聚集生长凝聚集团平均特征长度与粒子数关系研究

从统计的角度出发,在二维DLA模型的基础上,以正方形四边中点作为随机粒子产生位置的聚集生长凝聚集团进行研究,测量在不同粒子数情况下凝聚集团的平均特征长度,寻找平均特征长度与粒子数之间的关系。结果发现,平均特征长度与粒子数的双自然对数曲线基本成直线,理论上由该直线的斜率可以导出凝聚集团的分形维数为1.605,但是却比凝聚体的实际分维数偏小。

Study on Characteristic Length of Aggregate Growth Aggregation vs Particle Number

Beginning with the point of statistic and basing on the model of DLA, this paper studies the assemble-growth aggregation with foursquare four sides'' midpoint as random particles generate positions.Measuring aggregation''s average characteristic length for different particle numbers and searching the relation between the average characteristic length and the particle number.The results find that the double logarithm curve of average characteristic length and particle number is linear basically.Theoretically, we can deduce the fractal dimension of aggregation is 1.605 from the slope of this line, but it is smaller than real fractal dimension of aggregation.