Skip to main content
SpringerLink
Log in

Non linearities and fluctuations at the threshold of a hydrodynamic instability in nematics

  • A. Effets prétransitionnels et étude du point critique
  • Chapter
  • First Online:
Les instabilitiés hydrodynamiques en convection libre, forcée et mixte

Part of the book series: Lecture Notes in Physics ((LNP,volume 72))

  • 134 Accesses

Abstract

We present the results of a non-linear analysis above the threshold of the Piéranski-Guyon instability in Nematics [1] and derive a kind of “Ginsburg criterion” giving the extent of the “critical domain” where the classical mean field theory breaks down.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Piéranski and E. Guyon, Sol. St. Comm. 13, 435 (1973).

    Google Scholar 

  2. P. Piéranski and E. Guyon, Phys. Rev. A 9 404 (1974).

    Google Scholar 

  3. P. Manneville and E. Dubois-Violette, J. de Physique (Paris) 37, 285 (1976).

    Google Scholar 

  4. F.M. Leslie, J. Phys. D. (Applied Physics) 9, 925 (1976).

    Google Scholar 

  5. P. Manneville, Ph. D Thesis, to be presented-at the University of Paris-Sud, Orsay.

    Google Scholar 

  6. W.V.R. Malkus and G. Veronis, J. Fluid Mech. 4, 225 (1958).

    Google Scholar 

  7. L.D. Landau, C.R. Acad. Sci. URSS 44, 311 (1944); see: Collected Papers of L.D. Landau, D. Ter Haar ed., Pergamon Press (Oxford, 1965).

    Google Scholar 

  8. P.G. de Gennes, The Physics of Liquid Crystals, Clarendon Press (Oxford 1974).

    Google Scholar 

  9. Fluctuations, Instabilities and Phase Transitions, T. Riste ed., Plenum Press (New York, 1975).

    Google Scholar 

  10. P.G. de Gennes in ref. 9.

    Google Scholar 

  11. C. Normand, Y. Pomeau and M. Velarde, Rev. Mod. Phys. 49, 581 (1977).

    Google Scholar 

  12. I.W. Smith, Y. Galerne, S.T. Lagerwall, E. Dubois-Violette and G. Durand, J. de Physique (Paris) Colloque C1, 36, C1–237 (1975)

    Google Scholar 

  13. R. Graham, in ref. 9.

    Google Scholar 

  14. H.N.W. Lekkerkerker and W.G. Laidlaw: J. de Physique (Paris) 38, 1 (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Service de Physique du Solide et de Résonance Magnétique, Centre d'Etudes Nucléaires de Saclay, B.P. no 2, 91190, Gif-sur-Yvette, France

    Paul Manneville

Authors
  1. Paul Manneville
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jean-Claude Legros Jean Karl Platten

Rights and permissions

Reprints and permissions

Copyright information

© 1978 Springer-Verlag

About this chapter

Cite this chapter

Manneville, P. (1978). Non linearities and fluctuations at the threshold of a hydrodynamic instability in nematics. In: Legros, JC., Platten, J.K. (eds) Les instabilitiés hydrodynamiques en convection libre, forcée et mixte. Lecture Notes in Physics, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08652-8_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-08652-8_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08652-9

  • Online ISBN: 978-3-540-35932-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation