CNA 2001 Summer School

** **

**Noel J. Walkington**

**ABSTRACT**: Liquid crystals, fluids containing elastic particles, and polymer
fluids, all exhibit non trivial macroscopic behavior due to
interactions occurring on micro/mesoscopic scales. The derivation of
rational models for these materials is a non-trivial task and results
in formidable systems of partial differential equations. Of these
problems the most complete theory is for Ericksen's model of liquid
crystals, and I will begin with a discussion of this theory. I will
then consider fluids containing elastic particles and present an
approach which eliminates the need consider different coordinate
systems for the particles (Lagrangian) and fluid (Eulerian). This
naturally leads to ideas developed in the physics community to model
polymer fluids and suggest alternative models for liquid crystals.
These latter ideas are not widely known in the mathematical community
and their connection with continuum mechanics is not clear.

This is joint work with C. Liu (Pennsylvania State University, USA)

Noel J. Walkington

Department of Mathematical Sciences

Carnegie Mellon University

Pittsburgh, PA 15213

email: noelw@andrew.cmu.edu