Fig. 5.
Structural and dynamical anisotropy of the flocking liquid. (a) Radial distribution function g(r‖,r⊥) for a flocking liquid (p0 = 3.5, J = 2), evaluated along (g(0,r⊥), red solid line) and perpendicular (g(r‖,0), blue dotted line) the direction of flocking. The inset shows an intensity plot of the 2D g(r), with the horizontal axis chosen along the flocking direction. (b) Order parameter P (blue squares) as a function of J for p0 = 3.7. In the non-flocking state P = 0, while at the flocking transition, identified by the peak in the susceptibility χ (orange triangles), P becomes negative, indicating a tendency of the cells to elongate in the direction normal to that of mean motion. Inset: representative snapshot of a flocking liquid (J = 2, p0 = 3.7); the small arrows indicate the orientation of the principal axis of each cell and the large arrow is in the direction of flocking. (c,d) Maps of the displacements Δri averaged over a time τα = 102 for (b) J = 0 and (c) J = 2 in a system of 4900 cells. Ellipses are guides to the eye for highlighting the anisotropy of the collective rearrangements in the flocking state. The red arrow indicates the average migration direction. (e,f) Spatial correlations C(x‖,0) (red triangles) and C(0,x⊥) (blue circles) along axes longitudinal (x‖) and perpendicular (x⊥) to the direction of mean motion of a given sample for J = 0 (e) and J = 2 (f), averaged over 102 samples (see ESI for details).