Simulation of Three Dimensional Cellular Structures by New Triangulation Method for Vertex Model

We numerically study three-dimensional cellular structure by using the vertex model. We adopt a new triangulation method of cellular surface (model S), and compare it with two models (model N and model G). We find that they show similar scaling properties. Average face numbers of a cell are 13.92, 13.52, and 13.83 for model S, N, and G, respectively. We analytically obtain the lifetime of one regular polyhedral cell for each model. The distribution function of vertex velocity becomes a form of the log normal distribution. The vertex aberration from a flat cellular face is also investigated.