cold fluid limit. These simulations are run using the same [$N$-body ]{}framework but with an initial density and velocity power spectrum truncated below the scale of interest. This should lead to a suppression of small halos below a characteristic mass and the simulations ought to be able to reproduce all structures with a mass above this limit. They could thus quickly converge towards a solution. [@Colin2000; @Wang2007; @Colin2008] did, however, demonstrate that this is not the case and that spurious halos form and merge to form structures below the theoretical mass threshold. Various techniques are used in the literature to cure this problem. [@Lovell2012], for instance, filter their halo catalogues during the post-processing of their simulations. The end results are thus free from spurious halos but it does not solve the intrinsic discreteness problem of the [$N$-body ]{}technique.

More details about these challenges and a comprehensive review of the topic can be found in [@Dehnen2011]. Notice that this formalism is still a very active and lively area of research with alternative more advanced formulations being proposed frequently. Some authors [@Abell2012; @Shandarin2012] proposed recently to use tessellations of the 3D matter sheet in 6D space to track some of the phase 