Phys. Rev. Lett. 88, 138302 (2002) [3 pages]Universal Topological Properties of Two-Dimensional Trivalent Cellular PatternsReceived 13 November 2001; published 19 March 2002 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/μ2) = A+Bln(μ2), with the generalized Aboav parameter a and second moment of the number of cell edge distribution μ2. 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. © 2002 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.88.138302
DOI:
10.1103/PhysRevLett.88.138302
PACS:
82.70.Rr, 02.50.-r, 05.70.Ln
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