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We analyze high resolution simulations of compressible, MHD turbulence with properties resembling conditions in galaxy clusters. The flow is driven to turbulence Mach number $\mathcal{M}_t \sim 1/2$ in an isothermal medium with an initially very weak, uniform seed magnetic field ($\beta = P_g/P_B = 10^6$). Since cluster turbulence is likely to result from a mix of sheared (solenoidal) and compressive forcing processes, we examine the distinct turbulence properties for both cases. In one set of simulations velocity forcing is entirely solenoidal ($\nabla\cdot \delta {\vec u} = 0$), while in the other it is entirely compressive ($\nabla\times \delta {\vec u} = 0$). Both cases develop a mixture of solenoidal and compressive turbulent motions, since each generates the other. The development of compressive turbulent motions leads to shocks, even when the turbulence is solenoidally forced and subsonic. Shocks, in turn, produce and amplify vorticity, which is especially important in compressively forced turbulence. To clarify those processes we include a pair of appendices that look in detail at vorticity evolution in association with shocks. From our simulation analyses we find that magnetic fields amplified to near saturation levels in predominantly solenoidal turbulence can actually enhance vorticity on small scales by concentrating and stabilizing shear. The properties, evolution rates and relative contributions of the kinetic and magnetic turbulent elements depend strongly on the character of the forcing. Specifically, shocks are stronger, but vorticity evolution and magnetic field amplification are slower and weaker when the turbulence is compressively forced. We identify a simple relation to estimate characteristic shock strengths in terms of the turbulence Mach number and the character of the forcing. Our results will be helpful in understanding flow motions in galaxy clusters., Comment: 46 pages, 14 figures. Accepted for publication in the Astrophysical Journal

Cluster media are dynamical, not static; observational evidence suggests they are turbulent. High-resolution simulations of the intracluster media (ICMs) and of idealized, similar media help us understand the complex physics and astrophysics involved. We present a brief overview of the physics behind ICM turbulence and outline the processes that control its development. High-resolution, compressible, isothermal MHD simulations are used to illustrate important dynamical properties of turbulence that develops in media with initially very weak magnetic fields. The simulations follow the growth of magnetic fields and reproduce the characteristics of turbulence. These results are also compared with full cluster simulations that have examined the properties of ICM turbulence., Comment: 7 pages, 2 figures. To appear the proceedings of the conference "Non-thermal Phenomena in Colliding Galaxy Clusters" (Nice, 15-18 November, 2010), Memorie della Societa Astronomica Italiana, vol 82, n 3

Depending on mass and metallicity as well as evolutionary phase, stars occasionally experience convective-reactive nucleosynthesis episodes. We specifically investigate the situation when nucleosynthetically unprocessed, H-rich material is convectively mixed with a He-burning zone, for example in convectively unstable shell on top of electron-degenerate cores in AGB stars, young white dwarfs or X-ray bursting neutron stars. Such episodes are frequently encountered in stellar evolution models of stars of extremely low or zero metal content [...] We focus on the convective-reactive episode in the very-late thermal pulse star Sakurai's object (V4334 Sagittarii). Asplund etal. (1999) determined the abundances of 28 elements, many of which are highly non-solar, ranging from H, He and Li all the way to Ba and La, plus the C isotopic ratio. Our simulations show that the mixing evolution according to standard, one-dimensional stellar evolution models implies neutron densities in the He that are too low to obtain a significant neutron capture nucleosynthesis on the heavy elements. We have carried out 3D hydrodynamic He-shell flash convection [...] we assume that the ingestion process of H into the He-shell convection zone leads only after some delay time to a sufficient entropy barrier that splits the convection zone [...] we obtain significantly higher neutron densities (~few 10^15 1/cm^3) and reproduce the key observed abundance trends found in Sakurai's object. These include an overproduction of Rb, Sr and Y by about 2 orders of magnitude higher than the overproduction of Ba and La. Such a peculiar nucleosynthesis signature is impossible to obtain with the mixing predictions in our one-dimensional stellar evolution models. [...] We determine how our results depend on uncertainties of nuclear reaction rates, for example for the C13(\alpha, n)O16 reaction., Comment: ApJ in press, this revision contains several changes that improve clarity of presentation reflecting the suggestions made by the referee; this version represents no change in substance compared to version 1; some technical material has been moved to an appendix; an additional appendix deals in more detail with the combustion time scales; this version is practically identical to the ApJ version

The He-shell flash convection in AGB stars is the site for the high-temperature component of the s-process in low- and intermediate mass giants, driven by the Ne22 neutron source. [...] The upper convection boundary plays a critical role during the H-ingestion episode that may lead to neutron-bursts in the most metal-poor AGB stars. We address these problems through global 3-dimensional hydrodynamic simulations including the entire spherical He-shell flash convection zone (as oposed to the 3D box-in-a-star simulations). An important aspect of our current effort is to establish the feasibility of our appoach. We explain why we favour the explicit treatment over the anelastic approximation for this problem. The simulations presented in this paper use a Cartesian grid of 512^3 cells and have been run on four 8-core workstations for four days to simulate ~5000s, which corresponds to almost ten convective turn-over times. The convection layer extends radially at the simulated point in the flash evolution over 7 H_p pressure scale-heights and exceeds the size of the underlying core. Convection is dominated by large convective cells that fill more than an entire octant. [...], Comment: Talk contribution at Nuclei in the Cosmos X (2008, Mackinac Island, Michigan, USA)

We review the current state of modeling convective mixing in AGB stars. The focus is on results obtained through multi-dimensional hydrodynamic simulations of AGB convection, both in the envelope and the unstable He-shell. Using two different codes and a wide range of resolutions and modeling assumptions we find that mixing across convective boundaries is significant for He-shell flash convection. We present a preliminary quantitative analysis of this convectively induced extra mixing, based on a sub-set of our simulations. Other non-standard mixing will be discussed briefly., Comment: Invited conference paper given at "Why Galaxies Care About AGB Stars", Vienna, August 7-11, 2006, to appear in ASP Conference Series