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Abstract
We provide a comprehensive study on the planar (2D) orienta- tional distributions of nematic polymers under an imposed shear flow of ar- bitrary strength. We extend previous analysis for persistence of equilibria in steady shear and for transitions to unsteady limit cycles, from closure models (21) to the Doi-Hess 2D kinetic equation. A variation on the Boltzmann distri- bution analysis of Constantin et al. (3, 4, 5) and others (8, 22, 23) for potential flow is developed to solve for all persistent steady equilibria, and characterize parameter boundaries where steady states cease to exist, which predicts the transition to tumbling limit cycles.
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