Change of Scaling and Appearance of Scale-Free Size Distribution in Aggregation Kinetics by Additive Rules

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

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20 pages, 8 figures, submitted to Physica A: Statistical Mechanics and its Applications

Scientific paper

Here the idealized general model of aggregate growth is proposed on the basis of the simple additive rules that correspond to one-step aggregation process. Some factors that can influence the self-affine nature of the aggregating system of solitary agents (monomers) and their aggregates (clusters) were brought to light: the rate of monomer particle exchange between clusters, cluster geometry, and initial cluster size. 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. 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 analysis of simulated density and cumulative density distributions. The initial "singular" 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 asymmetric distribution of pile-ups. In contrast, the initial "singular" symmetric distributions of walls initially evolve by the diffusive scaling law and later it is replaced by the other linear scaling law with \textit{scale-free} exponential distributions without distinctive peaks. The conclusion was made as to applications of such approach for scaling analysis of cumulative density distributions in experimental data.

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