Simulating Fluids Exhibiting Microstructure 

Noel Walkington
Departments of Mathematical Sciences,
Carnegie Mellon University

Liquid crystals, fluid mixtures, fluids containing elastic particles,
and polymer fluids, all exhibit non-trivial macroscopic behavior due
to interactions occurring on micro/mesoscopic scales.  Frequently the
particles involved are small enough to be influenced by Brownian
motion so the classical equations of mechanics must be coupled to
appropriate Fokker Planck equation(s).  The derivation of rational
models for these materials is a non-trivial task and results in
formidable systems of partial differential equations.  This talk will
focus on the formulation and properties of such equations, and the
analysis of algorithms to approximate their solution.