Topology-dependent description of grain growth

A growth equation for individual grains is suggested by considering the interactions of the nearest-neighbor grains, which indicates that the average grain growth rate of a given topological class depends on the difference between the number of faces and the average number of faces of the nearest neighbors. For the convenience of its application, a practical equation is also proposed. They have been verified by the data of β-titanium grains, dry 3D foams, Monte Carlo Potts model simulation, vertex model simulation, and surface evolver simulation.