Non-self-similar behavior in the LSW theory of Ostwald ripening

Journal of Statistical Physics

Volumn 95, Issue 5-6, 1999, Pages 867-902

  Niethammer, Barbara ^a   Pego, Robert L ^b  

^a UNIVERSITY OF BONN   (Germany)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

Asymptotic behavior; Chaos; Domain coarsening; Kinetics of phase transitions; Self similarity; Stability

Indexed keywords

EID: 0033245858     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004546215920     Document Type: Article

References (17)

1. 1. C. Berg and G. Forst, Potential Theory on Locally Compact Abelian Groups (Springer-Verlag, New York, 1975).
2. 2. N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation, Encycl. Math. Appl., Vol. 27 (Cambridge University Press, Cambridge, 1987).
3. 3. L. C. Brown, A new examination of classical coarsening theory, Acta Metall. 37: 71-77 (1989).
4. 4. L. C. Brown, Reply to further comments by Hillert, Hunderi and Ryum on "A new examination of classical coarsening theory," Scripta Metall. Mater. 26:1939-1942 (1992).
5. 5. L. C. Brown, A new examination of volume fraction effects during particle coarsening. Acta Metall. Mater. 40:1293-1303 (1992).
6. 6. J. Carr and O. Penrose, Asymptotic behavior in a simplified Lifshitz-Slyozov equation. Physica D 124:166-176 (1998).
7. 7. J.-F. Collet and T. Goudon, On solutions of the Lifshitz-Slyozov model, preprint.
8. 8. B. Giron, B. Meerson, and P. V. Sasorov, Weak selection and stability of localized distributions in Ostwald ripening. Phys. Rev. E 58:4213-6 (1998).
9. 9. I. M. Lifshitz and V. V. Slyozov, The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids 19:35-50 (1961).
10. 10. B. Meerson and P. V. Sasorov, Domain stability, competition, growth and selection in globally constrained bistable systems. Phys. Rev. E 53:3491-4 (1996).
11. 11. B. Niethammer, Derivation of the LSW theory for Ostwald ripening by homogenization methods, to appear in Arch Rat. Mech. Anal.
12. 12. B. Niethammer and R. L. Pego, On the initial value problem in the Lifshitz Slyozov Wagner theory of Ostwald ripening, to appear in SIAM J. Math. Anal.
13. 13. O. Penrose, The Becker Döring equations at large times and their connection with the LSW theory of coarsening, J. Stat. Phys. 89:305-320 (1997).
14. 14. E. Seneta, Regularly Varying Functions, Lee. Notes in Math., Vol. 508 ( Springer-Verlag, New York, 1976).
15. 15. P. W. Voorhees, The theory of Ostwald ripening, J. Stat. Phys. 38:231-252 (1985).
16. 16 P. W. Voorhees, Ostwald ripening of two-phase mixtures, Ann. Rev. Mater. Sci. 22:197-215 (1992).
17. 17. C. Wagner, Theorie der Alterung von Niederschlägen durch Umlösen, Z. Elektrochem. 65:581-594 (1961).