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June 2005 Axial Symmetry and Classification of Stationary Solutions of Doi-Onsager Equation on the Sphere with Maier-Saupe Potential
Hailiang Liu, Hui Zhang, Pingwen Zhang
Commun. Math. Sci. 3(2): 201-218 (June 2005).

Abstract

We study the structure of stationary solutions to the Doi-Onsager equation with Maier-Saupe potential on the sphere, which arises in the modelling of rigid rod-like molecules of polymers. The stationary solutions are shown to be necessarily a set of axially symmetric functions, and a complete classification of parameters for phase transitions to these stationary solutions is obtained. It is shown that the number of stationary solutions hinges on whether the potential intensity crosses two critical values LOOK HERE!!!![PROPORTIONAL TO??] 1 about 6.731393 and LOOK HERE!!!![PROPORTIONAL TO??]2=7.5. Furthermore, we present explicit formulas for all stationary solutions.

Citation

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Hailiang Liu. Hui Zhang. Pingwen Zhang. "Axial Symmetry and Classification of Stationary Solutions of Doi-Onsager Equation on the Sphere with Maier-Saupe Potential." Commun. Math. Sci. 3 (2) 201 - 218, June 2005.

Information

Published: June 2005
First available in Project Euclid: 14 June 2005

zbMATH: 1092.76007
MathSciNet: MR2164198

Rights: Copyright © 2005 International Press of Boston

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Vol.3 • No. 2 • June 2005
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