title: Braiding a Flock: Winding Statistics of Interacting Flying Spins.
abstract: When animal groups move coherently in the form of a flock, their trajectories are not all parallel, the individuals exchange their position in the group. In this Letter, we introduce a measure of this mixing dynamics, which we quantify as the winding of the braid formed from the particle trajectories. Building on a paradigmatic flocking model we numerically and theoretically explain the winding statistics and show that it is predominantly set by the global twist of the trajectories as a consequence of a spontaneous symmetry breaking.
authors.affiliation: Laboratoire de Physique de l'École Normale Supérieure de Lyon, Université de Lyon, 46, allée d'Italie, 69007 Lyon, France.
authors.forename: Jean-Baptiste
authors.initials: JB
authors.lastname: Caussin
authors.affiliation: Laboratoire de Physique de l'École Normale Supérieure de Lyon, Université de Lyon, 46, allée d'Italie, 69007 Lyon, France.
authors.forename: Denis
authors.initials: D
authors.lastname: Bartolo
mesh_terms: D000818:Animals; D005426:Flight, Animal; D008954:Models, Biological; D008962:Models, Theoretical