Abstract and Applied Analysis
Volume 2008 (2008), Article ID 854725, 10 pages
Extendability of Equilibria of Nematic Polymers
1Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA 95064, USA
2Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USA
Received 9 May 2008; Accepted 30 October 2008
Academic Editor: Nobuyuki Kenmochi
Copyright © 2008 Hongyun Wang and Hong Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The purpose of this paper is to study the extendability of equilibrium states of
rodlike nematic polymers with the Maier-Saupe intermolecular potential. We formulate equilibrium states as solutions of a nonlinear system and calculate the determinant of the Jacobian matrix of the nonlinear system. It is found that the Jacobian matrix is nonsingular everywhere except at two equilibrium states. These two special equilibrium states correspond to two points in the phase diagram. One point is the folding point where the stable prolate branch folds into the unstable prolate branch; the other point is the intersection point of the nematic branch and the isotropic branch where the unstable prolate state becomes the unstable oblate state. Our result establishes the existence and uniqueness of equilibrium states in the presence of small perturbations away from these two special equilibrium states.