Validation criterion for noise-induced mechanism of sidebranching in directional solidification

European Physical Journal B

Volumn 21, Issue 2, 2001, Pages 229-240

  Pocheau, A ^a   Georgelin, M ^a  

^a AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

47.20 Hw Morphological instability; phase changes; 68.70 +w Whiskers and dendrites; 81.30 Fb Solidification

Indexed keywords

EID: 0013451449     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100510170199     Document Type: Article

References (34)

1. J.S. Langer, Rev. Mod. Phys. 52, 1 (1980); B. Billia, R. Trivedi, Handbook of Crystal Growth, Vol. 1, Chap. 14 (Elsevier Science Publishers, 1993).
2. J.S. Langer, Rev. Mod. Phys. 52, 1 (1980); B. Billia, R. Trivedi, Handbook of Crystal Growth, Vol. 1, Chap. 14 (Elsevier Science Publishers, 1993).
3. R. Pieters, Phys. Rev. A 37, 3126 (1988).
4. W. van Saarloos, B. Caroli, C. Caroli, J. Phys. I France 3, 741 (1993).
5. O. Martin, N. Goldenfeld, Phys. Rev. A 35, 1382 (1987).
6. Ya.B. Zel'dovich, A.G. Istratov, N.I. Kidin, V.B. Librovich, Combust. Science Technol. 24, 1 (1980).
7. P. Pelcé, Dynamics of curved fronts (Academic Press, New-York, 1988).
8. P. Pelcé, P. Clavin, Europhys. Lett. 3, 907 (1987).
9. R. Pieters, J.S. Langer, Phys. Rev. Lett. 56, 1948 (1986); J.S. Langer, Phys. Rev. A 36, 3350 (1987); M.N. Barber, A. Barbieri, J.S. Langer, Phys. Rev. A 36, 3340 (1987); B. Caroli, C. Caroli, B. Roulet, J. Phys. France 48, 1423 (1987).
10. R. Pieters, J.S. Langer, Phys. Rev. Lett. 56, 1948 (1986); J.S. Langer, Phys. Rev. A 36, 3350 (1987); M.N. Barber, A. Barbieri, J.S. Langer, Phys. Rev. A 36, 3340 (1987); B. Caroli, C. Caroli, B. Roulet, J. Phys. France 48, 1423 (1987).
11. R. Pieters, J.S. Langer, Phys. Rev. Lett. 56, 1948 (1986); J.S. Langer, Phys. Rev. A 36, 3350 (1987); M.N. Barber, A. Barbieri, J.S. Langer, Phys. Rev. A 36, 3340 (1987); B. Caroli, C. Caroli, B. Roulet, J. Phys. France 48, 1423 (1987).
12. R. Pieters, J.S. Langer, Phys. Rev. Lett. 56, 1948 (1986); J.S. Langer, Phys. Rev. A 36, 3350 (1987); M.N. Barber, A. Barbieri, J.S. Langer, Phys. Rev. A 36, 3340 (1987); B. Caroli, C. Caroli, B. Roulet, J. Phys. France 48, 1423 (1987).
13. S.K. Sarkar, Phys. Lett. A 117, 137 (1986).
14. X.W. Quian, H.Z. Cummins, Phys. Rev. Lett. 64, 3038 (1990).
15. L.M. Williams, M. Muschol, X. Quian, W. Losert, H.Z. Cummins, Phys. Rev. E 48, 489 (1993).
16. W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 35, 444 (1964).
17. M. Georgelin, A. Pocheau, Phys. Rev. E 57, 3189 (1998).
18. A. Dougherty, P.D. Kaplan, J. Gollub, Phys. Rev. Lett. 58, 1652 (1987).
19. P. Kurowski, C. Guthmann, S. de Cheveigné, Phys. Rev. A 42, 7368 (1990).
20. M. Georgelin, A. Pocheau, Eur. Phys. J. B 4, 169 (1998).
21. A. Pocheau, M. Georgelin, J. Cryst. Growth 206, 215 (1999).
22. in preparation.
23. J.D. Weeks, W. van Saarloos, Phys. Rev. A 42, 5056 (1990).
24. A. Karma, P. Pelcé, Phys. Rev. A 41, 6741 (1990).
25. i for the critical velocity approximates the exact one to 3%.
26. Both the liquidus slope and the solidus slope are assumed to be negative. For a positive liquidus slope and a positive solidus slope, the factor (1 - k) should be replaced by (k - 1) with k > 1.
27. P.G. Saffman, G.I. Taylor, Proc. Roy. Soc. A 245, 312 (1958).
28. P. Pelcé, A. Pumir, J. Cryst. Growth 73, 337 (1985).
29. T.F. Bower, H.D. Brody, M.C. Flemings, Trans. Met. Soc. AIME 236, 624 (1966); H.D. Brody, M.C. Flemings, Trans. Met. Soc. AIME 236, 615 (1966).
30. T.F. Bower, H.D. Brody, M.C. Flemings, Trans. Met. Soc. AIME 236, 624 (1966); H.D. Brody, M.C. Flemings, Trans. Met. Soc. AIME 236, 615 (1966).
31. J.W. McLean, P.G. Saffman, J. Fluid Mech. 102, 455 (1981).
32. J.D. Weeks, W. van Saarloos, M. Grant, J. Cryst. Growth 112, 244 (1991).
33. P.G. Saffman, G.I. Taylor, Proc. Roy. Soc. A 245, 312 (1958); P. Tabeling, G. Zocchi, A. Libchaber, J. Fluid Mech. 177, 67 (1987).
34. P.G. Saffman, G.I. Taylor, Proc. Roy. Soc. A 245, 312 (1958); P. Tabeling, G. Zocchi, A. Libchaber, J. Fluid Mech. 177, 67 (1987).