20
1 Polar Flocks
W ( m/s)
0
0 . 5
1
0
200
400
600
800
1000
j( m/s)
-0.5
0
0.5
0
0 . 5
1
0
100
200
300
j( m/s)
-0.2
-0.1
0
0.1
0.2
0
0.5
1
0
200
400
600
800
1000
-0.5
0
0.5
W ( m/s)
W ( m/s)
0
0.5
1
0
100
200
300
(
)
-0.2
-0.1
0
0.1
0.2
W ( m/s)
φ
φ
φ
φ
b
c
a
Fig. 1.16 (a) Collective motion of Quincke rollers. Arrows show the roller’s displacement between
two subsequent video frames (Bricard et al, 2013). (b) An active solid (black) propagates through
a polar liquid (gray) on a microfluidic racetrack; scale bar 2 mm. (c) Top: Snapshots at different
densities; scale bars 250 μm. Bottom: The dependence of the average particle flux W (blue) and
density φ (red) on time (normalized by the time taken by an active solid to circle around the race
track). Left to right: Coexistence between the active gas and a dense polar band at φ = 0.033;
propagating polar liquid phase at φ = 0.096; coexistence between the polar liquid and amorphous
active solid at φ = 0.49; the homogeneous active solid phase at φ = 0.70 (Geyer et al, 2019)
Fig. 1.17 (a) Computed phase diagram dependent on the average density φ 0 and the ratio b/a of
the exclusion range to the roller’s radius. (b) Snapshot of a computed vortex pattern. (c) A snapshot
of a computed swarm of length ξ. (d) A snapshot of the experimental vortex pattern. Arrows show
the roller’s displacement between two subsequent video frames (Bricard et al, 2015)