RESEARCH ABOUT FAULT DIAGNOSIS OF BEARING BASED ON INSTRINSIC TIME SCALE DECOMPOSITION AND CONVOLUTIONAL NEURAL NETWORK by XIAO JunQing, YUE MinNan, LI Chun, JIN JiangTao, XU ZiFei, MIAO WeiPao

“…Therefore, based on the experimental data of bearing damage and the fractal theory, the Intrinsic Time scale Decomposition（ITD） was used to extract the nonlinear features of vibration signals, and the effective fault feature components were selected. …”
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Node-Gosper Curve-Based Unknown Sensor Localization Using Single Mobile Anchor in Wireless Sensor Networks by Chi-Chang Chen, Sheng-Bo Wang

“…The node-Gosper curve is a fractal space-filling curve constructed by recursively replacing each node by a seven-segment generator curve. …”
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Atypical EEG Responses to Nonverbal Emotionally Charged Stimuli in Children with ASD by Galina V. Portnova, Aleksandra V. Maslennikova

“…Sounds of crying and laughter induced an atypical EEG response in children with ASD, with no change in alpha-band’s power and frequency observed in them; this was contrary to the observation in TD children. The decrease in the fractal dimension detected in children with ASD only for sounds of crying and laughter correlated with the accuracy of assessment of these stimuli.…”
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A Novel Four-Wing Hyperchaotic Complex System and Its Complex Modified Hybrid Projective Synchronization with Different Dimensions by Jian Liu, Shutang Liu, Fangfang Zhang

“…Some dynamic properties of the system have been described including Lyapunov exponents, fractal dimensions, and Poincaré maps. More importantly, we focus on a new type of synchronization method of modified hybrid project synchronization with complex transformation matrix (CMHPS) for different dimensional hyperchaotic and chaotic complex systems with complex parameters, where the drive and response systems can be asymptotically synchronized up to a desired complex transformation matrix, not a diagonal matrix. …”
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Anomalous diffusion and factor ordering in (1+1)-dimensional Lorentzian quantum gravity by E. Sanderson, R.L. Maitra, A.J. Liberatore

“…By computing the mean squared displacement of a diffusing particle, we find that diffusion is anomalous, behaving similarly to that on a porous substrate, network, or fractal over short distances. The walk dimension of the path for a particle diffusing in quantized space is calculated to have an infimum of 4, rising to arbitrarily large values depending on a parameter labeling the choice of factor ordering in the quantum Hamiltonian for our model and figuring in the asymptotic behavior of the wavefunction used to construct the quantum heat kernel. …”
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NUMERICAL STUDY ON TORSIONAL FRETTING WEAR OF ROUGH SURFACE by LIU JinSheng, LIU Juan, SHEN HuoMing

“…Based on the three-dimensional W-M fractal function, a three-dimensional rough surface was bulidt by SOLIDWORKS, and then the three-dimensional ball-rough surface contact numerical model of torsional fretting with the energy wear law being introduced by the user subroutine UMESHMOTION was established by ABAQUS. …”
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Characteristic Changes of Scale Invariance of Seismicity Prior to Large Earthquakes: A Constructive Review by Qiang Li, Gui-Ming Xu

“…Our suggestion is that when people try to obtain the precursory information before large earthquakes or to study the fractal property of seismicity by means of the previous scale invariance methods, the strengths and weaknesses of these methods have to be taken into consideration for the purpose of increasing research efficiency. …”
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Analysis of the n-Term Klein-Gordon Equations in Cantor Sets by Nikhil Sharma, Sunil Joshi, Pranay Goswami

“…Considering these points, the paper also provides an accurate and effective method to solve complex physical systems that display fractal or self-similar behavior across various scales. …”
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Half-line kink scattering in the ϕ 4 model with Dirichlet boundary conditions by Jairo S. Santos, Fabiano C. Simas, Adalto R. Gomes

“…The simulations reveal a rich variety of phenomena in the field dynamics, such as the formation of a kink-antikink pair, the generation of oscillons by the boundary perturbations, and the interaction between these objects and the boundary, which causes the emergence of boundary-induced resonant scatterings (for example, oscillon-boundary bound states and kink generation by oscillon-boundary collision) founded into complex fractal structures. Linear perturbation analysis was applied to interpret some aspects of the scattering process. …”
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Azimuthal Anisotropy in High-Energy Nuclear Collision: An Approach Based on Complex Network Analysis by Susmita Bhaduri, Dipak Ghosh

