Extendability of Equilibria of Nematic Polymers
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...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2008/854725 |
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| _version_ | 1832563686504398848 |
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| author | Hongyun Wang Hong Zhou |
| author_facet | Hongyun Wang Hong Zhou |
| author_sort | Hongyun Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-145bb565f5494b5cac44d81f80fe43c8 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-145bb565f5494b5cac44d81f80fe43c82025-02-03T01:12:48ZengWileyAbstract and Applied Analysis1085-33751687-04092008-01-01200810.1155/2008/854725854725Extendability of Equilibria of Nematic PolymersHongyun Wang0Hong Zhou1Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA 95064, USADepartment of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USAThe 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.http://dx.doi.org/10.1155/2008/854725 |
| spellingShingle | Hongyun Wang Hong Zhou Extendability of Equilibria of Nematic Polymers Abstract and Applied Analysis |
| title | Extendability of Equilibria of Nematic Polymers |
| title_full | Extendability of Equilibria of Nematic Polymers |
| title_fullStr | Extendability of Equilibria of Nematic Polymers |
| title_full_unstemmed | Extendability of Equilibria of Nematic Polymers |
| title_short | Extendability of Equilibria of Nematic Polymers |
| title_sort | extendability of equilibria of nematic polymers |
| url | http://dx.doi.org/10.1155/2008/854725 |
| work_keys_str_mv | AT hongyunwang extendabilityofequilibriaofnematicpolymers AT hongzhou extendabilityofequilibriaofnematicpolymers |