Wang Ziwei, Zhang Jie
Zhiyuan College, Shanghai Jiao Tong University, Shanghai 200240, China.
1] Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China [2] Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.
Sci Rep. 2015 Jan 30;5:8128. doi: 10.1038/srep08128.
We have investigated the spatiotemporal chaotic dynamics of unjamming and jamming of particles in a model experiment - a rotating drum partially filled with bidisperse disks to create avalanches. The magnitudes of the first Lyapunov vector δu(t) and velocity v(t) of particles are directly measured for the first time to yield insights into their spatial correlation Cδu,v, which is on statistical average slightly larger near the unjamming than the value near the jamming transition. These results are consistent with the recent work of Banigan et al (Nature Phys. 2013), and it is for the first time to validate their theoretical models in a real scenario. v(t) shows rich dynamics: it grows exponentially for unstable particles and keeps increasing despite stochastic interactions; after the maximum, it decays with large fluctuations. Hence the spatiotemporal chaotic dynamics of avalanche particles are entangled, causing temporal correlations of macroscopic quantities of the system. We propose a simple model for these observations.
我们在一个模型实验中研究了颗粒解堵和堵塞的时空混沌动力学——一个部分填充双分散圆盘的旋转鼓，以产生雪崩。首次直接测量了颗粒的第一李雅普诺夫向量δu(t)的大小和速度v(t)，以深入了解它们的空间相关性Cδu,v，统计平均值显示，在解堵附近，其值略大于堵塞转变附近的值。这些结果与Banigan等人（《自然物理学》，2013年）最近的工作一致，并且首次在实际场景中验证了他们的理论模型。v(t)显示出丰富的动力学：对于不稳定颗粒，它呈指数增长，尽管存在随机相互作用仍持续增加；在达到最大值后，它会伴随着大幅波动而衰减。因此，雪崩颗粒的时空混沌动力学相互纠缠，导致系统宏观量的时间相关性。我们针对这些观测结果提出了一个简单模型。
