title: Model of coarsening and vortex formation in vibrated granular rods.
abstract: Neicu et al. 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 the modified Cahn-Hilliard equation, while the tilt is described by the Ginzburg-Landau type equation. Our analysis shows that, in accordance with the Cahn-Hilliard dynamics, 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.
authors.affiliation: Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA.
authors.forename: Igor S
authors.initials: IS
authors.lastname: Aranson
authors.forename: Lev S
authors.initials: LS
authors.lastname: Tsimring