Emergence of fractals in aggregation with stochastic self-replication

We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully support all theoretical findings. In particular, we show ana...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2013-10, Vol.88 (4), p.042137-042137, Article 042137
Main Authors: Hassan, Md Kamrul, Hassan, Md Zahedul, Islam, Nabila
Format: Article
Language:English
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Summary:We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully support all theoretical findings. In particular, we show analytically that the particle size distribution function exhibits dynamic scaling and we verify it numerically using the idea of data collapse. Furthermore, the conditions under which the resulting system emerges as a fractal are found, the fractal dimension of the system is given, and the relationship between this fractal dimension and a conserved quantity is pointed out.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.88.042137