Efficient computation of dendritic microstructures using adaptive mesh refinement

Physical Review Letters

Volumn 80, Issue 15, 1998, Pages 3308-3311

  Provatas, Nikolas ^a   Goldenfeld, Nigel ^a   Dantzig, Jonathan ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1842576356     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.80.3308     Document Type: Article

References (28)

1. S.-C.Huang, and M. E.Glicksman, Acta Metall., 29, 701(1981).
2. M. E.Glicksman, Mater.Sci. Eng., 65, 45(1984).
3. J. S.Langer, Rev. Mod. Phys., 52, 1(1980).
4. J. S.Langer, in Chance and Matter, Lectures in the Theory of Pattern Formation, Les Houches Session XLVI, J. Souletie, J. Vannenimus, and R. Stora, (North-Holland, Amsterdam, 1987), p. 629.
5. D. A.Kessler, J.Koplik, and H.Levine, Adv. Phys., 37, 255(1988).
6. R.Brower, D.Kessler, J.Koplik, and H.Levine, Phys. Rev. Lett., 51, 1111(1983).
7. E.Ben-Jacob, N.Goldenfeld, J. S.Langer, and G.Schön, Phys. Rev. Lett., 51, 1930(1983).
8. E.Ben-Jacob, N.Goldenfeld, B. G.Kotliar, and J. S.Langer, Phys. Rev. Lett., 53, 2110(1984).
9. D.Kessler, J.Koplik, and H.Levine, Phys. Rev. A, 30, 3161(1984).
10. E.Brener, and V. I.Melnikov, Adv. Phys., 40, 53(1991).
11. Y.Pomeau, and M.Ben Amar, in Solids Far from Equilibrium, C. Godrèche, (Cambridge University Press, Cambridge, England, 1991), p. 365.
12. R.Almgren, J. Comp. Phys., 106, 337(1993).
13. G.Caginalp, Arch.Ration. Mech. Anal., 92, 205(1986)
14. G.Caginalp, Anal. Phys., 172, 136(1986)
15. G.Caginalp, and E.Socolovsky, SIAM J. Sci. Comput., 15, 106(1991).
16. J. B.Collins, and H.Levine, Phys. Rev. B, 31, 6119(1985).
17. J. A.Warren, and W. J.Boettinger, Acta Metall. Mater. A, 43, 689(1995).
18. A.Karma, Phys.Rev. E, 49, 2245(1994).
19. A. A.Wheeler, G. B.McFadden, and W. J.Boettinger, Proc. R. Soc. London A, 452, 495(1996).
20. R.Kobayashi, Physica (Amsterdam), 63D, 410(1993).
21. S-L.Wang, and R. F.Sekerka, Phys. Rev. E, 53, 3760(1996).
22. A.Karma, and W.-J.Rappel, Phys. Rev. E, 53, 3017(1996)
23. A. Karma, and Wouter-Jan Rappel, (to be published).
24. M.Fabbri, and V. R.Voller, J. Comput. Phys., 130, 256(1997).
25. G.Caginalp, and X.Chen, in On The Evolution Of Phase Boundaries, M. E. Gurtin, and G. B. McFadden, (Springer-Verlag, New York, 1992), p. 1.
26. R. J.Braun, and B. T.Murray, J. Cryst. Growth, 174, 41(1997).
27. N.Palle, and J. A.Dantzig, Metall. Trans. A, Phys. Metall. Mater. Sci., 27, 707(1996).
28. R.Almgren, W.-S.Dai, and V.Hakim, Phys. Rev. Lett., 71, 3461(1993).