The glass transition in a nutshell: A source of inspiration to describe the subcritical transition to turbulence

  • Olivier Dauchot
  • Eric BertinEmail author
Regular Article
Part of the following topical collections:
  1. Irreversible Dynamics: A topical issue dedicated to Paul Manneville


The starting point of the present work is the observation of possible analogies, both at the phenomenological and at the methodological level, between the subcritical transition to turbulence and the glass transition. Having recalled the phenomenology of the subcritical transition to turbulence, we review the theories of the glass transition at a very basic level, focusing on the history of their development as well as on the concepts they have elaborated. Doing so, we aim at attracting the attention on the above-mentioned analogies, which we believe could inspire new developments in the theory of the subcritical transition to turbulence. We then briefly describe a model inspired by one of the simplest and most inspiring models of the glass transition, the so-called Random Energy Model, as a first step in that direction.

Graphical abstract


Topical issue: Irreversible Dynamics: A topical issue dedicated to Paul Manneville 


  1. 1.
    O. Dauchot, E. Bertin, Phys. Rev. E 86, 036312 (2012).ADSCrossRefGoogle Scholar
  2. 2.
    B. Derrida, Phys. Rev. Lett. 45, 79 (1980).ADSCrossRefMathSciNetGoogle Scholar
  3. 3.
    Daniel D. Joseph, Stability of Fluid Motions (Springer, 1976).Google Scholar
  4. 4.
    Siegfried Grossmann, Rev. Mod. Phys. 72, 603 (2000).CrossRefGoogle Scholar
  5. 5.
    Olivier Dauchot, P. Manneville, J. Phys. II 7, 371 (1997).Google Scholar
  6. 6.
    V.A. Romanov, Funk. Anal. i Prolozen 7, 137 (1973).zbMATHGoogle Scholar
  7. 7.
    P.G. Drazin, W.H. Reid, Hydrodynamics Stability (Cambridge University Press, 1981).Google Scholar
  8. 8.
    Daniel Kivelson, Gilles Tarjus, Xiaolin Zhao, Steven A. Kivelson, Phys. Rev. E 53, 751 (1996).ADSCrossRefGoogle Scholar
  9. 9.
    Kerstin Avila, David Moxey, Alberto de Lozar, Marc Avila, Dwight Barkley, Björn Hof, Science 333, 192 (2011).ADSCrossRefGoogle Scholar
  10. 10.
    Kunihiko Kaneko, Prog. Theor. Phys. 73, 1033 (1985).ADSCrossRefGoogle Scholar
  11. 11.
    Hugues Chaté, P. Manneville, Spatiotemporal intermittency BT - Turbulence: A tentative dictionnary, in Turbulence: A tentative dictionnary, edited by P. Tabeling, O. Cardoso, Volume 341 (Plenum Press, 1994) page 111.Google Scholar
  12. 12.
    Hugues Chaté, P. Manneville, Europhys. Lett. 6, 591 (1988).ADSCrossRefGoogle Scholar
  13. 13.
    P.W. Colovas, C.D. Andereck, Phys. Rev. E 55, 2736 (1997).ADSCrossRefGoogle Scholar
  14. 14.
    S. Bottin, F. Daviaud, P. Manneville, Olivier Dauchot, Europhys. Lett. 43, 171 (1998).ADSCrossRefGoogle Scholar
  15. 15.
    S. Bottin, Hugues Chaté, Eur. Phys. J. B 6, 143 (1998).ADSCrossRefGoogle Scholar
  16. 16.
    Y. Pomeau, Physica D 23, 3 (1986).ADSCrossRefGoogle Scholar
  17. 17.
    P. Grassberger, J. Stat. Mech. 2006, P01004 (2006).CrossRefMathSciNetGoogle Scholar
  18. 18.
    Paul Manneville, Phys. Rev. E 79, 025301(R) (2009).CrossRefGoogle Scholar
  19. 19.
    Jimmy Philip, Paul Manneville, Phys. Rev. E 83, 36308 (2011).CrossRefGoogle Scholar
  20. 20.
    Dwight Barkley, Phys. Rev. E 84, 16309 (2011).CrossRefGoogle Scholar
  21. 21.
    H. Hinrichsen, Adv. Phys. 49, 815 (2000).ADSCrossRefGoogle Scholar
  22. 22.
    Olivier Dauchot, F. Daviaud, Phys. Fluids 7, 901 (1995).ADSCrossRefGoogle Scholar
  23. 23.
    S. Bottin, Olivier Dauchot, F. Daviaud, P. Manneville, Phys. Fluids 10, 2597 (1998).ADSCrossRefGoogle Scholar
  24. 24.
    M. Nagata, J. Fluid Mech. 217, 519 (1990).ADSCrossRefMathSciNetGoogle Scholar
  25. 25.
    R.M. Clever, F.H. Busse, J. Fluid Mech. 344, 137 (1997).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    A. Cherhabili, U. Ehrenstein, J. Fluid Mech. 342, 159 (1996).ADSCrossRefMathSciNetGoogle Scholar
  27. 27.
