scholarly journals Contact Distribution Function based Clustering Technique with Self-Organizing Maps

2018 ◽  
Vol 10 (3) ◽  
pp. 9-17
Author(s):  
G. Chamundeswari ◽  
◽  
G. P. S. Varma ◽  
Ch. Satyanarayana
Keyword(s):  
Distribution Function ◽  
Self Organizing Maps ◽  
Clustering Technique ◽  
Contact Distribution ◽  
Contact Distribution Function ◽  
Self Organizing

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 Random Laguerre tessellations

2008 ◽  
Vol 40 (03) ◽  
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 ON THE DILATED FACETS OF A POISSON-VORONOI TESSELLATION

2011 ◽  
Vol 30 (1) ◽  
pp. 31 ◽  
Author(s):  
Claudia Redenbach
Keyword(s):  
Distribution Function ◽  
Specific Surface ◽  
Voronoi Tessellation ◽  
Analytical Formula ◽  
Volume Density ◽  
Intrinsic Volumes ◽  
Closed Cell ◽  
Contact Distribution ◽  
Contact Distribution Function ◽  
Cell Foam

In this paper, the parallel set ΞR of the facets ((d−1)-faces) of a stationary Poisson-Voronoi tessellation in ℝ2 and ℝ3 is investigated. An analytical formula for the spherical contact distribution function of the tessellation allows for the derivation of formulae for the volume density and the specific surface area of ΞR. The densities of the remaining intrinsic volumes are studied by simulation. The results are used for fitting a dilated Poisson-Voronoi tessellation to the microstructure of a closed-cell foam.

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