计算机模拟研究油脂结晶网络的显微分形

Computer simulation research on microscopy fractal dimentions of grease crystallization network

以计算机编程模拟生成不同形状、尺寸、面积分数和分布模式的晶体显微图像,计算计盒维数(D_(B))、颗粒计数维数(D_(F))和分形布朗维数(D_(FBM)),并采用非参数回归分析和多重线性回归分析观察各个因素对各种分形维数的影响。结果表明:当晶体形状一定时,D_(B)随晶体尺寸和面积分数的增大而增大,且晶体的D_(B)主要由其晶体面积分数所决定;晶体的D_(FBM)主要由其尺寸所决定,晶体的面积分数对其影响较小。均匀分布条件下的D_(B)和D_(FBM)一般小于随机分布,聚集分布条件下的D_(B)和D_(FBM)一般大于随机分布。晶体的形状、尺寸、面积分数和分布模式对D_(F)均无显著影响。在油脂结晶的显微分形维数中,D_(B)可以用于表征晶体面积分数的变化,D_(FBM)可以用于表征晶体尺寸的变化。

The crystal microscopy images with different shapes,sizes,area fractions and distribution pat-terns were generated by computer programming simulation.Box counting dimension(D_(B)),particle count-ing dimension(D_(F))and fractal Brownian motion dimension(D_(FBM))were calculated,and the effects of various factors on various fractal dimensions were observed by non-parametric regression analysis and multiple linear regression analysis.The results showed that when the crystal shape was determined,the D_(B)increased with the increase of crystal size and area fraction,and the D_(B)was mainly determined by its crystal area fraction.The D_(FBM)was primarily determined by its size,and crystal area fraction had less influence on it D₃and Drum with uniform distribution were generally smaller than those with random distribution,and D_(B)and D_(FBM)with aggregate distribution were generally larger than those with random distribution.The crystals’shape,size,area fraction,and distribution patterns did not have significant effect on D_(F).In microscopy fractal dimension of grease crystallization,the D_(B)could be used to characterize the change in crystal area fraction,and the D_(FBM)could be used to characterize the change in crystal size.