Remote sensing of tropical tropopause layer radiation balance using A-train measurements

Determining the level of zero net radiative heating (LZH) is critical to understanding parcel trajectory in the Tropical Tropopause Layer (TTL) and associated stratospheric hydration processes. Previous studies of the TTL radiative balance have focused on using radiosonde data, but remote sensing measurements from polar-orbiting satellites may provide the relevant horizontal and vertical information for assessing TTL solar heating and infrared cooling rates, especially across the Pacific Ocean. CloudSat provides a considerable amount of vertical information about the distribution of cloud properties relevant to heating rate analysis. The ability of CloudSat measurements and ancillary information to constrain LZH is explored. We employ formal error propagation analysis for derived heating rate uncertainty given the CloudSat cloud property retrieval algorithms. Estimation of the LZH to within approximately 0.5 to 1 km is achievable with CloudSat, but it has a low-altitude bias because the radar is unable to detect thin cirrus. This can be remedied with the proper utilization of Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) lidar backscatter information. By utilizing an orbital simulation with the GISS data set, we explore the representativeness of non-cross-track scanning active sounders in terms of describing the LZH distribution. In order to supplement CloudSat, we explore the ability of Atmospheric Infrared Sounder (AIRS) and Advanced Microwave Scanning Radiometer-EOS (AMSR-E) to constrain LZH and find that these passive sounders are useful where the cloud top height does not exceed 7 km. The spatiotemporal distributions of LZH derived from CloudSat and CALIPSO measurements are presented which suggest that thin cirrus have a limited effect on LZH mean values but affect LZH variability

Tight-binding study of structure and vibrations of amorphous silicon

We present a tight-binding calculation that, for the first time, accurately describes the structural, vibrational and elastic properties of amorphous silicon. We compute the interatomic force constants and find an unphysical feature of the Stillinger-Weber empirical potential that correlates with a much noted error in the radial distribution function associated with that potential. We also find that the intrinsic first peak of the radial distribution function is asymmetric, contrary to usual assumptions made in the analysis of diffraction data. We use our results for the normal mode frequencies and polarization vectors to obtain the zero-point broadening effect on the radial distribution function, enabling us to directly compare theory and a high resolution x-ray diffraction experiment

Linear semigroups with coarsely dense orbits

Let $S$ be a finitely generated abelian semigroup of invertible linear operators on a finite dimensional real or complex vector space $V$. We show that every coarsely dense orbit of $S$ is actually dense in $V$. More generally, if the orbit contains a coarsely dense subset of some open cone $C$ in $V$ then the closure of the orbit contains the closure of $C$. In the complex case the orbit is then actually dense in $V$. For the real case we give precise information about the possible cases for the closure of the orbit.Comment: We added comments and remarks at various places. 14 page

The Fourth Positive System of Carbon Monoxide in the Hubble Space Telescope Spectra of Comets

The rich structure of the Fourth Positive System (A-X) of carbon monoxide accounts for many of the spectral features seen in long slit HST-STIS observations of comets 153P/Ikeya-Zhang, C/2001 Q4 (NEAT), and C/2000 WM1 (LINEAR), as well as in the HST-GHRS spectrum of comet C/1996 B2 Hyakutake. A detailed CO fluorescence model is developed to derive the CO abundances in these comets by simultaneously fitting all of the observed A-X bands. The model includes the latest values for the oscillator strengths and state parameters, and accounts for optical depth effects due to line overlap and self-absorption. The model fits yield radial profiles of CO column density that are consistent with a predominantly native source for all the comets observed by STIS. The derived CO abundances relative to water in these comets span a wide range, from 0.44% for C/2000 WM1 (LINEAR), 7.2% for 153P/Ikeya-Zhang, 8.8% for C/2001 Q4 (NEAT) to 20.9% for C/1996 B2 (Hyakutake). The subtraction of the CO spectral features using this model leads to the first identification of a molecular hydrogen line pumped by solar HI Lyman-beta longward of 1200A in the spectrum of comet 153P/Ikeya-Zhang. (Abridged)Comment: 12 pages, 11 figures, ApJ accepte

The Chandra Iron-L X-Ray Line Spectrum of Capella

An analysis of the iron L-shell emission in the publicly available spectrum of the Capella binary system, as obtained by the High Energy Transmission Grating Spectrometer on board the Chandra X-ray Observatory, is presented. The atomic-state model, based on the HULLAC code, is shown to be especially adequate for analyzing high-resolution x-ray spectra of this sort. Almost all of the spectral lines in the 10 - 18 Angstrom wavelength range are identified. It is shown that, for the most part, these lines can be attributed to emission from L-shell iron ions in the Capella coronae. Possibilities for electron temperature diagnostics using line ratios of Fe16+ are demonstrated. It is shown that the observed iron-L spectrum can be reproduced almost entirely by assuming a single electron temperature of kTe= 600 eV. This temperature is consistent with both the measured fractional ion abundances of iron and with the temperature derived from ratios of Fe16+ lines. A volume emission measure of 1053 cm-3 is calculated for the iron L-shell emitting regions of the Capella coronae indicating a rather small volume of 1029 cm3 for the emitting plasma if an electron density of 1012 cm-3 is assumed.Comment: Accepted to Ap

