Analytical Results for Size-Topology Correlations in 2D Disc and Cellular Packings
arXiv:1112.1108
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.
9 pages, 5 figures, accepted in Phys. Rev. Lett. (2011), http://prl.aps.org