致密颗粒物质中的轨迹纠缠
Trajectory entanglement in dense granular materials
摘要：
颗粒材料的颗粒尺度动力学通常由自扩散系数$D$表征。然而，这种措施放弃了集体和拓扑信息，已知是一个重要的特征，在密集的系统中的粒子轨迹。通过拓扑辫熵$\Sbraid$可以直接测量粒子时空轨迹的纠缠度，它以前曾被用来量化流体系统中的混合效率。在这里，我们调查的效用$\Sbraid$在表征一个致密的，驱动的颗粒状材料在附近的静态堵塞点$ϕ_J$的包装密度的动态。从二维颗粒材料内测量的颗粒轨迹，我们通常观察到$\Sbraid$是明确定义的和广泛的。然而，对于存在$ϕ\gtrsim 0.79$的系统，我们发现$\Sbraid$（如$D$）没有明确定义，这意味着这些系统在实验时间尺度上不是遍历的。$\Sbraid$和$D$都随堆积密度或围压的增加而减小，与所施加的边界条件无关。相关的编织因子提供了一种方法来识别多粒子现象，如集体重排。我们讨论了这种措施在表征颗粒系统的可能用途。
英文摘要：
The particle-scale dynamics of granular materials have commonly been characterized by the self-diffusion coefficient $D$. However, this measure discards the collective and topological information known to be an important characteristic of particle trajectories in dense systems. Direct measurement of the entanglement of particle space-time trajectories can be obtained via the topological braid entropy $\Sbraid$, which has previously been used to quantify mixing efficiency in fluid systems. Here, we investigate the utility of $\Sbraid$ in characterizing the dynamics of a dense, driven granular material at packing densities near the static jamming point $ϕ_J$. From particle trajectories measured within a two-dimensional granular material, we typically observe that $\Sbraid$ is well-defined and extensive. However, for systems where $ϕ\gtrsim 0.79$, we find that $\Sbraid$ (like $D$) is not well-defined, signifying that these systems are not ergodic on the experimental timescale. Both $\Sbraid$ and $D$ decrease with either increasing packing density or confining pressure, independent of the applied boundary condition. The related braiding factor provides a means to identify multi-particle phenomena such as collective rearrangements. We discuss possible uses for this measure in characterizing granular systems.
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