Smoothed corners and scattered waves

We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in $\mathbb R^3$. The method is local, only modifying the original surface in a neighborhood of the geometric singularity, and preserves desirable features like convexity and symmetry. The smoothness of the final surface is an explicit parameter in the method, and the bandlimit of the smoothed surface is proportional to its smoothness. Several numerical examples are provided in the context of acoustic scattering. In particular, we compare scattered fields from smoothed geometries in two dimensions with those from polygonal domains. We observe that significant reductions in computational cost can be obtained if merely approximate solutions are desired in the near- or far-field. Provided that it is sub-wavelength, the error of the scattered field is proportional to the size of the geometry that is modified

Debye Sources and the Numerical Solution of the Time Harmonic Maxwell Equations, II

In this paper, we develop a new integral representation for the solution of the time harmonic Maxwell equations in media with piecewise constant dielectric permittivity and magnetic permeability in R^3. This representation leads to a coupled system of Fredholm integral equations of the second kind for four scalar densities supported on the material interface. Like the classical Muller equation, it has no spurious resonances. Unlike the classical approach, however, the representation does not suffer from low frequency breakdown. We illustrate the performance of the method with numerical examples.Comment: 36 pages, 5 figure

Do the Poor Pay More for Healthy Food? An Empirical Economic Analysis

Food Consumption/Nutrition/Food Safety,

An Anomalous UV Extension in NGC6251

Deep U-band FOC images of the nuclear region of NGC6251 have revealed a region of extended emission which is most probably radiation scattered from a continuum source in the nucleus. This radiation lies interior to a dust ring, is nearly perpendicular to the radio jet axis, and is seen primarily in the FOC U and b filters. The extension has a low observed polarization($\le 10$), and is unlikely to arise from line emission. We know of no other examples similar to what we have found in NGC 6251, and we offer some tentative explanations. The nuclear morphology shows clear similarities to that seen in the nucleus of NGC 4261 except for the extended U-band radiation.Comment: 14 pages AAStex format + 4 figures; accepted for publication in ApJ Letter

A consistency condition for the vector potential in multiply-connected domains

A classical problem in electromagnetics concerns the representation of the electric and magnetic fields in the low-frequency or static regime, where topology plays a fundamental role. For multiply connected conductors, at zero frequency the standard boundary conditions on the tangential components of the magnetic field do not uniquely determine the vector potential. We describe a (gauge-invariant) consistency condition that overcomes this non-uniqueness and resolves a longstanding difficulty in inverting the magnetic field integral equation

Low Surface Brightness Galaxies around the HDF-S: II. Distances and volume densities

With this study we aim at the spectroscopic verification of a photometrically selected sample of Low Surface Brightness (LSB) galaxy candidates in a field around the Hubble Deep Field-South (HDF-S). The sample helps to extend the parameter space for LSB galaxies to lower central surface brightnesses and to provide better estimates on the volume densities of these objects. To derive redshifts for the LSB candidates, long-slit spectra were obtained covering a spectral range from 3400{\AA} to 7500{\AA}. The observations have been obtained using the ESO 3.6m telescope, equipped with the EFOSC2 spectrograph. From the measured radial velocities, distances could be estimated. With this distance information, it is possible to differentiate between true LSB galaxies and higher redshift High Surface Brightness (HSB) galaxies which may contaminate the sample. A correction for the surface brightnesses can then be applied, accounting for the cosmological dimming effect (``Tolman Dimming''). We show that ~70% of the LSB candidates, selected based on their location in the color-color space, are real LSB galaxies. Their position in the color-color diagrams, therefore, indicate that the LSB galaxies have a different stellar population mix resulting from a different star formation history compared to HSBs. Our LSB galaxy sample consists only of large disk galaxies with scale-length between 2.5kpc and 7.3kpc. We confirm the flat central surface brightness distribution of previous surveys and extend this distribution down to central surface brightnesses of 27 B mag arcsec^-2.Comment: 12 pages, 20 figures, accepted by A&

The star formation histories of red and blue low surface brightness disk galaxies

We study the star formation histories (SFH) and stellar populations of 213 red and 226 blue nearly face-on low surface brightness disk galaxies (LSBGs), which are selected from the main galaxy sample of Sloan Digital Sky Survey (SDSS) Data Release Seven (DR7). We also want to compare the stellar populations and SFH between the two groups. The sample of both red and blue LSBGs have sufficient signal-to-noise ratio in the spectral continua. We obtain their absorption-line indices (e.g. Mg_2, H\delta_A), D_n(4000) and stellar masses from the MPA/JHU catalogs to study their stellar populations and SFH. Moreover we fit their optical spectra (stellar absorption lines and continua) by using the spectral synthesis code STARLIGHT on the basis of the templates of Simple Stellar Populations (SSPs). We find that red LSBGs tend to be relatively older, higher metallicity, more massive and have higher surface mass density than blue LSBGs. The D_n(4000)-H\delta_A plane shows that perhaps red and blue LSBGs have different SFH: blue LSBGs are more likely to be experiencing a sporadic star formation events at the present day, whereas red LSBGs are more likely to form stars continuously over the past 1-2 Gyr. Moreover, the fraction of galaxies that experienced recent sporadic formation events decreases with increasing stellar mass. Furthermore, two sub-samples are defined for both red and blue LSBGs: the sub-sample within the same stellar mass range of 9.5 <= log(M_\star/M_\odot) <= 10.3, and the surface brightness limiting sub-sample with \mu_0(R) <= 20.7 mag arcsec^{-2}. They show consistent results with the total sample in the corresponding relationships, which confirm that our results to compare the blue and red LSBGs are robust.Comment: 9 pages, 7 figures, 2 tables, Accepted for publication in A&