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Propagation in Systems Far from Equilibrium: Introduction and Overview

  • P. Manneville
  • H. R. Brand
  • J. E. Wesfreid
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 41)

Abstract

At absolute thermodynamic equilibrium, a given macrosopic system rests in a structureless and time-independent state. It can be brought out of equilibrium in several ways. A first possibility is to prepare the system in a metastable state and to let the stable phase nucleate. This is the case of an undercooled liquid that solidifies as soon as a sufficiently large germ is present; at a given temperature the solid phase is more stable than the liquid phase and the fraction of the solid phase spontaneously increases, separated from the remaining liquid by a solidification front. In the same way, after ignition by a spark, a mixture of fresh gases releases its chemical potential energy by burning; a flame front propagates from burned towards unburned regions. Propagation of a front is the simplest way to restore uniformity at the expense of a metastable state. Questions of interest then relate to the propagation velocity and the morphology of the front, either unmodulated or modulated, and further, either cellular or irregular, i.e. e.g. dendritic (solidification) or turbulent (flame). It is important to realize that in such cases, the system can be assumed to be closed in the thermodynamic sense, but if it is actually closed, the propagation will stop after a while. In a conveniently designed open system, this kind of propagation of a front in a multi-phase medium can be maintained indefinitely. These topics form the basis of the first part of our workshop.

Keywords

Flame Front Phase Dynamic Pattern Selection Envelope Equation Solvability Mechanism 
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.

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References

  1. 1.
    H. Levine: Current status of the theory of dendrites.Google Scholar
  2. 2.
    S. de Cheveigné: Experiments in cellular instabilities in crystal growth.Google Scholar
  3. 3.
    Ch. Misbah: Velocity selection for needle crystals in the 2-D. one-sided model.Google Scholar
  4. 4.
    P. Clavin: Models for kinetic effects in the dynamics of interfaces.Google Scholar
  5. 5.
    Y. Couder: Anomalous Saffman-Taylor fingering.Google Scholar
  6. 6.
    P. Pelcé: Dendrite dynamics.Google Scholar
  7. 7.
    B. Billia: Pattern selection in directional solidification (from theory to experiments).Google Scholar
  8. 8.
    M. Ben Amar: Directional solidification.Google Scholar
  9. 9.
    H.K. Moffat: Vortex interaction with propagating fronts.Google Scholar
  10. 10.
    J. Ross: Experiment and theory of chemical waves.Google Scholar
  11. 11.
    S.C. Müller: New experiments on trigger wave propagation in the Belousov-Zhabotinskii reaction.Google Scholar
  12. 12.
    B. Malraison: Vacillation in electro-hydro-dynamical instabilities.Google Scholar
  13. 13.
    H.R. Brand: Phase dynamics - an overview and a perspective.Google Scholar
  14. 14.
    A. Pocheau: Phase turbulence and mean flow effects in Rayleigh-Bénard convection.Google Scholar
  15. 15.
    P. Metzener: Model systems for long scale convection.Google Scholar
  16. 16.
    P. Coullet: Codimension-one topological defects dynamics.Google Scholar
  17. 17.
    R. Ribotta: Localized instabilities in convection and nucleation of defects.Google Scholar
  18. 18.
    D. Walgraef: Phase dynamics near Hopf bifurcations in 2-D systems, the effect of external perturbations.Google Scholar
  19. 19.
    J. Lega: Waves’ topological defects.Google Scholar
  20. 20.
    A.C. Newell: Wave instabilities and turbulence.Google Scholar
  21. 21.
    E. Moses: Competing patterns in stationary convection of binary mixtures.Google Scholar
  22. 22.
    A. Joets: Propagation in convective instabilities.Google Scholar
  23. 23.
    I. Rehberg: Experimental observation of forced phase diffusion in convection experiments.Google Scholar
  24. 24.
    P. Manneville: Transition to turbulence in the Kuramoto-Sivashinsky equation.Google Scholar
  25. 25.
    J.L. Castillo: The Kuramoto-Velarde equation in Bénard-Marangoni convection with a deformable interface.Google Scholar
  26. 26.
    V. Steinberg: Vortex front propagation in Rayleigh-Bénard convection.Google Scholar
  27. 27.
    S. Linz: Convection in binary fluid layers between impervious horizontal boundaries.Google Scholar
  28. 28.
    G. Iooss: Primary and secondary bifurcations in the Couette-Taylor problem.Google Scholar
  29. 29.
    L. Kramer: Pattern selection in convective instabilities with an axial anisotropy.Google Scholar
  30. 30.
    C. Normand: Pattern selection in salt fingers.Google Scholar
  31. 31.
    G. Ahlers: Convection in binary mixtures.Google Scholar
  32. 32.
    J.C. Antoranz: Thermal convection in mixtures and lasers: model analogies with five and eight equation systems.Google Scholar
  33. 33.
    B. Zielinska: Convection in viscoelastic fluids.Google Scholar
  34. 34.
    P. Kolodner: Oscillatory traveling-wave convection in wine.Google Scholar
  35. 35.
    S. Fauve: Competing instabilities in a rotating layer of mercury heated from below.Google Scholar
  36. 36.
    C. Perez-Garcia: Pattern selection in Bénard-Marangoni convection.Google Scholar
  37. 37.
    C.D. Andereck: Flow regimes in the circular Couette system.Google Scholar
  38. 38.
    A. Aitta: New bifurcations in a partially filled, horizontal, rotating cylinder.Google Scholar
  39. 39.
    I. Mutabazi: Taylor-Couette instability in the flow between two horizontal concentric cylinders with a partially filled gap.Google Scholar
  40. 40.
    U. Dallmann: Linear and nonlinear primary and secondary instabilities in 3-D boundary layer flows.Google Scholar
  41. 41.
    P. Lallemand: Hydrodynamical simulation with lattice gases.Google Scholar
  42. 42.
    H. Peerhossaini: Formation of Görtler rolls in an unstable boundary layer over a concave wall.Google Scholar
  43. 43.
    V. Kottke: Influence of turbulence on the instability of laminar boundary tlayers to Taylor-Görtler vortices.Google Scholar
  44. 44.
    P. Huerre: Hydrodynamic instabilities in open shear flows: a bird’s eye view.Google Scholar
  45. 45.
    O. Thual: Experiments on the wake of a sphere in a stratified fluid.Google Scholar
  46. 46.
    W. Koch: Nonlinear limit cycle solutions - a rational method for transition prediction in shear flows?Google Scholar
  47. 47.
    M. Provensal: Von Karman instability in preturbulent regimes.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • P. Manneville
    • 1
  • H. R. Brand
    • 2
  • J. E. Wesfreid
    • 3
  1. 1.IRF-DPh-G/PSRM, CEN SaclayGif-sur-YvetteFrance
  2. 2.FB7, PhysikUniversität EssenEssenFed. Rep of Germany
  3. 3.ESPCI-LHMPParis Cedex 05France

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