{"title":"AN ANALOGICAL METHOD ON FRACTAL DIMENSION FOR THREE-DIMENSIONAL FRACTURE TORTUOSITY IN COAL BASED ON CT SCANNING","authors":"Gaofeng Liu, Zhen Zhang, Yunxing Cao, Xiaoming Wang, Huan Liu, Baolin Li, Nian Si, W. Guan","doi":"10.1142/s0218348x2350072x","DOIUrl":null,"url":null,"abstract":"In this work, we have given an analogical method for estimating the fractal dimension for three-dimensional fracture tortuosity (3D-FT). The comparison and error analysis of analogical and rigorous methods on fractal dimension for 3D-FT were carried out in this work. The fractal dimension [Formula: see text] for 3D-FT from the proposed analogical method is the function of 3D fracture average tortuosity ([Formula: see text] and average fracture length ([Formula: see text]. The analogical method for estimating fractal dimension ([Formula: see text] with high accuracy indicates good consistency with the rigorous method ([Formula: see text]. The fractal dimension ([Formula: see text] from the rigorous method is the embodiment of the physical meaning of [Formula: see text]. The fractal dimension ([Formula: see text] from the analogical method is relatively convenient for calculating the premise of ensuring accuracy.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":" ","pages":""},"PeriodicalIF":3.3000,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0218348x2350072x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, we have given an analogical method for estimating the fractal dimension for three-dimensional fracture tortuosity (3D-FT). The comparison and error analysis of analogical and rigorous methods on fractal dimension for 3D-FT were carried out in this work. The fractal dimension [Formula: see text] for 3D-FT from the proposed analogical method is the function of 3D fracture average tortuosity ([Formula: see text] and average fracture length ([Formula: see text]. The analogical method for estimating fractal dimension ([Formula: see text] with high accuracy indicates good consistency with the rigorous method ([Formula: see text]. The fractal dimension ([Formula: see text] from the rigorous method is the embodiment of the physical meaning of [Formula: see text]. The fractal dimension ([Formula: see text] from the analogical method is relatively convenient for calculating the premise of ensuring accuracy.
期刊介绍：
The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes.
Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality.
The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.
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