  The purpose of this note is to clarify the effect of the finite size of
spherical particles upon the characteristics of their spatial distribution
through a random Poisson process (RPP). This information is of special interest
when using RPP data as a reference for the analysis of the spatial structure of
a given (non-RPP) particulate system, in which case ignoring finite-size
effects upon the former may yield misleading conclusions. We perform Monte
Carlo simulations in triply-periodic spatial domains, and then analyze the
particle-centered Voronoi tesselations for solid volume fractions ranging from
10^(-5) to 0.3. We show that the standard-deviation of these volumes decreases
with the solid volume fraction, the deviation from the value of point sets
being reasonably approximated by an exponential function. As can be expected,
the domain size for which the random assemblies of finite-size particles are
generated has a constraining effect if the number of particles per realization
is chosen too small. This effect is quantified, and recommendations are given.
We have also revisited the case of random point sets (i.e. the limit of
vanishing particle diameter), for which we have confirmed the accuracy of the
earlier data by Tanemura [Forma, 18(4):221-247, 2003].
