Skip to main content

Field-Induced Instabilities in Nematic Liquid Crystals

  • Chapter
Nematics

Part of the book series: NATO ASI Series ((ASIC,volume 332))

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. C. Berry, Kazunori Se and Mohan Srinivasarao, Rheological, rheo-optical and light scattering studies on nematic solutions of PBT.

    Google Scholar 

  2. R. Cohen, Fractional step methods for liquid crystal problems, “Ph.D. Thesis,” University of Minnesota, 1988.

    Google Scholar 

  3. R. Cohen, S.-Y. Lin, M. Luskin, Relaxation and gradient methods for molecular orientation in liquid crystals, Computer Physics Commun. 53 (1989), 455–465.

    Article  MathSciNet  ADS  Google Scholar 

  4. R. Cohen and M. Taylor, Weak stability of the map x/|x| for liquid crystal functionals, Commun. in PDE (to appear).

    Google Scholar 

  5. P. G. de Gennes, “The Physics of Liquid Crystals”, Oxford, 1974.

    Google Scholar 

  6. J. L. Ericksen, Equilibrium theory of liquid crystals, in “Advances in Liquid Crystals 2, ed. G.H. Brown,” Academic Press, 1976.

    Google Scholar 

  7. J. L. Ericksen, Continuum theory of nematic liquid crystals, Res Mechanica 105 (1987), 381–392.

    Google Scholar 

  8. F.C. Frank, On the theory of liquid crystals, Disc. Faraday Soc. 25 (1958), 19–28.

    Article  Google Scholar 

  9. F. Freedericks and V. Zolina, Trans. Faraday Soc. 29 (1933), 919–930.

    Article  Google Scholar 

  10. R. Hardt, D. Kinderlehrer, F.-H. Lin, Existence and partial regularity of static liquid crystal configurations, Comm Math Physics 105 (1986), 547–570.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. F. Helein, Minima de la fonctionelle energie libre des cristaux liquides, C.R. Acad. Sc. Paris 305 (1987), 565–568.

    MathSciNet  MATH  Google Scholar 

  12. S.-Y. Lin, Numerical analysis for liquid crystal problems, “Ph.D. Thesis,” University of Minnesota, 1987.

    Google Scholar 

  13. C.W. Oseen, The theory of liquid crystals, Trans. Faraday Soc. 29 (1933), 883–889.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints 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

Publish with us

Policies and ethics