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. 15. Illustration of the optimal boundary conditions for simulations and experiments to test our predictions. The top and bottomwalls are reflecting, while periodic boundary conditions apply at the left and right walls (i.e., a bird that flies out to the right instantly reappears at the same height on the left). The mean direction of spontaneous flock motion, if any occurs, is clearly forced to be horizontal by these boundary conditions. In spatial dimensions d > 2, one should choose reflecting boundary conditions in d 1 directions, and periodic in the remaining direction, thereby forcing h~vi to point along that periodic direction.