Supernova Remnant in a Stratified Medium: Explicit, Analytical Approximations for Adiabatic Expansion and Radiative Cooling

We propose simple, explicit, analytical approximations for the kinematics of an adiabatic blast wave propagating in an exponentially stratified ambient medium, and for the onset of radiative cooling, which ends the adiabatic era. Our method, based on the Kompaneets implicit solution and the Kahn approximation for the radiative cooling coefficient, gives straightforward estimates for the size, expansion velocity, and progression of cooling times over the surface, when applied to supernova remnants (SNRs). The remnant shape is remarkably close to spherical for moderate density gradients, but even a small gradient in ambient density causes the cooling time to vary substantially over the remnant's surface, so that for a considerable period there will be a cold dense expanding shell covering only a part of the remnant. Our approximation provides an effective tool for identifying the approximate parameters when planning 2-dimensional numerical models of SNRs, the example of W44 being given in a subsequent paper.Comment: ApJ accepted, 11 pages, 2 figures embedded, aas style with ecmatex.sty and lscape.sty package

New method for critical failure prediction of complex systems

Rigorous analytical technique, called criticality determination methodology /or CD technique/ determines the probability that a given complex system will successfully achieve stated objectives. The CD technique identifies critical elements of the system by a failure mode and effects analysis

A Molecular Einstein Ring: Imaging a Starburst Disk Surrounding a Quasi-Stellar Object

Images of the CO 2-1 line emission, and the radio continuum emission, from the redshift 4.12 gravitationally lensed quasi-stellar object (QSO) PSS J2322+1944 reveal an Einstein ring with a diameter of 1.5". These observations are modeled as a star forming disk surrounding the QSO nucleus with a radius of 2 kpc. The implied massive star formation rate is 900 M_sun/year. At this rate a substantial fraction of the stars in a large elliptical galaxy could form on a dynamical time scale of 10^8 years. The observation of active star formation in the host galaxy of a high-redshift QSO supports the hypothesis of coeval formation of supermassive black holes and stars in spheroidal galaxies.Comment: 12 pages. to appear in Science, April 200

Small Energy Scale for Mixed-Valent Uranium Materials

We investigate a two-channel Anderson impurity model with a $5f^1$ magnetic and a $5f^2$ quadrupolar ground doublet, and a $5f^2$ excited triplet. Using the numerical renormalization group method, we find a crossover to a non-Fermi liquid state below a temperature $T^*$ varying as the $5f^2$ triplet-doublet splitting to the 7/2 power. To within numerical accuracy, the non-linear magnetic susceptibility and the $5f^1$ contribution to the linear susceptibility are given by universal one-parameter scaling functions. These results may explain UBe$_{13}$ as mixed valent with a small crossover scale $T^*$.Comment: 4 pages, 3 figures, REVTeX, to appear in Phys. Rev. Let

Hyperopic Cops and Robbers

We introduce a new variant of the game of Cops and Robbers played on graphs, where the robber is invisible unless outside the neighbor set of a cop. The hyperopic cop number is the corresponding analogue of the cop number, and we investigate bounds and other properties of this parameter. We characterize the cop-win graphs for this variant, along with graphs with the largest possible hyperopic cop number. We analyze the cases of graphs with diameter 2 or at least 3, focusing on when the hyperopic cop number is at most one greater than the cop number. We show that for planar graphs, as with the usual cop number, the hyperopic cop number is at most 3. The hyperopic cop number is considered for countable graphs, and it is shown that for connected chains of graphs, the hyperopic cop density can be any real number in $[0,1/2].

Rate of Spread of Introduced Rhodophytes Kappaphycus alvarezii, Kappaphycus striatum, and Gracilaria salicornia and Their Current Distribution in Kane'ohe Bay, O'ahu Hawai'i

Spread of the introduced macroalgae Kappaphycus alvarezii (Doty), Kappaphycus striatum Schmitz, and Graci/aria salicornia C. Ag. was measured on reefs in Kane'ohe Bay, O'ahu, Hawai'i. The red algae Kappaphycus alvarezii and Gracilaria salicornia were introduced to specific sites in Kane'ohe Bay in the 1970s. Since that time their distributions have increased, and the algae have spread through the bay. To assess the current extent of these algae in the bay and determine their rate of spread, we performed surveys with a manta towboard. In addition, abundance of these species was determined by detailed reef transects in the central bay in three habitats: barrier reef, patch reef, and fringing reef. All three species have become well established. These algae were found in all areas of Kane'ohe Bay. Distributions are not uniform within the central bay. Abundance of Kappaphycus spp. was highest on patch reefs in shallow water. Gracilaria salicornia was most abundant on the fringing reef. Kappaphycus alvarezii and K. striatum have spread 6km from their points of introduction in 1974, an average rate of spread of approximately 250 m yet. Gracilaria salicornia has spread over 5 km since its introduction in 1978, an average rate of spread of approximately 280 m yr -1. High abundance of these introduced species appears to be associated with moderate water motion

The Hubble Constant

Considerable progress has been made in determining the Hubble constant over the past two decades. We discuss the cosmological context and importance of an accurate measurement of the Hubble constant, and focus on six high-precision distance-determination methods: Cepheids, tip of the red giant branch, maser galaxies, surface brightness fluctuations, the Tully-Fisher relation and Type Ia supernovae. We discuss in detail known systematic errors in the measurement of galaxy distances and how to minimize them. Our best current estimate of the Hubble constant is 73 +/-2 (random) +/-4 (systematic) km/s/Mpc. The importance of improved accuracy in the Hubble constant will increase over the next decade with new missions and experiments designed to increase the precision in other cosmological parameters. We outline the steps that will be required to deliver a value of the Hubble constant to 2% systematic uncertainty and discuss the constraints on other cosmological parameters that will then be possible with such accuracy.Comment: To be published in Annual Reviews of Astronomy and Astrophysics, Vol. 48, 2010, consisting of 79 pages, 13 figures, 2 table