Generalization of the Aboav-Weaire law
H. Wang, G. Q. Liu · Europhysics Letters (EPL) · 2012
How cells are arranged in a three-dimensional celluar network is one of the classic problems of physics, biology and materials science. Based on the topological analyses on steady-state grain-growth structure, a generalization of the Aboav-Weaire law to layers beyond the first is suggested that the average number of faces per grain, mj(f), is related to the number of grains, qj(f), in thej-th layer of a center grain with f faces (on average). This result is verified by the data from the curvature flow simulation and assists in better understanding the arrangement of cells in three dimensions.