Grain growth in three dimensions depends on grain topology

While the growth rate of the average volume in a three-dimensional polycrystal is well understood, the growth rates of individual grains (which determine material properties through the topological and volume distributions) are not known. Using a three-dimensional Q-state Potts model simulation, I find that the average canonical growth rate of a grain depends linearly on its number of faces and is independent of its volume, a surprisingly simple and unexplained result.