Mean Densities and Spherical Contact Distribution Function of Inhomogeneous Boolean Models

2010 ◽  
Vol 28 (3) ◽  
pp. 480-504 ◽  
Author(s):  
Elena Villa
Keyword(s):  
Distribution Function ◽  
Boolean Models ◽  
Spherical Contact ◽  
Contact Distribution ◽  
Contact Distribution Function

scholarly journals ESTIMATING THE INTENSITY OF GERM-GRAIN MODELS WITH OVERLAPPING GRAINS

2011 ◽  
Vol 22 (1) ◽  
pp. 147 ◽  
Author(s):  
Hamid Ghorbani ◽  
Dietrich Stoyan
Keyword(s):  
Distribution Function ◽  
Silicon Wafer ◽  
Point Process ◽  
Poisson Point Process ◽  
Cluster Process ◽  
Spherical Contact ◽  
Grain Model ◽  
Contact Distribution ◽  
Contact Distribution Function

Formulas are derived for the spherical contact distribution of a planar germ-grain model Z with circular grains where the germs formeither a 'segment cluster' process or a 'line-based' Poisson point process. They are used in order to estimate the intensityl of the germprocess by means of the spherical contact distribution function. As an application the number of dislocations on a silicon wafer is estimated.

scholarly journals Contact and Chord Length Distribution Functions of the Poisson-Voronoi Tessellation in High Dimensions

2010 ◽  
Vol 42 (1) ◽  
pp. 48-68 ◽  
Author(s):  
L. Muche
Keyword(s):  
Voronoi Tessellation ◽  
Length Distribution ◽  
Distribution Functions ◽  
Chord Length ◽  
Dimensional Euclidean Space ◽  
Spherical Contact ◽  
Chord Length Distribution ◽  
Special Cases ◽  
Contact Distribution ◽  
Contact Distribution Function

In this paper we present formulae for contact distributions of a Voronoi tessellation generated by a homogeneous Poisson point process in the d-dimensional Euclidean space. Expressions are given for the probability density functions and moments of the linear and spherical contact distributions. They are double and simple integral formulae, which are tractable for numerical evaluation and for large d. The special cases d = 2 and d = 3 are investigated in detail, while, for d = 3, the moments of the spherical contact distribution function are expressed by standard functions. Also, the closely related chord length distribution functions are considered.

New Approximate Analytical Formula for the Solute-Solvent Contact Distribution Function in an Infinitely Dilute Binary Hard-Sphere Mixture

2008 ◽  
Vol 73 (3) ◽  
pp. 314-321 ◽  
Author(s):  
Stanislav Labík ◽  
William R. Smith
Keyword(s):  
Distribution Function ◽  
Hard Sphere ◽  
Pair Distribution Function ◽  
Analytical Formula ◽  
Diameter Ratio ◽  
Scaled Particle Theory ◽  
Perfect Agreement ◽  
Simulation Results ◽  
Contact Distribution ◽  
Contact Distribution Function

A new analytical expression for the contact value of the solute-solvent pair distribution function of a binary hard-sphere mixture at infinite dilution is proposed, based on scaled-particle-theory-like arguments. For high solute-solvent diameter ratio it predicts perfect agreement with the simulation results.

scholarly journals SPATIAL STATISTICS FOR SIMULATED PACKINGS OF SPHERES

2011 ◽  
Vol 20 (3) ◽  
pp. 203 ◽  
Author(s):  
Alexander Bezrukov ◽  
Dietrich Stoyan ◽  
Monika Bargieł
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Spatial Statistics ◽  
Volume Fraction ◽  
Pair Correlation ◽  
Simulation Methods ◽  
Coordination Numbers ◽  
Contact Distribution ◽  
Contact Distribution Function ◽  
Random Packings

This paper reports on spatial-statistical analyses for simulated random packings of spheres with random diameters. The simulation methods are the force-biased algorithm and the Jodrey-Tory sedimentation algorithm. The sphere diameters are taken as constant or following a bimodal or lognormal distribution. Standard characteristics of spatial statistics are used to describe these packings statistically, namely volume fraction, pair correlation function of the system of sphere centres and spherical contact distribution function of the set-theoretic union of all spheres. Furthermore, the coordination numbers are analysed.

scholarly journals Random Laguerre tessellations

2008 ◽  
Vol 40 (3) ◽  
pp. 630-650 ◽  
Author(s):  
Claudia Lautensack ◽  
Sergei Zuyev
Keyword(s):  
Distribution Function ◽  
Systematic Study ◽  
Poisson Processes ◽  
Voronoi Tessellations ◽  
Planar Case ◽  
Geometric Characteristics ◽  
Contact Distribution ◽  
Contact Distribution Function ◽  
Integral Formulae

A systematic study of random Laguerre tessellations, weighted generalisations of the well-known Voronoi tessellations, is presented. We prove that every normal tessellation with convex cells in dimension three and higher is a Laguerre tessellation. Tessellations generated by stationary marked Poisson processes are then studied in detail. For these tessellations, we obtain integral formulae for geometric characteristics and densities of the typical k-faces. We present a formula for the linear contact distribution function and prove various limit results for convergence of Laguerre to Poisson-Voronoi tessellations. The obtained integral formulae are subsequently evaluated numerically for the planar case, demonstrating their applicability for practical purposes.

scholarly journals Contact and Chord Length Distribution Functions of the Poisson-Voronoi Tessellation in High Dimensions

2010 ◽  
Vol 42 (01) ◽  
pp. 48-68 ◽  
Author(s):  
L. Muche
Keyword(s):  
Voronoi Tessellation ◽  
Length Distribution ◽  
Distribution Functions ◽  
Chord Length ◽  
Dimensional Euclidean Space ◽  
Spherical Contact ◽  
Chord Length Distribution ◽  
Special Cases ◽  
Contact Distribution ◽  
Contact Distribution Function

In this paper we present formulae for contact distributions of a Voronoi tessellation generated by a homogeneous Poisson point process in the d-dimensional Euclidean space. Expressions are given for the probability density functions and moments of the linear and spherical contact distributions. They are double and simple integral formulae, which are tractable for numerical evaluation and for large d. The special cases d = 2 and d = 3 are investigated in detail, while, for d = 3, the moments of the spherical contact distribution function are expressed by standard functions. Also, the closely related chord length distribution functions are considered.

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