Grain size distribution in two dimensions in the long time limit

It is shown that the inclusion of a “noise” term in the growth rate of individual grains leads to a stochastic model that provides a more realistic description of grain growth phenomenon. The resulting Fokker–Planck equation for the grain size distribution is solved numerically due to the difficulties in obtaining an analytical solution. The analysis is limited to two dimensions and assumes quasi-stationary distributions in the long time limit. The resulting grain size distribution is shown to be in agreement with that obtained from computer simulations, indicating the validity of the stochastic approach.