Mechanically stable sphere packings are generated in three-dimensional space using the discrete element method, which spans a wide range in structural order, ranging from fully amorphous to quasiordered structures, as characterized by the bond orientational order parameter. As the packing pressure $p$ varies from the marginally rigid limit at the jamming transition ($p\approx 0$) to that of more robust systems ($p\gg 0$), the coordination number $z$ follows a familiar scaling relation with pressure, namely, $\mathrm{\Delta }z=z-z_c\sim p^{1/2}$, where $z_c=2d=6$ ($d=3$ is the spatial dimension). While it has previously been noted that $\mathrm{\Delta }z$ does indeed remain the control parameter for determining the packing properties, here we show how the packing structure plays an influential role on the mechanical (elastic) properties of the packings. Specifically, we find that the elastic (bulk $K$ and shear $G$) moduli, generically referred to as $M$, become functions of both $\mathrm{\Delta }z$ and the structure, to the extent that $M-M_c\sim \mathrm{\Delta }z$. Here, $M_c$ are values of the elastic moduli at the jamming transition, which depend on the structure of the packings. In particular, the zero shear modulus, $G_c=0$, is a special feature of fully amorphous packings, whereas more ordered packings take larger positive values, $G_c>0$. The finite $G_c>0$ in the ordered packings excites acoustic vibrations which add to floppylike modes controlled by $\mathrm{\Delta }z$ and enhance the plateau in the vibrational density of states.

中文翻译：

---

接近干扰过渡的球形填料的结构和力学特性：从完全非晶态到准有序结构

机械稳定的球状填充物是使用离散元方法在三维空间中生成的，该方法的结构顺序范围很广，从完全无定形到准有序结构，其特征在于键的取向顺序参数。作为包装压力$p$ 不同于干扰过渡时的边缘刚性极限（$p\approx 0$）到更强大的系统（$p\gg 0$），协调号码 $ž$ 遵循与压力的熟悉的比例关系，即 $\mathrm{\Delta }ž=ž-{ž}_C〜p^{\mathrm{1个}/2}$，在哪里 ${ž}_C=2d=6$ （$d=3$是空间尺寸）。虽然以前已经注意到$\mathrm{\Delta }ž$确实确实保留了确定填料性能的控制参数，这里我们展示了填料结构如何对填料的机械（弹性）性能产生影响。具体来说，我们发现$ķ$ 和剪 $G$）模数，通常称为 $\mathrm{中号}$，成为两者的功能 $\mathrm{\Delta }ž$ 和结构，在一定程度上 $\mathrm{中号}-{\mathrm{中号}}_C〜\mathrm{\Delta }ž$。这里，${\mathrm{中号}}_C$是在卡塞过渡时的弹性模量值，它取决于填料的结构。特别是零剪切模量$G_C=0$是完全无定形填料的一个特征，而更有序的填料则具有较大的正值， $G_C>0$。有限的$G_C>0$ 在有序包装中激发声振动，从而增加了由软盘控制的软盘模式 $\mathrm{\Delta }ž$ 并增加了平台的振动态密度。