Collective Motion of Vibrated Polar Disks

We experimentally study a monolayer of vibrated disks with a built-in polar asymmetry which enables them to move quasibalistically on a large persistence length. Alignment occurs during collisions as a result of self-propulsion and hard core repulsion. Varying the amplitude of the vibration, we observe the onset of large-scale collective motion and the existence of giant number fluctuations with a scaling exponent in agreement with the predicted theoretical value.

Figure 1

Collective motion of self-propelled disks. Bottom left panel: a sketch of our polar particles. Main panel: a snapshot of an ordered regime observed in our flower-shape domain. The dark gray reveals the local alignment between particles {both perfect alignment [light grey (red)] and pergect antialignment [dark grey (blue)]}. The intrinsic polarity of the particles is indicated by the black arrows.

Figure 2

Individual dynamics for $\Gamma =2.7$. (a) Typical portions of polar particles trajectories inside the ROI. Black and grey (red) arrows indicate ${\overrightarrow{v}}_i^t$ and ${\overrightarrow{n}}_i^t$ at selected times. The domain area is about $15\times 15d$. (b) The same for symmetric particles. (c) Probability distribution function (PDF) with counterpropagating waves with a common linear polarization (lin-lin) of $\alpha$, the angle between ${\overrightarrow{v}}_i^t$ and ${\overrightarrow{n}}_i^t$. (d) Variation of angular diffusion coefficient $D_{\theta }$ with $\Gamma$.

Figure 3

Trajectories of two particles “during” a collision: they first collide almost head on, but repeated contacts [all along the grey (red) double-headed arrow] finally leave them almost aligned, despite their isotropic shape.

Figure 4

Collective dynamics. (a) Time series of order parameter $\Psi$ at $\Gamma =2.8$. (b) PDF (lin-lin) of $\Psi (t)$ at various $\Gamma$ values. (c) $⟨\Psi ⟩$ vs $\Gamma$ for polar and symmetric particles. (d) $\Delta n$ vs $n$ at $\Gamma =2.8$.