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21 pages, 1881 KB  
Article
Geometry-Driven Hydraulic Behavior of Pressure-Compensating Emitters for Water-Saving Agricultural Irrigation Systems
by Mohamed Ghonimy, Abdulaziz Alharbi, Nermin S. Hussein and Hisham M. Imam
Water 2026, 18(2), 244; https://doi.org/10.3390/w18020244 - 16 Jan 2026
Viewed by 198
Abstract
Water-saving agricultural irrigation systems depend heavily on the hydraulic stability of pressure-compensating (PC) emitters, whose performance is fundamentally shaped by internal flow-path geometry. This study analyzes six commercial PC emitters (E1E6) operated under pressures of 0.8–2.0 bar [...] Read more.
Water-saving agricultural irrigation systems depend heavily on the hydraulic stability of pressure-compensating (PC) emitters, whose performance is fundamentally shaped by internal flow-path geometry. This study analyzes six commercial PC emitters (E1E6) operated under pressures of 0.8–2.0 bar to quantify how key geometric descriptors influence hydraulic parameters critical for efficient water use, including actual discharge (qact), discharge coefficient (k), pressure exponent (x), emission uniformity (EU), and flow variability. All emitters had discharge deviations within ±7% of nominal values. Longer and more tortuous labyrinths enhanced compensation stability, while emitters with wider cross-sections and shorter paths produced higher throughput but weaker regulation efficiency. Linear mixed-effects modeling showed that effective flow area increased k, whereas normalized path length and tortuosity reduced both k and x. Predictive equations derived from geometric indicators closely matched measured values, with deviations below ±0.05 L/h for k and ±0.05 for x. These results establish a geometry-based hydraulic framework that supports emitter selection and design in water-saving agricultural irrigation, aligning with broader Agricultural Water–Land–Plant System Engineering objectives and contributing to more efficient and sustainable water-resource utilization. Full article
(This article belongs to the Special Issue Agricultural Water-Land-Plant System Engineering, 2nd Edition)
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14 pages, 1241 KB  
Article
Intermittency Analysis in Heavy-Ion Collisions: A Model Study at RHIC Energies
by Jin Wu, Zhiming Li and Shaowei Lan
Symmetry 2026, 18(1), 138; https://doi.org/10.3390/sym18010138 - 9 Jan 2026
Viewed by 142
Abstract
Large density fluctuations near the QCD critical point can be probed via intermittency analysis, which involves measuring scaled factorial moments (SFMs) of multiplicity distributions in relativistic heavy-ion collisions. Intermittency reflects the emergence of scale invariance and self-similar structures, which are closely related to [...] Read more.
Large density fluctuations near the QCD critical point can be probed via intermittency analysis, which involves measuring scaled factorial moments (SFMs) of multiplicity distributions in relativistic heavy-ion collisions. Intermittency reflects the emergence of scale invariance and self-similar structures, which are closely related to symmetry principles and their breaking near a second-order phase transition. We present a systematic model study of intermittency for charged hadrons in Au+Au collisions at sNN = 7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV. Using the cascade UrQMD model, we demonstrate that non-critical background effects can produce sizable SFMs and a large scaling exponent if they are not properly removed using the mixed-event subtraction method. To estimate the possible critical intermittency signal in experimental data, we employ a hybrid UrQMD+CMC model, in which fractal critical fluctuations are embedded into the UrQMD background. A direct comparison of the second-order SFM between the model and STAR experimental data suggests that a critical intermittency signal on the order of approximately 1.8% could be present in the most central Au+Au collisions at RHIC energies. This study provides practical guidance for evaluating background contributions in intermittency measurements and offers a quantitative estimate for the critical signal fraction present in the STAR data. Full article
(This article belongs to the Section Physics)
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16 pages, 5550 KB  
Article
Prediction of Hole Expansion Rate for V-Nb Bainitic High-Strength Steel
by Chuangwei Wang, Feilong Wang, Yonggang Mao, Liangyun Wang, Jie Yu, Jun Li and Huarong Qi
Materials 2025, 18(23), 5369; https://doi.org/10.3390/ma18235369 - 28 Nov 2025
Viewed by 351
Abstract
The hole expansion process of high-strength steel is influenced by multiple factors, including the deformation path, UTS/YS ratio, uniform elongation, sheet anisotropy, sheet thickness, strain rate, material micro-defects and the work hardening exponent. Based on forming limit curves or instability criteria, the prediction [...] Read more.
