AI 中文总结
该研究探究DLA团簇随机序列吸附的阻塞态，通过模拟分析团簇形状多样性对阻塞密度及涨落的影响，发现阻塞密度的幂律标度规律，且模型差异随团簇尺寸增大逐渐消失。
AI 中文摘要
受自然界及工程系统中分支分形沉积普遍存在的启发，我们研究了扩散限制聚集（DLA）团簇在正方形晶格上的不可逆吸附。我们通过系统控制不同实现方式之间及内部使用的不同形状数量，涵盖单分散和多分散模型变体，探究了团簇形状多样性对系统阻塞特性的作用。我们在团簇尺寸2≤k≤4096的宽范围内开展的大规模模拟显示，阻塞密度随团簇尺寸呈幂律递减，即p_j(k)-p_j^∞~k^(-α)。研究发现，α和p_j^∞均依赖于形状多样性程度，α的取值范围为0.374(2)至0.417(1)。观察到增加形状多分散性会促进更致密的堆积。重要的是，阻塞密度的涨落表现出不同的标度行为：对于固定的团簇形状集合，σ(L)~1/L；但当不同实现方式间刷新团簇形状集合时，涨落与L无关。此外，我们的结果表明，随着k增大，模型变体之间的差异会系统性减小，且由于DLA团簇的统计自相似性，当k→∞时这些差异预计会消失。
英文摘要
Motivated by the ubiquity of ramified fractal deposits in nature and engineered systems, we investigate the irreversible adsorption of diffusion-limited aggregation (DLA) clusters on a square lattice. We study the role of cluster shape diversity on jamming properties of the system by systematically controlling the number of distinct shapes used across and within realizations, encompassing both monodisperse and polydisperse model variants. Our large-scale simulations over a broad range of cluster sizes $2\leqslant k\leqslant4096$ show that the jamming density decreases with cluster size as a power-law $p_j(k)-p_j^\infty\sim k^{-α}$. Both $α$ and $p_j^\infty$ are found to depend on the degree of shape diversity, with $α$ ranging from $0.374(2)$ to $0.417(1)$. It is observed that increasing shape polydispersity promotes denser packing. Importantly, the fluctuations of the jamming density exhibit distinct scaling behavior: $σ(L)\sim1/L$ for a fixed pool of cluster shape(s), but remain $L$-independent when the pool of shape(s) is refreshed across different realizations. Furthermore, our results demonstrate that the differences between the model variants systematically diminish with increasing $k$ and are expected to vanish as $k\to\infty$ due to the statistical self-similarity of the DLA clusters.
