The Seepage Evolution Mechanism of Variable Mass of Broken Rock in Karst Collapse Column under the Influence of Mining Stress by Li Xiao-Lei, Li Xin-Lei, Wang Yue, Peng Wei-Hang, Fan Xuan, Cao Zheng-Zheng, Liu Rui-Fu

“…The test samples are prepared based on the fractal theory and the Talbol grading theory, and the seepage evolution law of fractured rock in collapse column under triaxial stress is studied, by employing the triaxial seepage test equipment. …”
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Particle-Size Distribution Models for the Conversion of Chinese Data to FAO/USDA System by Wei Shangguan, YongJiu Dai, Carlos García-Gutiérrez, Hua Yuan

“…The soil data were converted to the USDA (United States Department of Agriculture) standard using PSD models and the fractal concept. The performance of PSD models was affected by soil texture and classification of fraction schemes. …”
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Multifractal-Multiscale Analysis of Cardiovascular Signals: A DFA-Based Characterization of Blood Pressure and Heart-Rate Complexity by Gender by Paolo Castiglioni, Davide Lazzeroni, Paolo Coruzzi, Andrea Faini

“…Detrended Fluctuation Analysis (DFA) is a popular method for assessing the fractal characteristics of biosignals, recently adapted for evaluating the heart-rate multifractal and/or multiscale characteristics. …”
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Graph-Based Analysis of RNA Secondary Structure Similarity Comparison by Lina Yang, Yang Liu, Xiaochun Hu, Patrick Wang, Xichun Li, Jun Wu

“…A combinational method involving a discrete wavelet transform (DWT) and fractal dimension with sliding window is introduced to analyze and compare the graphs derived from feature extraction; after that, the distance matrix is generated. …”
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An efficient way to represent the processors and their connections in omega networks by Savari Prabhu, T. Jenifer Janany, Paul Manuel

“…We also compare these parameters with those of other predominant interconnection networks, such as the butterfly, Beneš, and fractal cubic networks, and we observe that the omega network has significantly lower values for these parameters compared to the other networks.…”
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Modeling of Two-Phase Flow in Rough-Walled Fracture Using Level Set Method by Yunfeng Dai, Zhifang Zhou, Jin Lin, Jiangbo Han

“…The roughness of the two-dimensional synthetic rough-walled fractures is controlled with different fractal dimension parameters. Described by the Navier–Stokes equations, the moving interface between crude oil and water is tracked using level set method. …”
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Experimental Study on Mechanism of Graphene Oxide-Modified Coral Sand Cement Mortar to Resist Sulfate Erosion by Bin Chen, Jianlin Zhang, Yanlin Zhao, Yiwei Lu

“…There were more orderly pore arrangement with less morphological complexity, when the dissolution amount of Ca(OH)2, porosity, total pore area, pore number, probability entropy, average form factor, and fractal dimension decreased. Coral sand cement mortar increases resistance to sulfate attack, which graphene oxide inhibits the formation of new dissolution pores and the expansion of original pores.…”
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Deformation Failure Characteristics of Coal Body and Mining Induced Stress Evolution Law by Zhijie Wen, Guanglong Qu, Jinhao Wen, Yongkui Shi, Chuanyang Jia

“…All this indicates that the pore distribution of coal body with different compressed volume has fractal character; it appears to be the linear relationship between propagation range of internal stress field and compressed volume of coal body and nonlinear relationship between the range of outburst coal mass and the number of pores which is influenced by mining pressure. …”
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Effects of Continuous Positive Airway Pressure on Sleep EEG Characteristics in Patients with Primary Central Sleep Apnea Syndrome by Cheng Zhang, Kun Chen, Guangfa Wang, Jue Zhang, Jing Ma

“…The raw sleep EEG data were analyzed based on two main factors: fractal dimension (FD) and zero-crossing rate of detrended FD. …”
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Evolution and Influencing Factors of Township Spatial Form: A Two-Dimensional Perspective by Yanpeng Gao, Wenjun Chen

