Power-Law Wrinkling Turbulence-Flame Interaction Model for Astrophysical Flames

We extend a model for turbulence-flame interactions (TFI) to consider astrophysical flames with a particular focus on combustion in type Ia supernovae. The inertial range of the turbulent cascade is nearly always under-resolved in simulations of astrophysical flows, requiring the use of a model in order to quantify the effects of subgrid-scale wrinkling of the flame surface. We provide implementation details to extend a well-tested TFI model to low-Prandtl number flames for use in the compressible hydrodynamics code FLASH. A local, instantaneous measure of the turbulent velocity is calibrated for FLASH and verification tests are performed. Particular care is taken to consider the relation between the subgrid rms turbulent velocity and the turbulent flame speed, especially for high-intensity turbulence where the turbulent flame speed is not expected to scale with the turbulent velocity. Finally, we explore the impact of different TFI models in full-star, three-dimensional simulations of type Ia supernovae.Comment: 20 pages, 12 figures, accepted to the Astrophysical Journa

White Dwarf Mergers on Adaptive Meshes I. Methodology and Code Verification

The Type Ia supernova progenitor problem is one of the most perplexing and exciting problems in astrophysics, requiring detailed numerical modeling to complement observations of these explosions. One possible progenitor that has merited recent theoretical attention is the white dwarf merger scenario, which has the potential to naturally explain many of the observed characteristics of Type Ia supernovae. To date there have been relatively few self-consistent simulations of merging white dwarf systems using mesh-based hydrodynamics. This is the first paper in a series describing simulations of these systems using a hydrodynamics code with adaptive mesh refinement. In this paper we describe our numerical methodology and discuss our implementation in the compressible hydrodynamics code CASTRO, which solves the Euler equations, and the Poisson equation for self-gravity, and couples the gravitational and rotation forces to the hydrodynamics. Standard techniques for coupling gravitation and rotation forces to the hydrodynamics do not adequately conserve the total energy of the system for our problem, but recent advances in the literature allow progress and we discuss our implementation here. We present a set of test problems demonstrating the extent to which our software sufficiently models a system where large amounts of mass are advected on the computational domain over long timescales. Future papers in this series will describe our treatment of the initial conditions of these systems and will examine the early phases of the merger to determine its viability for triggering a thermonuclear detonation.Comment: Accepted for publication in the Astrophysical Journa

Winter Conditions Influence Biological Responses of Migrating Hummingbirds

Conserving biological diversity given ongoing environmental changes requires the knowledge of how organisms respond biologically to these changes; however, we rarely have this information. This data deficiency can be addressed with coordinated monitoring programs that provide field data across temporal and spatial scales and with process-based models, which provide a method for predicting how species, in particular migrating species that face different conditions across their range, will respond to climate change. We evaluate whether environmental conditions in the wintering grounds of broad-tailed hummingbirds influence physiological and behavioral attributes of their migration. To quantify winter ground conditions, we used operative temperature as a proxy for physiological constraint, and precipitation and the normalized difference vegetation index (NDVI) as surrogates of resource availability. We measured four biological response variables: molt stage, timing of arrival at stopover sites, body mass, and fat. Consistent with our predictions, we found that birds migrating north were in earlier stages of molt and arrived at stopover sites later when NDVI was low. These results indicate that wintering conditions impact the timing and condition of birds as they migrate north. In addition, our results suggest that biologically informed environmental surrogates provide a valuable tool for predicting how climate variability across years influences the animal populations

Simulations of Astrophysical Fluid Instabilities

We present direct numerical simulations of mixing at Rayleigh-Taylor unstable interfaces performed with the FLASH code, developed at the ASCI/Alliances Center for Astrophysical Thermonuclear Flashes at the University of Chicago. We present initial results of single-mode studies in two and three dimensions. Our results indicate that three-dimensional instabilities grow significantly faster than two-dimensional instabilities and that grid resolution can have a significant effect on instability growth rates. We also find that unphysical diffusive mixing occurs at the fluid interface, particularly in poorly resolved simulations.Comment: 3 pages, 1 figure. To appear in the proceedings of the 20th Texas Symposium on Relativistic Astrophysic

Trend-based analysis of a population model of the AKAP scaffold protein

We formalise a continuous-time Markov chain with multi-dimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system