Universal topological properties of two-dimensional trivalent cellular patterns.
Universal topological properties of two-dimensional trivalent cellular patterns are found from shell analysis of soap froth and computer-generated Voronoi diagrams. We introduce a cluster analysis based on the shell model and find the universal relation ln(a/mu(2)) = A+Bln(mu(2)), with the generalized Aboav parameter a and second moment of the number of cell edge distribution mu(2). For the second, third, and fourth shells of the cluster, A and B are the same for all samples. Furthermore, A is increasing with shell number while B is a universal number, -0.90. For the first shell, the slope B is the same for soap froths, but slightly different from Voronoi graphs.
Szeto
K Y
KY
Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China.
Fu
Xiujun
X
Tam
W Y
WY
D002477:Cells / Q000000981:diagnostic imaging*; D008954:Models, Biological; D008962:Models, Theoretical; D014463:Ultrasonography