Distinguishing Solar Flare Types by Differences in Reconnection Regions

Observations show that magnetic reconnection and its slow shocks occur in solar flares. The basic magnetic structures are similar for long duration event (LDE) flares and faster compact impulsive (CI) flares, but the former require less non-thermal electrons than the latter. Slow shocks can produce the required non-thermal electron spectrum for CI flares by Fermi acceleration if electrons are injected with large enough energies to resonate with scattering waves. The dissipation region may provide the injection electrons, so the overall number of non-thermal electrons reaching the footpoints would depend on the size of the dissipation region and its distance from the chromosphere. In this picture, the LDE flares have converging inflows toward a dissipation region that spans a smaller overall length fraction than for CI flares. Bright loop-top X-ray spots in some CI flares can be attributed to particle trapping at fast shocks in the downstream flow, the presence of which is determined by the angle of the inflow field and velocity to the slow shocks.Comment: 15 pages TeX and 2 .eps figures, accepted to Ap.J.Let

Packing Returning Secretaries

We study online secretary problems with returns in combinatorial packing domains with $n$ candidates that arrive sequentially over time in random order. The goal is to accept a feasible packing of candidates of maximum total value. In the first variant, each candidate arrives exactly twice. All $2n$ arrivals occur in random order. We propose a simple 0.5-competitive algorithm that can be combined with arbitrary approximation algorithms for the packing domain, even when the total value of candidates is a subadditive function. For bipartite matching, we obtain an algorithm with competitive ratio at least $0.5721 - o(1)$ for growing $n$, and an algorithm with ratio at least $0.5459$ for all $n \ge 1$. We extend all algorithms and ratios to $k \ge 2$ arrivals per candidate. In the second variant, there is a pool of undecided candidates. In each round, a random candidate from the pool arrives. Upon arrival a candidate can be either decided (accept/reject) or postponed (returned into the pool). We mainly focus on minimizing the expected number of postponements when computing an optimal solution. An expected number of $\Theta(n \log n)$ is always sufficient. For matroids, we show that the expected number can be reduced to $O(r \log (n/r))$, where $r \le n/2$ is the minimum of the ranks of matroid and dual matroid. For bipartite matching, we show a bound of $O(r \log n)$, where $r$ is the size of the optimum matching. For general packing, we show a lower bound of $\Omega(n \log \log n)$, even when the size of the optimum is $r = \Theta(\log n)$.Comment: 23 pages, 5 figure

Advances on Matroid Secretary Problems: Free Order Model and Laminar Case

The most well-known conjecture in the context of matroid secretary problems claims the existence of a constant-factor approximation applicable to any matroid. Whereas this conjecture remains open, modified forms of it were shown to be true, when assuming that the assignment of weights to the secretaries is not adversarial but uniformly random (Soto [SODA 2011], Oveis Gharan and Vondr\'ak [ESA 2011]). However, so far, there was no variant of the matroid secretary problem with adversarial weight assignment for which a constant-factor approximation was found. We address this point by presenting a 9-approximation for the \emph{free order model}, a model suggested shortly after the introduction of the matroid secretary problem, and for which no constant-factor approximation was known so far. The free order model is a relaxed version of the original matroid secretary problem, with the only difference that one can choose the order in which secretaries are interviewed. Furthermore, we consider the classical matroid secretary problem for the special case of laminar matroids. Only recently, a constant-factor approximation has been found for this case, using a clever but rather involved method and analysis (Im and Wang, [SODA 2011]) that leads to a 16000/3-approximation. This is arguably the most involved special case of the matroid secretary problem for which a constant-factor approximation is known. We present a considerably simpler and stronger $3\sqrt{3}e\approx 14.12$-approximation, based on reducing the problem to a matroid secretary problem on a partition matroid

Numerical study of anharmonic vibrational decay in amorphous and paracrystalline silicon

The anharmonic decay rates of atomic vibrations in amorphous silicon (a-Si) and paracrystalline silicon (p-Si), containing small crystalline grains embedded in a disordered matrix, are calculated using realistic structural models. The models are 1000-atom four-coordinated networks relaxed to a local minimum of the Stillinger-Weber interatomic potential. The vibrational decay rates are calculated numerically by perturbation theory, taking into account cubic anharmonicity as the perturbation. The vibrational lifetimes for a-Si are found to be on picosecond time scales, in agreement with the previous perturbative and classical molecular dynamics calculations on a 216-atom model. The calculated decay rates for p-Si are similar to those of a-Si. No modes in p-Si reside entirely on the crystalline cluster, decoupled from the amorphous matrix. The localized modes with the largest (up to 59%) weight on the cluster decay primarily to two diffusons. The numerical results are discussed in relation to a recent suggestion by van der Voort et al. [Phys. Rev. B {\bf 62}, 8072 (2000)] that long vibrational relaxation inferred experimentally may be due to possible crystalline nanostructures in some types of a-Si.Comment: 9 two-column pages, 13 figure