Self-propelled non-linearly diffusing particles.Aggregation and continuum description.

We introduce a model of self-propelled particles carrying out a Brownian motion
with a diffusion coefficient which depends on the local density of particles within
a certain finite radius.
Numerical simulations show
that in a range of parameters the long-time spatial distribution of particles is non-homogeneous,
and clusters can be observed.
A number density equation, which explains
the emergence of the aggregates and indicates the values of the parameters for which they appear, is derived.
Numerical results of this continuum density equation are also shown.