  Inertial particles advected in chaotic flows often accumulate in strange
attractors. While moving in these fractal sets they usually approach each other
and collide. Here we consider inertial particles aggregating upon collision.
The new particles formed in this process are larger and follow the equation of
motion with a new parameter. These particles can in turn fragment when they
reach a certain size or shear forces become sufficiently large. The resulting
system consists of a large set of coexisting dynamical systems with a varying
number of particles. We find that the combination of aggregation and
fragmentation leads to an asymptotic steady state. The asymptotic particle size
distribution depends on the mechanism of fragmentation. The size distributions
resulting from this model are consistent with those found in rain drop
statistics and in stirring tank experiments.
