Three-dimensional Random Voronoi Tessellations: From Cubic Crystal Lattices to Poisson Point Processes

Details Three-dimensional Random Voronoi Tessellations: From Cubic Crystal Lattices to Poisson Point Processes Three-dimensional Random Voronoi Tessellations: From Cubic Crystal Lattices to Poisson Point Processes

2008-05-18

arxiv.org/abs/0805.2705v1

J. Stat. Phys., 134, 185-206 (2009)

Physics

Condensed Matter

Statistical Mechanics

18 pages, 7 figures

Scientific paper

10.1007/s10955-008-9668-y

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.

Affiliated with

Also associated with

No associations

Rating

Three-dimensional Random Voronoi Tessellations: From Cubic Crystal Lattices to Poisson Point Processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Three-dimensional Random Voronoi Tessellations: From Cubic Crystal Lattices to Poisson Point Processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Three-dimensional Random Voronoi Tessellations: From Cubic Crystal Lattices to Poisson Point Processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-65924