Clustering transition in a system of particles self-consistently driven by a shear flow

We introduce a simple model of active transport for an ensemble of particles
driven by an external shear flow.
Active refers to the fact that the flow of the particles is modified by
the distribution of particles itself.
The model consists in that the effective velocity of every particle is
given by the average of the external flow velocities felt by the particles
located at a distance less than a typical radius, $R$. Numerical analysis reveals
the existence of a transition to clustering depending on the parameters of the
external flow and on $R$. A continuum description in terms of the
number density of particles is derived,
and a linear stability analysis of the density equation is performed
in order to characterize the transitions observed in the model of interacting particles.