Skip to main content

Transitions Between Patterns of Different Symmetries

  • Chapter
Instabilities and Nonequilibrium Structures III

Part of the book series: Mathematics and Its Applications ((MAIA,volume 64))

Abstract

Beyond various pattern forming instabilities structures with different symmetries may be simultaneously stable. Several aspects of the transitions between such structures are studied in the framework of amplitude equations of the Ginzburg-Landau type. In particular, it is shown how boundary effects, external fields and internal fluctuations may affect these transitions. The relevance of these effects to specific experimental problems is discussed.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
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. P. Coullet and P. Huerre, “New Trends in Nonlinear Dynamics and Pattern Forming Phenomena: The Geometry of Nonequilibrium.,” Plenum, New York, 1990.

    MATH  Google Scholar 

  2. F. Busse and L. Kramer, “Nonlinear Evolution of Spatio-temporal Structures in Dissipative Continuous Systems,” Plenum, New York, to appear 1990.

    Book  Google Scholar 

  3. D. Walgraef, in “Nonlinear Phenomena in Materials Science,” G.Martin and L.P.Kubin, eds., Transtech, Aedermannsdorf (Switzerland), 1988, p. 77.

    Google Scholar 

  4. P.C. Hohenberg and M.C. Cross, in “Fluctuations and Stochastic Phenomena in Condensed Matter,” Lecture Notes in Physics 268, L.Garrido ed., Springer, New York, 1987.

    Google Scholar 

  5. E. Palm, J.Fluid Mech. 8 (1960), p. 183.

    Article  MATH  Google Scholar 

  6. F. Busse, J.Fluid Mech. 30 (1967), p. 625.

    Article  MATH  Google Scholar 

  7. M. Dubois, P. Bergé and J.E. Wesfreid, J.Physique 39 (1978), p. 1253.

    Article  Google Scholar 

  8. S. Ciliberto, E. Pampaloni and C. Perez-Garcia, Phys.Rev.Lett. 61 (1988), p. 1198.

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  10. M. Besterhorn and C. Perez-Garcia, Europhys.Lett. 4 (1987), p. 1365.

    Article  Google Scholar 

  11. M.N. Roppo, S.H. Davis and S. Rosenblatt, Phys.Fluids 27 (1984), p. 796.

    Article  MathSciNet  MATH  Google Scholar 

  12. P.C. Hohenberg and J. Swift, Phys.Rev. A35 (1987), p. 3855.

    Article  MathSciNet  Google Scholar 

  13. C.W. Meyer, G. Ahlers and D. Cannell, Phys.Rev.Lett. 59 (1987), p. 1577.

    Article  Google Scholar 

  14. L.M. Pismen, J. Chem.Phys. 72 (1980), p. 1900.

    Article  Google Scholar 

  15. D. Walgraef, G. Dewel and P. Borckmans, Adv.Chem.Phys. 49 (1982), p. 311.

    Article  Google Scholar 

  16. H. Haken, “Advanced Synergetics,” Springer, Berlin, 1983.

    Book  Google Scholar 

  17. P. Coullet, L. Gil and D. Repaux, in “Instabilities and Nonequilibrium Structures II,” E.Tirapegui and D.Villaroel, eds., Kluwer Acad. Publ., Dordrecht, 1989, p. 189.

    Book  Google Scholar 

  18. H. Riecke, J.D. Crawford and E. Knobloch, Phys.Rev.Lett. 61 (1988), p. 1942.

    Article  MathSciNet  Google Scholar 

  19. D. Walgraef, Europhys.Lett. 7 (1988), p. 485.

    Article  Google Scholar 

  20. I. Rehberg, S. Rasenat, J. Fineberg, M. De La Torre Juarez and V. Steinberg, Phys.Rev.Lett. 61 (1988), p. 2449.

    Article  Google Scholar 

  21. P. Coullet and D. Walgraef, Europhys.Lett. 10 (1989), p. 525.

    Article  Google Scholar 

  22. M.C. Cross, Phys.Rev.Lett. 57 (1986), p. 2935.

    Article  Google Scholar 

  23. P. Coullet, S. Fauve et E. Tirapegui, J. Physique (Paris) 46 (1985), p. 787.

    Article  Google Scholar 

  24. H.R. Brand, P.S. Lomdhal et A.C. Newell, Phys.Lett. 118A (1986), p. 67.

    Article  Google Scholar 

  25. H. Le Chatelier, C.R. Acad. Sci.(Paris) 108 (1889), p. 1046.

    Google Scholar 

  26. G. Van Tendeloo, J. Van Landuyt and S. Amelinckx, Phys.Status Solidi A33 (1976), p. 723.

    Article  Google Scholar 

  27. J.P. Bachheimer, J. Phys.Lett. 41 (1980), p. L559.

    Article  Google Scholar 

  28. G. Dolino, J.P. Bachheimer, B. Bergé, C. Zeyen, G. Van Tendeloo, J. Van Landuyt and S. Amelinckx, J.Phys.(Paris) 45 (1984), p. 901.

    Google Scholar 

  29. E. Snoeck, C. Roucau and P. Saint Gregoire, J. Phys.(Paris) 47 (1986), p. 2041.

    Article  Google Scholar 

  30. R. Blinc and A.P. Levanyuk, “Incommensurate Phases in Dielectrics,” North Holland, Amsterdam, 1986.

    Google Scholar 

  31. T.A. Aslanyan, A.P. Levanyuk, M. Vallade and J. Lajzerowicz, J.Phys.O: Solid State Phys. 17 (1983), p. 6505.

    Google Scholar 

  32. G. Dolino, P. Bastie, B. Bergé, M. Vallade, J. Bethke, L.P. Regnault and C. Zeyen, Europhys.Lett. 3 (1987), p. 601.

    Article  Google Scholar 

  33. O. Biham, D. Mukamel, J. Joner and X. Zhu, Phys.Rev.Lett. 59 (1987), p. 2439.

    Article  Google Scholar 

  34. T.A. Aslanyan and A.P. Levanyuk, Solid State Commun. 31 (1979), p. 547.

    Article  Google Scholar 

  35. P. Borckmans, G. Dewel and D. Walgraef, preprint (1990).

    Google Scholar 

  36. S.A. Brazovskii, Sov.Phys. (J.Exp.Theor.Phys.) 41 (1975), p. 85.

    Google Scholar 

  37. P. Bastie, F. Mogeon and C. Zeyen, Phys.Rev. B38 (1988), p. 786.

    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

Walgraef, D. (1991). Transitions Between Patterns of Different Symmetries. In: Tirapegui, E., Zeller, W. (eds) Instabilities and Nonequilibrium Structures III. Mathematics and Its Applications, vol 64. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3442-2_25

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-3442-2_25

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5522-2

  • Online ISBN: 978-94-011-3442-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics