Fatkullin, I. and Slastikov, V. (2005) A Note on the Onsager Model of Nematic Phase Transitions. Communications in Mathematical Sciences, 3 (1). pp. 21-26. ISSN 1539-6746. doi:10.4310/CMS.2005.v3.n1.a2. https://resolver.caltech.edu/CaltechAUTHORS:20170408-144655547
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Abstract
We study Onsager's free energy functional for nematic liquid crystals with an orientation parameter on a unit circle. For a class of interaction potentials we obtain explicit expressions for all critical points, analyze their stability, and construct the corresponding bifurcation diagram. We also derive asymptotic expansions of the equilibrium density of orientations near the critical and zero temperatures.
| Item Type: | Article | |||||||||
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| Additional Information: | © 2005 International Press of Boston. Received: October 26, 2004; accepted (in revised version): November 22, 2004. Communicated by Weinan E. The authors thank Weinan E of Princeton University for pointing out that similar results have been obtained in [6], which was not available in press when this work was completed. V. S. acknowledges support by NSF grant DMS-0405343. | |||||||||
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| Subject Keywords: | nematic phase transitions, Onsager model, Maier-Saupe potential | |||||||||
| Issue or Number: | 1 | |||||||||
| Classification Code: | AMS subject classifications. 82B27, 82D60 | |||||||||
| DOI: | 10.4310/CMS.2005.v3.n1.a2 | |||||||||
| Record Number: | CaltechAUTHORS:20170408-144655547 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170408-144655547 | |||||||||
| Official Citation: | Fatkullin, I.; Slastikov, V. A Note on the Onsager Model of Nematic Phase Transitions. Commun. Math. Sci. 3 (2005), no. 1, 21--26. http://projecteuclid.org/euclid.cms/1111095638. | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 76006 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | 1Science Import | |||||||||
| Deposited On: | 04 May 2017 21:00 | |||||||||
| Last Modified: | 15 Nov 2021 16:56 |
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