  We are observing, thanks to ALMA, the dust distribution in the region of
active planet formation around young stars. This is a powerful tool to connect
observations with theoretical models and improve our understandings of the
processes at play. We want to test how a multi-planetary system shapes its
birth disk and study the influence of the planetary masses and particle sizes
on the final dust distribution. Moreover, we apply our model to the HL Tau
system in order to obtain some insights on the physical parameters of the
planets that are able to create the observed features. We follow the evolution
of a population of dust particles, treated as Lagrangian particles, in
two-dimensional, locally isothermal disks where two equal mass planets are
present. The planets are kept in fixed orbits and they do not accrete mass. The
outer planet plays a major role removing the dust particles in the co-orbital
region of the inner planet and forming a particle ring which promotes the
development of vortices respect to the single planetary case. The ring and gaps
width depends strongly on the planetary mass and particle stopping times, and
for the more massive cases the ring clumps in few stable points that are able
to collect a high mass fraction. The features observed in the HL Tau system can
be explained through the presence of several massive cores that shape the dust
disk, where the inner planet(s) should have a mass on the order of 0.07 Jupiter
masses and the outer one(s) on the order of 0.35 Jupiter masses. These values
can be significantly lower if the disk mass turns out to be less than
previously estimated. Decreasing the disk mass by a factor 10 we obtain similar
gap widths for planets with a mass of 10 and 20 Earth masses respectively.
Although the particle gaps are prominent, the expected gaseous gaps would be
barely visible.
