ECONOMIC AND ENVIRONMENTAL IMPACTS OF NUTRIENT LOSS REDUCTIONS ON DAIRY AND DAIRY/POULTRY FARMS

Livestock Production/Industries,

Dimers on two-dimensional lattices

We consider close-packed dimers, or perfect matchings, on two-dimensional regular lattices. We review known results and derive new expressions for the free energy, entropy, and the molecular freedom of dimers for a number of lattices including the simple-quartic (4^4), honeycomb (6^3), triangular (3^6), kagome (3.6.3.6), 3-12 (3.12^2) and its dual [3.12^2], and 4-8 (4.8^2) and its dual Union Jack [4.8^2] Archimedean tilings. The occurrence and nature of phase transitions are also analyzed and discussed.Comment: Typos corrections in Eqs. (28), (32) and (43

Vacancy localization in the square dimer model

We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. With this formalism, we can address the question of the possible motion of the vacancy induced by dimer slidings. We find a probability 57/4-10Sqrt[2] for the vacancy to be strictly jammed in an infinite system. More generally, the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 9/8. On a finite system, the probability that a vacancy in the bulk can reach the boundary falls off as a power law of the system size with exponent 1/4. The resultant weak localization of vacancies still allows for unbounded diffusion, characterized by a diffusion exponent that we relate to that of diffusion on spanning trees. We also implement numerical simulations of the model with both free and periodic boundary conditions.Comment: 35 pages, 24 figures. Improved version with one added figure (figure 9), a shift s->s+1 in the definition of the tree size, and minor correction

The TAOS Project: Upper Bounds on the Population of Small KBOs and Tests of Models of Formation and Evolution of the Outer Solar System

We have analyzed the first 3.75 years of data from TAOS, the Taiwanese American Occultation Survey. TAOS monitors bright stars to search for occultations by Kuiper Belt Objects (KBOs). This dataset comprises 5e5 star-hours of multi-telescope photometric data taken at 4 or 5 Hz. No events consistent with KBO occultations were found in this dataset. We compute the number of events expected for the Kuiper Belt formation and evolution models of Pan & Sari (2005), Kenyon & Bromley (2004), Benavidez & Campo Bagatin (2009), and Fraser (2009). A comparison with the upper limits we derive from our data constrains the parameter space of these models. This is the first detailed comparison of models of the KBO size distribution with data from an occultation survey. Our results suggest that the KBO population is comprised of objects with low internal strength and that planetary migration played a role in the shaping of the size distribution.Comment: 18 pages, 16 figures, Aj submitte

Gravitational Stirring in Planetary Debris Disks

We describe gravitational stirring models of planetary debris disks using a new multi-annulus planetesimal evolution code. The current code includes gravitational stirring and dynamical friction; future studies will include coagulation, fragmentation, Poynting-Robertson drag, and other physical processes. We use the results of our calculations to investigate the physical conditions required for small bodies in a planetesimal disk to reach the shattering velocity and begin a collisional cascade. Our results demonstrate that disks composed primarily of bodies with a single size will not undergo a collisional cascade which produces small dust grains at 30-150 AU on timescales of 1 Gyr or smaller. Disks with a size distribution of bodies reach conditions necessary for a collisional cascade in 10 Myr to 1 Gyr if the disk is at least as massive as a minimum mass solar nebula and if the disk contains objects with radii of 500 km or larger. The estimated 500 Myr survival time for these disks is close to the median age of roughly 400 Myr derived for nearby stars with dusty disks.Comment: 23 pages of text + 16 Figures; to appear in the Astronomical Journal, January 200

