Proof of the Umbral Moonshine Conjecture

The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay-Thompson series are certain distinguished mock modular forms. Gannon has proved this for the special case involving the largest sporadic simple Mathieu group. Here we establish the existence of the umbral moonshine modules in the remaining 22 cases.Comment: 56 pages, to appear in Research in the Mathematical Science

Brayton heat exchanger unit development program (alternate design)

A Brayton Heat Exchanger Unit Alternate Design (BHXU-Alternate) consisting of a recuperator, a heat sink heat exchanger, and a gas ducting system, was designed and fabricated. The design was formulated to provide a high performance unit suitable for use in a long-life Brayton-cycle powerplant. Emphasis was on double containment against external leakage and leakage of the organic coolant into the gas stream. A parametric analysis and design study was performed to establish the optimum component configurations to achieve low weight and size and high reliability, while meeting the requirements of high effectiveness and low pressure drop. Layout studies and detailed mechanical and structural design were performed to obtain a flight-type packaging arrangement, including the close-coupled integration of the BHXU-Alternate with the Brayton Rotating Unit (BRU)

Quantum Dynamics of the Slow Rollover Transition in the Linear Delta Expansion

We apply the linear delta expansion to the quantum mechanical version of the slow rollover transition which is an important feature of inflationary models of the early universe. The method, which goes beyond the Gaussian approximation, gives results which stay close to the exact solution for longer than previous methods. It provides a promising basis for extension to a full field theoretic treatment.Comment: 12 pages, including 4 figure

Correlated radial velocity and X-ray variations in HD 154791/4U 1700+24

We present evidence for approximately 400-d variations in the radial velocity of HD 154791 (V934 Her), the suggested optical counterpart of 4U 1700+24. The variations are correlated with the previously reported approximately 400 d variations in the X-ray flux of 4U 1700+24, which supports the association of these two objects, as well as the identification of this system as the second known X-ray binary in which a neutron star accretes from the wind of a red giant. The HD 154791 radial velocity variations can be fit with an eccentric orbit with period 404 +/- 3 d, amplitude K=0.75 +/- 0.12 km/s and eccentricity e=0.26 +/- 0.15. There are also indications of variations on longer time scales >~ 2000 d. We have re-examined all available ASM data following an unusually large X-ray outburst in 1997-98, and confirm that the 1-d averaged 2-10 keV X-ray flux from 4U 1700+24 is modulated with a period of 400 +/- 20 d. The mean profile of the persistent X-ray variations was approximately sinusoidal, with an amplitude of 0.108 +/- 0.012 ASM count/s (corresponding to 31% rms). The epoch of X-ray maximum was approximately 40 d after the time of periastron according to the eccentric orbital fit. If the 400 d oscillations from HD 154791/4U 1700+24 are due to orbital motion, then the system parameters are probably close to those of the only other neutron-star symbiotic-like binary, GX 1+4. We discuss the similarities and differences between these two systems.Comment: 6 pages, 2 figures; accepted by Ap

A Lagrangian Integrator for Planetary Accretion and Dynamics (LIPAD)

We presented the first particle based, Lagrangian code that can follow the collisional/accretional/dynamical evolution of a large number of km-sized planetesimals through the entire growth process to become planets. We refer to it as the 'Lagrangian Integrator for Planetary Accretion and Dynamics' or LIPAD. LIPAD is built on top of SyMBA, which is a symplectic $N$-body integrator. In order to handle the very large number of planetesimals required by planet formation simulations, we introduce the concept of a `tracer' particle. Each tracer is intended to represent a large number of disk particles on roughly the same orbit and size as one another, and is characterized by three numbers: the physical radius, the bulk density, and the total mass of the disk particles represented by the tracer. We developed statistical algorithms that follow the dynamical and collisional evolution of the tracers due to the presence of one another. The tracers mainly dynamically interact with the larger objects (`planetary embryos') in the normal N-body way. LIPAD's greatest strength is that it can accurately model the wholesale redistribution of planetesimals due to gravitational interaction with the embryos, which has recently been shown to significantly affect the growth rate of planetary embryos . We verify the code via a comprehensive set of tests which compare our results with those of Eulerian and/or direct N-body codes.Comment: Accepted to the Astronomical Journal. See http://www.boulder.swri.edu/~hal/LIPAD.html for more detail including animation

Modeling the Formation of Giant Planet Cores I: Evaluating Key Processes

One of the most challenging problems we face in our understanding of planet formation is how Jupiter and Saturn could have formed before the the solar nebula dispersed. The most popular model of giant planet formation is the so-called 'core accretion' model. In this model a large planetary embryo formed first, mainly by two-body accretion. This is then followed by a period of inflow of nebular gas directly onto the growing planet. The core accretion model has an Achilles heel, namely the very first step. We have undertaken the most comprehensive study of this process to date. In this study we numerically integrate the orbits of a number of planetary embryos embedded in a swarm of planetesimals. In these experiments we have included: 1) aerodynamic gas drag, 2) collisional damping between planetesimals, 3) enhanced embryo cross-sections due to their atmospheres, 4) planetesimal fragmentation, and 5) planetesimal driven migration. We find that the gravitational interaction between the embryos and the planetesimals lead to the wholesale redistribution of material - regions are cleared of material and gaps open near the embryos. Indeed, in 90% of our simulations without fragmentation, the region near that embryos is cleared of planetesimals before much growth can occur. The remaining 10%, however, the embryos undergo a burst of outward migration that significantly increases growth. On timescales of ~100,000 years, the outer embryo can migrate ~6 AU and grow to roughly 30 Earth-masses. We also find that the inclusion of planetesimal fragmentation tends to inhibit growth.Comment: Accepted to AJ, 62 pages 11 figure

Activities of \gamma-ray emitting isotopes in rainwater from Greater Sudbury, Canada following the Fukushima incident

We report the activity measured in rainwater samples collected in the Greater Sudbury area of eastern Canada on 3, 16, 20, and 26 April 2011. The samples were gamma-ray counted in a germanium detector and the isotopes 131I and 137Cs, produced by the fission of 235U, and 134Cs, produced by neutron capture on 133Cs, were observed at elevated levels compared to a reference sample of ice-water. These elevated activities are ascribed to the accident at the Fukushima Dai-ichi nuclear reactor complex in Japan that followed the 11 March earthquake and tsunami. The activity levels observed at no time presented health concerns.Comment: 4 pages, 8 figure