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 SOME DENSE RANDOM PACKINGS GENERATED BY THE DEAD LEAVES MODEL

2019 ◽  
Vol 38 (1) ◽  
pp. 3
Author(s):  
Dominique Jeulin
Keyword(s):  
Correlation Function ◽  
Pair Correlation Function ◽  
Random Media ◽  
Volume Fraction ◽  
Pair Correlation ◽  
Sequential Model ◽  
Dead Leaves Model ◽  
The Dead ◽  
Dense Packings ◽  
Random Packings

The intact grains of the dead leaves model enables us to generate random media with non overlapping grains. Using the time non homogeneous sequential model with convex grains, theoretically very dense packings can be generated, up to a full covering of space. For these models, the theoretical volume fraction, the size distribution of grains, and the pair correlation function of centers of grains are given.

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.

Structure of Fe-Si-melts by X-ray Diffraction

1997 ◽  
Vol 52 (5) ◽  
pp. 415-419
Author(s):  
B. Sedelmeyer ◽  
S. Steeb
Keyword(s):  
Correlation Function ◽  
Pair Correlation Function ◽  
Pair Correlation ◽  
Molten Alloy ◽  
X Ray Diffraction ◽  
X Ray ◽  
Coordination Numbers ◽  
Crystalline Alloy ◽  
Connection Line

Abstract X-ray diffraction was done with molten Fe66,7 Si33,3 and molten Fe33,3 Si66,7 . The coordination numbers versus the concentration lie above the connection line between the coordination numbers of the unalloyed molten elements Fe and Si, respectively, which means a tendency for microsegregation. The pair correlation function of molten Fe66,7 Si33,3 was modeled using the data of crystalline Fe2 Si. At the same time, the pair correlation function of the molten alloy Fe33,3 Si66,7 can be modeled using the data of the corresponding crystalline alloy. Thus for molten Fe33,3 Si66,7 microsegregation into FeSi2 and Si or FeSi and for molten Fe66,7 Si33,3 microsegregation into Fe2 Si and Fe or FeSi exists.

scholarly journals Study of Colliding Particle-Pair Velocity Correlation in Homogeneous Isotropic Turbulence

2020 ◽  
Vol 10 (24) ◽  
pp. 9095
Author(s):  
Santiago Lain ◽  
Martin Ernst ◽  
Martin Sommerfeld
Keyword(s):  
Correlation Function ◽  
Turbulent Flow ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Pair Correlation ◽  
Average Kinetic Energy ◽  
Velocity Correlation ◽  
Particle Inertia ◽  
Particle Pair ◽  
Theoretical Approaches

This paper deals with the numerical analysis of the particle inertia and volume fraction effects on colliding particle-pair velocity correlation immersed in an unsteady isotropic homogeneous turbulent flow. Such correlation function is required to build reliable statistical models for inter-particle collisions, in the frame of the Euler–Lagrange approach, to be used in a broad range of two-phase flow applications. Computations of the turbulent flow have been carried out by means of Direct Numerical Simulation (DNS) by the Lattice Boltzmann Method (LBM). Moreover, the dependence of statistical properties of collisions on particle inertia and volumetric fraction is evaluated and quantified. It has been found that collision locations of particles of intermediate inertia, StK~1, occurs in regions where the fluid strain rate and dissipation are higher than the corresponding averaged values at particle positions. Connected with this fact, the average kinetic energy of colliding particles of intermediate inertia (i.e., Stokes number around 1) is lower than the value averaged over all particles. From the study of the particle-pair velocity correlation, it has been demonstrated that the colliding particle-pair velocity correlation function cannot be approximated by the Eulerian particle-pair correlation, obtained by theoretical approaches, as particle separation tends to zero, a fact related with the larger values of the relative radial velocity between colliding particles.

scholarly journals Spatial patterns of primary seed dispersal and adult tree distributions: Genipa americana dispersed by Cebus capucinus – CORRIGENDUM

2015 ◽  
Vol 32 (1) ◽  
pp. 88-88
Author(s):  
Kim Valenta ◽  
Mariah E. Hopkins ◽  
Melanie Meeking ◽  
Colin A. Chapman ◽  
Linda M. Fedigan
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Pair Correlation Function ◽  
Pair Correlation ◽  
Nearest Neighbour ◽  
Study Region ◽  
Adult Tree ◽  
The Mean ◽  
K Function ◽  
Typical Point

Within the second paragraph of page 494 incorrect language was used to characterize the summary characteristics used. Sentences 3–11 of this paragraph should have read:Second, we calculated three univariate summary characteristics: the nearest neighbour distribution function D(r), the pair-correlation function g(r) and the K-function K(r). The use of multiple summary characteristics holds increased power to characterize variation in spatial patterns (Wiegand et al. 2013). The univariate nearest neighbour distribution function D(r) can be interpreted as the probability that the typical adult tree has its nearest neighbouring adult tree within radius r (or alternatively, the probability that the typical defecation has its nearest neighbouring defecation within radius r). The univariate pair-correlation function g(r) is a non-cumulative normalized neighbourhood density function that gives the expected number of points within rings of radius r and width w centred on a typical point, divided by the mean density of points λ in the study region (Wiegand et al. 2009). We applied g(r) to trees and defecation point patterns separately, using a ring width of 10 m. The K-function K(r) provides a cumulative counterpart to the non-cumulative pair-correlation function g(r) by analysing dispersion and aggregation up to distance r rather than at distance r (Weigand & Moloney 2004). The K-function can be defined as the number of expected points (i.e. either trees or defecations) within circles of radius r extending from a typical point, divided by the mean density of points λ within the study region. Here, we apply the square root transformation L(r) to the K-function to remove scale dependence and stabilize the variance: $L( r ) = \scriptstyle\sqrt {\frac{{K( r )}}{\pi }} - r$ (Besag 1977, Wiegand & Moloney 2014).

Numerical Study of Nonequilibrium Diagram Theory

1972 ◽  
Vol 50 (4) ◽  
pp. 317-335 ◽  
Author(s):  
Gary R. Dowling ◽  
H. Ted Davis
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Kinetic Equation ◽  
Numerical Study ◽  
Pair Correlation ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
Collision Operator ◽  
Dense Fluid ◽  
Equilibrium Pair

In this paper we numerically analyze the first few diagrams in a Boltzmann-like collision operator that occurs in Severne's exact kinetic equation for the singlet distribution function. A similar analysis was used by Allen and Cole in deriving their singlet and doublet kinetic equations. Our analysis shows that the diagrams neglected by Allen and Cole in their kinetic equations are not negligible and these should be incorporated into dense fluid theories. The Allen–Cole kinetic transport coefficients and equilibrium pair correlation function are presented and calculated for dense argon. These results are not promising.

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.

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