  We present the results of cosmological simulations of large-scale structure
formation with massive neutrinos. The phase-space distribution of the cosmic
relic neutrinos is followed, for the first time, by directly integrating the
six-dimensional Vlasov-Poisson equations. Our novel approach allows us to
represent free streaming and clustering of neutrinos, and their gravitational
interaction with cold dark matter accurately. We thus obtain solutions for the
collisionless dynamics independent of conventional N-body methods. We perform a
suite of hybrid N-body/Vlasov simulations with varying the neutrino mass, and
systematically examine the dynamical effects of massive neutrinos on
large-scale structure formation. Our simulations show characteristic
large-scale clustering of the neutrinos and their coherent streaming motions
relative to dark matter. The effective local neutrino "temperature" around
massive galaxy clusters varies by several percent with respect to the cosmic
mean; the neutrinos in clusters can be hotter or colder depending on the
neutrino mass. We study a number of statistics of the large-scale structure and
of dark matter halos in comparison with those obtained by N-body simulations
and/or by perturbation theory. Our simulations mark an important milestone in
numerical cosmology, and pave a new way to study cosmic structure formation
with massive neutrinos.
