Abstract:Année de publication : 2010
We explore the noiseless Burgers dynamics in the inviscid limit, the so called "adhesion model'' in cosmology, in a regime where (almost) all the fluid particles are embedded within point-like massive halos. Taking advantage of the formulation of the dynamics in terms of Legendre transforms and convex hulls, for a properly taken inviscid limit, we study the evolution with time of the distribution of matter and the associated partitions of the Lagrangian and Eulerian spaces. We describe how the halo mass distribution derives from a triangulation in Lagrangian space, while the dual Voronoi-like tessellation in Eulerian space gives the boundaries of empty regions with shock nodes at their vertices. We then show that, at variance with the common lore, the adhesion model leads to halo fragmentations for space dimensions greater or equal to 2. This is most easily seen from the properties of the Lagrangian-space triangulation and we illustrate this process in the 2D case. In particular, we explain how point-like halos only merge through three-body collisions while two-body collisions always give rise to two new massive shock nodes (in 2D). This generalizes to higher dimensions and we briefly illustrate the 3D case. This leads to an original picture for the continuous formation of massive halos through successive halo fragmentations and mergings.