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

Matthew P. Miklius; Sascha Hilgenfeldt

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arXiv · 1112.1108

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

Matthew P. Miklius·Sascha Hilgenfeldt

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Abstract

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 Lemaître's law.

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Matthew P. Miklius, Sascha Hilgenfeldt. 2011-12-05. Analytical Results for Size-Topology Correlations in 2D Disc and Cellular Packings. https://arxiv.org/abs/1112.1108

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