Naima Hammoud's abstract:    Thin films on curved surfaces are widely observed in coating and painting processes and wetting problems. In this talk I will present both theoretical and experimental results of thin film flows on a curved substrate under the effect of gravitational, viscous, and surface tension forces. When the film is on the underside of the substrate, gravity works as a destabilizing force, and a Rayleigh-Taylor type instability is expected (i.e. dripping). We consider the stability of a uniform thin film coating the "inside" of a curved geometry (circular cylinder, sphere, torus, etc.), and using asymptotic techniques, we find that instabilities are only transient in nature, thus showing that curvature helps stabilize the film. Experimental results agree very well with our asymptotic theory. Haoshu Tian's abstract:  The default of one bank can cause other banks to default through two channels: financial contagion in the inter-bank liability network and fire sale in the asset selling market. When the defaulted bank cannot fully pay its debt, the loss is transmitted to other banks. When banks rush to sell the same asset simultaneously, they may fall into a Nash equilibrium in which banks compete for liquidity and sell their assets at an artificially low price. In this paper, a model that incorporates these two channels is developed and analyzed theoretically. An algorithm for finding the state in which both the inter-bank liability network and the market are in equilibrium is proposed and tested.
Joint work with Professor Weinan E.