论文标题
部分可观测时空混沌系统的无模型预测
Slow and fast particles in shear-driven jamming: critical behavior
论文作者
论文摘要
我们对剪切驱动的简单模型进行了大量的模拟，以二维的方式进行剪切驱动的干扰，以分析围绕干扰密度$ ϕ_j $的不同密度$ ϕ $的速度分布，并以不同的低剪切应变速率，$ \dotγ$。然后，我们发现速度分布由两个部分组成，这些部分与两个不同的物理过程相关，我们称之为缓慢的过程和快速过程，分别由较慢和更快的粒子主导。较早的缩放分析表明，剪切粘度$η$从下面接近干扰密度，该术语由两个不同的术语组成，我们提供了有力的证据，表明这些术语与两个不同的过程有关：领先的差异是由于快速过程所致，而校正到尺度的术语是由于缓慢的过程所致。由于观察到，在剪切驱动的干扰过渡及其周围的不同$ \dotγ$和$ ϕ $的速度分布中，对缓慢过程的分析可能是可能的，在低速下具有峰值，并且该分布的形状最高和略高于该峰值。然后，我们发现，由于过程在速度分布中的高度和峰位置而言，由于过程缓慢而表达对剪切粘度的贡献，并发现通过标准的临界缩放分析确定，这种贡献与校正到缩放项相匹配。一个进一步的观察是，集体粒子运动由缓慢的过程主导。与临界现象中通常的图像相反，与分歧相关长度和分化顺序参数之间的直接连接，我们发现相关性和剪切粘度脱短，因为它们是由不同的粒子集控制的，而剪切驱动的干扰是一种与众不同的关键现象。
We do extensive simulations of a simple model of shear-driven jamming in two dimensions to analyze the velocity distribution at different densities $ϕ$ around the jamming density $ϕ_J$ and at different low shear strain rates, $\dotγ$. We then find that the velocity distribution is made up of two parts which are related to two different physical processes which we call the slow process and the fast process as they are dominated by the slower and the faster particles, respectively. Earlier scaling analyses have shown that the shear viscosity $η$, which diverges as the jamming density is approached from below, consists of two different terms and we present strong evidence that these terms are related to the two different processes: the leading divergence is due to the fast process whereas the correction-to-scaling term is due to the slow process. The analysis of the slow process is possible thanks to the observation that the velocity distribution for different $\dotγ$ and $ϕ$ at and around the shear-driven jamming transition, has a peak at low velocities and that the distribution has a constant shape up to and slightly above this peak. We then find that it is possible to express the contribution to the shear viscosity due to the slow process in terms of height and position of the peak in the velocity distribution and find that this contribution matches the correction-to-scaling term, determined through a standard critical scaling analysis. A further observation is that the collective particle motion is dominated by the slow process. In contrast to the usual picture in critical phenomena with a direct link between the diverging correlation length and a diverging order parameter, we find that correlations and shear viscosity decouple since they are controlled by different sets of particles and that shear-driven jamming is thus an unusual kind of critical phenomenon.
