Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles

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We construct the hydrodynamic equations for suspensions of self-propelled particles (SPPs) with spontaneous orientational order, and make a number of striking, testable predictions:(i) SPP suspensions with the symmetry of a true nematic are always absolutely unstable at long wavelengths.(ii) SPP suspensions with polar, i.e., head-tail asymmetric, order support novel propagating modes at long wavelengths, coupling orientation, flow, and concentration. (iii) In a wavenumber regime accessible only in low Reynolds number systems such as bacteria, polar-ordered suspensions are invariably convectively unstable.(iv) The variance in the number N of particles, divided by the mean <N>, diverges as <N >²/³ in polar-ordered SPP suspensions.