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

TLDR: The hydrodynamic equations for suspensions of self-propelled particles (SPPs) with spontaneous orientational order are constructed, and a number of striking, testable predictions are made.

Abstract: Fish, birds, and swimming cells [1–3] are frequently found to move coherently in large groups [4–9] through the fluid medium they inhabit. Can general principles, like those used so successfully for ordered phases at equilibrium [10], reveal the laws governing the long-wavelength dynamics and fluctuations of these striking and ubiquitous examples of liquid-crystalline [11] order in suspensions of self-propelled particles (SPPs)? Although we know of no physics experiments on ordered SPP suspensions, Gruler [12] has studied ordered phases of living cells on a solid substrate, and finds ‘‘living liquid-crystalline’’ [13] phases corresponding to two distinct types of cells: apolar, that is, elongated but head-tail symmetric, and polar, distinguishing front from rear. The ordered phases formed by polar SPPs have a nonzero macroscopic drift velocity v 0 . Those formed by apolar SPPs have a macroscopic axis ^ n of