Exact results for nucleation-and-growth in one dimension

Abstract

We study statistical properties of the Kolmogorov-Avrami-Johnson-Mehl nucleation-and-growth model in one dimension. We obtain exact results for the gap density as well as the island distribution. When all nucleation events occur simultaneously, the island distribution has discontinuous derivatives on the rays x_n(t)=nt, n=1,2,3... We introduce an accelerated growth mechanism where the velocity increases linearly with the island size. We solve for the inter-island gap density and show that the system reaches complete coverage in a finite time and that the near-critical behavior of the system is robust, i.e., it is insensitive to details such as the nucleation mechanism.

9 pages, revtex, also available from http://arnold.uchicago.edu/~ebn/

References in corpus (4)

• Theory of Phase Ordering Kinetics
• Extremal Properties of Random Systems
• Theoretical and numerical studies of chemisorption on a line with precursor layer diffusion
• Space covering by growing rays

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