A Priori Assessment of Algebraic Flame Surface Density Models in the Context of Large Eddy Simulation for Nonunity Lewis Number Flames in the Thin Reaction Zones Regime by Mohit Katragadda, Nilanjan Chakraborty, R. S. Cant

“…The focus is on algebraic FSD models based on a power-law approach, and the effects of Lewis number on the fractal dimension D and inner cut-off scale ηi have been studied in detail. …”
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An Experimental Apparatus for Monitoring Radon during Compression of Coal/Rock Samples and Its Preliminary Application by Wei Zhang, Kaidi Xie, Yanchao Zhu, Yandong Zhang, Xu Duan, Jibo Zhu

“…Finally, suggestions for future research are proposed, including mathematical equations to express the correlations between different experimental parameters and fractal characteristics of radon release from porous media.…”
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Experimental Study on Dry Friction Damping Characteristics of the Steam Turbine Blade Material with Nonconforming Contacts by Jun Wu, Ruishan Yuan, Zhenwu He, Di Zhang, Yonghui Xie

“…The results show that the experimental result of the tangential contact stiffness is in good agreement with that of the theory result based on the fractal theory and the Hertz contact theory by Jiang et al., 2009. …”
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Numerical Investigation of Hydraulic Fracture Propagation Morphology in the Conglomerate Reservoir by Zehao Xu, Xiangjun Liu, Lixi Liang

“…This model was experimentally verified, and fractal theory was introduced to quantify the complexity of fracture morphology. …”
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Experimental Investigation into the Effects of Fracturing Fluid-Shale Interaction on Pore Structure and Wettability by Yan Zhang, Zhiping Li, Fengpeng Lai, Hao Wu, Gangtao Mao, Caspar Daniel Adenutsi

“…In this study, the pore structure and fluid distribution of shale samples were analyzed by utilizing low-pressure liquid nitrogen adsorption (LP-N2GA) and nuclear magnetic resonance (NMR). The fractal analysis showed that the pore structure of the sample was strongly heterogeneous. …”
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Effects of Thermal Treatment on Mineral Composition and Pore Structure of Coal by Bin Liu, Teng Teng, Zhenhua Jiao, Shaobo Li

“…Meanwhile, the volume of micropore increases first and then decreases during the process of thermal treatment. The fractal dimension of pore size ranges from 2.6 to 2.9 and increases linearly with the increasing temperature.…”
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A Systematic Method to Evaluate the Shear Properties of Soil-Rock Mixture considering the Rock Size Effect by Minghui Ren, Guangsi Zhao, Xianhao Qiu, Qinghua Xue, Meiting Chen

“…This paper proposes a systematic method to obtain the realistic shear strength of S-RM by detecting the rock size effect. Firstly, based on fractal theory, the rock size was determined as 5 mm by the multifractal property of granular size distribution. …”
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Micro- and Nanoscale Pore Structure Characterization of Carbonates from the Xiaoerbulake Formation in the Tarim Basin, Northwest China by Jingyi Wang, Qinhong Hu, Mengdi Sun, Zhongxian Cai, Cong Zhang, Tao Zhang

“…The structures (geometry and connectivity) of nm to μm-scale pore networks in outcrop samples of carbonates from Xiaoerbulake Formation in Tarim Basin of China were studied by using optical microscopy, field emission-scanning electron microscopy (FE-SEM), as well as mercury intrusion porosimetry (MIP) with fractal analyses of the data, and spontaneous imbibition tests (distilled water). …”
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Chaotic motion of particles in the spacetime of a Kerr black hole immersed in swirling universes by Deshui Cao, Lina Zhang, Songbai Chen, Qiyuan Pan, Jiliang Jing

“…Moreover, we observe clearly that, regardless of the spin parameter, there exist some self-similar fractal fine structures in the basins boundaries of attractors for the spacetime of a black hole immersed in swirling universes. …”
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Particle Flow Code Simulation of the Characteristics of Crack Evolution in Rock-Like Materials with Bent Cracks by Zhanguo Ma, Shixing Cheng, Peng Gong, Jun Hu, Yongheng Chen

“…Uniaxial compression generated tensile cracks in all the specimens with bent cracks, but in terms of failure mode, the specimens with 0 bend tended to suffer penetrating failure along the fracture strike, while the specimens with 1, 3, and 7 bend tended to suffer penetrating failure along the diagonal direction. Both the fractal dimension and bend number were positively correlated with strain; with the gradual increase of the stress percentage, the damage variable of the specimens gradually increased at a growing rate. …”
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Effect of Shale Sample Particle Size on Pore Structure Obtained from High Pressure Mercury Intrusion Porosimetry by Zhiye Gao, Longfei Duan, Qinhong Hu, Shuling Xiong, Tongwei Zhang

