Advanced microwave radiometer antenna system study

The practicability of a multi-frequency antenna for spaceborne microwave radiometers was considered in detail. The program consisted of a comparative study of various antenna systems, both mechanically and electronically scanned, in relation to specified design goals and desired system performance. The study involved several distinct tasks: definition of candidate antennas that are lightweight and that, at the specified frequencies of 5, 10, 18, 22, and 36 GHz, can provide conical scanning, dual linear polarization, and simultaneous multiple frequency operation; examination of various feed systems and phase-shifting techniques; detailed analysis of several key performance parameters such as beam efficiency, sidelobe level, and antenna beam footprint size; and conception of an antenna/feed system that could meet the design goals. Candidate antennas examined include phased arrays, lenses, and optical reflector systems. Mechanical, electrical, and performance characteristics of the various systems were tabulated for ease of comparison

Closed-form solutions of the Schroedinger equation for a class of smoothed Coulomb potentials

An infinite family of closed-form solutions is exhibited for the Schroedinger equation for the potential $V(r) = -Z/\sqrt{|r|^{2} + a^{2}}$. Evidence is presented for an approximate dynamical symmetry for large values of the angular momentum $l$.Comment: 13 pages LaTeX, uses included Institute of Physics style files, 3 PostScript figures. In press at J. Phys. B: At. Mol. Opt. Phys. (1997

Large-scale Breit-Pauli R-matrix calculations for transition probabilities of Fe V

Ab initio theoretical calculations are reported for the electric (E1) dipole allowed and intercombination fine structure transitions in Fe V using the Breit-Pauli R-matrix (BPRM) method. We obtain 3865 bound fine structure levels of Fe V and $1.46 x 10^6$ oscillator strengths, Einstein A-coefficients and line strengths. In addition to the relativistic effects, the intermediate coupling calculations include extensive electron correlation effects that represent the complex configuration interaction (CI). Fe V bound levels are obtained with angular and spin symmetries $SL\pi$ and $J\pi$ of the (e + Fe VI) system such that $2S+1$ = 5,3,1, $L \leq$ 10, $J \leq 8$. The bound levels are obtained as solutions of the Breit-Pauli (e + ion) Hamiltonian for each $J\pi$, and are designated according to the `collision' channel quantum numbers. A major task has been the identification of these large number of bound fine structure levels in terms of standard spectroscopic designations. A new scheme, based on the analysis of quantum defects and channel wavefunctions, has been developed. The identification scheme aims particularly to determine the completeness of the results in terms of all possible bound levels for applications to analysis of experimental measurements and plasma modeling. An uncertainty of 10-20% for most transitions is estimated.Comment: 31 pages, 1 figure, Physica Scripta (in press

Containing big soda: Countering inducements to buy large-size sugary drinks

Health concerns about overconsumption of large portions apply to a wide range of highly calorific foods and drinks. Yet, amongst all products, sugar-sweetened soft drinks and especially sugared soda are the ones which seem to raise the most ire because they contain little or no nutritional value beyond their sugar content and because of the way that vendors encourage excessive consumption by pricing jumbo-size portions to look like bargains while making smaller portions appear overpriced. This paper considers the logic of such extreme value size pricing and reveals why this marketing practice can harm economic welfare beyond public health concerns. The paper shows why policy interventions, including portion cap rules and soda taxes, seeking to reduce portion sizes and curb the consumption of large-size sugary drinks might fail when they do not fully take into account or appreciate the strategic responses that vendors might adopt to retain value size pricing

When does the zero fiber of the moment map have rational singularities?

Let $G$ be a complex reductive group and $V$ a $G$-module. There is a natural moment mapping $\mu\colon V\oplus V^*\to\mathfrak{g}^*$ and we denote $\mu^{-1}(0)$ (the shell) by $N_V$. We use invariant theory and results of Musta\c{t}\u{a} [Mus01] to find criteria for $N_V$ to have rational singularities and for the categorical quotient $N_V /\!\!/ G$ to have symplectic singularities, the latter results improving upon [HSS20]. It turns out that for ``most'' $G$-modules $V$, the shell $N_V$ has rational singularities. For the case of direct sums of classical representations of the classical groups, $N_V$ has rational singularities and $N_V /\!\!/ G$ has symplectic singularities if $N_V$ is a reduced and irreducible complete intersection. Another important special case is $V=p\,\mathfrak{g}$ (the direct sum of $p$ copies of the Lie algebra of $G$) where $p\geq 2$. We show that $N_V$ has rational singularities and that $N_V /\!\!/ G$ has symplectic singularities, improving upon results of [Bud19], [AA16], [Kap19] and [GH20]. Let $\pi=\pi_1(\Sigma)$ where $\Sigma$ is a closed Riemann surface of genus $p\geq 2$. Let $G$ be semisimple and let $\operatorname{Hom}(\pi,G)$ and $\mathscr X\!(\pi,G)$ be the corresponding representation variety and character variety. We show that $\operatorname{Hom}(\pi,G)$ is a complete intersection with rational singularities and that $\mathscr X\!(\pi,G)$ has symplectic singularities. If $p>2$ or $G$ contains no simple factor of rank $1$, then the singularities of $\operatorname{Hom}(\pi,G)$ and $\mathscr X\!(\pi,G)$ are in codimension at least four and $\operatorname{Hom}(\pi,G)$ is locally factorial. If, in addition, $G$ is simply connected, then $\mathscr X\!(\pi,G)$ is locally factorial.Comment: 21 pages. v2: 22 pages, clarified and improved arguments in Section 3, improved exposition and minor corrections. v3: 30 pages, reformatted, minor correction

FUSE spectroscopy of sdOB primary of the post common-envelope binary LB 3459 (AA Dor)

LB 3459 (AA Dor) is an eclipsing, close, post common-envelope binary consisting of an sdOB primary star and an unseen secondary with an extraordinarly low mass - formally a brown dwarf. A recent NLTE spectral analysis shows a discrepancy with the surface gravity, which is derived from analyses of radial-velocity and lightcurves. We aim at precisely determing of the photospheric parameters of the primary, especially of the surface gravity, and searching for weak metal lines in the far UV. We performed a detailed spectral analysis of the far-UV spectrum of LB 3459 obtained with FUSE by means of state-of-the-art NLTE model-atmosphere techniques. A strong contamination of the far-UV spectrum of LB 3459 by interstellar line absorption hampers a precise determination of the photospheric properties of its primary star. Its effective temperature (42 kK) was confirmed by the evaluation of new ionization equilibria. For the first time, phosphorus and sulfur have been identified in the spectrum of LB 3459. Their photospheric abundances are solar and 0.01 times solar, respectively. From the C III 1174-1177A multiplet, we can measure the rotational velocity of 35 +/- 5 km/sec of the primary of LB 3459 and confirm that the rotation is bound. From a re-analysis of optical and UV spectra, we determine a higher log g = 5.3 (cgs) that reduces the discrepancy in mass determination in comparison to analyses of radial-velocity and lightcurves. However, the problem is not completely solved.Comment: 10 pages, 15 figure

Driving and damping mechanisms in hybrid pressure-gravity modes pulsators

We study the energetic aspects of hybrid pressure-gravity modes pulsations. The case of hybrid beta Cephei-SPB pulsators is considered with special attention. In addition to the already known sensitivity of the driving mechanism to the heavy elements mixture (mainly the iron abundance), we show that the characteristics of the propagation and evanescent regions play also a major role, determining the extension of the stable gap in the frequency domain between the unstable low order pressure and high order gravity modes. Finally, we consider the case of hybrid delta Sct-gamma Dor pulsators.Comment: 7 pages, 9 figures, in the proceedings of the Helas II Conference: "Helioseismology, Asteroseismology and MHD Connections", Goettingen, August 200

Grain Physics and Rosseland Mean Opacities

Tables of mean opacities are often used to compute the transfer of radiation in a variety of astrophysical simulations from stellar evolution models to proto-planetary disks. Often tables, such as Ferguson et al. (2005), are computed with a predetermined set of physical assumptions that may or may not be valid for a specific application. This paper explores the effects of several assumptions of grain physics on the Rosseland mean opacity in an oxygen rich environment. We find that changing the distribution of grain sizes, either the power-law exponent or the shape of the distribution, has a marginal effect on the total mean opacity. We also explore the difference in the mean opacity between solid homogenous grains and grains that are porous or conglomorations of several species. Changing the amount of grain opacity included in the mean by assuming a grain-to-gas ratio significantly affects the mean opacity, but in a predictable way.Comment: 19 pages, 6 figures, accepted for publication in Ap

Stellar Population Models and Individual Element Abundances I: Sensitivity of Stellar Evolution Models

Integrated light from distant galaxies is often compared to stellar population models via the equivalent widths of spectral features--spectral indices--whose strengths rely on the abundances of one or more elements. Such comparisons hinge not only on the overall metal abundance but also on relative abundances. Studies have examined the influence of individual elements on synthetic spectra but little has been done to address similar issues in the stellar evolution models that underlie most stellar population models. Stellar evolution models will primarily be influenced by changes in opacities. In order to explore this issue in detail, twelve sets of stellar evolution tracks and isochrones have been created at constant heavy element mass fraction Z that self-consistently account for varying heavy element mixtures. These sets include scaled-solar, alpha-enhanced, and individual cases where the elements C, N, O, Ne, Mg, Si, S, Ca, Ti, and Fe have been enhanced above their scaled-solar values. The variations that arise between scaled-solar and the other cases are examined with respect to the H-R diagram and main sequence lifetimes.Comment: 33 pages, 13 figures, accepted to Ap

Universal amplitude ratios of two-dimensional percolation from field theory

We complete the determination of the universal amplitude ratios of two-dimensional percolation within the two-kink approximation of the form factor approach. For the cluster size ratio, which has for a long time been elusive both theoretically and numerically, we obtain the value 160.2, in good agreement with the lattice estimate 162.5 +/- 2 of Jensen and Ziff.Comment: 8 page