Liquid-crystals are intermediate phases between solid and liquid states

CDSNS Colloquium
Monday, March 14, 2011 - 11:00
1 hour (actually 50 minutes)
Skiles 005
University of Kansas
They may flow like fluids but under constraints of mechanical energies from their crystal aspects. As a result, they exhibit very rich phenomena that grant them  tremendous applications in modern technology.  Based on works of Oseen, Z\"ocher,  Frank and others, a continuum theory (not most general but satisfactory to a great extent) for liquid-crystals was formulated by Ericksen and Leslie in 1960s.  We will  first give a brief introduction to this classical theory and then focus on various important special settings in both static and dynamic cases. These special flows are rather simple for classical fluids but are quite  nonlinear for liquid-crystals.  We are able to apply abstract theory of nonlinear dynamical systems upon  revealing specific structures of the problems at hands.