Extending a Hybrid Godunov Method for Radiation Hydrodynamics to Multiple Dimensions

This paper presents a hybrid Godunov method for three-dimensional radiation hydrodynamics. The multidimensional technique outlined in this paper is an extension of the one-dimensional method that was developed by Sekora & Stone 2009, 2010. The earlier one-dimensional technique was shown to preserve certain asymptotic limits and be uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. This paper gives the algorithmic details for constructing a multidimensional method. A future paper will present numerical tests that demonstrate the robustness of the computational technique across a wide-range of parameter space.Comment: 25 page

The Use and Abuse of Special-Purpose Entities in Public Finance

States increasingly are raising financing indirectly through special-purpose entities (SPEs), variously referred to as authorities, special authorities, or public authorities. Notwithstanding their long history and increasingly widespread use, relatively little is known or has been written about these entities. This article examines state SPEs and their functions, comparing them to SPEs used in corporate finance. States, even more than corporations, use these entities to reduce financial transparency and avoid public scrutiny, seriously threatening the integrity of public finance. The article analyzes how regulation could be designed in order to control that threat while maintaining the legitimate financing benefits provided by these state entities

Tactic behaviors in bacterial dynamics

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.Includes bibliographical references (leaves 89-90).The locomotion of a wide class of motile bacteria can be mathematically described as a biased random walk in three-dimensional space. Fluid mechanics and probability theory are invoked to model the dynamics of bacteria swimming using tactic behaviors (movements or reorientation in response to chemical, physical or environmental stimuli) in flowing, viscous media. Physical descriptions are developed for bacterial chemotaxis (response to chemical agents) near particles exuding attractants, a small-scale process with global-scale implications for the biogeochemistry of the oceans. Three cases were investigated: a stationary particle, a slowly moving particle and a particle that generates a hydrodynamic wake in the form of attached vortices. The key finding of this thesis consists in the discovery of several scenarios in which motile bacteria swimming via random walks put themselves at a disadvantage in their quest for food with respect to non-motile pacteria. Thus, there exist threshold values in nutrient gradients and bacterial chemosensory ability below which bacteria would be better served if they did not swim. In the presence of vortices, it was discovered that bacteria can exploit the recirculating flow field to vastly increase their nutrient supply, but only if they alter their swimming behavior as a function of the concentration field.(cont.) Otherwise, slow bacteria completely miss the hydrodynamic wake (and the high nutrient region) behind a nearby moving particle, while fast bacteria end up colonizing the particle (i.e. clustering around the particle and potentially anchoring themselves to it). These processes are currently under investigation in laboratory experiments using high-speed digital photography, for which software (BacTrackTM) was written that can locate and track multiple bacteria over time, with the aim of providing trajectories and their statistics and ultimately establish the importance of these phenomena for marine ecology and biogeochemistry. Preliminary experiments were conducted with Escherichia coli being exposed to ultraviolet radiation, documenting the known result of E. coli being repelled by UV radiation and providing a successful test bed for the reliability of the tracking software.by Michael David Sekora.S.B

A Hybrid Godunov Method for Radiation Hydrodynamics

From a mathematical perspective, radiation hydrodynamics can be thought of as a system of hyperbolic balance laws with dual multiscale behavior (multiscale behavior associated with the hyperbolic wave speeds as well as multiscale behavior associated with source term relaxation). With this outlook in mind, this paper presents a hybrid Godunov method for one-dimensional radiation hydrodynamics that is uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. Moreover, one finds that the technique preserves certain asymptotic limits. The method incorporates a backward Euler upwinding scheme for the radiation energy density and flux as well as a modified Godunov scheme for the material density, momentum density, and energy density. The backward Euler upwinding scheme is first-order accurate and uses an implicit HLLE flux function to temporally advance the radiation components according to the material flow scale. The modified Godunov scheme is second-order accurate and directly couples stiff source term effects to the hyperbolic structure of the system of balance laws. This Godunov technique is composed of a predictor step that is based on Duhamel's principle and a corrector step that is based on Picard iteration. The Godunov scheme is explicit on the material flow scale but is unsplit and fully couples matter and radiation without invoking a diffusion-type approximation for radiation hydrodynamics. This technique derives from earlier work by Miniati & Colella 2007. Numerical tests demonstrate that the method is stable, robust, and accurate across various parameter regimes.Comment: accepted for publication in Journal of Computational Physics; 61 pages, 15 figures, 11 table

Detecting Variability in Massive Astronomical Time-Series Data I: application of an infinite Gaussian mixture model

We present a new framework to detect various types of variable objects within massive astronomical time-series data. Assuming that the dominant population of objects is non-variable, we find outliers from this population by using a non-parametric Bayesian clustering algorithm based on an infinite GaussianMixtureModel (GMM) and the Dirichlet Process. The algorithm extracts information from a given dataset, which is described by six variability indices. The GMM uses those variability indices to recover clusters that are described by six-dimensional multivariate Gaussian distributions, allowing our approach to consider the sampling pattern of time-series data, systematic biases, the number of data points for each light curve, and photometric quality. Using the Northern Sky Variability Survey data, we test our approach and prove that the infinite GMM is useful at detecting variable objects, while providing statistical inference estimation that suppresses false detection. The proposed approach will be effective in the exploration of future surveys such as GAIA, Pan-Starrs, and LSST, which will produce massive time-series data.Comment: accepted for publication in MNRA

A New Approach to Innovation & Growth in the Texas Technology Corridor

Texas faces the challenge of maintaining and growing its capacity to innovate at a time when global competitors are aggressively pursuing markets that have generated economic success for Texas companies in the recent past. Thus, the Digital Convergence Initiative (DCI), a university/private/public venture was established to spur innovation, collaboration, and competitiveness in the region among 1600 digital convergence organizations in the Texas Technology Corridor. This article reports on one of DCI's efforts: the deployment of a method for technology strategic planning developed in U.S. intelligence agencies and used by some of the largest and most successful U.S. corporations but never before deployed in the service of regional economic development.IC2 Institut