Topology-Driven Ordering of Flocking Matter

Physical Review X, vol. 11

Abstract

When interacting motile units self-organize into flocks, they realize one of the most robust ordered states found in nature.However, after 25 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 Æ1 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 charge 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.

Authors 5

1. Amélie Chardac

   École Normale Supérieure de Lyon · Centre National de la Recherche Scientifique · Laboratoire de Physique de l'ENS de Lyon

   Affiliation as printed

   Université Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342, Lyon, France

2. Ludwig A. Hoffmann Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, Netherlands

3. Yoann Poupart

   École Normale Supérieure de Lyon · Centre National de la Recherche Scientifique · Laboratoire de Physique de l'ENS de Lyon

   Affiliation as printed

   Université Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342, Lyon, France

4. Luca Giomi Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, Netherlands

5. Denis Bartolo

   École Normale Supérieure de Lyon · Centre National de la Recherche Scientifique · Laboratoire de Physique de l'ENS de Lyon

   Affiliation as printed

   Université Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342, Lyon, France