Nucleation and growth in one dimension, part I: The generalized Kolmogorov-Johnson-Mehl-Avrami model

Details Nucleation and growth in one dimension, part I: The generalized Kolmogorov-Johnson-Mehl-Avrami model Nucleation and growth in one dimension, part I: The generalized Kolmogorov-Johnson-Mehl-Avrami model

2004-08-12

arxiv.org/abs/cond-mat/0408260v2

Phys Rev E 71, 011908 (2005) and Feb 1 issue of Virtual Journal of Biological Physics

Physics

Condensed Matter

Soft Condensed Matter

9 pages, 9 figures

Scientific paper

10.1103/PhysRevE.71.011908

Motivated by a recent application of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model to the study of DNA replication, we consider the one-dimensional 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.

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