Tracing the Cosmic Web substructure with Lagrangian submanifold
  A new computational paradigm for the analysis of substructure of the Cosmic
Web in cosmological cold dark matter simulations is proposed. We introduce a
new data-field --- the flip-flop field ---which carries wealth of information
about the history and dynamics of the structure formation in the universe. The
flip-flop field is an ordered data set in Lagrangian space representing the
number of turns inside out sign reversals of an elementary volume of each
collisionless fluid element represented by a computational particle in a N-body
simulation. This field is computed using the Lagrangian submanifold, i.e. the
three-dimensional dark matter sheet in the six-dimensional space formed by
three Lagrangian and three Eulerian coordinates of the simulation particles. It
is demonstrated that the very rich substructure of dark matter haloes and the
void regions can be reliably and unambiguously recovered from the flip-flop
field.
