  Spatial distributions of heavy particles suspended in an incompressible
isotropic and homogeneous turbulent flow are investigated by means of high
resolution direct numerical simulations. In the dissipative range, it is shown
that particles form fractal clusters with properties independent of the
Reynolds number. Clustering is there optimal when the particle response time is
of the order of the Kolmogorov time scale $\tau_\eta$. In the inertial range,
the particle distribution is no longer scale-invariant. It is however shown
that deviations from uniformity depend on a rescaled contraction rate, which is
different from the local Stokes number given by dimensional analysis. Particle
distribution is characterized by voids spanning all scales of the turbulent
flow; their signature in the coarse-grained mass probability distribution is an
algebraic behavior at small densities.
