• Daniel Walgraef
Part of the Partially Ordered Systems book series (PARTIAL.ORDERED)


In experimental systems, when a spatially extended state becomes unstable by the increase of some control parameter, the new stable state may grow in different ways. It may grow globally from the noise that is always present in macroscopic systems, or it may propagate from special spatial locations such as impurities, nonuniformities, boundaries, and so on.


Unstable State Nematic Liquid Crystal Front Velocity Front Propagation Uniform State 
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. [9.1]
    D. G. Aaronson and H. F. Weinberger, Advances in Mathematics 30, 33 (1978).MathSciNetCrossRefGoogle Scholar
  2. [9.2]
    B. Shraiman and D. Bensimon, Physica Scripta T9, 123 (1985).ADSCrossRefGoogle Scholar
  3. [9.3]
    E. Ben Jacob, H. Brand, G. Dee, L. Kramer and J. S. Langer, Pattern propagation in nonlinear dissipative systems, Physica D14, 348 (1985).MathSciNetADSGoogle Scholar
  4. [9.4]
    A. J. Bernoff, Slowly varying fully nonlinear wavetrains in the Ginzburg-Landau equation, Physica D30, 363, (1988).MathSciNetADSGoogle Scholar
  5. [9.5]
    W. van Saarloos, Front propagation into unstable states: marginal stability as a dynamical mechanism for velocity selection, Phys. Rev. A37, 211 (1988).ADSGoogle Scholar
  6. [9.6]
    G. Dee and J. S. Langer, Propagating pattern selection, Phys.Rev.Lett. 50, 383 (1983).ADSCrossRefGoogle Scholar
  7. [9.7]
    J. Fineberg and V. Steinberg, Vortex-front propagation in Rayleigh-Bénard convection, Phys. Rev. Lett. 58, 1332 (1987).ADSCrossRefGoogle Scholar
  8. [9.8]
    G. Ahlers and D. S. Cannell, Vortex-front propagation in rotating Couette-Taylor flow, Phys. Rev. Leu. 50, 1583 (1983).ADSCrossRefGoogle Scholar
  9. [9.9]
    D. Walgraef, Structures Spatiales loin de l’Equilibre, Masson,Paris (1988).Google Scholar
  10. [9.10]
    A. Saul and K. Showalter in Oscillations and Travelling Waves in Chemical Systems, R. J. Field and H. Burger eds., Wiley, New York (1984), p. 419.Google Scholar
  11. [9.11]
    C. Schiller, Modelling Microstructures in Metals, PhD Thesis, Free University of Brussels (1989).Google Scholar
  12. [9.12]
    M. San Miguel, R. Montagne, A. Amengual and E. Hernandez-Garcia in Instabilities and Nonequilibrium Structures V. E. Tirapegui and W. Zeller eds., Kluwer, Dordrecht (1996).Google Scholar
  13. [9.13]
    B. L. Winkler, H. Richter, I. Rehberg, W. Zimmerman, L. Kramer and A. Bubka, Nonequilibrium patterns in the electric-field-induced splay Fredericksz transition, Phys. Rev. A43, 1940 (1991).ADSGoogle Scholar
  14. [9.14]
    F. Sagues and M. San Miguel, Transient patterns in nematic liquid crystals: domain-walls dynamics, Phys. Rev. A39, 6567 (1989).ADSGoogle Scholar
  15. [9.15]
    A. Amengual, E. Hernandez-Garcia and M. San Miguel, Ordering and finite-size effects in the dynamics of one-dimensional patterns, Phys. Rev. E47, 4151 (1993).ADSGoogle Scholar
  16. [9.16]
    Y. Kuramoto, Prog. Theor. Phys. 63, 1885 (1980).MathSciNetADSMATHCrossRefGoogle Scholar
  17. [9.17]
    M. Ben Amar, P. Pelcé, and P. Tabeling eds., On Growth and Form, Plenum Press, New York (1991).CrossRefGoogle Scholar
  18. [9.18]
    M. C. Cross and P. C. Hohenberg, Pattern formation outside equilibrium, Rev. Mod. Phys. 65, 854 (1993).ADSCrossRefGoogle Scholar
  19. [9.19]
    P. E. Cladis and P. Palffy-Muhoray, eds., Spatio-Temporal Patterns in Non-equilibrium Complex Systems, Santa Fe Institute, Proc. Vol. XXI, Addison-Wesley, Reading (1994).Google Scholar
  20. [9.20]
    B. Malomed, A. A. Nepomnyashchy and M. I. Tribelsky, Domain boundaries in convection patterns, Phys. Rev. A42, 7244 (1990).MathSciNetADSGoogle Scholar
  21. [9.21]
    E. Bodenschatz, D. S. Cannell, J. R. de Bruin, R. Ecke, Y. C. Hu, K. Lerman and G. Ahlers, Experiments on three systems with non-variational aspects, Physica D61, 77 (1992).ADSGoogle Scholar
  22. [9.22]
    L. Limat, P. Jenffer, B. Dagens, E. Touron, M. Fermigier and J.E. Wesfreid, Gravitational instabilities of thin liquid layers: dynamics and pattern selection, Physica D61, 166 (1992).ADSGoogle Scholar
  23. [9.23]
    W.van Saarloos, Front propagation into unstable states: linear versus nonlinear marginal stability and rate of convergence, Phys. Rev. A39, 6367 (1989).ADSGoogle Scholar
  24. [9.24]
    L. M. Pismen and A. A. Nepomnyashchy, Propagation of the hexagonal patterns, Europhys. Lett. 27, 433 (1994).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Daniel Walgraef
    • 1
  1. 1.Center for Nonlinear Phenomena and Complex SystemsUniversité Libre de BruxellesBruxellesBelgium

Personalised recommendations