絮凝体的DLA分形模拟及其分形维数的计算方法

运用有限扩散凝聚(DLA)模型对絮凝体的成长过程进行了二维模拟.模拟絮凝体分别采用密度函数法、回转半径法、图像分析法进行分形维数计算,分形维数均随模拟絮凝体尺寸的增大而减小.三种计算方法的结果显示,密度函数法和回转半径法得到的分形维数基本相当,但图像分析法所得到的分形维数较小,约为密度函数法和回转半径法所得到的分形维数的0.8左右,其原因可能是图像分析过程中计算机对图像的识别误差所致.以DLA模型模拟得到的絮凝体内部的孔隙率随絮凝体尺寸的增大而增加.絮凝体中孔隙率的增加是絮凝体密度减小、结构松散的主要原因,也是絮凝体分形维数降低的主要因素.

DLA SIMULATION OF FRACTAL FLOCS AND CALCULATION OF FRACTAL DIMENSION

In this paper, two-dimensional DLA model was studied on the morphological structure of floc growth, and the fractal dimension of the simulated flocs was calculated and compared by three different methods: density function, radius of gyration of simulated flocs and image analysis respectively.The results showed that the fractal dimension calculated by the three methods were all decreased with the increasing of floc size. Comparing the results of the fractal dimension calculated by the three methods, it could find that the fractal dimension calculated by density function correspond with that by radius of gyration of simulated flocs. However, the fractal dimension calculated by image analysis is somewhat smaller than that calculated by the above two methods, which is about 0.8 of the fractal dimension calculated by the two methods. The difference in the fractal dimension is probably resulted from the identification of floc image by computer in the process of image analysis. Furthermore, the porosity of the simulated flocs increased with the increasing of floc size, which is the main reason of the decrease in the density and fractal dimension of the flocs.