Vortex formation in the Vicsek model with internal chirality of self-propelling objects

TL;DR

This study investigates how internal chirality affects collective motion in a 2D Vicsek-like model by introducing a fixed angular bias $\theta_\chi$ to the noise. Using a large system with $\rho=0.50$ and $N=810000$, the authors vary $\theta_\chi$ and show that even tiny chirality can destroy traveling bands, while intermediate chirality leads to self-organized vortices and rotating flocks, and strong chirality yields coherent rotating groups with diffusive long-time dynamics due to vortex trapping. The work quantifies these transitions via MSD and VAF analyses and identifies regimes where vortex stability arises from inflow-outflow balance, highlighting a potential universality across active-matter models. These findings have implications for designing biomimetic active matter and micro- or nano-scale transport systems, where controlled vortex formation or suppression can be advantageous.

Abstract

Effect of internal chirality on collective motion of large number of active objects is studied by simulations of appropriately modified Vicsek model. We add a fixed angle to the noise and consider small ratios, p, between this angle and the maximal deviation from the average local direction of motion. When the above ratio is p=1/120, the traveling bands observed with the symmetrical noise are destroyed, and small bands moving in different directions appear. Circular rotating flocks of objects with the same orientation are formed for p=1/7.5. Stable vortexes in the stationary state were found from p=1/60 to p=1/20. Velocity autocorrelation function shows equilibrium between the inflow and the outflow to and from the vortex. Long-time evolution is significantly influenced by a temporary trapping of the objects in the vortex. The ballistic behavior for the symmetrical noise changes to the diffusive behavior for the chirality leading to the onset of vortexes.

Figures (7)

• Figure 1: Typical configuration in the stationary state in the system with the density $\rho=0.5$, the number of particles $N=810000$ and the chirality $\theta_\chi=0^o$. The velocity vectors of the particles (left panel) are represented by small arrows with different color representing different orientation of the particle. The color coding of the angle formed by the velocity vector with the horizontal axis is presented in the circle below. The thin, vertical, yellow straight line in the center of the left panel shows the average direction of motion of all active objects. The local density of the active objects (right panel) is represented by colorful spots, with the density increasing from the dark to the bright color. The color coding is shown in the color map below the local densities. Note the elongated bands of objects moving in the same direction, and a small fraction of objects dispersed outside the bands. (color online)
• Figure 2: Typical configuration in the stationary state in the system with the density $\rho=0.5$, the number of particles $N=810000$ and chirality $\theta_\chi=0.5^o$. In the left panel, the velocity vectors of the particles are represented by small arrows with different color representing different orientation of the particle. The color coding of the angle formed by the velocity vector with the horizontal axis is presented in the circle below the shown velocities. In the right panel, local density is shown for the same configuration, with the density coded according to the color map shown below the density distribution. (color online)
• Figure 3: (color online) The same as in Fig. \ref{['fig:small']} but for $\theta_\chi=8^o$.
• Figure 4: (color online) Typical configuration in the stationary state in the system with the density $\rho=0.5$, the number of particles $N=810000$ and chirality $\theta_\chi=1^o$. Left column: velocities of the particles in the whole system (top) and in a part of the system with the vortex zoomed in (bottom). The color coding of the velocity of the particles is shown in the circle below. Right column: local density in the same configuration in the whole system (top) and in a part of the system with the vortex zoomed in (bottom). The color coding of the local density is shown in the color map below.
• Figure 5: (color online) Typical configuration in the stationary state in the system with the density $\rho=0.5$, the number of particles $N=810000$ and chirality $\theta_\chi=3^o$. Velocities of the particles and local density are shown in the left and righ panel, respectively. For the coding of the velocity of the particles and the local density see Fig. \ref{['fig:small']}.