Model of coarsening and vortex formation in vibrated granular rods
  Neicu and Kudrolli observed experimentally spontaneous formation of the long-range orientational order and large-scale vortices in a system of vibrated macroscopic rods. We propose a phenomenological theory of this phenomenon, based on a coupled system of equations for local rods density and tilt. The density evolution is described by modified Cahn-Hilliard equation, while the tilt is described by the Ginzburg-Landau type equation. Our analysis shows that, in accordance to the Cahn-Hilliard dynamics, the islands of the ordered phase appear spontaneously and grow due to coarsening. The generic vortex solutions of the Ginzburg-Landau equation for the tilt correspond to the vortical motion of the rods around the cores which are located near the centers of the islands. 
Igor S. Aranson and Lev S. Tsimring