  To understand the earliest stages of planet formation, it is crucial to be
able to predict the rate and the outcome of dust grains collisions, be it
sticking and growth, bouncing, or fragmentation. The outcome of such collisions
depends on the collision speed, so we need a solid understanding of the rate
and velocity distribution of turbulence-induced dust grain collisions. The rate
of the collisions depends both on the speed of the collisions and the degree of
clustering experienced by the dust grains, which is a known outcome of
turbulence. We evolve the motion of dust grains in simulated turbulence, an
approach that allows a large turbulent inertial range making it possible to
investigate the effect of turbulence on meso-scale grains (millimeter and
centimeter). We find three populations of dust grains: one highly clustered,
cold and collisionless; one warm; and the third "hot". Our results can be fit
by a simple formula, and predict both significantly slower typical collisional
velocities for a given turbulent strength than previously considered, and
modest effective clustering of the collisional populations, easing difficulties
associated with bouncing and fragmentation barriers to dust grain growth.
Nonetheless, the rate of high velocity collisions falls off merely
exponentially with relative velocity so some mid- or high-velocity collisions
will still occur, promising some fragmentation.
