Comparison between a grain size distribution obtained by a Monte Carlo Potts Model and by an analytical mean field model

The evolution of the computer simulated Monte Carlo Potts model (MCPM) grain size distributions (GSD) of Battaile and Holm approached a quasi-stationary analytical distribution, φ*(u,ν,H0) = H0νH0/2(u2-νu+u)1+H0/2exp[ -H0ν/ √4ν-ν2(arctan(2u-ν/√4ν-ν 2) +arctan(ν/√4ν-ν2))], ν = 2, obtained by Rios based on the classical mean field theory. This is in agreement with previous work by Rios in which a GSD obtained by Surface Evolver simulation could also be described as an analytical distribution, φ*(u,ν,H0) = H0νH0/2(u2-νu+u)1+H0/2exp[- H0ν/ √4ν-ν2(arctan(2u-ν/√4ν-ν 2) +arctan(ν/√4ν-ν2))], ν = 2.65, belonging to the same one-parameter family of quasi-stationary solutions of the continuity equation. The fact that two computer simulated distributions obtained by different methods could be well described by the analytical mean field theory with reasonable values of ν indicates the consistency of the approaches.