In this project the principal investigator will continue his work on various problems in nonlinear continuum mechanics. In particular, he will look at the dynamics of elastic rods in three dimensions, the formation and evolution of "necks" in viscoelastic fibers, the equilibrium thermodynamics of periodic phases, and the minimum energy states of nematic liquid crystals. This work has enormous theoretical and technological implications. More and more one finds that technological advances are driven by improvements in the theory of nonlinear materials and the successful applications of that theory. In this project the principal investigator will continue his important studies of the mathematics and the physics that underlie various types of elastic, viscoelastic and crystalline materials. This work has applications to state-of-the-art problems in the production of high-strength polymers and liquid crystals of different shapes.