Discovery of an Unbound Hyper-Velocity Star in the Milky Way Halo

We have discovered a star, SDSS J090745.0+024507, leaving the Galaxy with a heliocentric radial velocity of +853+-12 km/s, the largest velocity ever observed in the Milky Way halo. The star is either a hot blue horizontal branch star or a B9 main sequence star with a heliocentric distance ~55 kpc. Corrected for the solar reflex motion and to the local standard of rest, the Galactic rest-frame velocity is +709 km/s. Because its radial velocity vector points 173.8 deg from the Galactic center, we suggest that this star is the first example of a hyper-velocity star ejected from the Galactic center as predicted by Hills and later discussed by Yu & Tremaine. The star has [Fe/H]~0, consistent with a Galactic center origin, and a travel time of <80 Myr from the Galactic center, consistent with its stellar lifetime. If the star is indeed traveling from the Galactic center, it should have a proper motion of 0.3 mas/yr observable with GAIA. Identifying additional hyper-velocity stars throughout the halo will constrain the production rate history of hyper-velocity stars at the Galactic center.Comment: 4 pages, submitted to ApJ Letter

First Results From The Taiwanese-American Occultation Survey (TAOS)

Results from the first two years of data from the Taiwanese-American Occultation Survey (TAOS) are presented. Stars have been monitored photometrically at 4 Hz or 5 Hz to search for occultations by small (~3 km) Kuiper Belt Objects (KBOs). No statistically significant events were found, allowing us to present an upper bound to the size distribution of KBOs with diameters 0.5 km < D < 28 km.Comment: 5 pages, 5 figure, accepted in Ap

Discovery of a Transiting Planet Near the Snow-Line

In most theories of planet formation, the snow-line represents a boundary between the emergence of the interior rocky planets and the exterior ice giants. The wide separation of the snow-line makes the discovery of transiting worlds challenging, yet transits would allow for detailed subsequent characterization. We present the discovery of Kepler-421b, a Uranus-sized exoplanet transiting a G9/K0 dwarf once every 704.2 days in a near-circular orbit. Using public Kepler photometry, we demonstrate that the two observed transits can be uniquely attributed to the 704.2 day period. Detailed light curve analysis with BLENDER validates the planetary nature of Kepler-421b to >4 sigmas confidence. Kepler-421b receives the same insolation as a body at ~2AU in the Solar System and for a Uranian albedo would have an effective temperature of ~180K. Using a time-dependent model for the protoplanetary disk, we estimate that Kepler-421b's present semi-major axis was beyond the snow-line after ~3Myr, indicating that Kepler-421b may have formed at its observed location.Comment: 14 pages, 10 figures, 3 tables. Accepted in Ap

Accretion in the Early Kuiper Belt II. Fragmentation

We describe new planetesimal accretion calculations in the Kuiper Belt that include fragmentation and velocity evolution. All models produce two power law cumulative size distributions, N_C propto r^{-q}, with q = 2.5 for radii less than 0.3-3 km and q = 3 for radii exceeding 1-3 km. The power law indices are nearly independent of the initial mass in the annulus, the initial eccentricity of the planetesimal swarm, and the initial size distribution of the planetesimal swarm. The transition between the two power laws moves to larger radii as the initial eccentricity increases. The maximum size of objects depends on their intrinsic tensile strength; Pluto formation requires a strength exceeding 300 erg per gram. Our models yield formation timescales for Pluto-sized objects of 30-40 Myr for a minimum mass solar nebula. The production of several `Plutos' and more than 10^5 50 km radius Kuiper Belt objects leaves most of the initial mass in 0.1-10 km radius objects that can be collisionally depleted over the age of the solar system. These results resolve the puzzle of large Kuiper Belt objects in a small mass Kuiper Belt.Comment: to appear in the Astronomical Journal (July 1999); 54 pages including 7 tables and 13 figure

Flickering in FU Orionis

We analyze new and published optical photometric data of FU Orionis, an eruptive pre-main sequence star. The outburst consists of a 5.5 mag rise at B with an e-folding timescale of roughly 50 days. The rates of decline at B and V are identical, 0.015 +- 0.001 mag per yr. Random fluctuations superimposed on this decline have an amplitude of 0.035 +- 0.005 mag at V and occur on timescales of 1 day or less. Correlations between V and the color indices U-B, B-V, and V-R indicate that the variable source has the optical colors of a G0 supergiant. We associate this behavior with small amplitude flickering of the inner accretion disk.Comment: 19 pages of text, 3 tables, and 6 figures to be published in the Astrophysical Journal, 10 March 200