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. 8. (A) The order parameter /, as defined in the text, versus the noise strength Dv. The arrow shows the value of Dv at which the fluctuations of the ordered state were calculated. (B) The scaling behavior of the equal time correlation function for the density fluctuations in the two limits can be calculated analytically (see [14,15] for details) in two dimensions. The lines illustrate the predicted slopes.