分形聚集生长性质研究

本文在分形生长DLA模型和有限步扩散反应置限聚集模型的基础上，考虑粒子扩散置限和粒子扩散有限步数的影响的同时，引入扩散粒子与种子或聚集集团粒子相遇时的聚集反应概率P，种子或聚集粒子对次近邻位置扩散粒子捐引作用引起扩散粒子向各方向的行走概率变化（行走偏向概率）WP，研究粒子随机行走的分形聚集生长性质，通过计算机模拟得到一系列的分形聚集生长图形，计算其相应的分形维数，结果表明：在粒子浓度较小时，分形生长为DLA生长，随粒子向外扩散置限范围dr，反应概率p和行走偏向概率wp 的增大，聚集体的分形维数df也随之增大；在粒子浓度较大时，一般聚集体呈密集结构，此时不具分形结构。

Study on the Properties of the Fractal Aggregation Growth

On the basis of the Diffusion Limited Aggregation (DLA) model and diffusion and reaction limited aggregation with finite steps model, we proposed a new fractal aggregation growth model by introducing the aggregation reaction probability and the walking deflection probability. The aggregation growth was simulated and the fractal dimension was calculated. When the particle density is not too big, it was found the DLA growth and the fractal dimension increases with diffusion confines, the aggregation reaction probability and the walking deflection probability increasing. When the particle density is big enough, it is no longer the fractal aggregation.