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Defects in nematic polymer hydrodynamics: survey of our work over the past 10 years

Wednesday 9th January 2013 - 11:50 to 12:30
INI Seminar Room 1
The organizers, Peter and David, asked me to give a basic introduction to defects in nematic hydrodynamics and to cover whatever aspects of our group's work I felt appropriate for a kickoff workshop. The lecture touches on highlights of work with Qi Wang and Xiaofeng Yang at South Carolina and Ruhai Zhou at Old Dominion University. The first topic covered is the remarkable (to us) shear-induced dynamics of nematic polymers revealed by numerical solutions -- of various second-moment tensor approximations, and of the fully resolved Doi-Hess-Smoluchowski equation for the orientational PDF. Next we study nematic distortions arising due to physical boundary conditions at stationary and moving boundaries, in both 1D and 2D simulations, again revealing persistent non-stationary behavior in large regions of parameter space. Phase diagrams analogous to the monodomain problem show transitions between stationary and non-stationary attractors. What is the role of defects? We employ defect core detection and tracking diagnostics that apply independent of space dimension, and in dimensions 2 or higher we assess topology only after a positive test for defect cores. The fundamental role of oblate defect cores is illustrated in both 1D and 2D unsteady attractors. In each topic, open problems potentially of interest for rigorous mathematics are raised, with the hope of follow-up discussion during the program.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons