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 $\pm 1$ 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 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.

中文翻译：

---

植绒物质的拓扑驱动排序

当相互作用的运动单元自组织成群时，它们实现了自然界中发现的最强大的有序状态之一。然而，经过 25 年的深入研究，控制活鸡群和人工鸡群排序动态的机制仍未解决。在这里，结合活性胶体实验、数值模拟和分析工作，我们解释了植绒液体如何治愈最初受到拓扑缺陷集合困扰的自发流动，以实现即使在二维中也能实现长程极性有序。我们证明了植绒物质的自相似排序是由连接所有区域的有生命的畴壁网络控制的。$\pm 1$漩涡并引导它们的湮灭动力学。至关重要的是，这种单一的定向结构与相互连接的领结形状的扩展密度模式的形成相呼应。我们确定这种双重结构源于自平流和密度梯度之间的相互作用。$-1$具有四个取向壁的拓扑电荷。然后我们解释了活跃的马格努斯力如何将所有拓扑电荷与扩展的畴壁联系起来，而弹性相互作用驱动它们沿着由此产生的极化奇点的丝状网络吸引。总之，我们的实验、数值和分析结果阐明了所有流动奇点的抑制和植绒物质中原始单向有序的出现。