The Freedericksz transition as a bifurcation problem

Dynamical Systems

Volumn 14, Issue 3, 1999, Pages 299-331

  Blake, G I ^a   Mullin, T ^a   Tavener, S J ^b  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); ELECTRIC FIELD EFFECTS; MAGNETIC FIELD EFFECTS; NAVIER STOKES EQUATIONS; NEMATIC LIQUID CRYSTALS; NUMERICAL METHODS; TWO DIMENSIONAL;

FREEDERICKSZ TRANSITION; NEWTONIAN FLUID; TAYLOR-COUETTE FLOW;

TRANSITION FLOW;

EID: 0033195623     PISSN: 14689367     EISSN: None     Source Type: Journal    
DOI: 10.1080/026811199282010     Document Type: Article

References (25)

1. Benjamin, T. B. (1978) Bifurcation phenomena in steady flows of a viscous liquid, part i. theory. Proceedings of the Royal Society London A 337, 1-26.
2. Brenner, S. C. and Scott, L. R. (1994) The Mathematical Theory of Finite Element Methods (Springer-Verlag, New York).
3. Cliffe, K. A. (1996) Entwife (release 6.3) reference manual: Entwife, initial data and solver data commands, AEAT-0823.
4. Cliffe, K. A. and Winters, K. H. (1984) A numerical study of the cusp catastrophe for Bénard convection in tilted cavities. J. Comp. Phys. 54, 531-534.
5. Dafermos, C. M. (1968) Stability of orientation patterns of liquid crystals subject to magnetic fields. SIAM Journal of Applied Mathematics 16, 1305-1318.
6. de Gennes, P. G. and Prost, J. (1993) The Physics of Liquid Crystals (Oxford University Press, Oxford).
7. Derfel, G. (1988) Field effects in nematic liquid crystals in terms of catastrophe theory. Liquid Crystals 93, 1411-1424.
8. Deuling, H. J. (1972) Deformation of nematic liquid crystals in an electric field. Mol. Cryst. Liq. Cryst. 19, 123-131.
9. Deuling, H. J. (1978) Elasticity of nematic liquid crystals. Solid State Physics Supplement, Vol. 14 (ed. L. Liebert; Academic Press, London), pp. 77-107.
10. Dunmur, D. and Toriyama, K. (1998) Elastic properties. Handbook of Liquid Crystals, Vol. 1 (eds J. Goodby, G. W. Gray and H. W. Spiess; Wiley, New York), pp. 253-280.
11. Ericksen, J. L. (1966) Inequalities in liquid crystal theory. Physics of Fluids 9, 1205-1207.
12. Frank, F. C. (1958) On the theory of liquid crystals. Discussions of the Faraday Society 25, 19-28.
13. Golubitsky, M. and Schaeffer, D. G. (1985) Singularities and Groups in Bifurcation Theory, Vol. I (Springer-Verlag, New York).
14. Gruler, H. and Meier, G. (1972) Electric field-induced deformations in oriented liquid crystals of the nematic type. Mol. Cryst. Liq. Cryst. 16, 299-310.
15. Kaiser, E. and Pesch, W. (1993) Amplitude equations for the electrohydrodynamic instability in nematic liquid crystals. Physical Review E 48, 4510-4528.
16. Keller, H. B. (1977) Numerical solution of bifurcation and nonlinear eigenvalue problems. Applications of Bifurcation Theory (ed. P. H. Rabinowitz; Academic Press, New York), pp. 359-384.
17. Leslie, F. M. (1970) Distortion of twisted orientation patterns in liquid crystals by magnetic fields. Mol. Cryst. Liq. Cryst. 12, 57-72.
18. Leslie, F. M. (1970) Some magneto-hydrostatic effects in nematic liquid crystals. Journal of Physics D: Applied Physics 3, 889-897.
19. Leslie, F. M. (1992) Continuum theory for nematic liquid crystals. Continuum Mechanics Thermodynamics 4, 167-175.
20. Moore, G. and Spence, A. (1980) The calculation of turning points of nonlinear equations. SIAM Journal of Numerical Analysis 17, 567-576.
21. Mullin, T. (1995) The Nature of Chaos (Clarendon Press, Oxford).
22. Mullin, T. and Kobine, J. J. (1996) Organised chaos in fluid dynamics. Nonlinear Mathematics and its Applications (ed. P. Aston; Cambridge University Press, London).
23. Saupe, A. (1960) Die biegungselastizitat der nematischen phase von azoxyanisol. Zeitschrift für Naurforschung 15a, 815-822.
24. Schiller, P. (1989) Perturbation theory for planar nematic twisted layers. Liquid Crystals 4, 69-78.
25. Werner, B. and Spence, A. (1984) The computation of symmetry breaking bifurcation points. SIAM Journal of Numerical Analysis 21, 388-399.