Skip to main content
SpringerLink
Log in
Book cover

Propagation in Systems Far from Equilibrium pp 206–224Cite as

Phase Dynamics — A Review and a Perspective

  • Conference paper

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 41))

Abstract

That there is a strong similarity between phase transitions in equilibrium systems (as e.g. the paramagnetic-ferromagnetic transition in magnetic systems or the superfluid-normal fluid transition in 4He) and nonequilibrium phase transitions is well established since the pioneering work of Graham and Haken [1] and de- Giorgio and Scully [2], who pointed out the analogy between second order phase transitions and the onset of laser action in the single mode laser in the field of quantum optics. Since then many examples of such a similarity have been found in nonequilibrium systems including fields such as quantum optics, hydrodynamic instabilities, autocatalytic chemical reactions, nonlinear oscillators in diverse fields etc.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Graham and H. Ilaken, Z.Phys. 237, 31 (1970)

    Article  ADS  Google Scholar 

  2. V. de Giorgio and M.O. Scully, Phys.Rev.A 2, 1170 (1970)

    Article  ADS  Google Scholar 

  3. C.D. Andereck, R. Dickman and II.L. Swinney, Phys.Fl. 26, 1395 (1983)

    Article  ADS  Google Scholar 

  4. C.D. Andereck, S.S. Liu and H.L. Swinney, J.Fluid Mech. 164, 155 (1986)

    Article  ADS  Google Scholar 

  5. M. Lowe and J.P. Gollub, Phys.Rev.A 31, 3895 (1985)

    Article  ADS  Google Scholar 

  6. A. Pocheau, V. Croquette, P. Le Gal and C. Poitou, Europhys.Lett. 3, 915 (1987)

    Article  ADS  Google Scholar 

  7. V. Croquette, P.Le Gal, A. Pocheau, and R. Guglielmetti, Europhys.Lett. 1, 393 (1986)

    Article  ADS  Google Scholar 

  8. G. Ahlers, D.S. Cannell and M.A. Dominguez-Lerma, Phys.Rev.Lett. 48, 368 (1982)

    Article  ADS  Google Scholar 

  9. J.E. Wesfreid, Y. Pomeau, M. Dubois, C. Normand and P. Berge, J.Phys. (France) 39, 725 (1978)

    Article  Google Scholar 

  10. G. Ahlers, D.S. Cannell, M.A. Dominguez-Lerma and R. Heinrichs, Physica D23, 202 (1986)

    ADS  Google Scholar 

  11. G.P. King and H.L. Swinney, Phys. Rev. A27, 1240 (1983)

    ADS  Google Scholar 

  12. G. Ahlers, D.S. Cannell and V. Steinberg, Phys.Rev.Lett. 54, 1373 (1985)

    Article  ADS  Google Scholar 

  13. Y. Pomeau and P. Manneville, J.Phys.Lett. 40, 609(1979)

    Article  MathSciNet  Google Scholar 

  14. J. Swift and P.C. Hohenberg, Phys.Rev.A 15, 319 (1977)

    Article  ADS  Google Scholar 

  15. J.E. Wesfreid and V. Croquette, Phys.Rev.Lett. 45, 634 (1980)

    Article  ADS  Google Scholar 

  16. V. Croquette and J.E. Wesfreid, p.399 in Symmetries and Broken Symmetries in Condensed Matter Physics, N. Boccara, Ed., IDSET, Paris, 1981

    Google Scholar 

  17. A.C. Newell and J.A. Whitehead, J.Fluid Mech. 38, 279 (1969)

    Article  MATH  ADS  Google Scholar 

  18. L.A. Segel, J.Fluid Mech. 38, 203 (1969)

    Article  MATH  ADS  Google Scholar 

  19. P. Ortoleva and J. Ross, J.Chem.Phys. 58, 5673 (1972)

    Article  ADS  Google Scholar 

  20. S. Zaleski, These de troisieme cycle, unpublished

    Google Scholar 

  21. H. Brand and M.C. Cross, Phys.Rev.A 27, 1237 (1983)

    Article  ADS  Google Scholar 

  22. P. Tabeling, J.Phys.Lett. 44, 665 (1983)

    Article  Google Scholar 

  23. H.A. Snyder, Phys.Fluids 11, 728 (1968)

    Article  ADS  Google Scholar 

  24. H.R. Brand, Prog.Theo.Phys. 71, 1096 (1984)

    Article  ADS  Google Scholar 

  25. G.I. Sivashinsky, Acta Astronaut. 6, 569 (1979)

    Article  MATH  Google Scholar 

  26. Y. Kuramoto and T. Tsuzuki, Prog.Theo.Phys. 55, 356 (1976)

    Article  ADS  Google Scholar 

  27. A.C. Newell and J.A. Whitehead, p.284 in Proceedings of the IUTAM Symposium in Herrenalb, 1969, H. Leipholz Ed., Springer, N.Y., 1971

