Tracing the Dark Matter Sheet in Phase Space
  The primordial velocity dispersion of dark matter is small compared to the
velocities attained during structure formation. The initial density
distribution is close to uniform and it occupies an initial sheet in phase
space that is single valued in velocity space. Because of gravitational forces
this three dimensional manifold evolves in phase space without ever tearing,
conserving phase-space volume and preserving the connectivity of nearby points.
N-body simulations already follow the motion of this sheet in phase space. This
fact can be used to extract full fine-grained phase-space-structure information
from existing cosmological N-body simulations. Particles are considered as the
vertices of an unstructured three dimensional mesh, moving in six dimensional
phase-space. On this mesh, mass density and momentum are uniquely defined. We
show how to obtain the space density of the fluid, detect caustics, and count
the number of streams as well as their individual contributions to any point in
configuration-space. We calculate the bulk velocity, local velocity
dispersions, and densities from the sheet - all without averaging over control
volumes. This gives a wealth of new information about dark matter fluid flow
which had previously been thought of as inaccessible to N-body simulations. We
outline how this mapping may be used to create new accurate collisionless fluid
simulation codes that may be able to overcome the sparse sampling and
unphysical two-body effects that plague current N-body techniques.
