Topology-driven ordering of flocking matter

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.

arXiv comment14 pages, 5 figures

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Cited by in corpus (12)

• Topological defects in solids with odd elasticity
• Metastability of Constant-Density Flocks
• Active Solids Model: Rigid Body Motion and Shape-changing Mechanisms
• Microscopic field theory for structure formation in systems of self-propelled particles with generic torques
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• Vortex line entanglement in active Beltrami flows
• Geometric frustration and pairing order transition in confined bacterial vortices
• Active viscoelastic nematics with partial degree of order
• Hydrodynamic bend instability of motile particles on a substrate
• Rolling at right angles: magnetic anisotropy enables dual-anisotropic active matter