Tessellating the Universe: the Zel'dovich and Adhesion tiling of space
  The adhesion approximation is a simple analytical model suggested for
explanation of the major geometrical features of the observed structure in the
galaxy distribution on scales from 1 to (a few)x100/h Mpc. It is based on
Burgers' equation and therefore allows analysis in considerable detail. A
particular version of the model that assumes the infinitesimal viscosity
naturally results in irregular tessellation of the universe. Generic elements
of the tessellation: vertices, edges, faces and three-dimensional tiles can be
associated with astronomical objects of different kinds: clusters,
superclusters and voids of galaxies. Point-like vertices contain the most of
the mass and one-dimensional edges (filaments) are the second massive elements.
The least massive are the two-dimensional faces and tiles (voids). The
evolution of the large-scale structure can be viewed as a continuous process
that transports mass predominantly from the high- to low-dimensional elements
of the tessellation. For instance, the mass from the cells flows into faces,
edges and vertices, in turn the mass from faces flows into edges and vertices,
etc. At the same time, the elements of the tessellation themselves are in
continuous motion resulting in mergers of some vertices, growth of some tiles
and shrinking and disappearance of the others as well as other metamorphoses.
