Universal properties of Voronoi tessellations of hard discs
- 7 December 1992
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 25 (23), 6169-6177
- https://doi.org/10.1088/0305-4470/25/23/014
Abstract
The authors describe a 2D mosaic obtained by the Voronoi tessellation of a monosize assembly of discs at different packing fractions. The experimental device (hard discs moving on an air table) produces, for every packing fraction, a succession of mosaics in statistical equilibrium, which constitutes a statistical ensemble. This ensemble is large enough for fluctuations from the most probable distributions to be negligible. They use the maximum entropy principle to get the distribution of the polygons in 2D mosaics generated from an assembly of hard discs. Steric exclusion yields an extra conservation law, which is sufficient to give a good agreement with the experimental data. A similar behaviour in the six-fold parameter seems to hold for other mosaics.Keywords
This publication has 19 references indexed in Scilit:
- Random packing of disks in two dimensionsPhysical Review A, 1990
- Cell-area distributions of planar Voronoi mosaicsMetallography, 1989
- Vertex models for two-dimensional grain growthPhilosophical Magazine Part B, 1989
- The arrangement of cells in “random” networksMetallography, 1982
- Adsorption of ferritinJournal of Colloid and Interface Science, 1980
- Random sequential adsorptionJournal of Theoretical Biology, 1980
- The arrangement of cells in a netMetallography, 1980
- Grain coordination in plane sections of polycrystalsActa Metallurgica, 1979
- The Monte-Carlo generation of random polygonsComputers & Geosciences, 1978
- Shape Distribution of Two-Dimensional Soap FrothsThe Journal of Chemical Physics, 1956