Coordination number for random distribution of parallel fibres

Abstract

This paper presents the results of computer simulations carried out to determine coordination numbers for a system of parallel cylindrical fibres distributed at random in a circular matrix according to twodimensional pattern created by random sequential addition scheme. Two different methods to calculate coordination number were utilized and compared. The first method was based on integration of pair distribution function. The second method was the modified sequential analysis. The calculations following from ensemble average approach revealed that these two methods give very close results for the same neighbourhood area irrespective of the wide range of radii used for calculation.

Nuclear size-regulated emergence of topological packing order on growing human lung alveolospheres

“…We define this critical transition point as 𝑥 0 . Specifically, we define the 𝑥 0 as the 𝑥 $!% at which point the integration of 𝑔(𝑠) from 0 to the first valley equals 1, 𝑁(𝑠 [40][41][42] , where 𝑠 * is the geodesic distance for the first valley.…”

Archives of Thermodynamics

“…Unfortunately, the RSA packing method of particles is based on statistical 'parked' [1] process and probability of direct contact of sampled particles tends to zero [8]. In such case it is not feasible to calculate useful coordination number by counting direct contact of particles [6,8]. To solve this problem a notion of the neighbourhood area was introduced.…”

“…Detailed description of the methods and their modifications used to evaluate CN, were described in paper [6]. It was shown there that the coordination number calculated from integration of the pair distribution function and the sequential analysis are equivalent for the same neighbourhood radius.…”

“…Moreover, no correlations between the effective thermal conductivity (ETC) and CN for two dimensional systems and in particular for the random sequential addition (RSA) packing scheme seem to exist in literature, where the RSA scheme is process of random adding of fibres one by one into matrix without intersecting others and composite boundaries [5]. Traditional attempt to CN as the mean number of direct contacts does not fulfil its role for the RSA and that is why both modified sequential analysis (SA) and pair distribution function (PDF) integration were further used [2,6]. The coordination number computed by the SA method is a simple sum of CNs for every object in the population divided by population magnitude [7].…”