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.
|Number of pages
|Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|Published - 2003
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics