(760 Torr, air) = 4.42 +/- 0.73 and Y(760 Torr, nitrogen) = 29.2 +/- 4.8 photons per electron per meter. Assuming that the fluorescence yield is proportional to the energy deposition of a charged particle traveling through air, good agreement with measurements at lower particle energies is observed.Comment: 22 pages, 14 figures, 2 tables, submitted to Astroparticle Physic

A Likelihood Method for Measuring the Ultrahigh Energy Cosmic Ray Composition

Air fluorescence detectors traditionally determine the dominant chemical composit ion of the ultrahigh energy cosmic ray flux by comparing the averaged slant depth of the shower maximum, $X_{max}$, as a function of energy to the slant depths expect ed for various hypothesized primaries. In this paper, we present a method to make a direct measurement of the expected mean number of protons and iron by comparing the shap es of the expected $X_{max}$ distributions to the distribution for data. The advantages of this method includes the use of information of the full distribution and its ability to calculate a flux for various cosmic ray compositi ons. The same method can be expanded to marginalize uncertainties due to choice of spectra, hadronic models and atmospheric parameters. We demonstrate the technique with independent simulated data samples from a parent sample of protons and iron. We accurately predict the number of protons and iron in the parent sample and show that the uncertainties are meaningful.Comment: 11 figures, 22 pages, accepted by Astroparticle Physic

Alternative Methods to Finding Patterns in HiRes Stereo Data

In this paper Ultra High Energy Cosmic Rays UHECRs data observed by the HiRes fluorescence detector in stereo mode is analyzed to search for events in the sky with an arrival direction lying on a great circle. Such structure is known as the arc structure. The arc structure is expected when the charged cosmic rays pass through the galactic magnetic field. The arcs searched for could represent a broad or a small scale anisotropy depending on the proposed source model for the UHECRs. The Arcs in this paper are looked for using Hough transform were Hough transform is a technique used to looking for patterns in images. No statistically significant arcs were found in this study

Milagro limits and HAWC sensitivity for the rate-density of evaporating Primordial Black Holes

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