Skip to main content
SpringerLink
Log in

Defects and Order to Disorder Transition in Non-Equilibrium Structures

  • Chapter
Book cover Microscopic Aspects of Nonlinearity in Condensed Matter

Part of the book series: NATO ASI Series ((NSSB,volume 264))

  • 146 Accesses

Abstract

The role of the defects in the transitions from order to disorder of the ordered states is investigated in a non-equilibrium system. The experimental system is a convective fluid driven to turbulence. Both the stationary and time-dependent homogeneous ordered states may become unstable against localized perturbations which create defects. Then, the defects may contribute either to the disorganization of the states, or they may mediate rapid transitions to fully ordered states of lower symmetry. This role can be understood from the topology and from the instability of the core of the defects and is reminiscent of the displacive transitions in solids.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. X.D. Yang, A. Joets, R. Ribotta, p. 194 in Propagation in Systems far from equilibrium, J.E. Wesfreid, H.R. Brand, P. Manneville, G. Albinet, N. Boccara Eds., Springer Series in Synergetics, Springer-Verlag, Berlin (1988).

    Chapter  Google Scholar 

  2. E. Dubois-Violette, P.G. de Gennes, O. Parodi, J. Phys. (Paris) 32, 305 (1971);

    Article  Google Scholar 

  3. P.G. de Gennes, “The Physics of Liquid Crystals”, Clarendon, Oxford (1974).

    Google Scholar 

  4. A. Joets and R. Ribotta, Phys. Rev. Lett. 60, 2164 (1988);

    Article  ADS  Google Scholar 

  5. also in “Propagation in Systems far from Equilibrium” J.E. Wesfreid, H.R. Brand, P. Manneville, G. Albinet and N. Boccara eds., Springer, Berlin (1988); and in the Proceedings of the 12th International Liquid Crystals Conference, Aug. 1988, Freiburg), Liquid Crystals, London (1988).

    Google Scholar 

  6. A. Joets, Thesis, Paris VII, 1984 (unpublished).

    Google Scholar 

  7. R. Ribotta, in “Nonlinear Phenomena in material Science”, p. 489, L. Kubin, G. Martin Eds., Solid State Phenomena, Vol. 324, Trans. Tech. Publications, Switzerland (1988).

