The rms peculiar velocity of galaxy clusters for different cluster   masses and radii
  We investigate the rms peculiar velocity of galaxy clusters in the Lambda cold dark matter ($\Lambda$CDM) and tau cold dark matter ($\tau$CDM) cosmological models using N-body simulations. Cluster velocities for different cluster masses and radii are examined. To identify clusters in the simulations we use two methods: the standard friends-of-friends (FOF) method and the method, where the clusters are defined as the maxima of the density field smoothed on the scale $R\sim 1h^{-1}$ Mpc (DENSMAX). If we use the DENSMAX method, the size of the selected clusters is similar for all clusters. We find that the rms velocity of clusters defined with the DENSMAX method is almost independent of the cluster density and similar to the linear theory expectations. The rms velocity of FOF clusters decreases with the cluster mass and radius. In the $\Lambda$CDM model, the rms peculiar velocity of massive clusters with an intercluster separation $d_{cl}=50h^{-1}$ Mpc is $\approx$15% smaller than the rms velocity of the clusters with a separation $d_{cl}=10h^{-1}$Mpc. 
Ivan Suhhonenko, Mirt Gramann