AN ANALOGICAL METHOD ON FRACTAL DIMENSION FOR THREE-DIMENSIONAL FRACTURE TORTUOSITY IN COAL BASED ON CT SCANNING

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-08-02 DOI:10.1142/s0218348x2350072x

Gaofeng Liu, Zhen Zhang, Yunxing Cao, Xiaoming Wang, Huan Liu, Baolin Li, Nian Si, W. Guan

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.

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基于ct扫描的煤三维断裂弯曲分形维数模拟方法

在这项工作中，我们给出了一种估计三维断裂弯曲(3D-FT)分形维数的类比方法。本文对三维傅里叶变换分形维数的类比法和严格法进行了比较和误差分析。所提出的类比方法的3D- ft分形维数[公式:见文]是三维裂缝平均弯曲度([公式:见文])和平均裂缝长度([公式:见文])的函数。估算分形维数的类比方法([公式:见文])具有较高的精度，与严格的方法([公式:见文])具有良好的一致性。分形维数([公式:见文])从严密的方法上体现了[公式:见文]的物理意义。类比法得到的分形维数([公式:见文])在保证精度的前提下，计算起来比较方便。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

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.