Phys. Rev. E 71, 011908 (2005) [8 pages]Nucleation and growth in one dimension. I. The generalized Kolmogorov-Johnson-Mehl-Avrami modelReceived 30 July 2004; published 21 January 2005 Motivated by a recent application of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model to the study of DNA replication, we consider the one-dimensional (1D) version of this model. We generalize previous work to the case where the nucleation rate is an arbitrary function I(t) and obtain analytical results for the time-dependent distributions of various quantities (such as the island distribution). We also present improved computer simulation algorithms to study the 1D KJMA model. The analytical results and simulations are in excellent agreement. © 2005 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.71.011908
DOI:
10.1103/PhysRevE.71.011908
PACS:
87.16.Ac, 05.40.−a, 02.50.Ey, 82.60.Nh
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