Weinan E
Department of Mathematics, Princeton University
We will present a molecular theory for inhomogeneous systems of rod-like molecules. This theory is an extension of the Doi theory for homogeneous system. By choosing appropriate interaction potential, this theory predicts both the nematic and various smectic phases. It can be used to study defect structures in liquid crystal phases. We will study the small Debroah number limit as well as the local limit for this model, and show that the classical Ericksen-Leslie equations are recovered if both limits are taken. We will also discuss how this formalism might be generalized to other systems of complex fluids.