A Reanalysis of the Hydrodynamic Theory of Fluid, Polar-Ordered Flocks

Abstract

I reanalyze the hydrodynamic theory of fluid, polar ordered flocks. I find new linear terms in the hydrodynamic equations which slightly modify the anisotropy, but not the scaling, of the damping of sound modes. I also find that the nonlinearities allowed {\it in equilibrium} do not stabilize long ranged order in spatial dimensions $d=2$; in accord with the Mermin-Wagner theorem. Nonequilibrium nonlinearities {\it do} stabilize long ranged order in $d=2$, as argued by earlier work. Some of these were missed by earlier work; it is unclear whether or not they change the scaling exponents in $d=2$.

6 pages, no figures. arXiv admin note: text overlap with arXiv:0909.1954

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• Novel type of phase transition in a system of self-driven particles
• Collective motion of self-propelled particles interacting without cohesion
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