AI 中文总结
该研究建立了适用于全径高比范围的圆柱内硬球密堆积分析理论，推导了任意规则晶格的堆积分数精确方程，提出优化圆柱取向的数学程序，为圆柱内球堆积提供通用理论基础。
AI 中文摘要
我们针对圆柱内硬球的密堆积问题建立了一套分析理论。从物理角度而言，该理论包含对密排三维固体的有限圆柱掩模，且适用于圆柱径高比的全范围，突破了仅关注窄宽度范围内极高圆柱的相关研究。我们明确推导了适用于任意规则晶格的堆积分数精确方程，该方程为理解前人研究中出现的体积分数振荡与标度行为提供了基础。此分析关系可作为严格下界，为进一步收紧下界，我们推导并实现了一套优化圆柱取向的高效数学程序。此外，我们提出了改进预测堆积结构的简单技术。总体而言，我们为所有容器尺寸下的球在圆柱内的堆积提供了通用理论基础。
英文摘要
We develop an analytical theory for the dense packing of hard spheres in cylinders. Physically, our theory consists of a finite cylindrical masking of a close-packed three-dimensional solid and covers the entire range of cylinder aspect ratios, thus going beyond efforts that are focused on very tall cylinders in a narrow range of widths. We explicitly derive an exact equation for resulting packing fractions, valid for any regular lattice, and it provides a basis to understand the oscillations and scaling of volume fractions that have appeared in previous works. Our analytical relation serves as a rigorous lower bound and to tighten it we derive, and implement, an efficient mathematical procedure to optimize the orientation of the cylinder. Furthermore, we suggest simple techniques to improve on the predicted packings. Overall, we provide a general theoretical foundation for the packing of balls in cylinders, valid for all container sizes.
Comments5 pages, 3 figures, plus supplemental material