“…Assessing the spatial and temporal evolution of rural settlements contributes to the promotion of rural scientific developments. This study used the fractal theory, center-of-gravity model, and spatial syntax to analyze the spatial and temporal evolution of Shenyang Ciyutuo Subdistrict and its influencing factors based on geospatial data from 2009‒2019, from the perspectives of internal characteristics and external morphological changes. …”
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Experimental Investigation on Nonlinear Flow Anisotropy Behavior in Fracture Media by Chun Zhu, Xiaoding Xu, Xiuting Wang, Feng Xiong, Zhigang Tao, Yun Lin, Jing Chen

“…The fracture was assumed to be a self-affine surface, and its roughness and anisotropy were quantified by the fractal dimension. According to the flow tortuosity effect, the nonlinear flow was characterized by hydraulic tortuosity and surface tortuosity power law relationships based on Forchheimer’s law. …”
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Quantitative Analysis of the Topological Structure of Rock Pore Network by Dayu Ye, Guannan Liu, Ning Luo, Feng Gao, Xinmin Zhu, Fengtian Yue

“…However, the prevailing methods for characterising the microstructure of rocks, such as the coordination number method and fractal theory, are still difficult to quantify the structural properties. …”
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THE COMPILATION OF SHANNON ENTROPY MEASUREMENT EQUATION FOR NONLINEAR DYNAMIC SYSTEMS BY USING THE INTERVAL ANALYSIS METHODS by Yu. P. Machekhin, Yu. S. Kurskoy

“…It’s proposed to use the fractal, entropic and temporal scales as tools for evaluation of a systems state. …”
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Continuous 1D single crystal growth with high aspect ratio by oriented aggregation of dendrite by Quan Wan, Maoqi Li, Yuhao Zhou, Meng Zhang, Zongpu Xu, Jie Wang, Yajun Shuai, Shuxu Yang, Mingying Yang

“…Here, we find that continuous 1D growth of crystals can be achieved during dendrite formation, where the fractal dendrite crystal growth intrinsically restricts side broadening. …”
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Identification of key regulators in pancreatic ductal adenocarcinoma using network theoretical approach. by Kankana Bhattacharjee, Aryya Ghosh

“…It was found that the PDAC network self-organizes into a scale-free fractal state with weakly hierarchical organization. …”
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Scale Effect on the Anisotropy of Acoustic Emission in Coal by Honghua Song, Yixin Zhao, Yaodong Jiang, Jiehao Wang

“…The TRFD and its anisotropy reduce as the specimen size increases, and the reduction of fractal dimension is most pronounced at the anisotropic angle of 45°. …”
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Human Development IX: A Model of the Wholeness of Man, His Consciousness, and Collective Consciousness by Søren Ventegodt, Tyge Dahl Hermansen, Trine Flensborg-Madsen, Erik Rald, Maj Lyck Nielsen, Joav Merrick

“…These phenomena are explained based on the concept of deep quantum chemistry and infinite dancing fractal spirals making up the energetic backbone of the world. …”
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A Study on Community Unit Scale Construction in China Under the Orientation of Green Production by Rui Zhang, Qingjian Zeng, Yanhang Lv, Huanjie Liu, Lixian Shi, Yukun Zhang

“…Ultimately, a quadratic optimization scale was devised for community units at varying levels based on fractal and management unit theory. This paper presents a new community unit scale constructed for use in large- and medium-sized areas in China, which serves as an illustrative example. …”
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An Experimental Study on the Microstructures of Cemented Paste Backfill during Its Developing Process by Bo Zhang, Jie Xin, Lang Liu, Lijie Guo, Ki-Il Song

“…The characteristics including pore size, pore shape, and orientation of the microstructures of CPB at different curing times were analyzed based on the SEM images. The porosity, fractal dimension, and probability entropy were characterized using the Particles and Pore Recognition and Analysis System (PPRAS). …”
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Study on the effect of acid fracturing fluid on pore structure of middle to high rank coal by Zhao Kang, Li Liangwei, Li Kun, Zuo Shaojie, Jiang Zhizhong

“…The new micropores produced by the acid fracturing fluid will increase the roughness of the fracture surface, but the widening of the original fracture will reduce the tortuosity of the fracture. Only the fractal dimension of lean coal has a significant change, about 6%. …”
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