Abstract and Applied Analysis
Volume 2008 (2008), Article ID 854725, 10 pages
doi:10.1155/2008/854725
Extendability of equilibria of nematic polymers
Hongyun Wang1
and Hong Zhou2
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
Abstract
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.