obtain a connection between the dimensionless $\tilde{G}$ and the relevant dimensional parameters of the box, $$\label{eq:Sigma}
  \varSigma_{\rm g} = 3600 \tilde{G}\,{\rm g\,cm^{-2}}
  \left( \frac{H/r}{0.05} \right) \left( \frac{M_\star}{\rm M_\odot}
  \right) \left( \frac{r}{5\,{\rm AU}} \right)^{-2} \, .$$ We assume a standard ratio of particle to gas column densities of 0.01. The self-gravity of the gas is ignored in both the Poisson equation and the gas equation of motion.

Collisions {#s:coll}
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Particle collisions become important inside dense particle clumps. In J07 the effect of particle collisions was included in a rather crude way by reducing the relative rms speed of particles inside a grid cell on the collisional time-scale, to mimic collisional cooling. Recently [@Rein+etal2010] found that the inclusion of particle collisions suppresses condensation of small scale clumps from the turbulent flow and favours the formation of larger structures.

[@Rein+etal2010] claimed that the lack of collisions is an inherent flaw in the superparticle approach. However, [@LithwickChiang2007] presented a scheme for the collisional evolution of particle rings whereby the collision between two particles occupying the same grid cell is determined by drawing a random number (to determine whether the two particles are at the same vertical position). We have extended this algorithm to 