AI 中文总结
该研究提出基于Adam优化器的\texttt{rcpgenerator}代码，实现极端尺寸比下的高维密堆积生成，性能优于传统方法，结果与实验及理论预测吻合。
AI 中文摘要
我们提出了\texttt{rcpgenerator}，这是一个开源代码，用于从任意指定的颗粒直径列表生成d维致密、无序、无重叠的密堆积结构。该方法采用Clarke-Wiley膨胀协议，但改用Adam优化器来松弛颗粒构型。通常，颗粒坐标使用单一全局步长更新，当尺寸比S≡D_max/D_min增大时，该步长必须缩小，这通常会导致优化停滞。Adam则为每个坐标提供自适应步长，在更宽的S范围内稳定优化时间。我们在三维周期性测试中展示了这一点：对于连续对数正态分布（N≈10^6个直径），尺寸比S可达~5×10^5；对于幂律分布，颗粒数可达N≈5.6×10^6，最密堆积的堆积分数φ≈0.87，在多核机器上每个案例耗时几分钟到几小时。对于截断对数正态、截断幂律和威布尔分布，所得的φ重现了先前数值结果以及无参数Farr-Groot预测中随分布形状和S变化的峰值、拐点位置等趋势，剩余偏移通常为0.005-0.01。此外，结果与振动床实验中测得的多峰堆积密度一致。代码及每张图背后的完整案例统计数据随论文一同发布。
英文摘要
We present \texttt{rcpgenerator}, an openly available code for generating $d$-dimensional dense, disordered, non-overlapping close packings from an arbitrary prescribed list of particle diameters. The method adapts the Clarke--Wiley inflation protocol, but instead uses the Adam optimizer to relax the particle configuration. Typically, particle coordinates are advanced with a single, global step size, which must shrink as the size ratio $S\equiv D_{\max}/D_{\min}$ grows, generally stalling the optimization. Adam instead gives each coordinate its own adaptive step size, stabilizing the optimization time across a broader range of $S$. We demonstrate this in three-dimensional periodic tests that reach $S\sim5\times10^{5}$ for a continuous lognormal distribution ($N\sim10^{6}$ diameters) and particle numbers up to $N\approx5.6\times10^{6}$ for power-law distributions, with the densest packings reaching $ϕ\simeq0.87$, each completed in minutes to hours on a multicore machine. Across truncated-lognormal, truncated-power-law, and Weibull distributions, the resulting $ϕ$ reproduces trends such as the locations of peaks and knees with distribution shape and $S$ found in prior numerical results and in the parameter-free Farr--Groot prediction, with a remaining offset typically $0.005$--$0.01$. Additionally, results are commensurate with multimodal packing densities measured in vibrated-bed experiments. The code and the complete per-case census behind every figure are released with the paper.
Comments11 pages, 10 figures, 3 tables, Code: https://github.com/KD-physics/RCPGenerator; data archived at Zenodo, doi:10.5281/zenodo.21435447
