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A Note on the Onsager Model of Nematic Phase Transitions

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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.4310/CMS.2005.v3.n1.a2DOIArticle
https://projecteuclid.org/euclid.cms/1111095638PublisherArticle
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.
Funders:
Funding AgencyGrant Number
NSFDMS-0405343
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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