Abstract
We derive formulas for critical field strengths from variational criteria for field-induced instabilities for nematic liquid crystals. We use these criteria to obtain analytical and numerical results for the Preedericks transition which shows that the spatially homogeneous solution is unstable to three-dimensional modes for magnetic field strengths smaller than that previously predicted by one-dimensional analyses.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. C. Berry, Kazunori Se and Mohan Srinivasarao, Rheological, rheo-optical and light scattering studies on nematic solutions of PBT.
R. Cohen, Fractional step methods for liquid crystal problems, “Ph.D. Thesis,” University of Minnesota, 1988.
R. Cohen, S.-Y. Lin, M. Luskin, Relaxation and gradient methods for molecular orientation in liquid crystals, Computer Physics Commun. 53 (1989), 455–465.
R. Cohen and M. Taylor, Weak stability of the map x/|x| for liquid crystal functionals, Commun. in PDE (to appear).
P. G. de Gennes, “The Physics of Liquid Crystals”, Oxford, 1974.
J. L. Ericksen, Equilibrium theory of liquid crystals, in “Advances in Liquid Crystals 2, ed. G.H. Brown,” Academic Press, 1976.
J. L. Ericksen, Continuum theory of nematic liquid crystals, Res Mechanica 105 (1987), 381–392.
F.C. Frank, On the theory of liquid crystals, Disc. Faraday Soc. 25 (1958), 19–28.
F. Freedericks and V. Zolina, Trans. Faraday Soc. 29 (1933), 919–930.
R. Hardt, D. Kinderlehrer, F.-H. Lin, Existence and partial regularity of static liquid crystal configurations, Comm Math Physics 105 (1986), 547–570.
F. Helein, Minima de la fonctionelle energie libre des cristaux liquides, C.R. Acad. Sc. Paris 305 (1987), 565–568.
S.-Y. Lin, Numerical analysis for liquid crystal problems, “Ph.D. Thesis,” University of Minnesota, 1987.
C.W. Oseen, The theory of liquid crystals, Trans. Faraday Soc. 29 (1933), 883–889.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Cohen, R., Luskin, M. (1991). Field-Induced Instabilities in Nematic Liquid Crystals. In: Coron, JM., Ghidaglia, JM., Hélein, F. (eds) Nematics. NATO ASI Series, vol 332. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3428-6_20
Download citation
DOI: https://doi.org/10.1007/978-94-011-3428-6_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5516-1
Online ISBN: 978-94-011-3428-6
eBook Packages: Springer Book Archive