Topology-driven ordering of flocking matter

TL;DR

This paper uncovers the mechanism behind the self-organization of flocking matter, revealing how topological defects are healed through a network of domain walls, leading to long-range order in two-dimensional active systems.

Contribution

It provides a comprehensive explanation combining experiments, simulations, and theory for the topological defect dynamics and ordering in flocking liquids, highlighting the role of domain walls and active forces.

Findings

Flocking liquids heal their flows via a network of domain walls linking topological defects.

The self-similar ordering involves interconnected density patterns resembling bow ties.

Active Magnus forces and elastic interactions govern defect annihilation and order emergence.

Abstract

When interacting motile units self-organize into flocks, they realize one of the most robust ordered state found in nature. However, after twenty five years of intense research, the very mechanism controlling the ordering dynamics of both living and artificial flocks has remained unsettled. Here, combining active-colloid experiments, numerical simulations and analytical work, we explain how flocking liquids heal their spontaneous flows initially plagued by collections of topological defects to achieve long-ranged polar order even in two dimensions. We demonstrate that the self-similar ordering of flocking matter is ruled by a living network of domain walls linking all $\pm 1$ vortices, and guiding their annihilation dynamics. Crucially, this singular orientational structure echoes the formation of extended density patterns in the shape of interconnected bow ties. We establish that this double structure emerges from the interplay between self-advection and density gradients dressing each $-1$ topological charges with four orientation walls. We then explain how active Magnus forces link all topological charges with extended domain walls, while elastic interactions drive their attraction along the resulting filamentous network of polarization singularities. Taken together our experimental, numerical and analytical results illuminate the suppression of all flow singularities, and the emergence of pristine unidirectional order in flocking matter.