H J Hilhorst

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By a new Monte Carlo algorithm we evaluate the sidedness probability p n of a planar Poisson-Voronoi cell in the range 3 ≤ n ≤ 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 → ∞. Our p n values all have between four and six significant digits. Accurate n(More)
In planar cellular systems m n denotes the average sidedness of a cell neighboring an n-sided cell. Aboav's empirical law states that nm n is linear in n. A downward curvature is nevertheless observed in the numerical nm n data of the Random Voronoi Froth. The exact large-n expansion of m n obtained in the present work, viz. m n = 4+3(π/n) 1 2 +. . .,(More)
We study the support (i.e. the set of visited sites) of a t step random walk on a two-dimensional square lattice in the large t limit. A broad class of global properties M (t) of the support is considered, including, e.g., the number S(t) of its sites; the length of its boundary; the number of islands of unvisited sites that it encloses; the number of such(More)
We consider a family of random line tessellations of the Euclidean plane introduced in a much more formal context by Hug and Schneider [Geom. Funct. Anal. 17, 156 (2007)] and described by a parameter α ≥ 1. For α = 1 the zero-cell (that is, the cell containing the origin) coincides with the Crofton cell of a Poisson line tessellation, and for α = 2 it(More)
  • H J Hilhorst, O Deloubrì Ere, M J Washenberger, U C Täuber
  • 2004
The kinetics of the q species pair annihilation reaction (A i + A j → ∅ for 1 ≤ i < j ≤ q) in d dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time regime the total particle density decays as ρ(t) ∼ t −α. For d = 1 the system segregates into single species domains, yielding a different value of α for(More)