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

Conditional strategies and the evolution of cooperation in spatial public goods games

The fact that individuals will most likely behave differently in different situations begets the introduction of conditional strategies. Inspired by this, we study the evolution of cooperation in the spatial public goods game, where besides unconditional cooperators and defectors, also different types of conditional cooperators compete for space. Conditional cooperators will contribute to the public good only if other players within the group are likely to cooperate as well, but will withhold their contribution otherwise. Depending on the number of other cooperators that are required to elicit cooperation of a conditional cooperator, the latter can be classified in as many types as there are players within each group. We find that the most cautious cooperators, such that require all other players within a group to be conditional cooperators, are the undisputed victors of the evolutionary process, even at very low synergy factors. We show that the remarkable promotion of cooperation is due primarily to the spontaneous emergence of quarantining of defectors, which become surrounded by conditional cooperators and are forced into isolated convex "bubbles" from where they are unable to exploit the public good. This phenomenon can be observed only in structured populations, thus adding to the relevance of pattern formation for the successful evolution of cooperation.Comment: 7 two-column pages, 7 figures; accepted for publication in Physical Review