9629133 E This work is supported by a Presidential Early Career Award for Scientists and Engineers. The research component will focus on the understanding and modeling of complex materials and complex fluids. This includes polymeric liquids (of which liquid crystal polymers are one example), turbulent flows, and flux flows in type-II superconductors, etc. The work on liquid crystals and polymers includes two aspects: (1) the phase separation process and (2) the hydrodynamics of liquid crystal polymers. The main issues for the first problem are the dynamics and morphology for polymerization driven phase transition and the interplay between phase separation and orientational order. For the second problem, the role of defects in the hydrodynamics of large molecule liquid crystals is of interest. The focus of the work on turbulent flows will be on turbulence models and large eddy simulation. The understanding of macroscopic instabilities of flux fronts and flux flows in type-II semiconductors requires a macroscopic theory of flux flows. A macroscopic theory for thin films has been developed by considering the hydrodynamics of interacting vortices in combination with a novel interfacial boundary condition. The approaches to these three problems involve similar steps: (1) establishing continuum models under the guidelines of nonequilibrium thermodynamics, (2) developing effective numerical methods, (3) using asymptotic analysis of simplified situations to provide insight, and (4) identifying prototypical problems for rigorous mathematical analysis. The investigator has worked toward enhancing the curriculum at his institution through the development of special courses in computational incompressible fluid mechanics and materials science and has been actively engaged in summer programs to enhance interactions among different groups (university faculty, high school teachers, students) in the mathematical sciences community. The Presid ent Early Career Awards for Scientists and Engineers (PECASE) were created to recognize demonstrated excellence and promise of future success in scientific or engineering research, and the potential for eventual leadership of the awardees in their respective fields. These awards are designed to produce a prominent cadre of scientists and engineers and to encourage their continued development.
