Comparisons studies between simulated variable density turbulent flows often consist of direct graphical representations where the level of agreement is determined by eye. This work demonstrates a formal validation methodology using an existing validation framework to examine the agreement between a simulated variable density jet flow and corresponding experimental data. Implicit large eddy simulations (ILES's) of a round jet and a plane jet with density ratio $s = 4.2$ were simulated using the compressible hydrodynamic code xRAGE. The jet growth, characterized by the spreading rates, was compared, and the difference between the simulations and the experiment was examined through jet structure diagnostics. The spreading rates were found to be larger than the experimental values, primarily due to resolution issues in the simulations, a fact that is quantified by the validation metric analysis.

Gamma-ray astronomy explores the most energetic photons in nature to address some of the most pressing puzzles in contemporary astrophysics. It encompasses a wide range of objects and phenomena: stars, supernovae, novae, neutron stars, stellar-mass black holes, nucleosynthesis, the interstellar medium, cosmic rays and relativistic-particle acceleration, and the evolution of galaxies. MeV gamma-rays provide a unique probe of nuclear processes in astronomy, directly measuring radioactive decay, nuclear de-excitation, and positron annihilation. The substantial information carried by gamma-ray photons allows us to see deeper into these objects, the bulk of the power is often emitted at gamma-ray energies, and radioactivity provides a natural physical clock that adds unique information. New science will be driven by time-domain population studies at gamma-ray energies. This science is enabled by next-generation gamma-ray instruments with one to two orders of magnitude better sensitivity, larger sky coverage, and faster cadence than all previous gamma-ray instruments. This transformative capability permits: (a) the accurate identification of the gamma-ray emitting objects and correlations with observations taken at other wavelengths and with other messengers; (b) construction of new gamma-ray maps of the Milky Way and other nearby galaxies where extended regions are distinguished from point sources; and (c) considerable serendipitous science of scarce events -- nearby neutron star mergers, for example. Advances in technology push the performance of new gamma-ray instruments to address a wide set of astrophysical questions.

We discuss the challenges of modeling X-ray bursts in multi-dimensions, review the different calculations done to date, and discuss our new set of ongoing simulations. We also describe algorithmic improvements that may help in the future to offset some of the expense of these simulations, and describe what may be possible with exascale computing.

We describe the AMReX suite of astrophysics codes and their application to modeling problems in stellar astrophysics. Maestro is tuned to efficiently model subsonic convective flows while Castro models the highly compressible flows associated with stellar explosions. Both are built on the block-structured adaptive mesh refinement library AMReX. Together, these codes enable a thorough investigation of stellar phenomena, including Type Ia supernovae and X-ray bursts. We describe these science applications and the approach we are taking to make these codes performant on current and future many-core and GPU-based architectures.

Based on accounting data, we propose an alternative measure, i.e. aggregate z-score and minus one z-score, for assessing systemic risk contributions. The z-score based systemic risk measure is developed on the idea that systemic risk contribution of each bank can be captured by the risk taking of a banking system including all banks and all-banks-but one, which is defined as the Leave-One-Out approach. Using an international sample of 61 large banks from 17 countries, we test the effectiveness of the z-score based approach in measuring systemic risk contributions, with the comparisons with commonly-used marketbased methods. The z-score based method can clearly identify greater systemic significance of global systemically important banks, although different measures cannot agree on the ranking of individual banks’ systemic significance. We find positive rank correlations between the z-score based approach and MES or ∆CoVaR. The easy computation of the zscore based measure and its ability to include both listed and unlisted banks contribute to the measurement of systemic risk, especially for banks without share market data available.

We perform the first detailed three-dimensional simulation of low Mach number convection preceding runaway thermonuclear ignition in a mixed H/He X-ray burst. Our simulations include a moderate-sized, approximate network that captures hydrogen and helium burning up through rp-process breakout. We look at the difference between two- and three-dimensional convective fields, including the details of the turbulent convection.

Our understanding of stars and their fates is based on coupling observations to theoretical models. Unlike laboratory physicists, we cannot perform experiments on stars, but rather must patiently take what nature allows us to observe. Simulation offers a means of virtual experimentation, enabling a detailed understanding of the most violent ongoing explosions in the Universe---the deaths of stars.

This is a White Paper in support of the mission concept of the Large Observatory for X-ray Timing (LOFT), proposed as a medium-sized ESA mission. We discuss the potential of LOFT for the study of thermonuclear X-ray bursts on accreting neutron stars. For a summary, we refer to the paper.

We present high-resolution, full-star simulations of the post-ignition phase of Type Ia supernovae using the compressible hydrodynamics code Castro. Initial conditions, including the turbulent velocity field and ignition site, are imported directly from a simulation of the last few hours of presupernova convection using a low Mach number code, Maestro. Adaptive mesh refinement allows the initial burning front to be modeled with an effective resolution of 36,864^3 zones ( 136 m/zone). The initial rise and expansion of the deflagration front are tracked until burning reaches the star's edge and the role of the background turbulence on the flame is investigated. The effect of artificially moving the ignition location closer to the star's center is explored. The degree to which turbulence affects the burning front decreases with increasing ignition radius since the buoyancy force is stronger at larger radii. Even central ignition — in the presence of a background convective flow field — is rapidly carried off-center as the flame is carried by the flow field. We compare our results to analytic models for burning thermals, and find that they reproduce the general trends of the bubble's size and mass, but underpredict the amount of buoyant acceleration due to simplifying assumptions of the bubble's properties. Overall, we find that the amount of mass that burns prior to flame break out is small, consistent with a "gravitationally confined detonation" occurring at a later epoch, but additional burning will occur following breakout that may modify this conclusion.

Type I X-ray Bursts (XRBs) are thermonuclear explosions of accreted material on the surfaces of a neutron stars in low mass X-ray binaries. Prior to the ignition of a subsonic burning front, runaway burning at the base of the accreted layer drives convection that mixes fuel and heavy-element ashes. In this second paper in a series, we explore the behavior of this low Mach number convection in mixed hydrogen/helium layers on the surface of a neutron star using two-dimensional simulations with the Maestro code. Maestro takes advantage of the highly subsonic flow field by filtering dynamically unimportant sound waves while retaining local compressibility effects, such as those due to stratification and energy release from nuclear reactions. In these preliminary calculations, we find that the rp-process approximate network creates a convective region that is split into two layers. While this splitting appears artificial due to the approximations of the network regarding nuclear flow out of the breakout reaction 18Ne(a,p)21Na, these calculations hint at further simplifications and improvements of the burning treatment for use in subsequent calculations in three dimensions for a future paper.

A leading model for Type Ia supernovae (SNe Ia) begins with a white dwarf near the Chandrasekhar mass that ignites a degenerate thermonuclear runaway close to its center and explodes. In a series of papers, we shall explore the consequences of ignition at several locations within such dwarfs. Here we assume central ignition, which has been explored before, but is worth revisiting, if only to validate those previous studies and to further elucidate the relevant physics for future work. A perturbed sphere of hot iron ash with a radius of similar to 100 km is initialized at the middle of the star. The subsequent explosion is followed in several simulations using a thickened flame model in which the flame speed is either fixed-within the range expected from turbulent combustion-or based on the local turbulent intensity. Global results, including the explosion energy and bulk nucleosynthesis (e.g., Ni-56 of 0.48-0.56 M-circle dot) turn out to be insensitive to this speed. In all completed runs, the energy released by the nuclear burning is adequate to unbind the star, but not enough to give the energy and brightness of typical SNe Ia. As found previously, the chemical stratification observed in typical events is not reproduced. These models produce a large amount of unburned carbon and oxygen in central low velocity regions, which is inconsistent with spectroscopic observations, and the intermediate mass elements and iron group elements are strongly mixed during the explosion.

Cosmologists have used the light curves of Type Ia supernovae (SN Ia) as tools for surveying vast distances. Previous simulations have used coarse resolution and artificial initial conditions that substantially influenced their outcome. Here, we have the unique advantage of being able to import the results from previous simulations of convection leading to ignition from our low Mach number code, MAESTRO, directly into our compressible code, CASTRO. These initial conditions include the location of ignition and the turbulence on the grid. In this video, we show the turbulence within the early "bubble" of a supernova via renderings of the magnitude of the vorticity within the simulation. We then focus on the highest values of the magnitude of vorticity to observe the formation of "vortex tubes".

We present multidimensional simulations of the early convective phase preceding ignition in a Type I X-ray burst using the low Mach number hydrodynamics code, MAESTRO. A low Mach number approach is necessary in order to perform long-time integration required to study such phenomena. Using MAESTRO, we are able to capture the expansion of the atmosphere due to large-scale heating while capturing local compressibility effects such as those due to reactions and thermal diffusion. We also discuss the preparation of one-dimensional initial models and the subsequent mapping into our multidimensional framework. Our method of initial model generation differs from that used in previous multidimensional studies, which evolved a system through multiple bursts in one dimension before mapping onto a multidimensional grid. In our multidimensional simulations, we find that the resolution necessary to properly resolve the burning layer is an order of magnitude greater than that used in the earlier studies mentioned above. We characterize the convective patterns that form and discuss their resulting influence on the state of the convective region, which is important in modeling the outburst itself.

The convective flow in the moments preceding the explosion of a Type Ia supernova determines where the initial flames that subsequently burn through the star first ignite. We continue our exploration of the final hours of this convection using the low Mach number hydrodynamics code, MAESTRO. We present calculations exploring the effects of slow rotation and show diagnostics that examine the distribution of likely ignition points. In the current calculations, we see a well-defined convection region persist up to the point of ignition, and we see that even a little rotation is enough to break the coherence of the convective flow seen in the radial velocity field. Our results suggest that off-center ignition may be favored, with ignition ranging out to a radius of 100 km and a maximum likelihood of ignition at a radius around 50 km.