论文标题
在临界尺寸下方的堵塞
Jamming below upper critical dimension
论文作者
论文摘要
在过去的几十年中，广泛的数值模拟证明，无摩擦的球形颗粒的临界指数在两个和三个维度中保持不变。这意味着上部临界维度为$ d_u = 2 $或更低。在这项工作中，我们研究了下部临界维度以下的堵塞过渡。我们研究了一个准二维系统：限制在狭窄通道中的磁盘。我们表明，该系统在干扰过渡点处是等静态的，就像在两个和三个维度的标准干扰系统的标准干扰过渡的情况下一样。然而，多余的接触数的缩放表明线性缩放。此外，即使在干扰过渡点，差距分布仍然有限。这些结果在两个维度和三个维度上与散装系统的结果有所不同。
Extensive numerical simulations in the past decades proved that the critical exponents of the jamming of frictionless spherical particles remain unchanged in two and three dimensions. This implies that the upper critical dimension is $d_u=2$ or lower. In this work, we study the jamming transition below the upper critical dimension. We investigate a quasi-one-dimensional system: disks confined in a narrow channel. We show that the system is isostatic at the jamming transition point as in the case of standard jamming transition of the bulk systems in two and three dimensions. Nevertheless, the scaling of the excess contact number shows the linear scaling. Furthermore, the gap distribution remains finite even at the jamming transition point. These results are qualitatively different from those of the bulk systems in two and three dimensions.
