load balancing. This problem is alleviated by the use of the PBDD scheme (orange/grey line).

PBDD works well as long as the single blocks do not achieve higher particle density than the optimally distributed particle number ${\tt
npar}/{\tt ncpus}$. In the case of strong clumping, e.g. due to self-gravity, the scheme is no longer as efficient. In such extreme cases one should ideally limit the local particle number in clumps by using sink particles.

Simulation parameters {#s:parameters}
=====================

The main simulations of the paper focus on the dynamics and self-gravity of solid particles moving in a gas flow which has developed turbulence through the magnetorotational instability [@BalbusHawley1991]. We have performed two moderate-resolution simulations (with $256^3$ grid points and $8\times10^6$ particles) and one high-resolution simulation ($512^3$ grid points and $64\times10^6$ particles). Simulation parameters are given in Table \[t:parameters\]. We use a cubic box of dimensions $(1.32 H)^3$.

Note that we use a sub-Keplerian speed difference of $\Delta v=0.05$ which is higher than $\Delta v=0.02$ presented in the main paper of J07. The ability of pressure bumps to trap particles is generally reduced with increasing $\Delta
v$ (see online supplementary information for J07). Particle clumping by streaming instabilities also becomes less efficient 