Fig. 3: Disorder to order transition.
From: Topological flocking models in spatially heterogeneous environments
Polar order parameter r versus noise intensity η at different obstacle densities ρo for different types of interaction neighborhoods, metric (a), k-nearest neighbors (kNN, k = 6 where k is the number of neighboring objects) (b), and Voronoi (c). d The snapshot shows a typical configuration forming in a system with Voronoi interaction in heterogeneous environments at low noise values, here η = 0.05, and ρo = 0.051. Black and red dots represent particles and obstacles respectively. The arrow shows the instantaneous polarization of the system. e, f Show magnification of the region displayed in (d). In e, black arrows show the particles' instantaneous moving direction. In f the underlying (undirected) Voronoi interaction network is depicted. A link exists between two particles, if they are neighbors in the Voronoi tessellation, and if at least one of them does not have an obstacle in its neighborhood. The green circles point out clusters that are connected by long links, i.e., long-distance interactions. Error bars represent the standard deviation of the polar order parameter over different realizations of the obstacle field (see “Methods”). Note that error bars are often comparable or smaller than the symbol size.
