Sheared nematic liquid crystal polymer monolayers
Discrete and continuous dynamical systems. Series B
We provide a comprehensive study on the planar (2D) orientational distributions of nematic polymers under an imposed shear flow of arbitrary strength. We extend previous analysis for persistence of equilibria in steady shear and for transitions to unsteady limit cycles, from closure models  to the Doi-Hess 2D kinetic equation. A variation on the Boltzmann distribution analysis of Constantin et al. [3, 4, 5] and others [8, 22, 23] for potential flow is developed to solve for all persistent
... or all persistent steady equilibria, and characterize parameter boundaries where steady states cease to exist, which predicts the transition to tumbling limit cycles. 2000 Mathematics Subject Classification. Primary: 82D60, 76A15; Secondary: 65Z05, 35Q99. Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.