“…Recently, a complex network based method of visibility graph has been applied to confirm the scale-freeness and presence of fractal properties in the process of multiplicity fluctuation. …”
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A Causal and Correlation Analysis between China Energy Futures and China Energy-Related Companies Stock Market by Yufang Liu, Chi Zhang, Wang Zhang

“…Subsequently, the source of fractal correlation was analysed with shuffled and surrogated sequences. …”
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Analytical Solutions of a Space-Time Fractional Derivative of Groundwater Flow Equation by Abdon Atangana, P. D. Vermeulen

“…Numerical solutions obtained via Adomian method are compared with the Barker generalized radial flow model for which a fractal dimension for the flow is assumed. Proposition for uncertainties in groundwater studies was given.…”
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Quantifying Optical Microangiography Images Obtained from a Spectral Domain Optical Coherence Tomography System by Roberto Reif, Jia Qin, Lin An, Zhongwei Zhi, Suzan Dziennis, Ruikang Wang

“…A technique for determining three measureable parameters (the fractal dimension, the vessel length fraction, and the vessel area density) is proposed and validated. …”
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Geometric Models for Isotropic Random Porous Media: A Review by Helmut Hermann, Antje Elsner

“…The methods presented are exemplified by applications: small-angle scattering of systems showing fractal-like behavior in limited ranges of linear dimension, optimization of nanoporous insulating materials, and improvement of properties of open-pore systems by atomic layer deposition of a second phase on the internal surface.…”
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Experimenting with twilight learnings and twilight writings for community engagement by Silvia Mugnaini, Åsa Ståhl, Leah Ireland

“…In this article, we show that a reflective community can start to emerge through sharing experiences and knowledges in a confined space that is simultaneously connected to society in a fractal scaling (O’Brien et al. 2023) way. Some of the participants grew so fond of reflecting together on hope, allies, uncertainties, pain and frustrations, that they continued to build the community by articulating themselves through follow-up interviews and through writing together in different ways. …”
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Effect of Recycled Bagasse on Cracking Behavior of Clay Materials by Wenlong Ma, Wenbo Liu, Yuanhang Wang, Binbin Yang

“…The cracks were extracted and calculated by digital image processing technology, and the crack characteristics of samples with different bagasse contents were studied by fractal dimension and crack entropy. The results show that when moisture content maintains 34%, the clay material forms only one main crack without bagasse, forms no crack with bagasse content of 9%, and forms a crack network with the bagasse content of 3%. …”
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A Collision Avoidance Method for Intelligent Ship Based on the Improved Bacterial Foraging Optimization Algorithm by Xingzhong Wang, Xinghua Kou, Jinfeng Huang, Xianchun Tan

“…An adaptive diminishing fractal dimension chemotactic step length is designed to replace the fixed step length to achieve the adaptive step length adjustment, an optimal swimming search method is proposed to solve the invalid searching and repeated searching problems of the traditional BFOA, and the adaptive migration probability is developed to take the place of the fixed migration probability to prevent elite individuals from being lost in BOFA. …”
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Wideband Polarization Conversion Metasurface for RCS Reduction of Antennas by Tao Hong, Ke Peng, Yue Gu, Wen Jiang, Shuxi Gong

“…A 3rd-order quadrate fractal structure (QFS) is designed as the PCM element that the polarization conversion ratio is greater than 80% from 10.45 GHz to 32.15 GHz (relative bandwidth of 101.9%). …”
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Modal Resonant Frequencies and Radiation Quality Factors of Microstrip Antennas by Jan Eichler, Pavel Hazdra, Miloslav Capek, Milos Mazanek

“…The chosen rectangular and fractal microstrip patch antennas above an infinite ground plane are analyzed by the theory of characteristic modes. …”
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A Single-Layer Dual-Band Reflectarray Cell for 5G Communication Systems by Sandra Costanzo, Francesca Venneri, Antonio Borgia, Giuseppe Di Massa

“…A reflectarray unit cell operating at 28/38 GHz is designed by adopting two pairs of miniaturized fractal patches, offering low losses (<0.7 dB) and almost full-phase ranges (≅320°) at both operating frequencies. …”
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