Asymptotic Derivation and Numerical Investigation of Time-Dependent Simplified Pn Equations

The steady-state simplified Pn (SPn) approximations to the linear Boltzmann equation have been proven to be asymptotically higher-order corrections to the diffusion equation in certain physical systems. In this paper, we present an asymptotic analysis for the time-dependent simplified Pn equations up to n = 3. Additionally, SPn equations of arbitrary order are derived in an ad hoc way. The resulting SPn equations are hyperbolic and differ from those investigated in a previous work by some of the authors. In two space dimensions, numerical calculations for the Pn and SPn equations are performed. We simulate neutron distributions of a moving rod and present results for a benchmark problem, known as the checkerboard problem. The SPn equations are demonstrated to yield significantly more accurate results than diffusion approximations. In addition, for sufficiently low values of n, they are shown to be more efficient than Pn models of comparable cost.Comment: 32 pages, 7 figure

Mapping the Asymmetric Thick Disk: The Hercules Thick Disk Cloud

The stellar asymmetry of faint thick disk/inner halo stars in the first quadrant first reported by Larsen & Humphreys (1996) and investigated further by Parker et al. (2003, 2004) has been recently confirmed by SDSS (Juric et al. 2008). Their interpretation of the excess in the star counts as a ringlike structure, however, is not supported by critical complimentary data in the fourth quadrant not covered by SDSS. We present stellar density maps from the Minnesota Automated Plate Scanner (MAPS) Catalog of the POSS I showing that the overdensity does not extend into the fourth quadrant. The overdensity is most probably not a ring. It could be due to interaction with the disk bar, evidence for a triaxial thick disk, or a merger remnant/stream. We call this feature the Hercules Thick Disk Cloud.Comment: 11 pages, 5 figures, to be published in Astrophysical Journal Letter

Smaller, Closer, Dirtier: Diesel Backup Generators in California

Quantifies the threat to air quality and human health by backup generators, and examines air quality in Los Angeles, San Diego, Sacramento, and Fresno, with some analysis of San Francisco as well

Mapping the Asymmetric Thick Disk I. A Search for Triaxiality

A significant asymmetry in the distribution of faint blue stars in the inner Galaxy, Quadrant 1 (l = 20 to 45 degrees) compared to Quadrant 4 was first reported by Larsen & Humphreys (1996). Parker et al (2003, 2004) greatly expanded the survey to determine its spatial extent and shape and the kinematics of the affected stars. This excess in the star counts was subsequently confirmed by Juric et al. (2008) using SDSS data. Possible explanations for the asymmetry include a merger remnant, a triaxial Thick Disk, and a possible interaction with the bar in the Disk. In this paper we describe our program of wide field photometry to map the asymmetry to fainter magnitudes and therefore larger distances. To search for the signature of triaxiality, we extended our survey to higher Galactic longitudes. We find no evidence for an excess of faint blue stars at l > 55 degrees including the faintest magnitude interval. The asymmetry and star count excess in Quadrant 1 is thus not due to a triaxial Thick Disk.Comment: 36 pages, 8 figures. Accepted by Astronomical Journa

Mapping the Asymmetric Thick Disk: II Distance, Size and Mass of the Hercules Thick Disk Cloud

The Hercules Thick Disk Cloud (Larsen et al. 2008) was initially discovered as an excess in the number of faint blue stars between quadrants 1 and 4 of the Galaxy. The origin of the Cloud could be an interaction with the disk bar, a triaxial thick disk or a merger remnant or stream. To better map the spatial extent of the Cloud along the line of sight, we have obtained multi-color UBVR photometry for 1.2 million stars in 63 fields approximately 1 square degree each. Our analysis of the fields beyond the apparent boundaries of the excess have already ruled out a triaxial thick disk as a likely explanation (Larsen, Humphreys and Cabanela 2010) In this paper we present our results for the star counts over all of our fields, determine the spatial extent of the over density across and along the line of sight, and estimate the size and mass of the Cloud. Using photometric parallaxes, the stars responsible for the excess are between 1 and 6 kiloparsecs from the Sun, 0.5 -- 4 kpc above the Galactic plane, and extends approximately 3-4 kiloparsecs across our line of sight. It is thus a major substructure in the Galaxy. The distribution of the excess along our sight lines corresponds with the density contours of the bar in the Disk, and its most distant stars are directly over the bar. We also see through the Cloud to its far side. Over the entire 500 square degrees of sky containing the Cloud, we estimate more than 5.6 million stars and 1.9 million solar masses of material. If the over density is associated with the bar, it would exceed 1.4 billion stars and more than than 50 million solar masses. Finally, we argue that the Hercules-Aquila Cloud (Belokurov et al. 2007) is actually the Hercules Thick Disk Cloud.Comment: 52 pages, 13 figure

