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Model of coarsening and vortex formation in vibrated granular rods

Igor S. Aranson·Lev S. Tsimring
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Abstract

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.

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Igor S. Aranson, Lev S. Tsimring. 2002-03-27. Model of coarsening and vortex formation in vibrated granular rods. https://doi.org/10.1103/physreve.67.021305

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