Cold Dark Matter I: The Formation of Dark Halos
  We use numerical simulations of critically-closed cold dark matter (CDM) models to study the effects of numerical resolution on observable quantities. We study simulations with up to $256^3$ particles using the particle-mesh (PM) method and with up to $144^3$ particles using the adaptive particle-particle --particle-mesh (P$^3$M) method. Comparisons of galaxy halo distributions are made among the various simulations. We also compare distributions with observations and we explore methods for identifying halos, including a new algorithm that finds all particles within closed contours of the smoothed density field surrounding a peak. The simulated halos show more substructure than predicted by the Press-Schechter theory. We are able to rule out all $\Omega=1$ CDM models for linear amplitude $\sigma_8\gsim 0.5$ because the simulations produce too many massive halos compared with the observations. The simulations also produce too many low mass halos. The distribution of halos characterized by their circular velocities for the P$^3$M simulations is in reasonable agreement with the observations for $150\kms\lsim V_{\rm circ} \lsim 350\kms$.}} 
James M. Gelb and Edmund Bertschinger