超球的最大随机塞包装的超均性跨空间维度的超球
Charles Emmett Maher1, Yang Jiao2,3, Salvatore Torquato1,4,5,6
1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
Physical review. E
|January 20, 2024
概括
最大随机塞 (MRJ) 状态是超均的,它们的结构因子S(k) 随着波数接近零,接近零. 更高的尺寸 (d≥3) 增加了MRJ包装的超均性,指数α = d-2.
科学领域:
- 物理 物理学 物理
- 材料科学 材料科学 材料科学
- 统计力学 统计力学
背景情况:
- 最大随机堵塞 (MRJ) 状态表示机械刚性,不重叠的物体最混乱的配置.
- MRJ 包装表现出超均性,其特点是抑制长波长密度波动,其中结构因子 S ((k) 作为波数趋向于零.
研究的目的:
- 调查在欧几里德维度d=3,4和5中产生高质量的严格塞状态的关键作用.
- 为了精确地确定MRJ状态的超均指数α,定义S(k) ~ ██████████████████████████████████████████████████████████████████████.
- 探索粒子数量,干扰和超均性之间的关系,以及声器的影响.
主要方法:
- 在维度d=3,4和5的严格塞配置的生成.
- 对结构因子S (k) 的分析,以量化超均性并提取指数α.
- 研究粒子数N和维度d对干扰和声器存在的影响.
主要成果:
- 高质量的严格堵塞状态对于准确的超均性分析和精确的α确定至关重要.
- 对于一个固定的维度d,增加粒子数N使塞变得更加困难,导致非超均的包装.
- 随着维度d的增加,声器的比例显著下降,这表明理想的MRJ状态是没有声器的.
- 分析表明,在d≥3的理想MRJ包装是超均的,α=d-2,随着d的增加变得更加超均.
- 在MRJ和Manna类随机密集 (RCP) 状态之间存在超均指数 (α) 的显著差异,特别是对于d=3,4和5.
结论:
- 真正的干扰与MRJ状态中的超均性密切相关.
- 尺寸d≥3的理想MRJ包装具有超均性,α=d-2.
- 这项研究强调了对算法的需求,以在三维中生成无的MRJ包装.
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