Self-oscillating synchronematic colloids

Self-oscillators that sustain periodic dynamics under constant input are ubiquitous in natural and engineered systems, where their interactions enable spatiotemporal coordination among many individual units. New forms of organization can emerge when these self-oscillating units are free to move and rotate, linking their spatial arrangement and orientation with their oscillation frequencies and phases. Here, we report experiments and simulations on populations of Quincke colloids that behave as self-oscillating units characterized by position, orientation, frequency, and phase. Hydrodynamic interactions among these colloids drive temporal synchronization and spatial alignment of their phases and orientations, giving rise to a new form of collective order that we term synchronematic. Within finite-size crystalline clusters, these non-reciprocal interactions promote global synchronization and circular alignment, with a collective frequency that increases with cluster size. Using the theory of weakly coupled oscillators, we derive a reduced-order model that captures the coupled evolution of phase and orientation and explains how synchronematic order depends sensitively on the particle configuration. Our results establish Quincke colloids as a model system for active oscillatory matter and reveal fundamental principles by which synchronization, alignment, and structure co-emerge---offering a framework for designing adaptive, frequency-tunable materials.

在自然与工程系统中，能够在恒定输入条件下维持周期动力学行为的自激振荡器无处不在，这类单元间的相互作用可实现众多独立个体之间的时空协调。当这些自振荡单元能够自由移动与旋转时，新的组织形式便会涌现，将其空间排布与取向与其振荡频率和相位紧密关联起来。本文报道了针对昆克胶体（Quincke colloids）群体的实验与模拟研究，这类胶体作为自振荡单元，其特征可由位置、取向、频率与相位加以表征。这些胶体之间的流体动力学相互作用，会驱动其相位与取向的时间同步及空间对齐，进而形成一种全新的集体序，我们将其命名为同步序（synchronematic）。在有限尺寸的晶态团簇中，这类非互易相互作用会促进全局同步与环形对齐，其集体频率随团簇尺寸的增大而升高。借助弱耦合振子（weakly coupled oscillators）理论，我们推导得到一个降阶模型，该模型能够捕捉相位与取向的耦合演化过程，并解释同步序如何敏感地依赖于粒子的排布构型。我们的研究确立了昆克胶体作为活性振荡物质的模型系统，并揭示了同步、对齐与结构协同涌现的基本原理——这为设计自适应、频率可调谐材料提供了理论框架。