Semianalytical Model for Flow Behavior Analysis of Unconventional Reservoirs with Complex Fracture Distribution by Dayou Shi, Zhengyuan Lu

“…The smaller the fractal dimension of the secondary fracture spacing is, the smaller the dimensionless flow rate will be. …”
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Study on the Failure Mechanism of Lower Cambrian Shale under Different Bedding Dips with Thermosolid Coupling by Wentao Wang, Zhonghu Wu, Huailei Song, Hengtao Cui, Yili Lou, Motian Tang, Hao Liu

“…The larger the fractal dimension was, the greater the crack rate of the specimen. …”
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Study on the Relationship between Fracture Morphology and Splitting Strength of Granite Based on Fabric Distribution by GuangSheng Du, ShiJiang Chen, Xiaoyi Chen, Yunfeng Gao, Hailong Wu

“…The relationship between strength, the fractal value of cross-section, and the fabric was analyzed, which was verified through experiment. …”
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The Meso-Analysis of the Rock-Burst Debris of Rock Similar Material Based on SEM by Manqing Lin, Lan Zhang, Xiqi Liu, Yuanyou Xia, Jiaqi He, Xiaosu Ke

“…It was found that the fractal dimensions of the crystal contours of the specimen’s detrital section had fractal characteristics, and the box-counting dimension based on the SEM image could quantitatively describe the rock-burst failure characteristics. …”
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Multifractal Framework Based on Blanket Method by Milorad P. Paskaš, Irini S. Reljin, Branimir D. Reljin

“…This paper proposes two local multifractal measures motivated by blanket method for calculation of fractal dimension. They cover both fractal approaches familiar in image processing. …”
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Construction of a Multimodal Neuroimaging Data Fusion System and Evaluation of Mental Fatigue Using Nonlinear Analysis by Rui Chen, Zhenzhong Li, Yi Lai

“…The state of human brain fatigue will make the brain function network more complicated. The fractal dimension with more network edges is around 2.2, while the fractal dimension with fewer network edges is around 1.6. …”
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Julia Sets and Their Control of Discrete Fractional SIRS Models by Miao Ouyang, Yongping Zhang

“…It is of crucial significance to study infectious disease phenomenon by using the discrete SIRS model with the Caputo deltas sense and fractal viewpoint. In this paper, Julia set of the discrete fractional SIRS model is established to analyze the fractal dynamics of this model. …”
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The Constitutive Model of Rockfill Based on Property-Dependent Plastic Potential Theory for Geomaterials by Xuefeng Li, Ruijie Li, Junhui Zhang, Qi Wang

“…According to the effect of the particle grading and crushing on the fractal dimension, the fractal theory and fabric tensor were introduced to establish the yield and failure criteria of the rockfill. …”
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The Dynamic Three-Dimensional Localization of Fields in Active Percolating Systems by Gennadiy Burlak

“…In such a system, the incipient percolating cluster generates a fractal radiating structure in which the field is radiated and scattered by the anisotropic inhomogeneity. …”
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Similarity Solution for Fractional Diffusion Equation by Jun-Sheng Duan, Ai-Ping Guo, Wen-Zai Yun

“…Fractional diffusion equation in fractal media is an integropartial differential equation parametrized by fractal Hausdorff dimension and anomalous diffusion exponent. …”
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Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions by Kasey Bray, Jerry Dwyer, Roger W. Barnard, G. Brock Williams

“…The dynamical systems of trigonometric functions are explored, with a focus on tz=tanz and the fractal image created by iterating the Newton map, Ftz, of  tz. …”
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Effect of Salt Content on the Evaporation and Cracking of Soil from Heritage Structures by Kai Cui, Xiaozheng Zhao, Mingming Hu, Chen Yang, Guanchang Xie

“…When 0%, 1%, 2%, and 4% NaCl are added, the residual water content of the samples is 3.15%, 4.23%, 4.82%, and 5.89%, respectively, which show an obvious trend of increasing water content; (2) the period with a stable fracture fractal dimension of the samples is shortened with an increase in NaCl concentration, and its maximum fractal dimension is reduced in turn; and (3) at a lower water content, NaCl crystallizes and precipitates in the pores of the soil, which provide a cementitious effect among the soil particles, thus inhibiting crack development.…”
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Analysis of Uniaxial Compression Mechanical Properties of Rubber Powder Recycled Coarse Aggregate Concrete Based on Strain Energy Theory by Lei Wang, Hailong Wang

“…Based on the strain energy theory, fractal theory, and grey correlation theory, the effects of the fractal dimension of the pore size of the rubber powder recycled concrete on the correlation of the strain energy parameters were investigated at different curing ages. …”
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Experimental Study on Dynamic Compression Characteristics of Red Sandstone under Wetting-Drying Cycles by Bin Du, Haibo Bai, Minglei Zhai, Shixin He

“…After different wetting-drying cycles, the fractal characteristics of red sandstone dynamic fragmentation were obvious, and the fractal dimension was 2.02–2.80, and the fractal dimension increased logarithmically with the strain rate. …”
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Effects of Turbulent Reynolds Number on the Performance of Algebraic Flame Surface Density Models for Large Eddy Simulation in the Thin Reaction Zones Regime: A Direct Numerical Si... by Mohit Katragadda, Nilanjan Chakraborty, R. S. Cant

“…A parameterisation of the fractal dimension is presented in which the effects of the Reynolds and the Karlovitz numbers are explicitly taken into account. …”
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Laboratory Investigation on Particle Breakage Characteristics of Calcareous Sands by Qingsheng Chen, Wan Peng, Ronghu Yu, Gaoliang Tao, Sanjay Nimbalkar

“…Einav’s relative breakage and fractal dimension were used as the particle breakage indices. …”
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Fractais em sala de aula: uma experiência com papel e tesoura, computador e espelho by Emerson Luiz Pereira, Rúbia Barcelos Amaral Zulatto

“…Na sequência, com um software educativo, Geometricks, visualizaram mais níveis de iteração deste fractal. Por fim, os alunos foram convidados, com uso de espelhos, a encontrar simetrias neste fractal. …”
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Shear-Dependent Yield Stress of Iron Ore Fine Tailings in Two-Step Flocculation Process by Ying Yang, Hongjiang Wang, Bern Klein, Aixiang Wu

“…Therefore, in the secondary broken phase, with the increase of shear, the decrease of yield stress, the floc strength factor, and fractal dimension were less obvious than that in the primary broken phase. …”
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Study on the Effect of Soft and Hard Coal Pore Structure on Gas Adsorption Characteristics by Xun Zhao, Tao Feng, Ping Wang, Ze Liao

“…We used box dimension algorithm to measure the fractal dimension and distribution of coal sample microstructure. …”
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The Correlation between Pore Structure and Macro Durability Performance of Road Concrete under Loading and Freeze-Thaw and Drying-Wetting Cycles by Sheng-bo Zhou, Jun-lin Liang, Wei-an Xuan, Ye Qiu

“…A negative correlation is shown between strength and fractal dimension and most probable pore size. Conversely, a positive correlation is shown between strength, porosity, and less harmful pore. …”
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