Chaos and Turbulent Nucleosynthesis Prior to a Supernova Explosion

Three-dimensional (3D), time dependent numerical simulations, of flow of matter in stars, now have sufficient resolution to be fully turbulent. The late stages of the evolution of massive stars, leading up to core collapse to a neutron star (or black hole), and often to supernova explosion and nucleosynthesis, are strongly convective because of vigorous neutrino cooling and nuclear heating. Unlike models based on current stellar evolutionary practice, these simulations show a chaotic dynamics characteristic of highly turbulent flow. Theoretical analysis of this flow, both in the Reynolds-averaged Navier-Stokes (RANS) framework and by simple dynamic models, show an encouraging consistency with the numerical results. It may now be possible to develop physically realistic and robust procedures for convection and mixing which (unlike 3D numerical simulation) may be applied throughout the long life times of stars. In addition, a new picture of the presupernova stages is emerging which is more dynamic and interesting (i.e., predictive of new and newly observed phenomena) than our previous one.Comment: 11 pages, 2 figures, Submitted to AIP Advances: Stardust, added figures and modest rewritin

Numerical simulations of heat explosion with convection in porous media

International audienceIn this article, we study the interaction between natural convection and heat explosion in porous media. The model consists of the heat equation with a nonlinear source term describing heat production due to an exothermic chemical reaction coupled with the Darcy law. Stationary and oscillating convection regimes and oscillating heat explosion are observed. The models with quasi-stationary and unstationary Darcy equation are compared

A wildland fire model with data assimilation

A wildfire model is formulated based on balance equations for energy and fuel, where the fuel loss due to combustion corresponds to the fuel reaction rate. The resulting coupled partial differential equations have coefficients that can be approximated from prior measurements of wildfires. An ensemble Kalman filter technique with regularization is then used to assimilate temperatures measured at selected points into running wildfire simulations. The assimilation technique is able to modify the simulations to track the measurements correctly even if the simulations were started with an erroneous ignition location that is quite far away from the correct one.Comment: 35 pages, 12 figures; minor revision January 2008. Original version available from http://www-math.cudenver.edu/ccm/report

3He-Driven Mixing in Low-Mass Red Giants: Convective Instability in Radiative and Adiabatic Limits

We examine the stability and observational consequences of mixing induced by 3He burning in the envelopes of first ascent red giants. We demonstrate that there are two unstable modes: a rapid, nearly adiabatic mode that we cannot identify with an underlying physical mechanism, and a slow, nearly radiative mode that can be identified with thermohaline convection. We present observational constraints that make the operation of the rapid mode unlikely to occur in real stars. Thermohaline convection turns out to be fast enough only if fluid elements have finger-like structures with a length to diameter ratio l/d > 10. We identify some potentially serious obstacles for thermohaline convection as the predominant mixing mechanism for giants. We show that rotation-induced horizontal turbulent diffusion may suppress the 3He-driven thermohaline convection. Another potentially serious problem for it is to explain observational evidence of enhanced extra mixing. The 3He exhaustion in stars approaching the red giant branch (RGB) tip should make the 3He mixing inefficient on the asymptotic giant branch (AGB). In spite of this, there are observational data indicating the presence of extra mixing in low-mass AGB stars similar to that operating on the RGB. Overmixing may also occur in carbon-enhanced metal-poor stars.Comment: 25 pages, 6 figures, modified version, accepted by Ap

Blow-up in a System of Partial Differential Equations with Conserved First Integral. Part II: Problems with Convection

A reaction-diffusion-convection equation with a nonlocal term is studied; the nonlocal operator acts to conserve the spatial integral of the unknown function as time evolves. The equations are parameterised by µ, and for µ = 1 the equation arises as a similarity solution of the Navier-Stokes equations and the nonlocal term plays the role of pressure. For µ = 0, the equation is a nonlocal reaction-diffusion problem. The aim of the paper is to determine for which values of the parameter µ blow-up occurs and to study its form. In particular, interest is focused on the three cases µ 1/2, and µ → 1. It is observed that, for any 0 ≤ µ ≤ 1/2, nonuniform global blow-up occurs; if 1/2 < µ < 1, then the blow-up is global and uniform, while for µ = 1 (the Navier-Stokes equations) there are exact solutions with initial data of arbitrarily large L_∞, L_2, and H^1 norms that decay to zero. Furthermore, one of these exact solutions is proved to be nonlinearly stable in L_2 for arbitrarily large supremum norm. An understanding of this transition from blow-up behaviour to decay behaviour is achieved by a combination of analysis, asymptotics, and numerical techniques