Power-law velocity distributions in granular gases

The kinetic theory of granular gases is studied for spatially homogeneous systems. At large velocities, the equation governing the velocity distribution becomes linear, and it admits stationary solutions with a power-law tail, f (v) approximately v(-sigma) . This behavior holds in arbitrary dimension for arbitrary collision rates including both hard spheres and Maxwell molecules. Numerical simulations show that driven steady states with the same power-law tail can be realized by injecting energy into the system at very high energies. In one dimension, we also obtain self-similar time-dependent solutions where the velocities collapse to zero. At small velocities there is a steady state and a power-law tail but at large velocities, the behavior is time dependent with a stretched exponential decay.