RESUMEN
We study the effect of the anisotropy of the cells on the topological properties of monodisperse two- and three-dimensional (3D) froths. These froths are built by Voronoï tessellation of actual assemblies of monosize disks (2D) and of many numerical packings of monosize disks (2D) and spheres (3D). We show that some topological properties of these froths can be simply related to the anisotropy of the cells.
RESUMEN
The Voronoi network is known to be a useful tool for the structural description of voids in the packings of spheres produced by computer simulations. In this article we extend the Voronoi-Delaunay analysis to packings of nonspherical convex objects. Main properties of the Voronoi network, which are known for systems of spheres, are valid for systems of any convex objects. A general numerical algorithm for calculation of the Voronoi network in three dimensions is proposed. It is based on the calculation of the trajectory of the imaginary empty sphere of variable size, moving inside a system (the Delaunay empty sphere method). Analysis of voids is presented for an ensemble of random straight lines and for a molecular dynamics model of liquid crystal. The spatial distribution of voids and a simple percolation analysis are obtained. The distributions of the bottleneck radii and the radii of spheres inscribed in the voids are calculated.
RESUMEN
By using molecular dynamics simulations on a large number of hard spheres and the Voronoï tessellation we characterize hard-sphere systems geometrically at any packing fraction eta along the different branches of the phase diagram. Crystallization of disordered packings occurs only for a small range of packing fraction. For the other packing fractions the system behaves as either a fluid (stable or metastable) or a glass. We have studied the evolution of the statistics of the Voronoï tessellation during crystallization and characterized the apparition of order by an order parameter (Q(6)) built from spherical harmonics.