    Joseph Skufca, James Yorke, Bruno Eckhardt, Phys. Rev. Lett. 96, 174101 (2006).ADSCrossRefGoogle Scholar
  28. 28.
    A. de Lozar, F. Mellibovsky, M. Avila, B. Hof, Phys. Rev. Lett. 108, 214502 (2012).ADSCrossRefGoogle Scholar
  29. 29.
    Yohann Duguet, Philipp Schlatter, Dan S. Henningson, Phys. Fluids 21, 111701 (2009).ADSCrossRefGoogle Scholar
  30. 30.
    Tobias M. Schneider, Daniel Marinc, Bruno Eckhardt, J. Fluid Mech. 646, 441 (2010).ADSCrossRefzbMATHGoogle Scholar
  31. 31.
    Tobias M. Schneider, Bruno Eckhardt, James A. Yorke, Phys. Rev. Lett. 99, 34502 (2007).ADSCrossRefGoogle Scholar
  32. 32.
    Jean-Philippe Bouchaud, L.F. Cugliandolo, J. Kurchan, M. Mezard, Out of equilibrium dynamics in spin-glasses and other glassy systems, in Spin Glasses and Random Fields, edited by A.P. Young (World Scientific, Singapore, 1998).Google Scholar
  33. 33.
    L. Angelani, R. Di Leonardo, G. Ruocco, A. Scala, F. Sciortino, Phys. Rev. Lett. 85, 5356 (2000).ADSCrossRefGoogle Scholar
  34. 34.
    Kurt Broderix, Kamal K. Bhattacharya, Andrea Cavagna, Annette Zippelius, Irene Giardina, Phys. Rev. Lett. 85, 5360 (2000).ADSCrossRefGoogle Scholar
  35. 35.
    Tomàs S. Grigera, Andrea Cavagna, Irene Giardina, Giorgio Parisi, Phys. Rev. Lett. 88, 055502 (2002).ADSCrossRefGoogle Scholar
  36. 36.
    Wim van Saarloos, Luca Cipelletti, Jean-Philippe Bouchaud, Giulio Biroli, Ludovic Berthier (Editors), Dynamical Heterogeneities in Glasses, Colloids, and Granular Media, International Series of Monographs on Physics Vol. 150 (Oxford University Press, Oxford, 2011).Google Scholar
  37. 37.
    David Chandler, Juan P. Garrahan, Annu Rev. Phys. Chem. 61, 191 (2010).CrossRefGoogle Scholar
  38. 38.
    F. Ritort, P. Sollich, Ad. Phys. 52, 219 (2003).ADSCrossRefGoogle Scholar
  39. 39.
    W. Götze, Liquids, Freezing and the Glass Transition, in Les Houches. Session LI, 1989, edited by J.P. Hansen, D. Levesque, J. Zinn-Justin (North-Holland, Amsterdam, 1991) p. 287.Google Scholar
  40. 40.
    P.G. Debenedetti, Metastable Liquids (Princeton University Press, Princeton, 1997).Google Scholar
  41. 41.
    E.-J. Donth, The Glass Transition: Relaxation Dynamics in Liquids and Disordered Materials (Springer, 2001).Google Scholar
  42. 42.
    P.G. Debenedetti, F.H. Stillinger, Nature 410, 259 (2001).ADSCrossRefGoogle Scholar
  43. 43.
    A. Cavagna, Phys. Rep. 476, 51 (2009).ADSCrossRefGoogle Scholar
  44. 44.
    Giulio Biroli, Jean-Philippe Bouchaud, The Random First-Order Transition Theory of Glasses: a critical assessment, in Structural Glasses and Supercooled Liquids: Theory, Experiment, and Applications, edited by P.G. Wolynes, V. Lubchenko (Wiley-Blackwell, 2010).Google Scholar
  45. 45.
    L. Berthier, Giulio Biroli, Rev. Mod. Phys. 83, 587 (2011).ADSCrossRefGoogle Scholar
  46. 46.
    W. Kauzmann, Chem. Rev. 43, 219 (1948).CrossRefGoogle Scholar
  47. 47.
    Julian H. Gibbs, Edmund A. DiMarzio, J. Chem. Phys. 28, 373 (1958).ADSCrossRefGoogle Scholar
  48. 48.
    G. Adam, J.H. Gibbs, J. Chem. Phys. 43, 139 (1965).ADSCrossRefGoogle Scholar
  49. 49.
    M. Goldstein, J. Chem. Phys. 51, 3728 (1969).ADSCrossRefGoogle Scholar
  50. 50.
    W. Götze, L. Sjögren, Rep. Prog. Phys. 55, 241 (1992).CrossRefGoogle Scholar
  51. 51.
    M. Mezard, G. Parisi, M. Virasoro, Spin glass theory and beyond: An Introduction to the Replica Method and Its Applications (World Scientific, 1987).Google Scholar
  52. 52.
    Giulio Biroli, Smarajit Karmakar, Itamar Procaccia, arXiv:1307.1205 (2013).
  53. 53.
    B. Derrida, Phys. Rev. Lett. 45, 79 (1980).ADSCrossRefMathSciNetGoogle Scholar
  54. 54.
    Bernard Derrida, Phys. Rev. B 24, 2613 (1981).ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.EC2MESPCI-ParisTech, UMR Gulliver 7083 CNRSParisFrance
  2. 2.Laboratoire de Physique, ENS Lyon, CNRSUniversité de LyonLyonFrance
  3. 3.Laboratoire Interdisciplinaire de PhysiqueUniversité Joseph Fourier Grenoble, CNRS UMR 5588Saint-Martin d’HèresFrance

Personalised recommendations