Velocity Selection for Needle Crystals in the 2-D One-Sided Model

  • C. Misbah
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 41)


When a solid grows at the expense of an undercooled melt the liquid-solid interface develops a dendritic shape, characterized by the propagation of a needle-shaped tip advancing at a constant velocity V and the persistent emission of side branches.


Surface Tension Imaginary Axis Symmetric Model Needle Crystal Constant Velocity Versus 
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  1. 1.
    M.E. Glicksman, R.J. Shaefer and J.D. Ayers: Metall. Trans. A7, 1747 (1976).Google Scholar
  2. S.C. Huang and M.E. Glicksman: Acta Metall. 29, 701 and 717 (1981).CrossRefGoogle Scholar
  3. 2.
    G.P. Ivantsov: Dokl. Akad. Nauk SSSR 58, 567 (1947).Google Scholar
  4. 3.
    R. Brower, D. Kessler, J. Koplik and H. Levine: Phys. Rev. Lett. 51, 1111 (1983); Phys. Rev. A29, 1335 (1984).CrossRefADSGoogle Scholar
  5. 4.
    E. Ben Jacob, N. Goldenfeld, J.S. Langer and G. Shön: Phys. Rev. Lett. 51, 1930 (1983); Phys. Rev. A29 330 (1984).CrossRefADSGoogle Scholar
  6. Ben Jacob, N. Goldenfeld, R.G. Koltiar and J.S. Langer: Phys. Rev. Lett. 53, 2110 (1984).CrossRefADSGoogle Scholar
  7. 5.
    J.S. Langer: Phys. Rev. A33, (1986), 435ADSGoogle Scholar
  8. 6.
    B. Caroli, C. Caroli, B. Roulet and J.S. Langer: Phys. Rev. A33. 442 (1986).ADSMathSciNetGoogle Scholar
  9. 7.
    M. Ben Amar and Y. Pomeau: Europhys. Lett. 2, 307 (1986).CrossRefADSGoogle Scholar
  10. 8.
    A. Barbieri, D.C. Hong and J.S. Langer: Phys. Rev. A35. 1802 (1987).ADSGoogle Scholar
  11. 9.
    D. Kessler and H. Levine: Phys. Rev. Lett. 57, 3069 (1986).CrossRefADSGoogle Scholar
  12. 10.
    D. Bensimon, P. Pelcé, and B.I. Shraiman: Dynamics of curved fronts and pattern selection, preprint (1987).Google Scholar
  13. 11.
    H. Honjo, S. Ohta and Y. Sawada: Phys. Rev. Lett. 55, 841 (5).Google Scholar
  14. 12.
    M.D. Kruskal and H. Segur: Asymptotics beyond all orders in a model of dendritic crystals, preprint (1985), A.R.A.P. Tech. Memo, 85–25.Google Scholar
  15. 13.
    A. Karma: Ph. D. Thesis, University of California, Santa Barbara (1985), and also A. Karma and M. Mardes (unpublished).Google Scholar
  16. 14.
    J.S. Langer and H. Müller-Krumbhaar: Acta Metall. 26, 1681, 1689, 1697 (1978).CrossRefGoogle Scholar
  17. 15.
    P. Pelcé and Y. Pomeau: Studies in Appl. Math. 74, 83 (1986).Google Scholar
  18. 16.
    J.M. Vanden Broeck: Phys. Fluids 26 2033 (1983).CrossRefADSMathSciNetGoogle Scholar
  19. 17.
    M. Ben Amar and B. Moussalam, preprint.Google Scholar
  20. 18.
    C. Misbah (unpublished).Google Scholar
  21. 19.
    V.L. Pokrovskii and I.M. Khalatnikov: Soviet Phys. JETP 13, 1207 (1961).Google Scholar
  22. 20.
    B Caroli, C. Caroli, C. Misbah and B. Roulet: J. Physique 48, 547 (1987).CrossRefGoogle Scholar
  23. 21.
    C. Misbah: to be published in J. Physique (August 1987).Google Scholar
  24. 22.
    Y. Saito, G. Goldbeck-Wood and H. Müller-Krumbhaar, Phys. Rev. Lett. 58, 1541 (1987).CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • C. Misbah
    • 1
  1. 1.Groupe de Physique des Solides de l’E.N.S., associé au C.N.R.S.Université ParisParis Cedex 05France

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