论文标题
d = 2和d = 3中随机关闭填料的显式分析解决方案
Explicit Analytical Solution for Random Close Packing in d=2 and d=3
论文作者
论文摘要
我们基于相同的方法，介绍了$ d = 3 $和$ d = 2 $的随机关闭包装（RCP）的体积分数的分析推导。使用适当修改的硬球统计，用于硬球，我们获得了$ ϕ _ {\ mathrm {rcp}} = 0.65896 $ in $ d = 3 $ in $ d = 3 $和$ ϕ _ {\ mathrm {rcp}}} = 0.88648 in $ d = 2 $。这些值很好地在文献中使用不同的方法（实验和数值模拟）和协议中报告的值的间隔内。 This order-agnostic derivation suggests some considerations related to the nature of RCP: (i) RCP corresponds to the onset of mechanical rigidity where the finite shear modulus emerges, (ii) the onset of mechanical rigidity marks the maximally random jammmed state and dictates $ϕ_{\mathrm{RCP}}$ via the coordination number $z$, (iii) disordered packings使用$ ϕ> ϕ _ {\ mathrm {rcp}} $可以以创建订单为代价，而在FCC限制处的$ z = 12 $作为边界条件。
We present an analytical derivation of the volume fractions for random close packing (RCP) in both $d=3$ and $d=2$, based on the same methodology. Using suitably modified nearest neigbhour statistics for hard spheres, we obtain $ϕ_{\mathrm{RCP}}=0.65896$ in $d=3$ and $ϕ_{\mathrm{RCP}}=0.88648$ in $d=2$. These values are well within the interval of values reported in the literature using different methods (experiments and numerical simulations) and protocols. This order-agnostic derivation suggests some considerations related to the nature of RCP: (i) RCP corresponds to the onset of mechanical rigidity where the finite shear modulus emerges, (ii) the onset of mechanical rigidity marks the maximally random jammmed state and dictates $ϕ_{\mathrm{RCP}}$ via the coordination number $z$, (iii) disordered packings with $ϕ>ϕ_{\mathrm{RCP}}$ are possible at the expense of creating some order, and $z=12$ at the FCC limit acts as a boundary condition.
