Critical points of the Onsager functional on a sphere

Nonlinearity

Volumn 18, Issue 6, 2005, Pages 2565-2580

  Fatkullin, I ^a   Slastikov, V ^b,c  

^a University of Arizona   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

^c UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 26944481099     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/18/6/008     Document Type: Article

References (22)

1. Bhandar A S and Wiest J M 2003 Mesoscale constitutive modeling of magnetic dispersions J. Colloid Interface Sci. 257 371-82
2. Bhave A V, Menon R K, Armstrong R C and Brown R A 1993 A constitutive equation for liquid-crystalline polymer solutions J. Rheol. 37 413-41
3. Constantin P, Kevrekidis I G and Titi E S 2004 Asymptotic states of a Smoluchowski equation Arch. Rat. Mech. Anal. 174 365-84
4. Constantin P, Kevrekidis I G and Titi E S 2004 Remarks on a Smoluchowski equation Discrete Cont. Dyn. Syst. 11 101-12
5. Constantin P and Vukadinovic J 2005 Note on the number of steady states for a 2D Smoluchowski equation Nonlinearity 18 441-3
6. de Gennes P G and Prost J 1993 The Physics of Liquid Crystals (Oxford: Oxford University Press)
7. Doi M 1981 Molecular dynamics and rheological properties of concentrated solutions of rodlike polymers in isotropic and liquid crystalline phases J. Polym. Sci. Polym. Phys. Edn 19 229-43
8. Doi M and Edwards S F 1986 The Theory of Polymer Dynamics (Oxford: Oxford University Press)
9. Fatkullin I and Slastikov V 2005 A note on the Onsager model of nematic phase transitions Commun. Math. Sci. 3 21-6
10. Forest M G, Wang Q and Zhou R 2004 The weak shear kinetic phase diagram for nematic polymers Rheol. Acta 43 17-37
11. Freiser M J 1970 Ordered states of a nematic liquid Phys. Rev. Lett. 24 1041-3
12. Gradshteyn I S and Ryzhik I M 1965 Table of Integrals, Series, and Products (New York: Academic)
13. Grosberg A Yu and Khokhlov A R 1994 Statistical Physics of Macromolecules (New York: AIP Press)
14. Kayser R F Jr and Raveché H J 1978 Bifurcation in Onsager's model of isotropic-nematic transition Phys. Rev. A 17 2067-72
15. Krasnosel'skii M A 1964 Topological Methods in the Theory of Nonlinear Integral Equations (Oxford: Pergamon)
16. Kröger M 2004 Simple models for complex nonequilibrium fluids Phys. Rep. 390 453-551
17. Larson R G and Ottinger H C 1991 Effect of molecular elasitcity on out-of-plane orientations in shearing flows of liquid-crystalline polymers Macromolecules 24 6270-82
18. Luo C, Zhang H and Zhang P 2005 The structure of equilibrium solutions of the one-dimensional Doi equation Nonlinearity 18 379-89
19. Maier W and Saupe A 1958 Eine einfache molekulare Theorie des nematischen kristallinflüssigen Zustandes Z. Naturf. a 13 564
20. Onsager L 1949 The effects of shape on the interaction of colloidal particles Ann. NY Acad. Sci. 51 627-59
21. Wang Q 1997 Biaxial steady states and their stability in shear flows of liquid crystal polymers J. Rheol. 41 943-70
22. Zeidler E 1984 Nonlinear Functional Analysis and its Applications III: Variational Methods and Optimization (Berlin: Springer)