In the next paragraph we give the results of the simulations of the
randomly driven granular gas model. We have used event driven
Molecular Dynamics simulations in : in these simulations the
position of the particles are precisely known, the collisions happen
if and only if the conditions (3.4) are
verified, in other words the model is exactly reproduced by the
simulator. In some of the runs performed, at low values of
and high values of the ratio
(approaching the
cooling limit) we have observed a dramatic increase of the collision
rate resulting in very poor performances of the algorithm: we have
discarded the results of these simulations considering them the
evidence of a sort of inelastic collapse (this fact is reflected in
the figures, where some points are missing). To simulate a larger
number of particles in more than one dimension, we have performed a
number of Direct Simulation Monte Carlo: this is an algorithm
introduced (by Bird, see for example [30]) to reproduce the
solution of the Boltzmann equation and assumes the Molecular Chaos,
i.e. disregards correlations of colliding particles. In Appendix A we
give a detailed description of Molecular Dynamics of hard spheres in
and of Direct Simulation Monte Carlo in
and
. Here we
just warn the reader to be careful and notice the captions of the
figures. Where ``DSMC'' appears, it must be clear that an important
assumption (Molecular Chaos) has been made. However the compatibility
of the results with MD in
and also many agreements with
experimental measurements has convinced us that the Bird algorithm is
very well suited to study qualitatively dilute granular
gases. Finally, we stress the fact that even if a granular gas is well
described by the Boltzmann equation (this is the message/anticipation
of this brief introduction), nothing is said about the hydrodynamic
description, where further assumption are needed (e.g. low values of
the gradients, scale separation, etc).