    Google Scholar 

  28. A.C. Newell, p.244 in Synergetics, H. Haken Ed., Springer, N.Y. 1979.

    Google Scholar 

  29. A.C. Newell, p.157 in Lectures in Applied Mathematics, Vol.15, M. Kac Ed., American Mathematical Society, Rh.I. 1974

    Google Scholar 

  30. H.R. Brand, P.S. Lomdahl and A.C. Newell, Phys.Lett.A 118, 67 (1986)

    Article  ADS  Google Scholar 

  31. H.R. Brand, P.S. Lomdahl and A.C. Newell, Physica D 23, 345 (1986)

    Article  MATH  ADS  Google Scholar 

  32. D. Walgraef, Phys.Rev.A 34, 3270 (1986)

    Article  ADS  Google Scholar 

  33. P. Hall, Phys.Rev.A 29, 2921 (1984)

    Article  ADS  Google Scholar 

  34. Y. Kuramoto, Prog.Theo.Phys. 71, 1183 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  35. M. Gorman and H.L. Swinney, J.Fluid Mech. 117, 123 (1982)

    Article  ADS  Google Scholar 

  36. K. Bhler, Z.Angew.Math.Mech. 64, T180 (1984)

    Google Scholar 

  37. C. Nouar, R. Devienne, G. Cognet and M. Lebouche, Abstracts of the 4th Taylor Vortex Flow Working Party, Karlsruhe, W. Germany, 1985, K. Bhler, M. Wimmer and J. Zierep, Eds.

    Google Scholar 

  38. P. Tabeling and C. Trakas, in Cellular Structures in Instabilities, J.E. Wesfreid and S. Zaleski Eds., Lecture Notes in Physics, Springer, N.Y. 1984

    Google Scholar 

  39. H.R. Brand, Phys.Rev.A 31, 3454 (1985)

    Article  ADS  Google Scholar 

  40. H.R. Brand, Phys.Rev.A 32, 3551 (1985)

    Article  ADS  Google Scholar 

  41. P.G. de Gennes, The physics of liquid crystals, Clarendon Press, Oxford, 1982

    Google Scholar 

  42. T.C. Lubensky, Phys.Rev.A 6, 452 (1972)

    Article  ADS  Google Scholar 

  43. H.R. Brand and II. Pleiner, J.Phys.(France) 45, 563 (1984)

    Article  Google Scholar 

  44. H. Brand and H. Pleiner, J.Phys.(France) 41, 553 (1980)

    Article  MathSciNet  Google Scholar 

  45. P. Lallemand, S. Zaleski and P. Tabeling, Phys.Rev.A 32, 655 (1984)

    Google Scholar 

  46. H. Brand and P. Bak, Phys.Rev.A 27, 1062 (1983)

    Article  ADS  Google Scholar 

  47. M. Lowe, B.S. Albert and J.P. Gollub, J.Fluid Mech. 173, 253 (1986)

    Article  ADS  Google Scholar 

  48. P. Coullet, Phys.Rev.Lett. 56, 724 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  49. P. Coullet and C. Elphick, Phys.Lett.A 121, 233 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  50. D. Shechtman, I. Blech, D. Gratias and J.W. Cahn, Phys.Rev.Lett. 53, 1951 (1984)

    Article  ADS  Google Scholar 

  51. P. Bak, Phys.Rev.Lett. 54, 1517 (1985)

    Article  ADS  Google Scholar 

  52. H.R. Brand, P.C. Hohenberg and V. Steinberg, Phys.Rev.A 30, 2548 (1984)

    Article  ADS  Google Scholar 

  53. H.R. Brand, Phys.Rev.Lett. 57, 2768 (1986)

    Article  ADS  Google Scholar 

  54. P. Coullet and S. Fauve, p.290 in Macroscopic Modelling of Turbulent Flows, U. Frisch et al, Eds., Lecture Notes in Physics, Vol.230, Springer, N.Y. 1985

