用分形和多重分形分析表征合成多孔介质图像

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS GEM-International Journal on Geomathematics Pub Date : 2023-09-13 DOI:10.1007/s13137-023-00237-6
Pablo Pavón-Domínguez, Marina Díaz-Jiménez
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引用次数: 1

摘要

多孔图像的分形和多重分形分析允许通过尺度不变的理解来描述多孔介质。已经有许多工作使用这些分析技术来描述各种各样的真实多孔介质。然而,这些研究通常是比较的,难以辨别孔隙大小和孔隙分布在分形和多重分形分析结果中的作用。本文从分形和多重分形的角度对不同的合成多孔介质进行了深入的研究,其中孔隙大小及其在介质中的分布都是参数化的。从而生成了一组合成的二值图像,获得了具有不同固定孔径和不同孔径率的确定性和随机结构。为了完成上述分析,还计算了缺度。结果表明,分形维数随孔隙大小的增大而增大,当孔隙分布服从随机分布时,分形维数比服从确定性分布时更高。而当孔隙非常大时,无论孔隙分布如何,分形维数都是相似的。从多重分形方法来看,孔隙大小与多重分形程度呈负相关。事实上,在不同孔径的混合图像中也发现,小孔隙的比例越大,多重分形的程度越大。相反,当大孔隙比一定时,由于大孔隙的合并,多重分形程度也会增加。
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Characterization of synthetic porous media images by using fractal and multifractal analysis
Abstract Fractal and multifractal analysis of porous images allow the description of porous media through a scale-invariant understanding. There have been numerous works that have used these analysis techniques for the description of a great variety of real porous media. However, these studies are usually comparative, being difficult to discern the role played by the pore size and pore distribution in the results of fractal and multifractal analysis. This works develops an in-depth study of different synthetic porous media from a fractal and multifractal approach, in which both the pore size and its distribution in the medium are parameterized. Thus, a set of synthetic binary images have been generated obtaining deterministic and random structures with different fixed pore sizes and also with different rates of pore sizes. Lacunarity is also calculated in order to complete the aforementioned analysis. Results evinces that fractal dimension increases with pore size and that it is higher when the pore distribution obeys a random distribution versus a deterministic one. However, when the pore size is very large, fractal dimension is similar regardless of the pore distribution. From a multifractal approach, pore size is negatively correlated with the degree of multifractality. In fact, in images with mixtures of different pore sizes it is also found that the greater the ratio of small pores, the greater degree of multifractality. By contrast, when the ratio of large pores is relevant, the degree of multifractality also increases due to the merging of macro-pores.
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来源期刊
GEM-International Journal on Geomathematics
GEM-International Journal on Geomathematics MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
3.50
自引率
0.00%
发文量
18
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