Cell Dynamics Simulation of Kolmogorov-Johnson-Mehl-Avrami Kinetics of   Phase Transformation
  In this study, we use the cell dynamics method to test the validity of the Kormogorov-Johnson-Mehl-Avrami (KJMA) theory of phase transformation. This cell dynamics method is similar to the well-known phase-field model, but it is a more simple and efficient numerical method for studying various scenarios of phase transformation in a unified manner. We find that the cell dynamics method reproduces the time evolution of the volume fraction of the transformed phase predicted by the KJMA theory. Specifically, the cell dynamics simulation reproduces a double-logarithmic linear KJMA plot and confirms the integral Avrami exponents $n$ predicted from the KJMA theory. Our study clearly demonstrates that the cell dynamics approach is not only useful for studying the pattern formation but also for simulating the most basic properties of phase transformation. 
Masao Iwamatsu, Masato Nakamura