## Impurity in a Maxwellian Unforced Granular Fluid,

### E. Ben-Naim and P.L. Krapivsky

We investigate velocity statistics of an impurity immersed in a
uniform granular fluid. We consider the cooling phase, and obtain
scaling solutions of the inelastic Maxwell model analytically.
First, we analyze identical fluid-fluid and fluid-impurity collision
rates. We show that light impurities have similar velocity
statistics as the fluid background, although their temperature is
generally different. Asymptotically, the temperature ratio increases
with the impurity mass, and it diverges at some critical mass.
Impurities heavier than this critical mass essentially scatter of a
static fluid background. We then analyze an improved inelastic
Maxwell model with collision rates that are proportional to the
{\it average} fluid-fluid and fluid-impurity relative velocities.
Here, the temperature ratio remains finite, and the system is always
in the light impurity phase. Nevertheless, ratios of sufficiently
high order moments $\langle v^n_{\rm impurity}\rangle/\langle
v^n_{\rm fluid}\rangle$ may diverge, a consequence of the
multiscaling asymptotic behavior.

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