Higher-order finite element methods for elliptic problems with interfaces

We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of the problem. We prove optimal error estimates of the methods on general quasi-uniform and shape regular meshes in maximum norms. In addition, we apply the method to a Stokes interface problem, adding correction terms for the velocity and the pressure, obtaining optimal convergence results.Comment: 26 pages, 6 figures. An earlier version of this paper appeared on November 13, 2014 in http://www.brown.edu/research/projects/scientific-computing/reports/201

Dynamics of alliance formation and the egalitarian revolution

Arguably the most influential force in human history is the formation of social coalitions and alliances (i.e., long-lasting coalitions) and their impact on individual power. In most great ape species, coalitions occur at individual and group levels and among both kin and non-kin. Nonetheless, ape societies remain essentially hierarchical, and coalitions rarely weaken social inequality. In contrast, human hunter-gatherers show a remarkable tendency to egalitarianism, and human coalitions and alliances occur not only among individuals and groups, but also among groups of groups. Here, we develop a stochastic model describing the emergence of networks of allies resulting from within-group competition for status or mates between individuals utilizing dyadic information. The model shows that alliances often emerge in a phase transition-like fashion if the group size, awareness, aggressiveness, and persuasiveness of individuals are large and the decay rate of individual affinities is small. With cultural inheritance of social networks, a single leveling alliance including all group members can emerge in several generations. Our results suggest that a rapid transition from a hierarchical society of great apes to an egalitarian society of hunter-gatherers (often referred to as "egalitarian revolution") could indeed follow an increase in human cognitive abilities. The establishment of stable group-wide egalitarian alliances creates conditions promoting the origin of cultural norms favoring the group interests over those of individuals.Comment: 37 pages, 15 figure

PAH Formation in O-rich Planetary Nebulae

Polycyclic aromatic hydrocarbons (PAHs) have been observed in O-rich planetary nebulae towards the Galactic Bulge. This combination of oxygen-rich and carbon-rich material, known as dual-dust or mixed chemistry, is not expected to be seen around such objects. We recently proposed that PAHs could be formed from the photodissociation of CO in dense tori. In this work, using VISIR/VLT, we spatially resolved the emission of the PAH bands and ionised emission from the [SIV] line, confirming the presence of dense central tori in all the observed O-rich objects. Furthermore, we show that for most of the objects, PAHs are located at the outer edge of these dense/compact tori, while the ionised material is mostly present in the inner parts of these tori, consistent with our hypothesis for the formation of PAHs in these systems. The presence of a dense torus has been strongly associated with the action of a central binary star and, as such, the rich chemistry seen in these regions may also be related to the formation of exoplanets in post-common-envelope binary systems.Comment: 14, accepted for publication in the MNRAS Journa