Skip to main content
SpringerLink
Log in

Pattern Selection in Convective Instabilities with Axial Anisotropy

  • Conference paper
Propagation in Systems Far from Equilibrium

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 41))

Abstract

We examine the possible stable patterns slightly above threshold of quasi-two-dimensional pattern-forming systems with an axial anisotropy. Special attention is given to the electrohydrodynamic instability in nematic liquid crystals, where extensive calculations have been done, and to systems where the anisotropy can be turned on continuously.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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. F. H. Busse: Rep. Prog. Phys. 41, 28 (1978); and in Hydrodynamic Instabilites and the Transition to Turbulence, 2nd ed., H. L. Swinney and J. P. Gollub, eds. (Springer, Berlin 1986).

    Article  Google Scholar 

  2. M. C. Cross and A. C. Newell: Physica 10D, 299 (1984).

    ADS  MathSciNet  Google Scholar 

  3. M. S. Heutmaker, P. N. Fraenkel and J. P. Gollub: Phys. Rev. Lett. 54, 1369 (1985)

    Article  ADS  Google Scholar 

  4. G. Ahlers, D. S. Cannell and V. Steinberg: Phys. Rev. Lett. 54, 1373 (1985)

    Article  ADS  Google Scholar 

  5. P. Le Gal, A. Pocheau and V. Croquette: Phys. Rev. Lett. 54, 2501 (1985) and 55, 1094 (1985).

    Article  ADS  Google Scholar 

  6. See e.g. W. J. A. Goossens: Advances in Liquid Crystals, edited by G. H. Brown (Academic, New York 1978), Vol.3, p.1.

    Google Scholar 

  7. A. Joets and R. Ribotta: in Cellular Structures in Instabilities, J. E. Wesfreid and S. Zaleski, eds. (Springer, Berlin 1984) p.294; J. Physique 47, 595 (1986)

    Chapter  Google Scholar 

  8. R. Ribotta, A. Joets and Lin Lei: Phys. Rev. Lett. 56, 1595 (1986).

    Article  ADS  Google Scholar 

  9. M. Lowe and J. P. Gollub: Phys. Rev. Lett. 55, 2575 (1985)

    Article  ADS  Google Scholar 

  10. Y. Tsuchiya and S. Horie: J. Phys. Soc. Japan 55, 2945 (1986)

    Article  ADS  Google Scholar 

  11. H. Yamazaki, S. Kai and K. Hirakawa: J. Phys. Soc. Jap. 56, 1 (1987).

    Article  ADS  Google Scholar 

  12. W. Zimmermann and L. Kramer: Phys. Rev. Lett. 55, 402 (1985).

    Article  ADS  Google Scholar 

  13. E. Bodenschatz, W. Zimmermann and L. Kramer: preprint (1988).

    Google Scholar 

  14. E. Dubois-Violette: C. R. hebd. seanc. Acad. Sci. 21, 275, 923 (1971).

    Google Scholar 

  15. E. Dubois-Violette: Solid State Comm. 14, 767 (1974).

    Article  ADS  Google Scholar 

  16. E. Dubois-Violette, E. Guyon and P. Pieranski: Mol. Cryst. Liq. Cryst. 26, 193 (1976).

    Article  Google Scholar 

  17. A. Joets, L. Kramer, R. Ribotta, J. Salan and W. Zimmermann: to be published.

    Google Scholar 

  18. W. Pesch and L. Kramer: Z. Phys. B63, 121 (1986).

    Article  ADS  Google Scholar 

  19. L. Kramer, E. Bodenschatz, W. Pesch and W. Zimmermann: In The Physics of Structure Formation, ed. by W. Güttinger and G. Dangelmayr, Springer Ser. Syn., Vol. 37 (Springer, Berlin, Heidelberg 1987).

    Google Scholar 

  20. S. Chandrasekhar: Hydrodynamic and Hydromagnetic Stability (Clarendon Press, Oxford, 1961) p.186.

    MATH  Google Scholar 

  21. B. Lehnert and N. C. Little: Tellus 9, 97 (1957).

    Article  ADS  Google Scholar 

  22. For recent experiments on the influence of a horizontal magnetic field on Rayleigh-Bénard convection see S. Fauve, C. Laroche and A. Libschaber: J. Physique Lett. 42, L-455 (1981); 45, L-101 (1984).

