加和规则下聚集动力学中标度的变化和无标度粒径分布的出现
Change of Scaling and Appearance of Scale-Free Size Distribution in Aggregation Kinetics by Additive Rules
摘要：
基于与一步聚集过程相对应的简单可加规则，考虑了理想化的一般聚集增长模型。在桌面网格分布式计算环境中，对这两种理想情况进行了分析和蒙特卡罗模拟，分析了不同聚集场景下的“堆”和“墙”簇分布。通过对累积分布函数的分析，确定了由“零团簇尺寸”边界条件驱动的聚集动力学的几个方面（标度变化、尺寸分布类型的变化和无标度尺寸分布的出现）。具有\textit{minimum}活性表面（奇点）的“堆积”情况可以模拟位错的堆积聚集，并且具有\textit{maximum}活性表面的情况可以模拟位错在壁中的排列。标度律的变化（堆积和墙壁）和无标度分布（墙壁）的可用性进行了分析，并通过模拟概率密度和累积分布函数的标度，拟合，矩和自举分析确认。初始的“奇异”\textit{symmetric}堆积分布由“无限”扩散标度律演化，随后被另一个具有\textit{asymmetric}堆积分布的“半无限”扩散标度律所取代。与此相反，最初的“奇异”\textit{symmetric}分布的墙壁最初演变的扩散标度律，后来它被替换的其他弹道（线性）标度律与\textit{scale-free}指数分布没有明显的峰值。结论是可能的应用，这种方法的缩放，拟合，矩，并在模拟和实验数据中的分布的自举分析。
英文摘要：
The idealized general model of aggregate growth is considered on the basis of the simple additive rules that correspond to one-step aggregation process. The two idealized cases were analytically investigated and simulated by Monte Carlo method in the Desktop Grid distributed computing environment to analyze "pile-up" and "wall" cluster distributions in different aggregation scenarios. Several aspects of aggregation kinetics (change of scaling, change of size distribution type, and appearance of scale-free size distribution) driven by "zero cluster size" boundary condition were determined by analysis of evolving cumulative distribution functions. The "pile-up" case with a \textit{minimum} active surface (singularity) could imitate piling up aggregations of dislocations, and the case with a \textit{maximum} active surface could imitate arrangements of dislocations in walls. The change of scaling law (for pile-ups and walls) and availability of scale-free distributions (for walls) were analytically shown and confirmed by scaling, fitting, moment, and bootstrapping analyses of simulated probability density and cumulative distribution functions. The initial "singular" \textit{symmetric} distribution of pile-ups evolves by the "infinite" diffusive scaling law and later it is replaced by the other "semi-infinite" diffusive scaling law with \textit{asymmetric} distribution of pile-ups. In contrast, the initial "singular" \textit{symmetric} distributions of walls initially evolve by the diffusive scaling law and later it is replaced by the other ballistic (linear) scaling law with \textit{scale-free} exponential distributions without distinctive peaks. The conclusion was made as to possible applications of such approach for scaling, fitting, moment, and bootstrapping analyses of distributions in simulated and experimental data.
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