  We present a detailed numerical study of the impact that cosmological models
featuring a direct interaction between the Dark Energy component that drives
the accelerated expansion of the Universe and Cold Dark Matter can have on the
linear and nonlinear stages of structure formation. By means of a series of
collisionless N-body simulations we study the influence that each of the
different effects characterizing these cosmological models - which include
among others a fifth force, a time variation of particle masses, and a
velocity-dependent acceleration - separately have on the growth of density
perturbations and on a series of observable quantities related to linear and
nonlinear cosmic structures, as the matter power spectrum, the gravitational
bias between baryons and Cold Dark Matter, the halo mass function and the halo
density profiles. We perform our analysis applying and comparing different
numerical approaches previously adopted in the literature, and we address the
partial discrepancies recently claimed in a similar study by Li & Barrow
(2010b) with respect to the first outcomes of Baldi et al. (2010), which are
found to be related to the specific numerical approach adopted in the former
work. Our results fully confirm the conclusions of Baldi et al. (2010) and show
that when linear and nonlinear effects of the interaction between Dark Energy
and Cold Dark Matter are properly disentangled, the velocity-dependent
acceleration is the leading effect acting at nonlinear scales, and in
particular is the most important mechanism in lowering the concentration of
Cold Dark Matter halos.
