New Monte Carlo method for planar Poisson-Voronoi cells

Details New Monte Carlo method for planar Poisson-Voronoi cells New Monte Carlo method for planar Poisson-Voronoi cells

2006-12-16

arxiv.org/abs/cond-mat/0612422v1

J.Phys. A: Math.Theor. 40 (2007) 2615

Physics

Condensed Matter

Statistical Mechanics

35 pages including 10 figures and 4 tables

Scientific paper

By a new Monte Carlo algorithm we evaluate the sidedness probability p_n of a planar Poisson-Voronoi cell in the range 3 \leq n \leq 1600. The algorithm is developed on the basis of earlier theoretical work; it exploits, in particular, the known asymptotic behavior of p_n as n\to\infty. Our p_n values all have between four and six significant digits. Accurate n dependent averages, second moments, and variances are obtained for the cell area and the cell perimeter. The numerical large n behavior of these quantities is analyzed in terms of asymptotic power series in 1/n. Snapshots are shown of typical occurrences of extremely rare events implicating cells of up to n=1600 sides embedded in an ordinary Poisson-Voronoi diagram. We reveal and discuss the characteristic features of such many-sided cells and their immediate environment. Their relevance for observable properties is stressed.

Affiliated with

Also associated with

No associations

Rating

New Monte Carlo method for planar Poisson-Voronoi cells 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 New Monte Carlo method for planar Poisson-Voronoi cells, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New Monte Carlo method for planar Poisson-Voronoi cells will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-368929