Dry Active Matter on a Sphere

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When flocks of birds migrate southwards imagine larger and larger swarms moving together on a shrinking globe, until one gigantic flock covers the entire planet. What becomes of their motion if they reach the pole? We propose to build and analyse a model of active particles confined to move on the surface of a sphere. Unlike in the plane where all particles can align with each and travel with the same velocity parallel to each other, motion on the sphere is far more peculiar. This is a direct consequence of the famous Hairy ball theorem that states that "you can't comb a hairy ball flat without creating a cowlick". Translated into the language of active motion, it is not possible for the entire flock to travel with a uniform velocity on the surface of a sphere. As a result, one expects to observe a rich and complex set of motion patterns emerging from the intricate interplay between the curvature and particles' alignment. It is our aim to identify, understand and classify those motion patterns.