Flocking rods in a sea of beads: swarms through physical interactions

Original papers: Flocking at a distance in active granular matter


Many living creatures, such as birds, sheep, and fish, make coherent flocks or swarms. Flocking animals travel together, coordinating their speed and turns in an often visually striking manner. This can have benefits for the animals – flocking birds can use aerodynamics to fly more efficiently, sheep can move together as a group to evade predators, and fish can use collective sensing to find preferred locations in their environment. Flocks emerge in biological systems because animals try to follow their neighbors.

But how about non-living things? Can they spontaneously form swarms without any biological motive?

In “Flocking at a distance in active granular matter”, Nitin Kumar and colleagues investigate how non-living rods can form flocks just like animals do. They create a flock of self-propelled rods in a sea of spheres and show how a small concentration of these rods can transport a large load of passive spheres.

In this study, the active agents are cone-shaped brass rods, as in Figure 1a, that move through a layer of aluminum beads. The rods and beads are placed in a flower-shaped dish, as shown in Figure 1b, and covered by a glass lid. The surface vibrates, making the rods bounce up and down. Friction between the floor and ceiling propels a rod in the direction of its tip. Thus, each otherwise immobile rod moves by itself. Because the rod shape isn’t perfect, it turns a little with each movement, and randomly wanders around the surface.

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Figure 1: (a) Schematic of a cone-shaped rod. (b) Experimental setup of brass rods moving through aluminum beads. The flower shape is used to prevent rod clumping at the walls. Figure adapted from the original article.

 

At low concentrations of both rods and beads, the rods wander around randomly and independently of one another. Past some critical concentration of either, however, the rods suddenly align and swarm around the surface in a random direction. Once the rods begin swarming clockwise or counterclockwise, they do not change which way they swarm.

A comparison of randomly moving and aligned rods is shown in Figures 2a and 2b. The motile rods drag the inactive beads alongside them. The flow of the beads then reorients rods throughout the surface, until the rods are aligned. This is similar to what happens in biological flocks, where each animal tries to follow their nearest neighbors. Small turns of individuals turn the entire flock, forming beautiful patterns.

The researchers created a “phase diagram” of rod and bead concentrations in the experiment (Figure 2c). At rod and bead concentrations below the black line, the rods move randomly. When either rod or bead concentration is increased, swirling begins. Increasing the number of rods increases the number of agents that can interact with each other. Increasing the number of beads increases the density of material through which the rod forces propagate. Finally, if the concentrations are too high, the system becomes jammed, and the rods can’t move enough to align in the first place.

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Figure 2: (a) Randomly moving rods. (b) Aligned rods swirling in the same direction. (c) Phase diagram showing transitions between the different behaviors of the rods and beads depending on how concentrated they are. Image adapted from the original article.

So far we’ve just discussed the motion of the rods. But what about the beads themselves? The flocking rods push them in a coherent pattern, the velocity field of which is shown in Figure 3. The rods don’t just align – they also affect their surroundings, and transport the beads as cargo.

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Figure 3: Velocity field of beads that are pushed around by swirling rods.

To figure out how rods align and swarm, Kumar and colleagues developed a mathematical model for the sea of beads and rods as a “fluid” of moving beads (since there are many more beads than rods) and simulated the motion of all the rods and beads. They identified two key parameters in their equations that corresponded to:

  • Adding more rods or stronger rods results in more beads being dragged, increasing the force on each rod.
  • The “weathercock effect” affects how easily rods turn to follow the flow of the beads surrounding them. A rod with an off-center pivot (as in Figure 4) that experiences a force from the surrounding beads will turn in the direction of the forcing.

The interplay of rods pushing beads, and beads reorienting rods, form a swarm.

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Figure 4: “Weathercock effect” reorients rods with an off-center pivot in the direction of the flow of the surrounding beads.

This study shows that simple mechanical interactions can cause swarms. Living creatures, such as fish and bacteria, may have taken advantage of the swarms caused by their interactions with each other to survive as they evolved.

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