Gravitational Collapse in an Expanding Universe: Scaling Relations for   Two-Dimensional Collapse Revisited
  We investigate non-linear scaling relations for two-dimensional gravitational collapse in an expanding background using a 2D TreePM code and study the strongly non-linear regime ($\bar\xi \leq 200$) for power law models. Evolution of these models is found to be scale-invariant in all our simulations. We find that the stable clustering limit is not reached, but there is a model independent non-linear scaling relation in the asymptotic regime. This confirms results from an earlier study which only probed the mildly non-linear regime ($\bar\xi \leq 40$). The correlation function in the extremely non-linear regime is a less steep function of scale than reported in earlier studies. We show that this is due to coherent transverse motions in massive haloes. We also study density profiles and find that the scatter in the inner and outer slopes is large and that there is no single universal profile that fits all cases. We find that the difference in typical density profiles for different models is smaller than expected from similarity solutions for halo profiles and transverse motions induced by substructure are a likely reason for this difference being small. 
S. Ray, J.S. Bagla and T. Padmanabhan