Planar Voronoi cells and the failure of Aboav's law
Résumé
Aboav's law is a quantitative expression of the empirical fact that in planar cellular structures many-sided cells tend to have few-sided neighbors. This law is nonetheless violated in the most widely used model system, {\it viz.} the Poisson-Voronoi tessellation. We obtain the correct law for this model: Given an $n$-sided cell, any of its neighbors has on average $m_n$ sides where $m_n=4+3(\pi/n)^{-\frac{1}{2}}+\ldots$ in the limit of large $n$. This expression is quite accurate also for nonasymptotic $n$ and we discuss its implications for the analysis of experimental data.
Loading...