The horizon problem for prevalent surfaces

We investigate the box dimensions of the horizon of a fractal surface defined by a function $f \in C[0,1]^2$. In particular we show that a prevalent surface satisfies the `horizon property', namely that the box dimension of the horizon is one less than that of the surface. Since a prevalent surface has box dimension 3, this does not give us any information about the horizon of surfaces of dimension strictly less than 3. To examine this situation we introduce spaces of functions with surfaces of upper box dimension at most \alpha, for \alpha $\in$ [2,3). In this setting the behaviour of the horizon is more subtle. We construct a prevalent subset of these spaces where the lower box dimension of the horizon lies between the dimension of the surface minus one and 2. We show that in the sense of prevalence these bounds are as tight as possible if the spaces are defined purely in terms of dimension. However, if we work in Lipschitz spaces, the horizon property does indeed hold for prevalent functions. Along the way, we obtain a range of properties of box dimensions of sums of functions

Measuring the atomic composition of planetary building blocks

Volatile molecules are critical to terrestrial planetary habitability, yet difficult to observe directly where planets form at the midplanes of protoplanetary disks. It is unclear whether the inner 1 AU of disks are volatile-poor or if this region is resupplied with ice-rich dust from colder disk regions. Dust traps at radial pressure maxima bounding disk gaps can cut off the inner disk from such volatile reservoirs. However, the trap retention efficiency and atomic composition of trapped dust have not been measured. We present a new technique to measure the absolute atomic abundances in gas accreting onto T Tauri stars and infer the bulk atomic composition and distribution of midplane solids retained in the disk around the young star TW Hya. We identify line emission from gas-phase material inside the dust sublimation rim of TW Hya. Gaussian decomposition of the strongest H Paschen lines isolates the inner disk hydrogen emission. We measure several key elemental abundances, relative to hydrogen, using a chemical photoionization model and infer dust retention in the disk. With a 1D transport model, we determine approximate radial locations and retention efficiencies of dust traps for different elements. Volatile and refractory elements are depleted from TW Hya's hot gas by factors of ~10^2 and up to 10^5, respectively. Dust traps beyond the CO and N2 snowline cumulatively sequester 96% of the total dust, while the trap at 2 AU retains 3% of the initial dust mass. The high depletions of Si, Mg, and Ca are explained by a third trap at 0.3 AU. TW Hya has a significant volatile reservoir rich in C- and N-ices in its outer ring structure. However, the lack of C resupply may leave the terrestrial planet-forming region dry and carbon-poor. Any planets that form within the silicate dust trap at 0.3 AU may resemble Earth in terms of the degree of their volatile depletion.Comment: Accepted for publication in A&A Letters. 6 pages, 3 figures, plus appendice

High velocity clouds in the Galactic All Sky Survey I. Catalogue

We present a catalogue of high-velocity clouds (HVCs) from the Galactic All Sky Survey (GASS) of southern-sky neutral hydrogen, which has 57 mK sensitivity and 1 km/s velocity resolution and was obtained with the Parkes Telescope. Our catalogue has been derived from the stray-radiation corrected second release of GASS. We describe the data and our method of identifying HVCs and analyse the overall properties of the GASS population. We catalogue a total of 1693 HVCs at declinations < 0 deg, including 1111 positive velocity HVCs and 582 negative velocity HVCs. Our catalogue also includes 295 anomalous velocity clouds (AVCs). The cloud line-widths of our HVC population have a median FWHM of ~19 km/s, which is lower than found in previous surveys. The completeness of our catalogue is above 95% based on comparison with the HIPASS catalogue of HVCs, upon which we improve with an order of magnitude in spectral resolution. We find 758 new HVCs and AVCs with no HIPASS counterpart. The GASS catalogue will shed an unprecedented light on the distribution and kinematic structure of southern-sky HVCs, as well as delve further into the cloud populations that make up the anomalous velocity gas of the Milky Way.Comment: 21 pages, 14 figures, accepted for publication in ApJ

Distinct Signatures For Coulomb Blockade and Aharonov-Bohm Interference in Electronic Fabry-Perot Interferometers

Two distinct types of magnetoresistance oscillations are observed in two electronic Fabry-Perot interferometers of different sizes in the integer quantum Hall regime. Measuring these oscillations as a function of magnetic field and gate voltages, we observe three signatures that distinguish the two types. The oscillations observed in a 2.0 square micron device are understood to arise from the Coulomb blockade mechanism, and those observed in an 18 square micron device from the Aharonov-Bohm mechanism. This work clarifies, provides ways to distinguish, and demonstrates control over, these distinct physical origins of resistance oscillations seen in electronic Fabry-Perot interferometers.Comment: related papers at http://marcuslab.harvard.ed

The VLA Galactic Plane Survey

The VLA Galactic Plane Survey (VGPS) is a survey of HI and 21-cm continuum emission in the Galactic plane between longitude 18 degrees 67 degr. with latitude coverage from |b| < 1.3 degr. to |b| < 2.3 degr. The survey area was observed with the Very Large Array (VLA) in 990 pointings. Short-spacing information for the HI line emission was obtained by additional observations with the Green Bank Telescope (GBT). HI spectral line images are presented with a resolution of 1 arcmin x 1 arcmin x 1.56 km/s (FWHM) and rms noise of 2 K per 0.824 km/s channel. Continuum images made from channels without HI line emission have 1 arcmin (FWHM) resolution. VGPS images are compared with images from the Canadian Galactic Plane Survey (CGPS) and the Southern Galactic Plane Survey (SGPS). In general, the agreement between these surveys is impressive, considering the differences in instrumentation and image processing techniques used for each survey. The differences between VGPS and CGPS images are small, < 6 K (rms) in channels where the mean HI brightness temperature in the field exceeds 80 K. A similar degree of consistency is found between the VGPS and SGPS. The agreement we find between arcminute resolution surveys of the Galactic plane is a crucial step towards combining these surveys into a single uniform dataset which covers 90% of the Galactic disk: the International Galactic Plane Survey (IGPS). The VGPS data will be made available on the World Wide Web through the Canadian Astronomy Data Centre (CADC).Comment: Accepted for publication in The Astronomical Journal. 41 pages, 13 figures. For information on data release, colour images etc. see http://www.ras.ucalgary.ca/VGP