Hassan Md Kamrul, Hassan Md Zahedul, Islam Nabila
Department of Physics, University of Dhaka, Dhaka 1000, Bangladesh.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Oct;88(4):042137. doi: 10.1103/PhysRevE.88.042137. Epub 2013 Oct 24.
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.
我们提出并研究了一个简单模型，该模型描述了具有随机自我复制的布朗粒子的聚集动力学。同时给出了精确解和标度理论以及数值模拟，这些充分支持了所有理论结果。特别地，我们通过解析证明了粒径分布函数呈现动态标度，并使用数据塌缩的概念进行了数值验证。此外，还找到了所得系统呈现为分形的条件，给出了系统的分形维数，并指出了该分形维数与一个守恒量之间的关系。
