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

Gamma-Ray Bursts: The Underlying Model

A pedagogical derivation is presented of the ``fireball'' model of gamma-ray bursts, according to which the observable effects are due to the dissipation of the kinetic energy of a relativistically expanding wind, a ``fireball.'' The main open questions are emphasized, and key afterglow observations, that provide support for this model, are briefly discussed. The relativistic outflow is, most likely, driven by the accretion of a fraction of a solar mass onto a newly born (few) solar mass black hole. The observed radiation is produced once the plasma has expanded to a scale much larger than that of the underlying ``engine,'' and is therefore largely independent of the details of the progenitor, whose gravitational collapse leads to fireball formation. Several progenitor scenarios, and the prospects for discrimination among them using future observations, are discussed. The production in gamma- ray burst fireballs of high energy protons and neutrinos, and the implications of burst neutrino detection by kilometer-scale telescopes under construction, are briefly discussed.Comment: In "Supernovae and Gamma Ray Bursters", ed. K. W. Weiler, Lecture Notes in Physics, Springer-Verlag (in press); 26 pages, 2 figure

Hospital Performance, the Local Economy, and the Local Workforce: Findings from a US National Longitudinal Study

Blustein and colleagues examine the associations between changes in hospital performance and their local economic resources. Locationally disadvantaged hospitals perform poorly on key indicators, raising concerns that pay-for-performance models may not reduce inequality

No short-cut in assessing trial quality: a case study

Assessing the quality of included trials is a central part of a systematic review. Many check-list type of instruments for doing this exist. Using a trial of antibiotic treatment for acute otitis media, Burke et al., BMJ, 1991, as the case study, this paper illustrates some limitations of the check-list approach to trial quality assessment. The general verdict from the check list type evaluations in nine relevant systematic reviews was that Burke et al. (1991) is a good quality trial. All relevant meta-analyses extensively used its data to formulate therapeutic evidence. My comprehensive evaluation, on the other hand, brought to the surface a series of serious problems in the design, conduct, analysis and report of this trial that were missed by the earlier evaluations. A check-list or instrument based approach, if used as a short-cut, may at times rate deeply flawed trials as good quality trials. Check lists are crucial but they need to be augmented with an in-depth review, and where possible, a scrutiny of the protocol, trial records, and original data. The extent and severity of the problems I uncovered for this particular trial warrant an independent audit before it is included in a systematic review