Driven by physical questions pertaining to quantifying particle dynamics, microscopy can now resolve complex systems at the single-particle level, from cellular organisms to individual ions. Yet, available analysis techniques face challenges reconstructing trajectories in dense and heterogeneous systems where accurately labeling particles is difficult. Furthermore, the inescapable finite field of view of experiments hinders the measurement of collective effects. Inspired by Smoluchowski, we introduce a broadly applicable analysis technique that probes dynamics of interacting particle suspensions based on a remarkably simple principle: counting particles in finite observation boxes. Using colloidal experiments, advanced simulations, and theory, we first demonstrate that statistical properties of fluctuating counts can be used to determine self-diffusion coefficients, so alleviating the hurdles associated with trajectory reconstruction. We also provide a recipe for practically extracting the diffusion coefficient from experimental data at variable particle densities, which is sensitive to steric and hydrodynamic interactions. Remarkably, by increasing the observation box size, counting naturally enables the study of collective dynamics in dense suspensions. Using our novel analysis of particle counts, we uncover a surprising enhancement of collective behavior due to hydrodynamics as well as a new length scale which can be connected with hyperuniform structure. Our counting framework, the “countoscope,” thus enables efficient measurements of self and collective dynamics in dense suspensions and opens the way to quantifying dynamics and identifying novel physical mechanisms in diverse complex systems where single particles can be resolved.

中文翻译：

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Countoscope：在没有轨迹的情况下测量自我和集体动力


在与量化粒子动力学相关的物理问题的驱动下，显微镜现在可以在单粒子水平上解析复杂系统，从细胞生物到单个离子。然而，现有的分析技术面临着在致密和非均质系统中重建轨迹的挑战，在这些系统中，准确标记颗粒很困难。此外，实验不可避免的有限视野阻碍了集体效应的测量。受 Smoluchowski 的启发，我们引入了一种广泛适用的分析技术，该技术基于一个非常简单的原理来探测相互作用的粒子悬浮液的动力学：在有限观测框中计数粒子。使用胶体实验、高级模拟和理论，我们首先证明了波动计数的统计特性可用于确定自扩散系数，从而减轻与轨迹重建相关的障碍。我们还提供了一个配方，用于从可变粒子密度的实验数据中实际提取扩散系数，该粒子密度对空间和流体动力学相互作用很敏感。值得注意的是，通过增加观察框的大小，计数自然而然地能够研究密集悬浮液中的集体动力学。利用我们对粒子计数的新颖分析，我们揭示了由于流体动力学以及可以与超均匀结构相关的新长度尺度，集体行为的惊人增强。因此，我们的计数框架，即“countoscope”，能够有效地测量致密悬浮液中的自身和集体动力学，并为量化动力学和识别各种复杂系统中的新物理机制开辟了道路，在这些系统中，单个粒子可以被解析。