Swarming

Co-alignment between particles then couples the channels so that they tend to counter-rotate. We study channels arranged to mimic a geometrically frustrated antiferromagnet and show how the effects of this frustration allow us to better distinguish between SPP models. There is now experimental evidence that nearest-neighbour interactions in many swarms are metric free, but the models that control density rely on attractive and repulsive forces with associated length scales.

We propose a solution that involves a metric-free motional bias on those individuals that are topologically identified to be on the surface of the swarm. We and a novel power-law scaling of the real-space density with the number of individuals N as well as a familiar order-to-disorder transition. We argue that local interactions alone are insufficient to explain the organisation of large flocks of birds and expand the strictly metric free model to mimic the information set and abilities of a starling in a murmuration.

We postulate that large flocks self-organise to the maximum density at which a typical individual is still able to see out of the flock in many directions; such flocks are marginally opaque. The emergence of marginal opacity constrains how individuals interact with each other within swarms. It also provides a mechanism for global interactions: An individual can respond to the projection of the flock that it sees.

We then present evidence for marginal opacity in starling murmurations observed around the UK.