Singular Energy Distributions in Driven and Undriven Granular Media
E. Ben-Naim and A. Zippelius
We study the kinetic theory of driven and undriven granular gases,
taking into account both translational and rotational degrees of
freedom. We obtain the high-energy tail of the stationary bivariate
energy distribution, depending on the total energy $E$ and the ratio
$x=\sqrt{E_w/E}$ of rotational energy $E_w$ to total energy.
Extremely energetic particles have a unique and well-defined
distribution $f(x)$ which has several remarkable features: $x$ is
not uniformly distributed as in molecular gases; $f(x)$ is not
smooth but has multiple singularities. The latter behavior is
sensitive to material properties such as the collision parameters,
the moment of inertia and the collision rate. Interestingly, there
are preferred ratios of rotational-to-total energy. In general,
$f(x)$ is strongly correlated with energy and the deviations from a
uniform distribution grow with energy. We also solve for the energy
distribution of freely cooling Maxwell Molecules and find
qualitatively similar behavior.
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