Analytical Results for Size-Topology Correlations in 2D Disc and Cellular Packings

Details Analytical Results for Size-Topology Correlations in 2D Disc and Cellular Packings Analytical Results for Size-Topology Correlations in 2D Disc and Cellular Packings

2011-12-05

arxiv.org/abs/1112.1108v1

Physics

Condensed Matter

Soft Condensed Matter

9 pages, 5 figures, accepted in Phys. Rev. Lett. (2011), http://prl.aps.org

Scientific paper

Random tilings or packings in the plane are characterized by a size distribution of individual elements (domains) and by the statistics of neighbor relations between the domains. Most systems occurring in nature or technology have a unimodal distribution of both areas and number of neighbors. Empirically, strong correlations between these distributions have been observed and formulated as universal laws. Using only the local, correlation-free granocentric model approach with no free parameters, we construct accurate analytical descriptions for disc crystallization, size-topology correlations, and Lema\^itre's law.

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