Low Mach Number Modeling of Type Ia Supernovae

We introduce a low Mach number equation set for the large-scale numerical simulation of carbon-oxygen white dwarfs experiencing a thermonuclear deflagration. Since most of the interesting physics in a Type Ia supernova transpires at Mach numbers from 0.01 to 0.1, such an approach enables both a considerable increase in accuracy and savings in computer time compared with frequently used compressible codes. Our equation set is derived from the fully compressible equations using low Mach number asymptotics, but without any restriction on the size of perturbations in density or temperature. Comparisons with simulations that use the fully compressible equations validate the low Mach number model in regimes where both are applicable. Comparisons to simulations based on the more traditional anelastic approximation also demonstrate the agreement of these models in the regime for which the anelastic approximation is valid. For low Mach number flows with potentially finite amplitude variations in density and temperature, the low Mach number model overcomes the limitations of each of the more traditional models and can serve as the basis for an accurate and efficient simulation tool.Comment: Accepted for publication in the Astrophysical Journal 31 pages, 5 figures (some figures degraded in quality to conserve space

Privacy and the Press since Time, Inc. v. Hill

In this article, the authors do not propose to discuss the innumerable ways in which one\u27s privacy is invaded or to survey the entire sweep of the law of privacy, but rather attempt to trace briefly its development, with particular emphasis on how the law has affected the mass media since the Supreme Court decided its first privacy case, Time, Inc. v. Hill, in 1967. In so doing, we hope to add somewhat to the understanding of this unsettled area of law

Patch-based Adaptive Mesh Refinement for Multimaterial Hydrodynamics

We present a patch-based direct Eulerian adaptive mesh refinement (AMR) algorithm for modeling real equation-of-state, multimaterial compressible flow with strength. Our approach to AMR uses a hierarchical, structured grid approach first developed by (Berger and Oliger 1984), (Berger and Oliger 1984). The grid structure is dynamic in time and is composed of nested uniform rectangular grids of varying resolution. The integration scheme on the grid hierarchy is a recursive procedure in which the coarse grids are advanced, then the fine grids are advanced multiple steps to reach the same time, and finally the coarse and fine grids are synchronized to remove conservation errors during the separate advances. The methodology presented here is based on a single grid algorithm developed for multimaterial gas dynamics by (Colella et al. 1993), refined by(Greenough et al. 1995), and extended to the solution of solid mechanics problems with significant strength by (Lomov and Rubin 2003). The single grid algorithm uses a second-order Godunov scheme with an approximate single fluid Riemann solver and a volume-of-fluid treatment of material interfaces. The method also uses a non-conservative treatment of the deformation tensor and an acoustic approximation for shear waves in the Riemann solver. This departure from a strict application of the higher-order Godunov methodology to the equation of solid mechanics is justified due to the fact that highly nonlinear behavior of shear stresses is rare. This algorithm is implemented in two codes, Geodyn and Raptor, the latter of which is a coupled rad-hydro code. The present discussion will be solely concerned with hydrodynamics modeling. Results from a number of simulations for flows with and without strength will be presented

The role of breast cancer oestrogen/progesterone receptor status in bone mineral density

This abstract was presented at the Osteoporosis Conference 2016, 7th - 9th November 2016, Birmingham, UK. This is the accepted manuscript version of the abstract. The final version is available online from Springer at: https://doi.org/10.1007/s00198-016-3743-zPublished versio

A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Grids using Directional Operator Splitting

An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional operator splitting, implementation of the scheme is rather straightforward. Extending the method for static walls from Klein et al., Phil. Trans. Roy. Soc., A367, no. 1907, 4559-4575 (2009), the scheme calculates fluxes needed for a conservative update of the near-wall cut-cells as linear combinations of standard fluxes from a one-dimensional extended stencil. Here the standard fluxes are those obtained without regard to the small sub-cell problem, and the linear combination weights involve detailed information regarding the cut-cell geometry. This linear combination of standard fluxes stabilizes the updates such that the time-step yielding marginal stability for arbitrarily small cut-cells is of the same order as that for regular cells. Moreover, it renders the approach compatible with a wide range of existing numerical flux-approximation methods. The scheme is extended here to time dependent rigid boundaries by reformulating the linear combination weights of the stabilizing flux stencil to account for the time dependence of cut-cell volume and interface area fractions. The two-dimensional tests discussed include advection in a channel oriented at an oblique angle to the Cartesian computational mesh, cylinders with circular and triangular cross-section passing through a stationary shock wave, a piston moving through an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil profile.Comment: 30 pages, 27 figures, 3 table

An adaptive projection method for the modeling of unsteady, low-Mach number combustion

In this paper the authors present an adaptive projection method for modeling unsteady, low-Mach reacting flow in an unconfined region. The equations they solve are based on a model for low-Mach number combustion that consists of the evolution equations for density, species concentrations, enthalpy, and momentum coupled with a constraint on the divergence of the flow. The algorithm is based on a projection methodology in which they first advance the evolution equations and then solve an elliptic equation to enforce the divergence constraint. The adaptive mesh refinement (AMR) scheme uses a time-varying, hierarchical grid structure composed of uniform rectangular grids of varying resolution. The integration scheme on the grid hierarchy is a recursive procedure in which a coarse grid is advanced, fine grids are advanced multiple steps to reach the same time as the coarse grid, and the coarse and the fine grids are synchronized. The method is valid for multiple grids on each level and multiple levels of refinement. The method is currently implemented for laminar, axisymmetric flames with a reduced kinetics mechanism and a Lewis number of unity. Two methane-air flames, one steady and the other flickering, are presented as numerical examples

Keck Planet Finder: design updates

The Keck Planet Finder (KPF) is a fiber-fed, high-resolution, high-stability spectrometer in development at the UC Berkeley Space Sciences Laboratory for the W.M. Keck Observatory. KPF is designed to characterize exoplanets via Doppler spectroscopy with a goal of a single measurement precision of 0.3 m s-1 or better, however its resolution and stability will enable a wide variety of astrophysical pursuits. Here we provide post-preliminary design review design updates for several subsystems, including: the main spectrometer, the fabrication of the Zerodur optical bench; the data reduction pipeline; fiber agitator; fiber cable design; fiber scrambler; VPH testing results and the exposure meter