An abstract class of two-dimensional geometry-driven free boundary problems is considered in which the evolution of the Cauchy transform of the time-evolving domain satisfies a partial differential equation of conservation type. This idea generalizes an association between free boundary problems and the inverse gravitational problem. It is shown that this class of free boundary problems admits ...

We study experimentally the shape of a granular heap formed pouring a granular material into a vertical Hele-Shaw cell and analyze the effect of the grain impact energy. We propose a continuous model for the steady profile of the heap that explicitly considers energy dissipation of flowing grains through inelastic collisions. We solve the model analytically and analyze the resulting height prof...

In this paper we study a mathematical model for the motion of a Stokesian fluid in a Hele-Shaw cell surrounded by a gas at uniform pressure. The model is based on a non-Newtonian version of Darcy’s law for the bulk fluid, as suggested in [9, 12]. Besides a general existence and uniqueness result for classical solutions, it is also shown that classical solutions exist globally and tend to circle...

Advances in computing have enabled microsecond all-atom molecular dynamics trajectories of protein folding that can be used to compare with and test critical assumptions of theoretical models. We show that recent simulations by the Shaw group (10, 11, 14, 15) are consistent with a key assumption of an Ising-like theoretical model that native structure grows in only a few regions of the amino ac...

Submitted for the DFD11 Meeting of The American Physical Society Hydrodynamic instability induced by a precipitation reaction in a Hele-Shaw cell YUKI ISHII, YUICHIRO NAGATSU, Nagoya Institute of Technology, 466-8555, Japan, ANNE DE WIT, Nonlinear Physical Chemistry Unit, CP 231, Université Libre de Bruxelles (ULB), 1050 Brussels, Belgium — We experimentally demonstrate hydrodynamic fingering d...