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Phys Rev Lett. 2015 Dec 18;115(25):258101. doi: 10.1103/PhysRevLett.115.258101. Epub 2015 Dec 17.

Hydrodynamics of Turning Flocks.

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Physics Department, Syracuse University, Syracuse, New York 13244, USA.
Syracuse Biomaterials Institute, Syracuse University, Syracuse, New York 13244, USA.


We present a hydrodynamic model of flocking that generalizes the familiar Toner-Tu equations to incorporate turning inertia of well-polarized flocks. The continuum equations controlled by only two dimensionless parameters, orientational inertia and alignment strength, are derived by coarse-graining the inertial spin model recently proposed by Cavagna et al. The interplay between orientational inertia and bend elasticity of the flock yields anisotropic spin waves that mediate the propagation of turning information throughout the flock. The coupling between spin-current density to the local vorticity field through a nonlinear friction gives rise to a hydrodynamic mode with angular-dependent propagation speed at long wavelengths. This mode becomes unstable as a result of the growth of bend and splay deformations augmented by the spin wave, signaling the transition to complex spatiotemporal patterns of continuously turning and swirling flocks.

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