论文标题
在干扰下的非棕色球的放松动力学
Relaxation dynamics of non-Brownian spheres below jamming
论文作者
论文摘要
我们从数字上研究了在空间尺寸中堵塞的非摩擦球的放松动力和相关的关键性$ d = 2 $，$ 3 $，$ 4 $和$ 8 $，以及在平均田野玛利亚豪尔班模型中。我们发现与无骨填料的放松相关的放松时间的非平凡有限尺寸和体积分数依赖性。特别是，放松时间显示出对数的分歧，系统大小在干扰下的任何密度下都可以分歧，并且没有关键指数可以表征其接近阻塞的行为。在平均场上，放松时间定义明确：它与临界指数的干扰有所不同，我们在数值上确定，并且与较早的平均场预测有所不同。我们使用一个极值统计论点合理化有限的$ d $对数差异，其中放松时间由系统中最连接的区域主导。同样的论点表明，较早的命题是，放松动力学和剪切粘度是直接相关的大型系统中的。非棕色包装的剪切粘度在热力学极限的所有$ d $中都明确定义，但是很大的有限尺寸效果会困扰其接近障碍的测量。
We numerically study the relaxation dynamics and associated criticality of non-Brownian frictionless spheres below jamming in spatial dimensions $d=2$, $3$, $4$, and $8$, and in the mean-field Mari-Kurchan model. We discover non-trivial finite-size and volume fraction dependences of the relaxation time associated to the relaxation of unjammed packings. In particular, the relaxation time is shown to diverge logarithmically with system size at any density below jamming, and no critical exponent can characterise its behaviour approaching jamming. In mean-field, the relaxation time is instead well-defined: it diverges at jamming with a critical exponent that we determine numerically and differs from an earlier mean-field prediction. We rationalise the finite $d$ logarithmic divergence using an extreme-value statistics argument in which the relaxation time is dominated by the most connected region of the system. The same argument shows that the earlier proposition that relaxation dynamics and shear viscosity are directly related breaks down in large systems. The shear viscosity of non-Brownian packings is well-defined in all $d$ in the thermodynamic limit, but large finite-size effects plague its measurement close to jamming.
