Figure 3
From: Delay in the dispersal of flocks moving in unbounded space using long-range interactions
(a) Order parameter Ψ as a function of the density ρ for the 3D Vicsek model with periodic boundary conditions (black curve) and in open space (red dotted line). Note the complete absence of ordered states for the case without boundaries. ρ0 = 0.3 is the initial density used to generate the plots in Fig. 2. This value corresponds to highly ordered states in the standard Vicsek model. (b) Ψ as a function of the average long-range connectivity κ for systems moving in open space with short-range interactions implemented metrically (black curve with circles) and topologically (red curve with triangles). In both cases, note the onset of collective order for relatively low values of κ. The complete set of the parameters used in the simulations is listed in Supplementary Tables S2 and S3.
