Evolution of pattern complexity in the Cahn-Hilliard theory of phase separation

Acta Materialia

Volumn 53, Issue 3, 2005, Pages 693-704

  Gameiro, Marcio ^a   Mischaikow, Konstantin ^a   Wanner, Thomas ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b GEORGE MASON UNIVERSITY   (United States)

Author keywords

Coarsening; Dynamic phenomena; Microstructure; Phase field models; Spinodal decomposition

Indexed keywords

ALGEBRA; ALLOYS; BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; DECOMPOSITION; MATHEMATICAL MODELS; MICROSTRUCTURE; PHASE SEPARATION;

COARSENING; COMPUTATIONAL ALGEBRA; DYNAMIC PHENOMENA; PATTERN COMPLEXITY; PHASE FIELD MODELS; SPINODAL DECOMPOSITION;

COMPLEXATION;

EID: 10444284320     PISSN: 13596454     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.actamat.2004.10.022     Document Type: Article

References (38)

1. Arns CH, Knackstedt MA, Pinczewski WV, Mecke KR. Phys Rev E 2001;63(3):031112.
2. Binder K. In: Arnold L, editor. Stochastic nonlinear systems. Berlin: Springer; 1981. p. 62-71.
3. Blömker D, Maier-Paape S, Wanner T. Commun Math Phys 2001;223(3):553-82.
4. Cahn JW. J Chem Phys 1959;30:1121-4.
5. Cahn JW. J Chem Phys 1965;42:93-9.
6. Cahn JW. Trans Metall Soc AIME 1968;242:166-80.
7. Cahn JW, Milliard JE. J Chem Phys 1958;28:258-67.
8. Cahn JW, Milliard JE. J Chem Phys 1959;31:688-99.
9. Cerezo A, Hetherington MG, Hyde JM, Miller MK. Scripta Metall Mater 1991;25:1435-40.
10. Cook H. Acta Metall 1970;18:297-306.
11. Frigo M, Johnson SG. Proc ICASSP 1998 1998;3:1381-4.
12. Gameiro M, Kalies W, Mischaikow K. Phys Rev E 2004;70(3):035203.
13. Garcke H, Niethammer B, Rumpf M, Weikard U. Acta Mater 2003;51(10):2823-30.
14. Hairer E, Wanner G. Solving ordinary differential equations II. Berlin: Springer; 1991.
15. Hilfer R. Transport Porous Med 2002;46(2-3):373-90.
16. Hilliard JE. In: Aaronson HI, editor. Phase transformations. Metals Park (OH): American Society for Metals; 1970. p. 497-560.
17. Hyde JM, Miller MK, Hetherington MG, Cerezo A, Smith GDW, Elliott CM. Acta Metall Mater 1995;43:3403-13.
18. Hyde JM, Miller MK, Hetherington MG, Cerezo A, Smith GDW, Elliott CM. Acta Metall Mater 1995;43:3415-26.
19. Ioannidis MA, Chatzis I. J Colloid Interface Sci 2000;229(2):323-34.
20. Kaczynski T, Mischaikow K, Mrozek M. Computational homology. Applied mathematical sciences, vol. 157. New York: Springer; 2004.
21. Kalies W, Pilarczyk P. Computational homology program. Available from: http://www.math.gatech.edu/~chom/, 2003.
22. Kong TY, Rosenfeld A. Comput Vision Graph Image Process 1989;48(3):357-93.
23. Langer JS. Ann Phys 1971;65:53-86.
24. Leßle P, Dong M, Schmauder S. Comput Mater Sci 1999;15(4):455-65.
25. Leßle P, Dong M, Soppa E, Schmauder S. Scripta Mater 1998;38(9):1327-32.
26. Löchte L, Gitt A, Gottstein G, Hurtado I. Acta Mater 2000;48(11):2969-84.
27. Maier-Paape S, Wanner T. Commun Math Phys 1998;195(2):435-64.
28. Maier-Paape S, Wanner T. Arch Ration Mech Anal 2000;151(3):187-219.
29. Mendoza R, Alkemper J, Voorhees PW. In: Rappaz M, Beckermann C, Trivedi R, editors. Solidification processes and microstructures: a symposium in honor of Wilfried Kurz. TMS; 2004. p. 123-29.
30. Miller MK, Hyde JM, Hetherington MG, Cerezo A, Smith GDW, Elliott CM. Acta Metall Mater 1995;43:3385-401.
31. Quarteroni A, Valli A. Numerical approximation of partial differential equations. Berlin: Springer; 1994.
32. Ramanarayan H, Abinandanan TA. Acta Mater 2003;51(16):4761-72.
33. Sander E, Wanner T. J Stat Phys 1999;95(5-6):925-48.
34. Sander E, Wanner T. SIAM J Appl Math 2000;60(6): 2182-2202.
35. Shardlow T. Numer Func Anal Opt 1999;20(1-2):121-45.
36. Torquato S. Annu Rev Mater Res 2002;32:77-111.
37. Ujihara T, Osamura K. Acta Mater 2000;48(7):1629-37.
38. Wanner T. Trans Am Math Soc 2004;356(6):2251-79.