    Google Scholar 

  8. A. Joets, R. Ribotta, J. Phys. (Paris) 47, 595 (1986).

    Article  Google Scholar 

  9. A. Joets, R. Ribotta, Europhysics Lett. 10, 721 (1989).

    Article  ADS  Google Scholar 

  10. A. Joets, X.D. Yang, R. Ribotta, Physica 23D, 235 (1986).

    ADS  Google Scholar 

  11. R. Ribotta, A. Joets, J. Phys. (Paris) 47, 739 (1986).

    Article  Google Scholar 

  12. R. Ribotta, A. Joets, L. Lei, Phys. Rev. Lett. 56, 1595 (1986).

    Article  ADS  Google Scholar 

  13. S. Kai, K. Hirakawa, Sol. State Com. 18, 1573 (1976)

    Article  ADS  Google Scholar 

  14. A.C. Newell and J.A. Whitehead, J. Fluid. Mech., 38, 279 (1969).

    Article  ADS  MATH  Google Scholar 

  15. L.A. Segel, J. Fluid Mech., 38, 203 (1969).

    Article  ADS  MATH  Google Scholar 

  16. A.C. Newell, Lect. Appl. Math. 15, 157 (1974).

    MathSciNet  Google Scholar 

  17. E. Bodenschatz, W. Zimmermann, L. Kramer, J. de Phys. (Paris), 49, 1975 (1988).

    Google Scholar 

  18. G.B. Whitham, “Linear and Nonlinear Waves”, John Wiley & Sons, New York (1974);

    MATH  Google Scholar 

  19. J. Lighthill, “Waves in Fluids”, Cambridge Univ. Press, Cambridge (1978).

    MATH  Google Scholar 

  20. P. Coullet, C. Elphick, L. Gil, and J. Lega, Phys. Rev. Lett. 59, 884 (1987);

    Article  ADS  Google Scholar 

  21. P. Coullet, and J. Lega, Europhys. Lett. 7, 511 (1988).

    Article  ADS  Google Scholar 

  22. T.B. Benjamin and J.E. Feir, J. Fluid Mech. 27, 417 (1967);

    Article  ADS  MATH  Google Scholar 

  23. J.T. Stuart and R.C. DiPrima, R.C., Proc. R. Soc. Lond. A 362, 27 (1978);

    Article  ADS  Google Scholar 

  24. C.S. Bretherton and E.A. Spiegel, Phys. Lett. 96A, 152 (1983).

    ADS  Google Scholar 

  25. K. Kawasaki, T. Ohta, Physica 116A, 573 (1982);

    MathSciNet  ADS  Google Scholar 

  26. N. Bekki and K. Nozaki, Phys. Lett. A110, 133 (1985).

    ADS  Google Scholar 

  27. G. Toulouse, M. Kléman, J. Phys. Lett. (Paris) 37, 149 (1976).

    Article  Google Scholar 

  28. N. D. Mermin, Rev. Mod. Phys. 51, 591 (1979).

    Article  MathSciNet  ADS  Google Scholar 

  29. J. Friedel, Dislocations, Pergamon Press, London (1964).

    MATH  Google Scholar 

  30. F.R.N. Nabarro, Theory of Crystal Dislocations, Clarendon Press, Oxford (1969).

    Google Scholar 

  31. J.S. Bowles and J.K. Mackenzie, Acta Metal. 2, 129 (1954);

    Article  Google Scholar 

  32. ibid., 2, 224 (1954);

    Article  Google Scholar 

  33. J.W. Christian, “The Theory of Transformations in Metals and Alloys”, Pergamon Press, Oxford (1965).

    Google Scholar 

  34. A. Joets, R. Ribotta, in “New trends in nonlinear dynamics and pattern forming phenomena: the geometry of nonequilibrium”, P. Coullet and P.Huerre (eds.), Nato ASI series B, Plenum Press (1989) (Cargese Workshop Aug. 1988); also in the Proceedings of “Nonlinear coherent structures in physics, mechanics and biological systems” (Paris, June 1988), J. de Phys. C3, 50, 171 (1989).

    Google Scholar 

  35. R. Ribotta, A. Joets, in “Partially Integrable Evolution Equations in Physics”, R. Conte and N. Boccara eds. Nato ASI Series, Kluwer Acad. Pub., C-310, 279 (1990).

    Google Scholar 

  36. J. Lega, Thesis, Université de Nice (1989), unpublished.

    Google Scholar 

  37. D. Walgraef, Europhys. Lett., 7, 485 (1988).

    Article  ADS  Google Scholar 

  38. E. Knobloch, Phys. Rev. A 34, 1538 (1986).

    Article  ADS  Google Scholar 

  39. J. Lajzerowicz and J. J. Niez in “Solitons in Condensed Matter Physics”, A. R. Bishop, T. Schneider eds., Springer Series in Solid State Science, 8, Berlin (1978).

    Google Scholar 

  40. P. Coullet, L. Gil, D. Repaux, Phys. Rev. Lett., 62, 2957 (1989).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique des Solides, Université de Paris-Sud, Bât. 510, 91405, Orsay Cedex, France

    R. Ribotta & A. Joets

Authors
  1. R. Ribotta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Joets
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Los Alamos National Laboratory, Los Alamos, New Mexico, USA

    A. R. Bishop

  2. Landau Institute for Theoretical Physics, Academy of Sciences of the USSR, Moscow, USSR

    V. L. Pokrovsky

  3. University of Florence, Florence, Italy

    V. Tognetti

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Plenum Press, New York

About this chapter

Cite this chapter

Ribotta, R., Joets, A. (1991). Defects and Order to Disorder Transition in Non-Equilibrium Structures. In: Bishop, A.R., Pokrovsky, V.L., Tognetti, V. (eds) Microscopic Aspects of Nonlinearity in Condensed Matter. NATO ASI Series, vol 264. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5961-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-5961-6_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-5963-0

  • Online ISBN: 978-1-4684-5961-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation