Emergence of fractal in aggregation with stochastic self-replication

Abstract

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 verified it numerically using the idea of data-collapse. Besides, 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.

8 pages, 8 figures

References in corpus (1)

• Condensation-Driven Aggregation in One Dimension

Cited by in corpus (5)

• Self-similarity, Aboav-Weaire's and Lewis' laws in weighted planar stochastic lattice
• Stochastic Fractal and Noether's Theorem
• Dyadic Cantor set and its kinetic and stochastic counterpart
• Multi-multifractality and dynamic scaling in stochastic porous lattice
• Dynamic scaling and stochastic fractal in nucleation and growth processes