Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles: living liquid crystals

We construct the hydrodynamic equations for nematic as well as vectorially ordered suspensions of self-propelled particles (SPPs), using symmetry and conservation principles, and make a number of striking, testable predictions: (i) Nematic SPP suspensions are always absolutely unstable at long wavelengths. (ii) Vectorially ordered SPP suspensions 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, vector-ordered suspensions are invariably convectively unstable. (iv) The variance in the number of particles, scaled by the mean $N$, diverges as $N^{2/3}$ in vectorially ordered SPP suspensions.