Skip to main content

Scaling for an interfacial instability

  • Conference paper
  • First Online:
  • 167 Accesses

Part of the book series: Lecture Notes in Physics ((LNP,volume 319))

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. A. Jackson and J. D. Hunt, Acta Metall. 13:1215 (1965).

    Google Scholar 

  2. F. Heslot and A. Libchaber, Phys. Scr. T9:126 (1985).

    Google Scholar 

  3. P. G. Saffman and G. I. Taylor, Proc. Roy. Soc. (London) A245:312 (1958).

    Google Scholar 

  4. P. Tabeling and A. Libchaber, Phys. Rev. A33:794 (1986).

    Google Scholar 

  5. S. C. Huang and M. E. Glicksman, Acta Metall. 29:701 (1981); 29:717 (1981).

    Google Scholar 

  6. J. S. Langer, Rev. Mod. Phys. 52:1 (1980).

    Google Scholar 

  7. See, e.g., D. Kessler, J. Koplik and H. Levine, Phys. Rev. A30:3161 (1984); E. Ben-Jacob, N. Goldenfeld, B. G. Kotliar and J. S. Langer, Phys. Rev. Lett. 53:2110 (1984).

    Google Scholar 

  8. S. K. Sarkar and D. Jasnow, Phys. Rev. A35:4900 (1987).

    Google Scholar 

  9. A. Karma, Phys. Rev. Lett. 57:858 (1986).

    Google Scholar 

  10. T. Dombre and V. Hakim, Phys. Rev. A36:2811 (1987).

    Google Scholar 

  11. M. Ben-Amar and B. Moussallam, Phys. Rev. Lett. 60:317 (1988).

    Google Scholar 

  12. D. A. Kessler and H. Levine, U.C.S.D. preprint (1988).

    Google Scholar 

  13. T. A. Witten and L. M. Sander, Phys. Rev. Lett. 47:1400 (1981).

    Google Scholar 

  14. T. A. Witten and L. M. Sander, Phys. Rev. B27:5685 (1983).

    Google Scholar 

  15. See, e.g.,articles in Kinetics of Aggregation and Gelation, edited by F. Family and D. P. Landau (North Holland, New York, 1984).

    Google Scholar 

  16. D. Bensimon, L. P. Kadanoff, S. Liang, B. Schraiman and C. Tang, Rev. Mod. Phys. 58:977 (1986).

    Google Scholar 

  17. T. Vicsek, Phys. Rev. Lett. 53:2281 (1984).

    Google Scholar 

  18. L. A. Turkevich and H. Scher, Phys. Rev. Lett. 55:1026 (1985).

    Google Scholar 

  19. W. W. Mullins and R. F. Sekerka, J. Appl. Phys. 34:323 (1963); 35:444(1964).

    Google Scholar 

  20. L. P. Kadanoff, J. Stat. Phys. 39:267 (1985).

    Google Scholar 

  21. See, e.g., J. Marro, J. L. Lebowitz and M. H. Kalos, Phys. Rev. Lett. 43:282 (1979); J. L. Lebowitz, J. Marro and M. H. Kalos, Acta Metall. 30:297 (1982); for additional background and references see J. D. Gunton, M. San Miguel and P. S. Sahni in Phase Transitions and Critical Phenomena, ed. by C. Domb and J. L. Lebowitz (Academic, New York, 1983)v.8.

    Google Scholar 

  22. For an interesting new approach and a thorough discussion of background and references, the reader is referred to the work of Y. Oono and S. Puri, Phys. Rev. A (in press).

    Google Scholar 

  23. Previous accounts have appeared in H. Guo and D. Jasnow, Phys. Rev. 34:5027 (1986).

    Google Scholar 

  24. D. Jasnow, Superlattices and Microstructures 3:581 (1987).

    Google Scholar 

  25. J. S. Langer and L. Turski, Acta Metall. 25:267 (1977).

    Google Scholar 

  26. D. Jasnow, D. A. Nicole and T. Ohta, Phys. Rev. A23:3192 (1981).

    Google Scholar 

  27. A. Onuki, K.P. Sekimoto and D. Jasnow, Prog. Theor. Phys. 74:685 (1985).

    Google Scholar 

  28. A brief discussion of roughening with references is contained in D. Jasnow, Rept. Prog. Phys. 47:1059 (1984).

    Google Scholar 

  29. K. Kawasaki, Phys. Rev. 145:224 (1966).

    Google Scholar 

  30. See, e.g., A. B. Bortz, M. H. Kalos, J. L. Lebowitz and M. A. Zendejas, Phys. Rev. B10:535 (1974); A. Sadiq, Phys. Rev. b(:2299 (1974); additional references may be found in K. W. Kehr and K. Binder in Applications of the Monte Carlo Method in Statistical Physics, ed. K. Binder (Springer-Verlag, New York, 1984).

    Google Scholar 

  31. S. Katz, J. L. Lebowitz and H. Spohn, J. Stat. Phys. 34:323 (1984); 38:725 (1985).

    Google Scholar 

  32. A. Hernandez-Machado and D. Jasnow, Phys. Rev. 37:656 (1988).

    Google Scholar 

  33. For a review of hyperscaling in critical phenomena see, e.g., M. E. Fisher in Lecture Notes in Physics Vol. 186, Critical Phenomena, (ed. F. J. W. Hahne, Springer-Verlag, N. Y., 1983).

    Google Scholar 

  34. K. Leung and J. L. Cardy, J. Stat. Phys. 44:567 (1986).

    Google Scholar 

  35. J. W. Cahn and J. E. Hilliard, J. Chem. Phys. 28:258 (1958).

    Google Scholar 

  36. See, e. g., D. B. Abrahamand P. Reed, J. Phys. A10:L121 (1977); K.K. Mon and D. Jasnow, Phys. Rev. A31:4008 (1985); J. Stat. Phys. 41:273 (1985).

    Google Scholar 

  37. M. P. A. Fisher, D. S. Fisher and J. D. Weeks, Phys. Rev. Lett. 48:368 (1982).

    Google Scholar 

  38. J. B. Collins and H. Levine, Phys. Rev. B31:6119 (1985).

    Google Scholar 

  39. E. Ben-Jacob, N. Goldenfeld, J. S. Langer and G. Schon, Phys. Rev. Lett. 51:1930 (1983).

    Google Scholar 

  40. G. Caginalp, Phys. Rev. B (in press); University of Pittsburgh preprint (1988).

    Google Scholar 

  41. K. Kitahara, Y. Oono and D. Jasnow, Mod. Phys. Lett. B (in press).

    Google Scholar 

  42. Y. Oono and S. Puri, Phys. Rev. Lett. 58:836 (1987).

    Google Scholar 

  43. A. Hernandez-Machado, unpublished.

    Google Scholar 

  44. J. S. Langer, N. Bar-On and H. D. Miller, Phys. Rev. A11:1417 (1975).

    Google Scholar 

  45. L. M. Sander, P. Ramanial and E. Ben-Jacob, Phys. Rev. A32:3160 (1985)

    Google Scholar 

  46. S. Sarkar, unpublished.

    Google Scholar 

  47. H. Guo, unpublished.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Luis Garrido

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Jasnow, D. (1988). Scaling for an interfacial instability. In: Garrido, L. (eds) Far from Equilibrium Phase Transitions. Lecture Notes in Physics, vol 319. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50643-8_44

Download citation

  • DOI: https://doi.org/10.1007/3-540-50643-8_44

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50643-0

  • Online ISBN: 978-3-540-46060-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics