Nematic polymers have a more or less rigid backbone, and
alignment among the molecules gives rise to the nematic order.
With attributes of both ordinary liquids and crystalline solids,
nematic polymers have highly unusual flow behaviors, which bear
upon their processing as high-performance materials.
In this talk, I will describe finite-difference simulations
of a fascinating array of instabilities that may occur in a
sheared nematic polymer. Using the Leslie-Ericksen theory,
we solve the momentum and constitutive equations and thus
directly simulate the loss of stability of a solution and the
evolution of a new and stable one, which usually has a lower
degree of symmetry. In particular, we will explore the formation
of orientational defects as a consequence of flow-structure
coupling.
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