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 generaliz...

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Bibliographic Details
Published inPhysical review letters Vol. 88; no. 13; p. 138302
Main Authors Szeto, K Y, Fu, Xiujun, Tam, W Y
Format Journal Article
LanguageEnglish
Published United States 01.04.2002
Subjects
Cells - diagnostic imaging
Models, Biological
Models, Theoretical
Ultrasonography
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Summary: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.
ISSN:0031-9007
DOI:10.1103/PhysRevLett.88.138302