  I simulate the evolution of a stellar system hosting two stellar populations
whose initial set up is defined according to the two main scenarios proposed
for the origin of multiple populations in Galactic globular clusters: (i)
formation of a second generation from a cooling flow of pristine+polluted gas
and (ii) accretion of polluted gas onto the proto-stellar disks of a fraction
of low-mass stars. For this purpose, Monte Carlo simulations containing from
$10^{5}$ up to $3\cdot 10^{6}$ particles have been run including the effect of
stellar evolution, binary interactions, external tidal field and a detailed
modelling of the proto-stellar disk structure. The early accretion of gas onto
proto-stellar disks is unable to produce discrete populations and to alter the
chemical composition of a significant ($>10\%$) fraction of stars unless a disk
lifetime larger ($t_{disk}\sim20~Myr$) than that predicted by models is
assumed. Moreover, in this scenario the mixing timescale of the two populations
is too short to reproduce the observed segregation of the chemically enriched
population. On the other hand, simulations run within the cooling flow scenario
can evolve after a Hubble time into stellar systems with a first-to-second
population mass ratio similar to that observed in globular clusters, provided
that an initial filling-factor $r_{h}/r_{J}>0.15$ is adopted. However, in the
weak tidal field regime a radial segregation of the second population stronger
than what observed in Milky Way globular clusters at large Galactocentric
distances is predicted. This discrepancy disappears in simulations following
eccentric orbits in a realistic axisymmetric potential.
