We review the past decade s theoretical and experimental studies of flocking: the collective, coherent motion of large numbers of self-propelled ‘‘particles’’ (usually, but not always, living organisms). Like equilibrium condensed matter systems, flocks exhibit distinct ‘‘phases’’ which can be classified by their symmetries. Indeed, the phases that have been theoretically studied to date each have exactly the same symmetry as some equilibrium phase (e.g., ferromagnets, liquid crystals). This… CONTINUE READING
Fig. 5. Sketch of the asymptotic phase diagram in the zero-density limit. Due to the large separation of scales in b, the phase diagram is broken into two panels to show details of the transition regions. Filled circles indicate points determined numerically in  for a system of size L = 180, q = 1/16, see text for the parameters of the model.