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 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 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.
- Received 10 March 2021
- Revised 4 June 2021
- Accepted 27 July 2021
DOI:https://doi.org/10.1103/PhysRevX.11.031069
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
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Highlights in Experimental Statistical, Biological, and Soft-Matter Physics
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Popular Summary
Active-matter physics describes the mesmerizing dynamics of interacting motile bodies such as bird flocks, cell colonies, and even ensembles of synthetic “swimmers.” However, after 25 years of intense research, the mechanism controlling the ordering dynamics of living and artificial flocks remains unsettled. Here, we combine experiments on active-colloid flocks, numerical simulations, and analytical analysis to show how flocks smooth over their initial multidirectional flows.
The question is deceptively simple: Starting from a homogeneous ensemble of uncoordinated motile particles, how does their velocity field, initially marred by many singularities, heal and reach pristine order at all scales? To answer this question, we needed to solve another outstanding challenge of active matter physics: describing the geometry and the dynamics of topological defects in flocking liquids. In doing so, we show that flocking matter annihilates its defects by linking the with polarization walls separating regions of incompatible flow directions. This filamentous structure mirrors the emergence of density patterns—shaped like interconnected bow ties—that stabilize long-lived domain walls. Finally, we explain how the intimate interplay between density gradients, self-advection, and elasticity heals the distortions and discontinuities of flocking matter.
We solved the problem of flock ordering in two dimensions. Future work needs to extend this analysis to three dimensions and address how the interplay between density fluctuations and self-propulsion alter the fundamental topological excitations of higher-dimensional active matter.