论文标题
测试用于干扰非球体颗粒的平均场理论：接触数，间隙分布和振动密度
Testing mean-field theory for jamming of non-spherical particles: Contact number, gap distribution, and vibrational density of states
论文作者
论文摘要
我们对非球形粒子在两个维度上的干扰过渡进行数值模拟。特别是，当粒子的形状与完美的磁盘略微偏离时，我们系统地研究了干扰过渡点处的物理量如何行为。对于有效的数值模拟，我们首先使用参考磁盘的扰动理论得出了GAP函数的分析表达。从磁盘开始，我们观察到粒子形状变形的效果，即傅立叶系列$ \ sin（nθ）$的$ n $ th订单项。我们表明，状态振动密度的接触数量，间隙分布和特征频率等几个物理量显示了与参考磁盘线性偏差有关的幂律行为。幂律行为不取决于$ n $，并且与非球形颗粒的抑制作用的平均场理论完全一致。该结果表明，对于几乎可以通过傅立叶序列表示形状的几乎球形粒子，平均场理论通常具有非常普遍的作用。
We perform numerical simulations of the jamming transition of non-spherical particles in two dimensions. In particular, we systematically investigate how the physical quantities at the jamming transition point behave when the shapes of the particle deviate slightly from the perfect disks. For efficient numerical simulation, we first derive an analytical expression of the gap function, using the perturbation theory around the reference disks. Starting from disks, we observe the effects of the deformation of the shapes of particles by the $n$-th order term of the Fourier series $\sin(nθ)$. We show that the several physical quantities, such as the number of contacts, gap distribution, and characteristic frequencies of the vibrational density of states, show the power-law behaviors with respect to the linear deviation from the reference disks. The power-law behaviors do not depend on $n$ and are fully consistent with the mean-field theory of the jamming of non-spherical particles. This result suggests that the mean-field theory holds very generally for nearly spherical particles whose shape can be expressed by the Fourier series.