Instantaneous Pair Theory for High-Frequency Vibrational Energy Relaxation in Fluids

Notwithstanding the long and distinguished history of studies of vibrational energy relaxation, exactly how it is that high frequency vibrations manage to relax in a liquid remains somewhat of a mystery. Both experimental and theoretical approaches seem to say that there is a natural frequency range associated with intermolecular motions in liquids, typically spanning no more than a few hundred cm^{-1}. Landau-Teller-like theories explain how a solvent can absorb any vibrational energy within this "band", but how is it that molecules can rid themselves of superfluous vibrational energies significantly in excess of these values? We develop a theory for such processes based on the idea that the crucial liquid motions are those that most rapidly modulate the force on the vibrating coordinate -- and that by far the most important of these motions are those involving what we have called the mutual nearest neighbors of the vibrating solute. Specifically, we suggest that whenever there is a single solvent molecule sufficiently close to the solute that the solvent and solute are each other's nearest neighbors, then the instantaneous scattering dynamics of the solute-solvent pair alone suffices to explain the high frequency relaxation. The many-body features of the liquid only appear in the guise of a purely equilibrium problem, that of finding the likelihood of particularly effective solvent arrangements around the solute. These results are tested numerically on model diatomic solutes dissolved in atomic fluids (including the experimentally and theoretically interesting case of I_2 in Xe). The instantaneous pair theory leads to results in quantitative agreement with those obtained from far more laborious exact molecular dynamics simulations.Comment: 55 pages, 6 figures Scheduled to appear in J. Chem. Phys., Jan, 199

Non-linear optomechanical measurement of mechanical motion

Precision measurement of non-linear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of non-linear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator by exploiting the intrinsic non-linearity of the radiation pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100~pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can be used to experimentally explore collapse models of the wavefunction and the potential for mechanical-resonator-based quantum information and metrology applications.Comment: 8 pages, 4 figures, extensive supplementary material available with published versio

A dynamical and kinematical model of the Galactic stellar halo and possible implications for galaxy formation scenarios

We re-analyse the kinematics of the system of blue horizontal branch field (BHBF) stars in the Galactic halo (in particular the outer halo), fitting the kinematics with the model of radial and tangential velocity dispersions in the halo as a function of galactocentric distance r proposed by Sommer-Larsen, Flynn & Christensen (1994), using a much larger sample (almost 700) of BHBF stars. The basic result is that the character of the stellar halo velocity ellipsoid changes markedly from radial anisotropy at the sun to tangential anisotropy in the outer parts of the Galactic halo (r greater than approx 20 kpc). Specifically, the radial component of the stellar halo's velocity ellipsoid decreases fairly rapidly beyond the solar circle, from approx 140 +/- 10 km/s at the sun, to an asymptotic value of 89 +/- 19 km/s at large r. The rapid decrease in the radial velocity dispersion is matched by an increase in the tangential velocity dispersion, with increasing r. Our results may indicate that the Galaxy formed hierarchically (partly or fully) through merging of smaller subsystems - the 'bottom-up' galaxy formation scenario, which for quite a while has been favoured by most theorists and recently also has been given some observational credibility by HST observations of a potential group of small galaxies, at high redshift, possibly in the process of merging to a larger galaxy (Pascarelle et al 1996).Comment: Latex, 16 pages. 2 postscript figures. Submitted to the Astrophysical Journal. also available at http://astro.utu.fi/~cflynn/outerhalo.htm

Quantum Coherent String States in AdS_3 and SL(2,R) WZWN Model

In this paper we make the connection between semi-classical string quantization and exact conformal field theory quantization of strings in 2+1 Anti de Sitter spacetime. More precisely, considering the WZWN model corresponding to SL(2,R) and its covering group, we construct quantum {\it coherent} string states, which generalize the ordinary coherent states of quantum mechanics, and show that in the classical limit they correspond to oscillating circular strings. After quantization, the spectrum is found to consist of two parts: A continuous spectrum of low mass states (partly tachyonic) fulfilling the standard spin-level condition necessary for unitarity |j|< k/2, and a discrete spectrum of high mass states with asymptotic behaviour m^2\alpha'\propto N^2 (N positive integer). The quantization condition for the high mass states arises from the condition of finite positive norm of the coherent string states, and the result agrees with our previous results obtained using semi-classical quantization. In the k\to\infty limit, all the usual properties of coherent or {\it quasi-classical} states are recovered. It should be stressed that we consider the circular strings only for simplicity and clarity, and that our construction can easily be used for other string configurations too. We also compare our results with those obtained in the recent preprint hep-th/0001053 by Maldacena and Ooguri.Comment: Misprints corrected. Final version to appear in Phys. Rev.