Braiding a flock: winding statistics of interacting flying spins

TL;DR

This paper introduces a measure based on braid theory to quantify the mixing dynamics in flocking animals, revealing that the winding statistics are mainly determined by the global twist resulting from spontaneous symmetry breaking.

Contribution

It presents a novel braid-based measure for analyzing flock mixing dynamics and provides a theoretical explanation linking winding statistics to symmetry breaking.

Findings

Winding statistics are primarily influenced by the global twist of trajectories.

The measure captures the mixing behavior in flocking models.

Spontaneous symmetry breaking underpins the winding dynamics.

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.