The clusters shown in the figure appear naturally
after some time when an initially homogeneous dissipative
gas cools by itself or when the sytem is driven, i.e.
energy is injected into
the system at a low rate. With Stefan Luding
we studied in detail the growth of the clusters and the evolution
of the granular temperature as
published in Chaos, Vol.9, 673-681 (1999).
In this case also the
velocity distribution is not Maxwellian anymore.
With Matthias Müller we used Event-driven Molecular Dynamics
and DSMC to obtain these distributions as published in the
proceedings of a workshop in
Jülich in 1996.
With Rafaele Cafiero and
Stefan Luding we found that
deviations from the Maxwell distribution also exist
when the system is apparently still homogeneous and that
the dependence of these deviation from the driving
can be calculated (Phys. Rev. Lett. Vol.84, p.6014-6017 (2000)).
Interesting is in particular the case of driving through particle
rotation (submitted to Phys. Rev. E) .
More details can be found in the
paper published in Physica A, Vol.295, p.93-100 (2001).
Very interesting is also that when energy is injected with
Maxwellian distribution into the rotational degrees of freedom
then the resulting translational velocities have again a
non-Maxwellian distribution as documented in our
paper published in Europhys. Lett. Vol.60, p.854-860
(2002). A review on these issues will be
published as proceedings of a CECAM workshop or in the
paper published in Rev. Mexicana de Fisica, Vol.49, Suppl.3,
p.29-32 (2003). Finally, with Olaf Herbst and Annette Zippelius
we also studied the case when the dissipative gas has
Coulomb friction as presented in a
preprint . You can also download a
talk that I gave in several occasions on the subject.
It is in fact not easy to justify the definition of a granular
temperature because of this strong deviation from equilibrium
thermodynamics. In a
paper published in J. Physique II Vol.3, p.427-433 (1993).