Defects and Order to Disorder Transition in Non-Equilibrium Structures

  • R. Ribotta
  • A. Joets
Part of the NATO ASI Series book series (NSSB, volume 264)


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.


Normal Roll Singular Line Progressive Wave Phase Jump Shear Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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).CrossRefGoogle Scholar
  2. 2.
    E. Dubois-Violette, P.G. de Gennes, O. Parodi, J. Phys. (Paris) 32, 305 (1971);CrossRefGoogle Scholar
  3. 2a.
    P.G. de Gennes, “The Physics of Liquid Crystals”, Clarendon, Oxford (1974).Google Scholar
  4. 3.
    A. Joets and R. Ribotta, Phys. Rev. Lett. 60, 2164 (1988);ADSCrossRefGoogle Scholar
  5. 3a.
    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. 4.
    A. Joets, Thesis, Paris VII, 1984 (unpublished).Google Scholar
  7. 5.
    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. 6.
    A. Joets, R. Ribotta, J. Phys. (Paris) 47, 595 (1986).CrossRefGoogle Scholar
  9. 7.
    A. Joets, R. Ribotta, Europhysics Lett. 10, 721 (1989).ADSCrossRefGoogle Scholar
  10. 8.
    A. Joets, X.D. Yang, R. Ribotta, Physica 23D, 235 (1986).ADSGoogle Scholar
  11. 9.
    R. Ribotta, A. Joets, J. Phys. (Paris) 47, 739 (1986).CrossRefGoogle Scholar
  12. 10.
    R. Ribotta, A. Joets, L. Lei, Phys. Rev. Lett. 56, 1595 (1986).ADSCrossRefGoogle Scholar
  13. 11.
    S. Kai, K. Hirakawa, Sol. State Com. 18, 1573 (1976)ADSCrossRefGoogle Scholar
  14. 12.
    A.C. Newell and J.A. Whitehead, J. Fluid. Mech., 38, 279 (1969).ADSMATHCrossRefGoogle Scholar
  15. 12a.
    L.A. Segel, J. Fluid Mech., 38, 203 (1969).ADSMATHCrossRefGoogle Scholar
  16. 12b.
    A.C. Newell, Lect. Appl. Math. 15, 157 (1974).MathSciNetGoogle Scholar
  17. 13.
    E. Bodenschatz, W. Zimmermann, L. Kramer, J. de Phys. (Paris), 49, 1975 (1988).Google Scholar
  18. 14.
    G.B. Whitham, “Linear and Nonlinear Waves”, John Wiley & Sons, New York (1974);MATHGoogle Scholar
  19. 14a.
    J. Lighthill, “Waves in Fluids”, Cambridge Univ. Press, Cambridge (1978).MATHGoogle Scholar
  20. 15.
    P. Coullet, C. Elphick, L. Gil, and J. Lega, Phys. Rev. Lett. 59, 884 (1987);ADSCrossRefGoogle Scholar
  21. 15a.
    P. Coullet, and J. Lega, Europhys. Lett. 7, 511 (1988).ADSCrossRefGoogle Scholar
  22. 16.
    T.B. Benjamin and J.E. Feir, J. Fluid Mech. 27, 417 (1967);ADSMATHCrossRefGoogle Scholar
  23. 16a.
    J.T. Stuart and R.C. DiPrima, R.C., Proc. R. Soc. Lond. A 362, 27 (1978);ADSCrossRefGoogle Scholar
  24. 16b.
    C.S. Bretherton and E.A. Spiegel, Phys. Lett. 96A, 152 (1983).ADSGoogle Scholar
  25. 17.
    K. Kawasaki, T. Ohta, Physica 116A, 573 (1982);MathSciNetADSGoogle Scholar
  26. 17a.
    N. Bekki and K. Nozaki, Phys. Lett. A110, 133 (1985).ADSGoogle Scholar
  27. 18.
    G. Toulouse, M. Kléman, J. Phys. Lett. (Paris) 37, 149 (1976).CrossRefGoogle Scholar
  28. 18a.
    N. D. Mermin, Rev. Mod. Phys. 51, 591 (1979).MathSciNetADSCrossRefGoogle Scholar
  29. 19.
    J. Friedel, Dislocations, Pergamon Press, London (1964).MATHGoogle Scholar
  30. 19a.
    F.R.N. Nabarro, Theory of Crystal Dislocations, Clarendon Press, Oxford (1969).Google Scholar
  31. 20.
    J.S. Bowles and J.K. Mackenzie, Acta Metal. 2, 129 (1954);CrossRefGoogle Scholar
  32. 20a.
    ibid., 2, 224 (1954);CrossRefGoogle Scholar
  33. 20b.
    J.W. Christian, “The Theory of Transformations in Metals and Alloys”, Pergamon Press, Oxford (1965).Google Scholar
  34. 21.
    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. 22.
    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. 23.
    J. Lega, Thesis, Université de Nice (1989), unpublished.Google Scholar
  37. 24.
    D. Walgraef, Europhys. Lett., 7, 485 (1988).ADSCrossRefGoogle Scholar
  38. 25.
    E. Knobloch, Phys. Rev. A 34, 1538 (1986).ADSCrossRefGoogle Scholar
  39. 26.
    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. 27.
    P. Coullet, L. Gil, D. Repaux, Phys. Rev. Lett., 62, 2957 (1989).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • R. Ribotta
    • 1
  • A. Joets
    • 1
  1. 1.Laboratoire de Physique des SolidesUniversité de Paris-SudFrance

Personalised recommendations