MacWilliams Identities for mm-tuple Weight Enumerators

Since MacWilliams proved the original identity relating the Hamming weight enumerator of a linear code to the weight enumerator of its dual code there have been many different generalizations, leading to the development of $m$-tuple support enumerators. We prove a generalization of theorems of Britz and of Ray-Chaudhuri and Siap, which build on earlier work of Kl{\o}ve, Shiromoto, Wan, and others. We then give illustrations of these $m$-tuple weight enumerators.Comment: 17 pages. Accepted to SIAM Journal on Discrete Mathematic

3-D Models of Embedded High-Mass Stars: Effects of a Clumpy Circumstellar Medium

We use 3-D radiative transfer models to show the effects of clumpy circumstellar material on the observed infrared colors of high mass stars embedded in molecular clouds. We highlight differences between 3-D clumpy and 1-D smooth models which can affect the interpretation of data. We discuss several important properties of the emergent spectral energy distribution (SED): More near-infrared light (scattered and direct from the central source) can escape than in smooth 1-D models. The near- and mid-infrared SED of the same object can vary significantly with viewing angle, depending on the clump geometry along the sightline. Even the wavelength-integrated flux can vary with angle by more than a factor of two. Objects with the same average circumstellar dust distribution can have very different near-and mid-IR SEDs depending on the clump geometry and the proximity of the most massive clump to the central source. Although clumpiness can cause similar objects to have very different SEDs, there are some observable trends. Near- and mid-infrared colors are sensitive to the weighted average distance of clumps from the central source and to the magnitude of clumpy density variations (smooth-to-clumpy ratio). Far-infrared emission remains a robust measure of the total dust mass. We present simulated SEDs, colors, and images for 2MASS and Spitzer filters. We compare to observations of some UCHII regions and find that 3-D clumpy models fit better than smooth models. In particular, clumpy models with fractal dimensions in the range 2.3-2.8, smooth to clumpy ratios of <50%, and density distributions with shallow average radial density profiles fit the SEDs best.Comment: accepted to ApJ; version with full-res figures: http://www.astro.virginia.edu/~ri3e/clumpy3d.pd

Photometry of SN 2002ic and Implications for the Progenitor Mass-Loss History

We present new pre-maximum and late-time optical photometry of the Type Ia/IIn supernova 2002ic. These observations are combined with the published V-band magnitudes of Hamuy et al. (2003) and the VLT spectrophotometry of Wang et al. (2004) to construct the most extensive light curve to date of this unusual supernova. The observed flux at late time is significantly higher relative to the flux at maximum than that of any other observed Type Ia supernova and continues to fade very slowly a year after explosion. Our analysis of the light curve suggests that a non-Type Ia supernova component becomes prominent $\sim20$ days after explosion. Modeling of the non-Type Ia supernova component as heating from the shock interaction of the supernova ejecta with pre-existing circumstellar material suggests the presence of a $\sim1.7 10^{15}$ cm gap or trough between the progenitor system and the surrounding circumstellar material. This gap could be due to significantly lower mass-loss $\sim15 (v_w/10 km/s)^{-1}$ years prior to explosion or evacuation of the circumstellar material by a low-density fast wind. The latter is consistent with observed properties of proto-planetary nebulae and with models of white-dwarf + asymptotic giant branch star progenitor systems with the asymptotic giant branch star in the proto-planetary nebula phase.Comment: accepted for publication in Ap

Brewster-angle measurements of sea-surface reflectance using a high resolution spectroradiometer

This paper describes the design, construction and testing of a ship-borne spectroradiometer based on an imaging spectrograph and cooled CCD array with a wavelength range of 350-800 nm and 4 nm spectral sampling. The instrument had a minimum spectral acquisition time of 0.1 s, but in practice data were collected over periods of 10 s to allow averaging of wave effects. It was mounted on a ship's superstructure so that it viewed the sea surface from a height of several metres at the Brewster angle (53 degrees) through a linear polarizing filter. Comparison of sea-leaving spectra acquired with the polarizer oriented horizontally and vertically enabled estimation of the spectral composition of sky light reflected directly from the sea surface. A semi-empirical correction procedure was devised for retrieving water-leaving radiance spectra from these measurements while minimizing the influence of reflected sky light. Sea trials indicated that reflectance spectra obtained by this method were consistent with the results of radiance transfer modelling of case 2 waters with similar concentrations of chlorophyll and coloured dissolved organic matter. Surface reflectance signatures measured at three locations containing blooms of different phytoplankton species were easily discriminated and the instrument was sufficiently sensitive to detect solar-stimulated fluorescence from surface chlorophyll concentrations down to 1 mg m−3

2-D Radiative Transfer in Protostellar Envelopes: I. Effects of Geometry on Class I Sources

We present 2-D radiation transfer models of Class I Protostars and show the effect of including more realistic geometries on the resulting spectral energy distributions and images. We begin with a rotationally flattened infalling envelope as our comparison model, and add a flared disk and bipolar cavity. The disk affects the spectral energy distribution most strongly at edge-on inclinations, causing a broad dip at about 10 um (independent of the silicate feature) due to high extinction and low scattering albedo in this wavelength region. The bipolar cavities allow more direct stellar+disk radiation to emerge into polar directions, and more scattering radiation to emerge into all directions. The wavelength-integrated flux, often interpreted as luminosity, varies with viewing angle, with pole-on viewing angles seeing 2-4 times as much flux as edge-on, depending on geometry. Thus, observational estimates of luminosity should take into account the inclination of a source. The envelopes with cavities are significantly bluer in near-IR and mid-IR color-color plots than those without cavities. Using 1-D models to interpret Class I sources with bipolar cavities would lead to an underestimate of envelope mass and an overestimate of the implied evolutionary state. We compute images at near-, mid-, and far-IR wavelengths. We find that the mid-IR colors and images are sensitive to scattering albedo, and that the flared disk shadows the midplane on large size scales at all wavelengths plotted. Finally, our models produce polarization spectra which can be used to diagnose dust properties, such as albedo variations due to grain growth. Our results of polarization across the 3.1 um ice feature agree well with observations for ice mantles covering 5% of the radius of the grains.Comment: Accepted for publication in ApJ, 37 pages, 13 figures (several figures reduced in quality; find original version at http://gemelli.colorado.edu/~bwhitney/preprints.html

Smoothed Particle Hydrodynamics Simulations of Apsidal and Nodal Superhumps

In recent years a handful of systems have been observed to show "negative" (nodal) superhumps, with periods slightly shorter than the orbital period. It has been suggested that these modes are a consequence of the slow retrograde precession of the line of nodes in a disk tilted with respect to the orbital plane. Our simulations confirm and refine this model: they suggest a roughly axisymmetric, retrogradely-precessing, tilted disk that is driven at a period slightly less than half the orbital period as the tidal field of the orbiting secondary encounters in turn the two halves of the disk above and below the midplane. Each of these passings leads to viscous dissipation on one face of an optically-thick disk -- observers on opposite sides of the disk would each observe one brightening per orbit, but 180 degrees out of phase with each other.Comment: 11 pages. Accepted for publication in The ApJ Letter

Laser-wakefield accelerators as hard x-ray sources for 3D medical imaging of human bone

A bright μm-sized source of hard synchrotron x-rays (critical energy Ecrit > 30 keV) based on the betatron oscillations of laser wakefield accelerated electrons has been developed. The potential of this source for medical imaging was demonstrated by performing micro-computed tomography of a human femoral trabecular bone sample, allowing full 3D reconstruction to a resolution below 50 μm. The use of a 1 cm long wakefield accelerator means that the length of the beamline (excluding the laser) is dominated by the x-ray imaging distances rather than the electron acceleration distances. The source possesses high peak brightness, which allows each image to be recorded with a single exposure and reduces the time required for a full tomographic scan. These properties make this an interesting laboratory source for many tomographic imaging applications

Nonequilibrium molecular dynamics simulation of rapid directional solidification

We present the results of non-equilibrium molecular dynamics simulations for the growth of a solid binary alloy from its liquid phase. The regime of high pulling velocities, $V$, for which there is a progressive transition from solute segregation to solute trapping, is considered. In the segregation regime, we recover the exponential form of the concentration profile within the liquid phase. Solute trapping is shown to settle in progressively as $V$ is increased and our results are in good agreement with the theoretical predictions of Aziz [J. Appl. Phys. {\bf 53}, 1158 (1981)]. In addition, the fluid advection velocity is shown to remain directly proportional to $V$, even at the highest velocities considered here ($V\simeq10$ms$^{-1}$).Comment: Submitted to Phys. Rev.