Three important results are in order: the decrease of the flock length, L F, echoes that of the global order parameter and vanishes rather smoothly at φ o ⋆ ( Fig. 2c). Therefore, the time variations of, the longitudinal current averaged over the transverse direction, give an accurate description of the coarse-grained shape of the flocks ( Fig. 2b). The flock speed c F is unaltered by disorder and remains very close to the roller velocity for all φ o < φ o ⋆ ( Fig. 2a). For sake of clarity we focus here on the roller current as the main observable. This morphology can be equivalently captured by the variations of the local density, current, or polarization fields, as demonstrated in the Supplementary Information. To do so, we consider the evolution of the flock morphology along the propagation direction upon increasing disorder. Our first goal is to elucidate this loss of orientational order. Accordingly J x monotonically decreases with φ o and vanishes at φ o ⋆ ( Fig. 1d). A natural order parameter for the flocking transition is the magnitude J x of the roller current J( r, t) projected on the x-axis, and averaged over time and space. The roller fraction is set to a constant value above the flocking threshold in a obstacle-free channel, ρ = (1.02 ± 0.06) × 10 −2. In all that follows, the sole control parameter of our experiments is the obstacle fraction φ o. As expected, dense flocks are more robust to disorder and φ o ⋆ increases monotonically with the roller fraction ρ ( Fig. 1c). Correlated motion persists only at short scales, as illustrated in Supplementary Movie 3. However, as φ o exceeds a critical value, φ o ⋆, the obstacle collisions suppress any form of global orientational order and macroscopic transport. When the obstacle packing fraction φ o is small, collective motion still emerges according to the same nucleation and propagation scenario (see Fig. 1b and Supplementary Movie 2). Error bars, 1 standard deviation (s.d.) (17 different flocks).Ĭan flocks propagate in disorder media? How does this broken-symmetry phase survive to geometrical disorder? To answer these questions, we include randomly distributed circular obstacles of radius a = 5 μm in the microfluidic channel. Orientational order is suppressed in the shaded region. J x/ J 0 is plotted as a function of the fraction of obstacles. d, The x-component of the roller current is normalized by J 0 measured in an obstacle-free channel. Error bars: smaller than the symbols (defined as the difference between the minimal value of ρ above which flocking was observed and the maximal value below which isotropic motion only was observed). The symbols represent the variations of φ o ⋆ with ρ. c, Flocking phase diagram in the ( ρ, φ o) plane. Obstacle packing fraction: φ o = 2.45 × 10 −2. The arrows are located at the colloid positions and point along the orientation of their velocity. b, Close-up on the head of a colloidal swarm propagating past random obstacles (black dots). Dotted rectangle: region in which the velocity measurements of b are performed. Further increasing the disorder, we demonstrate that collective motion is suppressed in the form of a first-order phase transition generic to all polar active materials.Ī, Stitched fluorescent images of a 7-mm-long colloidal flock cruising in a rectangular channel. We elucidate how disorder and bending elasticity compete to channel the flow of polar flocks along sparse river networks akin those found beyond plastic depinning in driven condensed matter 21. To do so, we combine experiments and analytical theory to examine motile colloids cruising between randomly positioned microfabricated obstacles. Here we explain how collective motion survives in geometrical disorder. In stark contrast, aside from rare exceptions 15, 16, 17, our physical understanding of flocking has so far been limited to homogeneous media 18, 19, 20. How do flocks, herds and swarms move through disordered environments? The answer to this question is crucial not only to animal groups in the wild, but also to effectively all applications of collective robotics and active materials composed of synthetic motile units 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.
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