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.
Highlights
Dazzling nonequilibrium steady states are consistently observed in soft condensed matter assembled from motile units [1,2,3,4], but their lively dynamics comes at a high price
Numerical simulations, and analytical work, we explain how flocks of self-propelled particles suppress the topological excitations of their flow field and self-organize in one of the most stable ordered phases observed in nature
This atypical phase-ordering dynamics is ruled by the emergence of domain-wall networks shaped by self-advection and density gradient around −1 topological charges
Summary
Dazzling nonequilibrium steady states are consistently observed in soft condensed matter assembled from motile units [1,2,3,4], but their lively dynamics comes at a high price. Flocks generically refer to collections of interacting polar units collectively moving along the same average direction [7] as observed over more than 6 orders of magnitude in scale, from kilometer-long insect swarms to colloidal and molecular flocks cruising through microfluidic devices [10,11,12,13,14] Both living and synthetic flocks support self-advected density and velocity fluctuations captured by Toner-Tu hydrodynamics [1,7,9], thereby realizing one of the most stable broken-symmetry phases observed in nature, in vitro and in silico: Flocks can support long-ranged polar order both in three and two dimensions, even when challenged by thermal fluctuations and quenched isotropic disorder [9,15,16,17]. We show that a self-similar dynamics emerges from the annihilation of Æ1 vortices along a filamentous network of domain walls with no counterparts in passive materials This lively orientational structure is mirrored by very characteristic density patterns having the shape of interconnected bow ties generic to all realizations of Toner-Tu fluids. Orientational elasticity attracts all topological defects along this emergent filamentous structure which eventually vanishes to form a material assembled from self-propelled units all flocking along the same direction
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