Nucleation and growth in one dimension
Nucleation and growth in one dimension
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, we show that the island distribution has discontinuous derivatives on the rays ${\mathit{x}}_{\mathit{n}}$(t)=nt, n=1,2,3... . We introduce an …