    Chapter  Google Scholar 

  55. P. Coullet and S. Fauve, Phys.Rev.Lett. 55, 2857 (1985)

    Article  ADS  Google Scholar 

  56. B.I. Shraiman, Phys.Rev.Lett. 57, 325 (1986)

    Article  ADS  Google Scholar 

  57. G.I. Sivashinsky, Ann.Rev.Fluid Mech. 15, 179 (1983)

    Article  ADS  Google Scholar 

  58. V.L. Gertsberg and G.I. Sivashinsky, Prog.Theor.Phys. 66, 1219 (1981)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  59. E.D. Siggia and A. Zippelius, Phys.Rev.Lett. 47, 835 (1981)

    Article  ADS  Google Scholar 

  60. P. Coullet and P. Huerre, Physica D 23, 27 (1986)

    Article  MATH  ADS  Google Scholar 

  61. M.C. Cross, Phys.Rev.A 27, 490 (1983)

    Article  ADS  Google Scholar 

  62. H.R. Brand and A.C. Newell, to be published

    Google Scholar 

  63. R.E. Rosenzweig, Advances in Electronics and Electron Physics, 48, 103 (1980)

    Google Scholar 

  64. P. Leiderer, W. Ebner and V.B. Shikin, Surf.Sci. 113, 405 (1982)

    Article  ADS  Google Scholar 

  65. M. Boucif, J.E. Wesfreid and E. Guyon, J.Phys.Lett. 45, 413 (1984)

    Article  Google Scholar 

  66. H.R. Brand and J.E. Wesfreid, submitted for publication

    Google Scholar 

  67. H.R. Brand, Phys.Rev.A 35, 4461 (1987)

    Article  ADS  Google Scholar 

  68. J.M. Luijkx, J.K. Platten and J.C. Legros, Int.J.Heat and Mass Transfer 24, 1287 (1981)

    Article  Google Scholar 

  69. M. Wimmer, Z.Angew.Math.Mech. 63, T299 (1983)

    Google Scholar 

  70. M. Wimmer, Z.Angew.Math.Mech. 65, T255 (1985)

    ADS  Google Scholar 

  71. A. Pocheau, this volume

    Google Scholar 

  72. M.C. Cross and A.C. Newell, Physica D 10, 299 (1984)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  73. H.R. Brand and K. Kawasaki, J.Phys.A 17, 905 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  74. K. Kawasaki and H.R. Brand, Ann.Phys.(N.Y.) 160, 420 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  75. K. Kawasaki, Prog.Theo.Phys.Suppl. 79, 161 (1984)

    Article  ADS  Google Scholar 

  76. L. Kramer, E. Ben-Jacob, H. Brand and M.C. Cross, Phys.Rev.Lett. 49, 1891 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  77. D.S. Cannell, M.A. Dominguez-Lerma and G. Ahlers, Phys.Rev.Lett. 50, 1365 (1983)

    Article  ADS  Google Scholar 

  78. H. Riecke and H.G. Paap, Phys.Rev.A 33, 547 (1986)

    Article  ADS  Google Scholar 

  79. H. Chat and P. Manneville, Phys.Rev.Lett. 58, 112 (1987)

    Article  ADS  Google Scholar 

  80. P. Manneville and J.M. Piquemal, Phys.Rev.A 28, 1774 (1983)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FB 7, Physik, Universität Essen, D-4300, Essen 1, Fed. Rep. of Germany

    H. R. Brand

  2. Center for Nonlinear Studies, MS-B258, Los Alamos National Laboratory, University of California, Los Alamos, NM, 87545, USA

    H. R. Brand

Authors
  1. H. R. Brand
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratoire d’Hydrodynamique et Mécanique Physique, E.S.P.C.I. Paris, 10, rue Vauquelin, F-75231, Paris Cedex 05, France

    José E. Wesfreid

  2. Fachbereich 7 (Physik), Universität Essen, D-4300, Essen 1, Fed. Rep. of Germany

    Helmut R. Brand

  3. IRF-DPh-G/PSRM, CEN-Saclay, F-91191, Gif-sur-Yvette, France

    Paul Manneville

  4. Lab. de Recherches en Combustion, Université de Provence, Centre St. Jérôme, F-13397, Marseille Cedex 13, France

    Gilbert Albinet

  5. Centre de Physique Théorique, F-74310, Les Houches, France

    Nino Boccara

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brand, H.R. (1988). Phase Dynamics — A Review and a Perspective. In: Wesfreid, J.E., Brand, H.R., Manneville, P., Albinet, G., Boccara, N. (eds) Propagation in Systems Far from Equilibrium. Springer Series in Synergetics, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73861-6_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-73861-6_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-73863-0

  • Online ISBN: 978-3-642-73861-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation