The simulation of curvature driven growth in grain boundary systems is becoming an important tool in understanding the behavior of microstructure evolution and there is much distinguished work in this subject. Here we address the mesoscale simulation of large systems of grain boundaries subject to the Mullins equation of curvature driven growth with the Herring force balance equation imposed at triple junctions. We discuss several novel features of our approach which we anticipate will render it a flexible, scalable, and robust tool to aid in microstructural prediction. What is the result of the simulation? We discuss what such a simulation is capable of predicting, taking as a prototype the histogram of relative area population as it changes through the simulation. We do not use this data to seek the best distribution, like Hillert, Rayleigh, or lognormal. Instead we treat the set of distributions as the solution of an inverse problem for a time varying function and determine the equation they satisfy. This results in a coarse graining of the complex simulation to simpler system governed by a Fokker-Planck Equation. Even so, fundamental questions concerning the predictability of simulations of large metastable systems arise from these considerations.
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Kinderlehrer, D., Livshits, I., Manolache, F. et al. An Approach to the Mesoscale Simulation of Grain Growth. MRS Online Proceedings Library 652, 15 (2000). https://doi.org/10.1557/PROC-652-Y1.5