极性活性物质中的拓扑混合与编织普适性
Topological Mixing and Braiding Universality in Polar Active Matter
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中文总结 AI 辅助
研究以受限细菌悬浮液为模型，用有限时间编织指数（FTBE）量化拓扑混合，揭示其随密度的三种 regime 转变，建立FTBE与有效扩散率的平方根缩放关系，归为路径线编织普适性类。
中文摘要 AI 辅助
将活性物质的自主运动学与其涌现的宏观输运联系起来，受到高分辨率欧拉速度场要求的限制。此处，我们使用受限细菌悬浮液作为模型活性流体，将荧光示踪细胞的稀疏拉格朗日轨迹映射为(2+1)维几何编织，该编织直接编码流动的时空纠缠。我们使用有限时间编织指数（FTBE）作为代理，量化受限细菌悬浮液的拓扑熵和混沌混合。在适度受限的湿系统中，我们发现流体动力学耦合驱动结构从稀释活性气体转变为相干涡旋，最终转变为活性湍流，揭示了三种不同的、依赖于密度的拓扑混合 regime。相反，通过极端受限截断流体动力学屏蔽长度，系统向干活性物质极限转变。在该极限下，密集的面内空间碰撞抑制不可约纠缠，并在高粒子密度下大幅降低FTBE。通过评估每次相遇产生的拓扑复杂性，我们揭示了从离散几何相遇 regime 到面积逃逸机制的转变。最后，我们建立了FTBE与有效扩散率之间的平方根缩放关系，将活性流体的自维持混合归入路径线编织普适性类。
英文摘要
Connecting the autonomous kinematics of active matter to its emergent macroscopic transport is constrained by the requirement for high-resolution Eulerian velocity fields. Here, we use confined bacterial suspensions as a model active fluid, mapping the sparse Lagrangian trajectories of fluorescent spy cells into (2+1)-dimensional geometric braids that directly encode the spatiotemporal entanglement of the flow. We use the finite-time braiding exponent (FTBE) as a proxy to quantify the topological entropy and chaotic mixing of confined bacterial suspensions. In moderately confined wet systems, we find that hydrodynamic coupling drives a structural transition from a dilute active gas to coherent vortices, and ultimately to active turbulence, revealing three distinct density-dependent regimes of topological mixing. Conversely, truncating the hydrodynamic screening length via extreme confinement drives the system toward a dry active matter limit. In this limit, dense in-plane steric collisions suppress irreducible entanglement and substantially reduce the FTBE at high particle densities. By evaluating the topological complexity generated per encounter, we reveal a transition from a discrete geometric encounter regime to an areal escape mechanism. Finally, we establish a square-root scaling between the FTBE and the effective diffusivity, placing the self-sustained mixing of active fluids into the pathline braiding universality class.
发表机构
- Northwest University（西北大学）
- Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）
机构由 AI 辅助整理，请以论文原文为准。
