Planar Voronoi cells and the failure of Aboav's law
| dc.creator | Hilhorst, Hendrik-Jan | |
| dc.date | 2005-09-15 | |
| dc.date.accessioned | 2026-07-07T03:06:38Z | |
| dc.date.available | 2026-07-07T03:06:38Z | |
| dc.description | 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 $m\_n=4+3(π/n)^{-{1/2}}+...$ 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. | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0509409 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0509409 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/26886 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Planar Voronoi cells and the failure of Aboav's law | |
| dc.type | text |