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.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Exact Phase Solutions of Nonlinear Oscillators on Two-dimensional Lattice

We present various exact solutions of a discrete complex Ginzburg-Landau (CGL) equation on a plane lattice, which describe target patterns and spiral patterns and derive their stability criteria. We also obtain similar solutions to a system of van der Pol's oscillators.Comment: Latex 11 pages, 17 eps file

Hole Solutions in the 1d Complex Ginzburg-Landau Equation

The cubic Complex Ginzburg-Landau Equation (CGLE) has a one parameter family of traveling localized source solutions. These so called 'Nozaki-Bekki holes' are (dynamically) stable in some parameter range, but always structually unstable: A perturbation of the equation in general leads to a (positive or negative) monotonic acceleration or an oscillation of the holes. This confirms that the cubic CGLE has an inner symmetry. As a consequence small perturbations change some of the qualitative dynamics of the cubic CGLE and enhance or suppress spatio-temporal intermittency in some parameter range. An analytic stability analysis of holes in the cubic CGLE and a semianalytical treatment of the acceleration instability in the perturbed equation is performed by using matching and perturbation methods. Furthermore we treat the asymptotic hole-shock interaction. The results, which can be obtained fully analytically in the nonlinear Schroedinger limit, are also used for the quantitative description of modulated solutions made up of periodic arrangements of traveling holes and shocks.Comment: 20 pages (RevTex) , 7 figures (postscript

Interaction of Vortices in Complex Vector Field and Stability of a ``Vortex Molecule''

We consider interaction of vortices in the vector complex Ginzburg--Landau equation (CVGLE). In the limit of small field coupling, it is found analytically that the interaction between well-separated defects in two different fields is long-range, in contrast to interaction between defects in the same field which falls off exponentially. In a certain region of parameters of CVGLE, we find stable rotating bound states of two defects -- a ``vortex molecule".Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Flagella bending affects macroscopic properties of bacterial suspensions

To survive in harsh conditions, motile bacteria swim in complex environment and respond to the surrounding flow. Here we develop a PDE model describing how the flagella bending affects macroscopic properties of bacterial suspensions. First, we show how the flagella bending contributes to the decrease of the effective viscosity observed in dilute suspension. Our results do not impose tumbling (random re-orientation) as it was done previously to explain the viscosity reduction. Second, we demonstrate a possibility of bacterium escape from the wall entrapment due to the self-induced buckling of flagella. Our results shed light on the role of flexible bacterial flagella in interactions of bacteria with shear flow and walls or obstacles