  The evolution of an isolated over-density represents a useful toy model to
test the accuracy of a cosmological N-body code in the non linear regime as it
is approximately equivalent to that of a truly isolated cloud of particles,
with same density profile and velocity distribution, in a non expanding
background. This is the case as long as the system size is smaller than the
simulation box side, so that its interaction with the infinite copies can be
neglected. In such a situation, the over-density rapidly undergoes to a global
collapse forming a quasi stationary state in virial equilibrium. However, by
evolving the system with a cosmological code (GADGET) for a sufficiently long
time, a clear deviation from such quasi-equilibrium configuration is observed.
This occurs in a time t_{LI} that depends on the values of the simulation
numerical parameters such as the softening length and thetime-stepping
accuracy, i.e. it is a numerical artifact related to the limited spatial and
temporal resolutions. The analysis of the Layzer-Irvine cosmic energy equation,
confirms that this deviation corresponds to an unphysical dynamical regime. By
varying the numerical parameters of the simulation and the physical parameters
of the system we show that the unphysical behaviour originates from badly
integrated close scatterings of high velocity particles. We find that, while
the structure may remain virialized in the unphysical regime, its density and
velocity profiles are modified with respect to the quasi-equilibrium
configurations, converging however to well defined shapes, the former
characterised by a Navarro Frenk White-type behaviour.
