Mathematical models of triple junctions

Interface Science

Volumn 7, Issue 3, 1999, Pages 243-249

  Taylor, Jean E ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; GRAIN GROWTH; INTERFACIAL ENERGY; MATHEMATICAL MODELS; POLYCRYSTALLINE MATERIALS;

TRIPLE LINE ENERGY;

INTERFACES (MATERIALS);

EID: 0033312063     PISSN: 09277056     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1008717225195     Document Type: Article

References (37)

1. J.A.F. Plateau, Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires (Gauthier-Villars, Paris, 1863).
2. A. Heppes, Isogonale sphärischen Netze, Ann. Univ. Sci. Budapest Eötvös Sec. Math. 7, 41-48 (1964).
3. Ernest Lamarle, Mém. Acad. R. Belg 35, 3-104 (1864).
4. Jean E. Taylor, Annals of Mathematics 103, 489-539 (1976).
5. Jesse Douglas, Trans. Amer. Math. Soc. 33, 263-321 (1931).
6. Frederick J. Almgren, Jr., Memoirs of the American Mathematical Society 165 (1975).
7. E.R. Reifenberg, Acta Math. 104, 1-92 (1960).
8. E.R. Reifenberg, Ann. of Math. 80, 1-14 (1964).
9. Robert Kanigel, The Scientist (published by the New York Academy of Sciences) March 1993, and republished in Math Horizons (published by the Mathematical Association of America), Sept. 1994.
10. Brian White, Regularity of the singular sets in immiscible fluid interfaces and solutions to other Plateau-type problems. Miniconference on geometry and partial differential equations (Canberra, 1985), 244-249, Proc. Centre Math. Anal. Austral. Nat. Univ. 10, Austral. Nat. Univ. Canberra, 1986.
11. Brian White, J. Geom. Anal. 6(1), 151-161 (1996).
12. Jean E. Taylor, Comm. in Partial Differential Equations 2, 323-357 (1977).
13. D.W. Hoffman and J.W Cahn, Surf. Sci. 31, 368 (1972).
14. Gary Lawlor and Frank Morgan, Pacific J. Math. 166, 55-83 (1994).
15. Jean E. Taylor, in The Selected Works of John W. Cahn, edited by W.C. Carter and W.C. Johnson (TMS Warrendale, PA, 1998), pp. 289-292.
16. Jean E. Taylor, Annals of Mathematics 103, 541-546 (1976).
17. Kenneth A. Brakke, Experiment. Math. 1(2), 141-165 (1992).
18. Jean E. Taylor and John W. Cahn, Physica D 112, 381-411 (1998).
19. Hong-Kai Zhao, T. Chan, B. Merriman, and S. Osher, J. Comput. Phys. 127(1), 179-195 (1996).
20. Frank Morgan and Jean E. Taylor, Scripta Metall. Mater. 25, 1907-1910 (1991).
21. Frank Morgan, Proc. Amer. Math. Soc. 122, 1153-1161 (1994).
22. Frank Morgan, Math. Ann. 299, 697-714 (1994).
23. J. Willard Gibbs, The Collected Works of J.W. Gibbs (Longmans, Green and Co., New York, 1928), Vol. 1, p. 298.
24. S.G. Srinivasan, John W. Cahn, Hannes Jónsson, and Gretchen Kalonji, Acta Mat. 47(9), 2821-2829 (1999).
25. Kenneth Brakke and Frank Morgan, Instability of the wet X soap film, J. Geometric Analysis, to appear. Preprint available from http://www.susqu.edu/facstaff/b/brakke/papers.
26. Kenneth Brakke, Instability of the wet cube cone soap film, preprint. Available from http://www.susqu.edu/facstaff/b/ brakke/papers.
27. Joel Hass and Frank Morgan, Math Z. 223, 185-196 (1996).
28. B. Widom, Physica A 263, 500-515 (1999).
29. Jean E. Taylor, Acta Metall. Mater. 40, 1475-1485 (1992).
30. William K. Allard, Ann. of Math. (2) 95, 417-491 (1972).
31. William K. Allard, Amer. J. Math. 105, 1255-1276 (1983).
32. Jean E. Taylor, John W. Cahn, and Carol A. Handwerker, Acta Metall. Mater. 40, 1443-1474 (1992).
33. Fred Almgren, Jean Taylor, and Lihe Wang, Curvature Driven Flows: SIAM Journal of Control and Optimization 31, 386-437 (1993).
34. NungKwan Yip, Ph.D. thesis, Princeton University, 1996.
35. David Caraballo, Thesis, Princeton University, 1996.
36. Jean E. Taylor, J. Stat. Phys., to appear.
37. Amy Novick-Cohen, Triple junction motion for a Allen-Cahn/Cahn-Hilliard system, Physica D. 136, (2000), to appear.