Numerically investigating the morphology of the supernova remnant SN 1006 in the ambient medium with a density discontinuity

ABSTRACT Multiband observations on the Type Ia supernova remnant SN 1006 indicate peculiar properties in its morphologies of emission in the radio, optical, and X-ray bands. In the hard X-rays, the remnant is bilateral with two opposite bright limbs with prominent protrusions. Moreover, a filament has been detected at the radio, optical, and soft X-ray wavelengths. The reason for these peculiar features in the morphologies of the remnant is investigated using 3D HD simulations. With the assumption that the supernova ejecta are evolved in the ambient medium with a density discontinuity, the radius of the remnant’s boundary is smaller in the tenuous medium, and the shell consists of two hemispheres with different radii. Along particular line of sights, protrusions appear on the periphery of the remnants since the emission from the edge of the hemisphere with a larger radius is located outside that from the shell of the small hemisphere. Furthermore, the north-west filament of SN 1006 arises as a result of the intersection of the line of sight and the shocked material near the edges of the two hemispheres. It can be concluded that the protrusions on the north-east and south-west limbs and the north-west filament in the morphologies of SN 1006 can be reproduced as the remnants interacting with the medium with a density discontinuity.

Homicides and the Age of Criminal Responsibility: A Density Discontinuity Approach

We employ a density discontinuity design to evaluate the deterrence effect of more severe punishments around the legal age of criminal responsibility in Brazil. Motivated by the criminology literature, we propose a novel proxy based on the inherent risk underlying criminal activities. Using violent death rates as a proxy for an individual's involvement in violent crime, we find no discernible deterrence effects. We additionally study arrest data from the country's third most populous state, Rio de Janeiro, and discuss the advantages of our proxy in light of potential underreporting biases from using criminal records.

On the Aspects of a Convergent Shock Wave Impinging a Perturbed Density Interface

The detailed characterization of a fluid flow following a convergent shock wave impinging a perturbed density interface is an extremely complex task as this flow combines geometry effects, compressibility effects and turbulence. Nonetheless, more understanding is necessary to be able to develop models that help accurately predict the flow behavior when occurring in engineering applications. Such an application is Inertial Confinement Fusion (ICF), where turbulent mixing induced by the interaction of the shock wave with the fuel pellet is detrimental to the fusion process. This interaction triggers mixing due to baroclinic vorticity deposition at the density interface in a phenomenon known as the Richtmyer-Meshkov Instability (RM). Next, the Rayleigh-Taylor Instability (RT) is driving the final growth of the mixing layer limited by secondary instabilities such as the Kelvin-Helmholtz Instability (KH). These classical hydrodynamic instabilities (HI) trigger the mixing process that leads ultimately to a highly-mixed fluid layer. For this study, we simulate a cylindrical Sulfur hexafluoride (SF6) target immersed into an air medium. The incident shock wave is regarded as a Chisnell-type converging shock wave impinging into a perturbed cylindrical density discontinuity generated with a wave-like spatial perturbation spectra. Parameters of interest are the growth rate and width of the mixing layer at the density discontinuity. This study aims at describing and quantifying relevant aspects of these flows coupling mixing layer growth with perturbation modes.

Manipulation Testing Based on Density Discontinuity

In this article, we introduce two community-contributed commands, rddensity and rdbwdensity, that implement automatic manipulation tests based on density discontinuity and are constructed using the results for local-polynomial density estimators in Cattaneo, Jansson, and Ma (2017b, Simple local polynomial density estimators, Working paper, University of Michigan). These new tests exhibit better size properties (and more power under additional assumptions) than other conventional approaches currently available in the literature. The first command, rddensity, implements manipulation tests based on a novel local-polynomial density estimation technique that avoids prebinning of the data (improving size properties) and allows for restrictions on other features of the model (improving power properties). The second command, rdbwdensity, implements several bandwidth selectors specifically tailored for the manipulation tests discussed herein. We also provide a companion R package with the same syntax and capabilities as rddensity and rdbwdensity.