The arrangement of cells in 3- and 4-regular planar networks formed by random straight linesReport as inadecuate




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Abstract : The relation between mi, the average number of sides in cells adjacent to i-sided cells, and i, was investigated in planar networks of two types, generated by random, Poisson distributed, straight lines. When the lines are continuous, a 4-regular network results. If the lines are interrupted to form T-junctions, a 3-regular network is obtained. In the first case, two types of cell adjacency can be defined and for both mi varies approximately linearly with 1-i. The same applies to the 3-regular network. The linear relations Aboav-s law can be put in a general form, involving the second moment of the distribution of cell polygonalities and a single parameter, a, as suggested by Weaire.

Keywords : lattice theory and statistics random processes





Author: M. A. Fortes P.N. Andrade

Source: https://hal.archives-ouvertes.fr/



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