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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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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Abstract 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.
AbstractList 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.
Author Szeto, K Y
Fu, Xiujun
Tam, W Y
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SubjectTerms Cells - diagnostic imaging
Models, Biological
Models, Theoretical
Ultrasonography
Title Universal topological properties of two-dimensional trivalent cellular patterns
URI https://www.ncbi.nlm.nih.gov/pubmed/11955131
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