Topology-Driven Ordering of Flocking Matter
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 ±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 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.
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BibTeX
@article{chardac2026topologydriven,
title = {{Topology-Driven Ordering of Flocking Matter}},
author = {Amélie Chardac and Ludwig Hoffmann and Yoann Poupart and Luca Giomi and Denis Bartolo},
journal = {Physical Review X},
year = {2026},
month = sep,
doi = {10.1103/physrevx.11.031069},
eprint = {2103.03861},
archivePrefix = {arXiv},
url = {https://hal.science/hal-04965940v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Topology-Driven Ordering of Flocking Matter
AU - Amélie Chardac
AU - Ludwig Hoffmann
AU - Yoann Poupart
AU - Luca Giomi
AU - Denis Bartolo
PY - 2026
DA - 2026/09/17
JO - Physical Review X
DO - 10.1103/physrevx.11.031069
UR - https://hal.science/hal-04965940v1
AB - 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 ±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 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.
SN - 2160-3308
ER -