Demonstrating Discreteness and Collision Error in Cosmological N-body   Simulations of Dark Matter Gravitational Clustering
  Two-body scattering and other discreteness effects are unimportant in cosmological gravitational clustering in most scenarios, since the dark matter has a small particle mass. The collective field should determine evolution: Two-body scattering in simulations violates the Poisson-Vlasov equations. We test this in PM, P$^3$M, Tree, and NGPM codes, noting that a collisionless code will preserve the one-dimensional character of plane wave collapse. We find collisionality vanishing as the softening parameter approaches the mean interparticle separation. Solutions for the problem are suggested, involving greater computer power, PM-based nested grid codes, and a more conservative approach to resolution claims. 
A.L. Melott and S.F. Shandarin (Univ. Kansas), R.J. Splinter (Univ.   Kentucky), and Y. Suto (Univ. Tokyo)