Nucleation and growth in one dimension. I. The generalized Kolmogorov-Johnson-Mehl-Avrami model

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 71, Issue 1, 2005, Pages

  Jun, Suckjoon ^a,b   Zhang, Haiyang ^a   Bechhoefer, John ^a  

^a SIMON FRASER UNIVERSITY   (Canada)

^b FOM INSTITUTE AMOLF   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTALLIZATION KINETICS; FINITE SYSTEM SIZE; KOLOMOGOROV-JOHNSON-MEHL-AVRAMI (KJMA) MODEL; NUCLEATION RATE;

ALGORITHMS; COMPUTER SIMULATION; DNA; GENETIC ENGINEERING; MATHEMATICAL MODELS; NUCLEATION; PROBLEM SOLVING;

PHASE TRANSITIONS;

DNA; MACROMOLECULE;

CHEMICAL MODEL; CHEMISTRY; COMPARATIVE STUDY; COMPUTER SIMULATION; CRYSTALLIZATION; DIMERIZATION; DNA REPLICATION; EVALUATION STUDY; MACROMOLECULE; PROCEDURES; STATISTICAL MODEL; ULTRASTRUCTURE;

COMPUTER SIMULATION; CRYSTALLIZATION; DIMERIZATION; DNA; DNA REPLICATION; MACROMOLECULAR SUBSTANCES; MODELS, CHEMICAL; MODELS, STATISTICAL;

EID: 41349107964     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.71.011908     Document Type: Article

References (36)

1. A. N. Kolmogorov, Izv. Akad. Nauk SSSR, Ser. Fiz. 1, 335 (1937).
2. W. A. Johnson and P. A. Mehl, Trans. AIME 135, 416 (1939).
3. M. Avrami, J. Chem. Phys. 7, 1103 (1939); 8, 212 (1940); 9, 177 (1941).
4. M. Avrami, J. Chem. Phys. 7, 1103 (1939); 8, 212 (1940); 9, 177 (1941).
5. M. Avrami, J. Chem. Phys. 7, 1103 (1939); 8, 212 (1940); 9, 177 (1941).
6. J. W. Christian, The Theory of Phase Transformations in Metals and Alloys (Pergamon Press, New York, 1981).
7. C. P. Yang and J. F. Nagle, Phys. Rev. A 37, 3993 (1988).
8. T. Huang, T. Tsuji, M. R. Kamal, and A. D. Rey, Phys. Rev. E 58, 789 (1998).
9. M. Fanfoni and M. Tomellini, Nuovo Cimento D 20, 1171 (1998).
10. G. Korniss and T. Caraco, J. Theor. Biol.(to be published).
11. B. Kämpfer, Ann. Phys. (Leipzig) 9, 1 (2000).
12. J. W. Evans, Rev. Mod. Phys. 65, 1281 (1993).
13. R. A. Ramos, P. A. Rikvold, and M. A. Novotny, Phys. Rev. B 59, 9053 (1999).
14. H. Orihara and Y. Ishibashi, J. Phys. Soc. Jpn. 61, 1919 (1992).
15. J. W. Cahn, in Thermodynamics and Kinetics of Phase Transformations, edited by J. S. Im, B. Park, A. L. Greer, and G. B. Stephonion, MRS Symposia Proceedings No. 358(Materials Research Society, Pittsburgh, 1999, p. 425; Trans. Indian Inst. Met. 50, 573 (1997).
16. J. W. Cahn, in Thermodynamics and Kinetics of Phase Transformations, edited by J. S. Im, B. Park, A. L. Greer, and G. B. Stephonion, MRS Symposia Proceedings No. 358(Materials Research Society, Pittsburgh, 1999, p. 425; Trans. Indian Inst. Met. 50, 573 (1997).
17. A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 3, 109 (1958).
18. B. Derrida, C. Godrèche, and I. Tekutieli, Europhys. Lett. 12, 385 (1990).
19. J. Herrick, S. Jun, J. Bechhoefer, and A. Bensimon, J. Mol. Biol. 320, 741 (2002).
20. K. Sekimoto, Physica A 125, 261 (1984); 135, 328 (1986); Int. J. Mod. Phys. B 5, 1843 (1991).
21. K. Sekimoto, Physica A 125, 261 (1984); 135, 328 (1986); Int. J. Mod. Phys. B 5, 1843 (1991).
22. K. Sekimoto, Physica A 125, 261 (1984); 135, 328 (1986); Int. J. Mod. Phys. B 5, 1843 (1991).
23. E. Ben-Naim and P. L. Krapivsky, Phys. Rev. E 54, 3562 (1996).
24. P. L. Krapivsky, Phys. Rev. B 45, 12699 (1992).
25. J. Krug, P. Meakin, and T. Halpin-Healy, Phys. Rev. A45, 638 (1992).
26. E. Ben-Naim, A. R. Bishop, I. Daruka, and P. L. Krapivsky, J. Phys. A 31, 5001 (1998).
27. M. L. Boas, Mathematical Methods in the Physical Sciences 2nd ed. (Wiley, New York, 1983), p. 350.
28. G. Arfken and H. Weber, Mathematical Methods for Physicists, 4th ed. (Academic Press, San Diego, 1993, Sec. 15.12.
29. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, New York, 1992).
30. S. Jun, J. Herrick, A. Bensimon, and J. Bechhoefer, Cell Cycle 3, 223 (2004).
31. Even for a 1D nucleation-and-growth system, spatial correlations can exist. For a theoretical study of deviations from the KJMA, see, for example, [30]. Blow et al. [31] and Jun et al. [25] present experimental evidence for size correlations of domain statistics in biological systems.
32. A slightly different way to record individual hole sizes has been used by Ben-Naim and Krapivsky[18].
33. WaveMetrics, Inc., P.O. Box 2088, Lake Oswego, OR 97035, USA. http://www.wavemetrics.com.
34. S. Jun and J. Bechhoefer, following papers, Phys. Rev. E71, 011909 (2005).
35. M. Tomellini, M. Fanfoni, and M. Volpe, Phys. Rev. B 62, 11 300 (2000).
36. J. J. Blow, P. J. Gillespie, D. Francis, and D. A. Jackson, J. Cell Biol. 152, 15 (2001).