Phase-field model of dendritic sidebranching with thermal noise

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 4 A, 1999, Pages 3614-3625

  Karma, Alain ^a   Rappel, Wouter Jan ^b  

^a NORTHEASTERN UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000752997     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.60.3614     Document Type: Article

References (48)

1. W. Kurz and D. J. Fisher, Fundamentals of Solidification (Trans Tech, Aedermannsdorf, Switzerland, 1989).
2. R. Trivedi and W. Kurz, Int. Mater. Rev. 39, 49 (1994).
3. C. Huang and M. E. Glicksman, Acta Metall. 29, 701 (1981); 29, 717 (1981).
4. C. Huang and M. E. Glicksman, Acta Metall. 29, 701 (1981); 29, 717 (1981).
5. P. Pelce, Ph.D. thesis, Université de Provence, 1986.
6. P. Pecle and P. Clavin, Europhys. Lett. 3, 907 (1987).
7. Ya. B. Zel'dovich, A. G. Istratov, N. I. Kidin, and V. B. Librovich, Combust. Sci. Technol. 24, 1 (1980).
8. R. Pieters and J. S. Langer, Phys. Rev. Lett. 56, 1948 (1986).
9. M. Barber, A. Barbieri, and J. S. Langer, Phys. Rev. A 36, 3340 (1987).
10. D. Kessler and H. Levine, Europhys. Lett. 4, 215 (1987).
11. J. S. Langer, Phys. Rev. A 36, 3350 (1987).
12. E. Brener and D. Temkin, Phys. Rev. E 51, 351 (1995).
13. A. Dougherty, P. D. Kaplan, and J. P. Gollub, Phys. Rev. Lett. 58, 1652 (1987).
14. U. Bisang and J. H. Bilgram, Phys. Rev. Lett. 75, 3898 (1995).
15. R. Almgren, W. S. Dai, and V. Hakim, Phys. Rev. Lett. 71, 3461 (1993).
16. E. Brener, Phys. Rev. Lett. 71, 3653 (1993).
17. J. C. LaCombe, M. B. Koss, V. E. Fradkov, and M. E. Glicksman, Phys. Rev. E 52, 2778 (1995).
18. A. A. Wheeler, B. T. Murray, and R. Schaefer, Physica D 66, 243 (1993).
19. J. A. Warren and W. J. Boettinger, Acta Metall. Mater. 43, 689 (1995).
20. S-L. Wang and R. F. Sekerka, Phys. Rev. E 53, 3760 (1996).
21. B. T. Murray, A. A. Wheeler, and M. E. Glicksman, J. Cryst. Growth 47, 386 (1995).
22. A. Karma and W. J. Rappel, Phys. Rev. E 53, R3017 (1996); Phys. Rev. Lett. 77, 4050 (1996); Phys. Rev. E 57, 4323 (1998).
23. A. Karma and W. J. Rappel, Phys. Rev. E 53, R3017 (1996); Phys. Rev. Lett. 77, 4050 (1996); Phys. Rev. E 57, 4323 (1998).
24. A. Karma and W. J. Rappel, Phys. Rev. E 53, R3017 (1996); Phys. Rev. Lett. 77, 4050 (1996); Phys. Rev. E 57, 4323 (1998).
25. N. Provatas, N. Goldenfeld, and J. Dantzig, Phys. Rev. Lett. 80, 3308 (1998); J. Comp. Phys. (to be published).
26. N. Provatas, N. Goldenfeld, and J. Dantzig, Phys. Rev. Lett. 80, 3308 (1998); J. Comp. Phys. (to be published).
27. T. Ihle and H. Muller-Krumbhaar, Phys. Rev. E 49, 2972 (1994).
28. J. S. Langer, Directions in Condensed Matter, edited by G. Grinstein and G. Mazenko (World Scientific, Singapore, 1986), p. 164.
29. J. B. Collins and H. Levine, Phys. Rev. B 31, 6119 (1985).
30. B. I. Halperin, P. C. Hohenberg, and S-K. Ma, Phys. Rev. B 10, 139 (1974).
31. A. Karma, Phys. Rev. Lett. 70, 3439 (1993); Phys. Rev. E 48, 3441 (1993).
32. A. Karma, Phys. Rev. Lett. 70, 3439 (1993); Phys. Rev. E 48, 3441 (1993).
33. L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon, New York, 1980).
34. G. Caginalp and X. Chen, in On the Evolution of Phase Boundaries, edited by M. E. Gurtin and G. B. McFadden, The IMA Volumes in Mathematics and Its Applications Vol. 43 (Springer-Verlag, New York, 1992), p. 1.
35. The coupling constant is denoted by Λ, in place of λ in Ref. [21], since λ is used here to denote the wavelength of fluctuations or the spacing between sidebranches.
36. R. Kobayashi, Physica D 63, 410 (1993); Experimental Math. 3, 60 (1994).
37. R. Kobayashi, Physica D 63, 410 (1993); Experimental Math. 3, 60 (1994).
38. S-L. Wang, R. F. Sekerka, A. A. Wheeler, B. T. Murray, S. R. Coriell, R. J. Braun, and G. B. McFadden, Physica D 69, 189 (1993).
39. M. E. Glicksman and N. B. Singh, J. Cryst. Growth 98, 277 (1989).
40. M. Muschol, D. Liu, and H. Z. Cummins, Phys. Rev. A 46, 1038 (1992).
41. J. S. Langer, in Chance and Matter, Lectures on the Theory of Pattern Formation, Les Houches, Session XLVI, edited by J. Souletie, J. Vannimenus, and R. Stora (North-Holland, Amsterdam, 1987), pp. 629-711; D. Kessler, J. Koplik, and H. Levine, Adv. Phys. 37, 255 (1988); E. A. Brener and V. I. Melnikaov, ibid. 40, 50 (1991).
42. J. S. Langer, in Chance and Matter, Lectures on the Theory of Pattern Formation, Les Houches, Session XLVI, edited by J. Souletie, J. Vannimenus, and R. Stora (North-Holland, Amsterdam, 1987), pp. 629-711; D. Kessler, J. Koplik, and H. Levine, Adv. Phys. 37, 255 (1988); E. A. Brener and V. I. Melnikaov, ibid. 40, 50 (1991).
43. J. S. Langer, in Chance and Matter, Lectures on the Theory of Pattern Formation, Les Houches, Session XLVI, edited by J. Souletie, J. Vannimenus, and R. Stora (North-Holland, Amsterdam, 1987), pp. 629-711; D. Kessler, J. Koplik, and H. Levine, Adv. Phys. 37, 255 (1988); E. A. Brener and V. I. Melnikaov, ibid. 40, 50 (1991).
44. D. A. Kessler and H. Levine, Phys. Rev. B 33, 7867 (1986).
45. D. I. Meiron, Phys. Rev. A 33, 2704 (1986).
46. M. Ben Amar and B. Moussallam, Physica D 25, 155 (1987).
47. A. Karma (unpublished).
48. Q. Li and C. Beckermann, Phys. Rev. E 57, 3176 (1998).