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

Abstract

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.

arXiv comment9 pages, 9 figures

References in corpus (6)

• Test of the Kolmogorov-Johnson-Mehl-Avrami picture of metastable decay in a model with microscopic dynamics
• Kinetic model of DNA replication in eukaryotic organisms
• Exact results for nucleation-and-growth in one dimension
• Nucleation and growth in one dimension, part II: Application to DNA replication kinetics
• Cosmic Phase Transitions
• Mean Field Theory of Polynuclear Surface Growth

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• How Xenopus laevis embryos replicate reliably: investigating the random-completion problem
• Cell size distribution in a random tessellation of space governed by the Kolmogorov-Johnson-Mehl-Avrami model: Grain size distribution in crystallization
• How Xenopus laevis replicates DNA reliably even though its origins of replication are located and initiated stochastically
• Beyond the constraints underlying Kolmogorov-Johnson-Mehl-Avrami theory related to the growth laws
• Inferring the spatiotemporal DNA replication program from noisy data
• Solid phase crystallization under continuous heating: kinetic and microstructure scaling laws
• Quench dynamics of a dissipative Rydberg gas in the classical and quantum regime
• Kinetics of phase transformations with heterogeneous correlated-nucleation
• Cell-size distribution and scaling in a one-dimensional KJMA lattice model with continuous nucleation
• Nonequilibrium grain size distribution with generalized growth and nucleation rates
• Genome replication in asynchronously growing microbial populations