“…The amount and proportion of mercury retention during mercury extrusion process increase with the decrease of shale particle size, which is closely related to the increased ink-bottle effect in shale sample with smaller particle size. In addition, the fractal dimension of Barnett Shale is positively related to the particle size, which indicates that the heterogeneity of pore structure is stronger in shale sample with larger particle size. …”
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Morphology Effect of Surface Structures on Microchannel Flow Using Lattice Boltzmann Method by Ge Zhang, Bo Liu, Aiguo Xu, Yiming Shan, Yingjun Li

“…Further research is carried based on more complex channels with arrays of fractal-character artificial elements. As elements in the channel can be divided into main summits and subsummits, their different roles of the effect on the fluid flow is investigated. …”
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Gender equity as a key element for agroecological transitions: Neo‐rural women as managers of agroecological initiatives by Beatriz Vizuete, Marina García‐Llorente, Irene Pérez‐Ramírez, Elisa Oteros‐Rozas

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Study of Macro- and Mesodamage of Remolded Loess under Alternating Dry and Wet Conditions in an Acid Rain Environment by Wanjun Ye, Yuntao Wu, Yang Bai

“…At the microscopic level, the clay mineral particles among soil particles decrease in size, the contact mode between soil particles develops from stable to unstable, the particles are gradually rounded, and the fractal dimension decreases. Chemical erosion and physical erosion are special features of this experiment. …”
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Numerically pricing American and European options using a time fractional Black–Scholes model in financial decision-making by Omid Nikan, Jalil Rashidinia, Hossein Jafari

“…The time fractional Black–Scholes equation (TFBSE) is designed to evaluate price fluctuations within a correlated fractal transmission system. This model prices American or European put and call options on non-dividend-paying stocks. …”
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Analysis and Prediction of Grouting Reinforcement Performance of Broken Rock Considering Joint Morphology Characteristics by Guanglin Liang, Linchong Huang, Chengyong Cao

“…Given the significant influence of rock joint morphology on mechanical behavior, this study employs the frequency spectrum fractal dimension (D) and the frequency domain amplitude integral (Rq) as quantitative descriptors of joint morphology. …”
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Research on Seepage Characteristics of Y-Shaped Fractures under Different Fracture Roughness by Ruifeng Tang, Jing Xie, Shouning Xue, Zhilong Zhang, Junjun Liu, Bengao Yang

“…In this work, based on the W-M fractal function, a Y-shaped fracture model with different roughness is established. …”
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Mechanistic controls on permeability evolution in thermally-upgraded low-maturity oil shales: Application of machine learning outputs by Bo He, Lingzhi Xie, Xin Liu, Jun Liu, Derek Elsworth

“…Heating enhances permeability by increasing both the number and total cross-sectional area (SEM) of pores. Fractal dimensions indicate that the pore microstructure is anisotropic in the bedding-parallel and bedding-perpendicular directions and is upgraded by elevated temperature. …”
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Development of Porosity and Copper(II) Ion Adsorption Capacity by Activated Nano-Carbon Xerogels in Relation to Treatment Schemes by Badie S. Girgis, Mohamed N. Alaya, Iman Y. El-Sherif, Amina A. Attia, Nady A. Fathy

“…The samples were characterized by different techniques including CHO elemental analysis, transmission electron microscopy (TEM) and nitrogen adsorption studies at 77 K, with the data obtained in the latter case being analyzed using the BET equation and the α S -method, as well as the fractal dimension approach. The porosities of the obtained carbons were considerably enhanced by chemical activation (mostly within the micropore range), while steam activation promoted the porosities to a lesser extent. …”
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Experimental Study on the Property Degradation and Failure Mechanism of Weakly Cemented Sandstone under Dry-Wet Cycles by Zhaoyang Song, Lihui Sun, Shouye Cheng, Zhiqiang Liu, Jie Tan, Fangbo Ning

“…With an increase in the number of dry-wet cycles, the crack is mainly caused by the main crack penetration failure, and the secondary crack is significantly reduced. The fractal dimension decreases with an increase in the dry-wet cycles and reaches its maximum at 0 dry-wet cycles, which means that 0 dry-wet cycles witness the most complex morphology of fractures within the weakly cemented sandstone. …”
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