    Article  Google Scholar 

  23. J. Salan and E. Guyon: J. Fluid Mech. 126, 13 (1983).

    Article  ADS  Google Scholar 

  24. P. Pieranski and E. Guyon: Phys. Rev. Lett. 39, 1281 (1977)

    Article  ADS  Google Scholar 

  25. E. Guazelli and E. Guyon: J. Physique 43, 985 (1982)

    Article  Google Scholar 

  26. E. Guazelli and A.-J. Koch: J. Physique 46, 673 (1985).

    Article  Google Scholar 

  27. E. Dubois-Violette and F. Rothen: J. Physique 10, 1039 (1978)

    Google Scholar 

  28. J. Sadik, F. Rothen, W. Bestgen and E. Dubois-Violette: J. Physique 42, 915 (1981)

    Article  Google Scholar 

  29. A.-J. Koch, F. Rothen, J. Sadik and J. Prost: Phil. Mag. A48, 727 (1983).

    Google Scholar 

  30. E. Guazelli, G. Dewel, P. Borckmann and W. Walgraef: to be published.

    Google Scholar 

  31. P. A. Penz and G. W. Ford: Phys. Rev. A6, 414 (1972).

    ADS  Google Scholar 

  32. Experimental values of the material constants for MBBA at 25°C: Elastic constants \(\text k^{11} - 6.66 \times 10^{-12}\text{N}\), \(\text k^{22} - 4.2 \times 10^{-12}\text{N}\) and \(\text k^{33} - 8.61 \times 10^{-12}\text{N}\) are taken from H. W. de Jeu et al.: Mol. Cryst. & Liq. Cryst. 37, 269 (1976). Viscosities \(\alpha_1 = - 18.1 \times 10^{-3}\text{kg m}^{-1}\,\text{s}^{-1}\), \(\alpha_2 = - 110.4 \times 10^{-3}\text{kg m}^{-1}\,\text{s}^{-1}\), \(\alpha_3 = - 1.1 \times 10^{-3}\text{kg m}^{-1}\,\text{s}^{-1}\), \(\alpha_4 = 82.6 \times 10^{-3}\text{kg m}^{-1}\,\text{s}^{-1}\), \(\alpha_5 = 77.9 \times 10^{-3}\text{kg m}^{-1}\,\text{s}^{-1}\), \(\alpha_6 = - 33.6 \times 10^{-3}\text{kg m}^{-1}\,\text{s}^{-1}\) are taken from H. Kneppe et al.: J. Chem. Phys. 77, 3203 (1982). We have chosen \(3\bar\in = (2\in_{\,_\bot} + \in_{\,_{\text{,,}}}) = 15.22\), \(\in_a = - 0.53\), \(\sigma_{\,_\bot} = 10^{-8} \Omega^{-1} \text{ m}^{-1}\) and \(\sigma_{||}/\sigma_{\,_\bot} = 1.5\) unless stated otherwise.

    Google Scholar 

  33. A. Joets and R. Ribotta: this volume.

    Google Scholar 

  34. N. V. Madhusudana, V. A. Raghunathan and K. R. Sumathy, Pramäna J. Phys. 28, L 311 (1987).

    Article  ADS  Google Scholar 

  35. W. Thom, W. Zimmermann and L. Kramer: preprint (1988).

    Google Scholar 

  36. Y. P. Bobylev and S. A. Pikin: Zh. Eksp. Theor. Fiz. 72, 369 (1977) [English transl: Sov. Phys.-JETP 45, 195 (1977)]

    Google Scholar 

  37. Y. P. Bobylev, V. G. Chigrinov and S. A. Pikin: J. Physique Coll. 40, C3–331 (1979)

    Google Scholar 

  38. M. I. Barnik, L. M. Blinov, A. N. Trufanov and B. A. Umanskii: Zh. Eksp. Theor. Fiz. 73, 1936 (1977) [English transl.: Sov. Phys.-JETP 46, 1016 (1977)]; J. Physique 39, 417 (1978).

    Google Scholar 

  39. F. Lonberg and R. B. Meyer: Phys. Rev. Lett. 55, 718 (1985)

    Article  ADS  Google Scholar 

  40. E. Miraldi, C. Oldano and A. Strigazzl: Phys. Rev. A34, 4348 (1986)

    ADS  Google Scholar 

  41. W. Zimmermann and L. Kramer: Phys. Rev. Lett. 56, 2655 (1986)

    Article  ADS  Google Scholar 

  42. U. D. Kini: J. Physique 47, 693 (1986); 47, 1829 (1986).

    Article  Google Scholar 

  43. R. M. Hornreich, M. Luban and S. Shtrikam: Phys. Rev. Lett. 35, 1678 (1975); Physica 86A, 465 (1977).

    Article  ADS  Google Scholar 

  44. See e.g. V. Steinberg, this conference. E. Ben-Jacob, H. Brand, G. Dee, L. Kramer and J. S. Langer: Physica 14D, 348 (1985).

    ADS  MathSciNet  Google Scholar 

  45. E. D. Siggia and A. Zippelius: Phys. Rev. A24, 1036 (1981)

    ADS  Google Scholar 

  46. Y. Pomeau, S. Zaleski and P. Manneville: Phys. Rev. A27, 2710 (1983).

    ADS  MathSciNet  Google Scholar 

  47. G. Tesauro and M. C. Cross: Phys. Rev. A34, 1363 (1986).

    ADS  Google Scholar 

  48. E. Bodenschatz, W. Pesch and L. Kramer: preprint (1988).

    Google Scholar 

  49. P. Coullet: this volume; P. Coullet, C. Elphick and D. Repaux: Phys. Rev. Lett. 58, 431 (1987).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physikalisches Institut, Universität Bayreuth, Postfach 101251, D-8580, Bayreuth, Fed. Rep. of Germany

    L. Kramer, W. Zimmermann, E. Bodenschatz & W. Pesch

Authors
  1. L. Kramer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Zimmermann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Bodenschatz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. W. Pesch
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratoire d’Hydrodynamique et Mécanique Physique, E.S.P.C.I. Paris, 10, rue Vauquelin, F-75231, Paris Cedex 05, France

    José E. Wesfreid

  2. Fachbereich 7 (Physik), Universität Essen, D-4300, Essen 1, Fed. Rep. of Germany

    Helmut R. Brand

  3. IRF-DPh-G/PSRM, CEN-Saclay, F-91191, Gif-sur-Yvette, France

    Paul Manneville

  4. Lab. de Recherches en Combustion, Université de Provence, Centre St. Jérôme, F-13397, Marseille Cedex 13, France

    Gilbert Albinet

  5. Centre de Physique Théorique, F-74310, Les Houches, France

    Nino Boccara

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kramer, L., Zimmermann, W., Bodenschatz, E., Pesch, W. (1988). Pattern Selection in Convective Instabilities with Axial Anisotropy. In: Wesfreid, J.E., Brand, H.R., Manneville, P., Albinet, G., Boccara, N. (eds) Propagation in Systems Far from Equilibrium. Springer Series in Synergetics, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73861-6_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-73861-6_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-73863-0

  • Online ISBN: 978-3-642-73861-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation