8,600 research outputs found
The Palm measure and the Voronoi tessellation for the Ginibre process
We prove that the Palm measure of the Ginibre process is obtained by removing
a Gaussian distributed point from the process and adding the origin. We obtain
also precise formulas describing the law of the typical cell of
Ginibre--Voronoi tessellation. We show that near the germs of the cells a more
important part of the area is captured in the Ginibre--Voronoi tessellation
than in the Poisson--Voronoi tessellation. Moment areas of corresponding
subdomains of the cells are explicitly evaluated.Comment: Published in at http://dx.doi.org/10.1214/09-AAP620 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Weighted Poisson-Delaunay Mosaics
Slicing a Voronoi tessellation in with a -plane gives a
-dimensional weighted Voronoi tessellation, also known as power diagram or
Laguerre tessellation. Mapping every simplex of the dual weighted Delaunay
mosaic to the radius of the smallest empty circumscribed sphere whose center
lies in the -plane gives a generalized discrete Morse function. Assuming the
Voronoi tessellation is generated by a Poisson point process in ,
we study the expected number of simplices in the -dimensional weighted
Delaunay mosaic as well as the expected number of intervals of the Morse
function, both as functions of a radius threshold. As a byproduct, we obtain a
new proof for the expected number of connected components (clumps) in a line
section of a circular Boolean model in $\mathbb{R}^n
Elastic moduli of model random three-dimensional closed-cell cellular solids
Most cellular solids are random materials, while practically all theoretical
results are for periodic models. To be able to generate theoretical results for
random models, the finite element method (FEM) was used to study the elastic
properties of solids with a closed-cell cellular structure. We have computed
the density () and microstructure dependence of the Young's modulus ()
and Poisson's ratio (PR) for several different isotropic random models based on
Voronoi tessellations and level-cut Gaussian random fields. The effect of
partially open cells is also considered. The results, which are best described
by a power law (), show the influence of randomness
and isotropy on the properties of closed-cell cellular materials, and are found
to be in good agreement with experimental data.Comment: 13 pages, 13 figure
High-order 3D Voronoi tessellation for identifying Isolated galaxies, Pairs and Triplets
Geometric method based on the high-order 3D Voronoi tessellation is proposed
for identifying the single galaxies, pairs and triplets. This approach allows
to select small galaxy groups and isolated galaxies in different environment
and find the isolated systems. The volume-limited sample of galaxies from the
SDSS DR5 spectroscopic survey was used. We conclude that in such small groups
as pairs and triplets the segregation by luminosity is clearly observed:
galaxies in the isolated pairs and triplets are on average two times more
luminous than isolated galaxies. We consider the dark matter content in
different systems. The median values of mass-to-luminosity ratio are 12
M_sol/L_sol for the isolated pairs and 44 M_sol/L_sol for the isolated
triplets; 7 (8) M_sol/L_sol for the most compact pairs (triplets). We found
also that systems in the denser environment have greater rms velocity and
mass-to-luminosity ratio.Comment: 11 pages, 7 figures, Accepted 2008 October 25 in MNRA
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