The hole expansion process of high-strength steel is influenced by multiple factors, including the deformation path, UTS/YS ratio, uniform elongation, sheet anisotropy, sheet thickness, strain rate, material micro-defects and the work hardening exponent. Based on forming limit curves or instability criteria, the prediction of the hole expansion ratio (HER) often requires extensive initial boundary conditions that complicate the result. In this study, V-Nb bainitic steel was subjected to hot continuous rolling and underwent water quenching with different coiling temperatures, then subsequently followed by thermal simulation and mechanical testing to fit the work hardening exponent (n) and to obtain the necking deformation instability curve. The radial displacement at the hole edge during simulation was predicted with the ratio of ultimate tensile strength to fracture strength. Furthermore, based on the tensile fracture failure criterion, the HER was predicted with the true fracture strain derived from uniaxial tensile tests. Comparison between the simulated results and actual hole expansion tests shows that the crack resistance in the post-uniform stage, strain hardening capacity and deformation compatibility between the microstructure and matrix are critical factors. And the proposed model achieves a prediction accuracy of over 85% for the V-Nb bainitic high-strength steel. Full article
(This article belongs to the Section Metals and Alloys)
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19 pages, 385 KB  
Article
Thermodynamics of Fluid Elements in the Context of Turbulent Isothermal Self-Gravitating Molecular Clouds in Virial Equilibrium
by Sava D. Donkov, Ivan Zhivkov Stefanov and Valentin Kopchev
Universe 2025, 11(12), 383; https://doi.org/10.3390/universe11120383 - 21 Nov 2025
Viewed by 329
Abstract
In this paper, we continue the study of the thermodynamics of fluid elements in isothermal turbulent self-gravitating systems, presented by molecular clouds. We build the model again on the hypothesis that, locally, the turbulent kinetic energy per fluid element can be substituted for [...] Read more.
In this paper, we continue the study of the thermodynamics of fluid elements in isothermal turbulent self-gravitating systems, presented by molecular clouds. We build the model again on the hypothesis that, locally, the turbulent kinetic energy per fluid element can be substituted for the macro-temperature of a gas of fluid elements. Also, we presume that the cloud has a fractal nature. The virial theorem is applicable to our system too (hence it is in a dynamical equilibrium). But, in contrast to the previous work, where the turbulent kinetic energy clearly dominates over the gravity, in the present paper, we assume that the virial relation 2Ekin+Egrav=0 holds for the entire cloud. Hence, the cloud is a dense and strongly self-gravitating object. On that basis, we calculate the internal and the total energy per fluid element. Writing down the first principle of thermodynamics, we obtain the explicit form of the entropy increment. It demonstrates untypical behavior. In the range 0β<0.4, for the turbulent scaling exponent, the entropy increment is positive, but in the interval 0.4<β1, it is negative, and for βcr=0.4, it is zero. The latter two regimes (negative and zero) cannot be explained from the classical point of view. However, we give some arguments for the reasons for these irregularities, and the main is that our cloud is an open self-organizing system driven by the gravity. Moreover, we study the system for critical points under the conditions of three thermodynamic ensembles: micro-canonical, canonical, and grand canonical. Only the canonical ensemble exhibits a critical point, which is a maximum of the free energy and corresponds to an unstable equilibrium of the system. Analysis of the equilibrium potentials also shows that the system resides in unstable states under all the conditions. We explain these results by prompting the hypothesis that the virialized cloud is in the final unstable state before its contraction and subsequent fragmentation or collapse. Full article
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13 pages, 6602 KB  
Article
Deep Learning of the Biswas–Chatterjee–Sen Model
by José F. S. Neto, David S. M. Alencar, Lenilson T. Brito, Gladstone A. Alves, Francisco Welington S. Lima, Antônio M. Filho, Ronan S. Ferreira and Tayroni F. A. Alves
Entropy 2025, 27(11), 1173; https://doi.org/10.3390/e27111173 - 20 Nov 2025
Viewed by 390
Abstract
We investigate the critical properties of kinetic continuous opinion dynamics using deep learning techniques. The system consists of N continuous spin variables in the interval [1,1]. Dense neural networks are trained on spin configuration data generated via [...] Read more.
We investigate the critical properties of kinetic continuous opinion dynamics using deep learning techniques. The system consists of N continuous spin variables in the interval [1,1]. Dense neural networks are trained on spin configuration data generated via kinetic Monte Carlo simulations, accurately identifying the critical point on both square and triangular lattices. Classical unsupervised learning with principal component analysis reproduces the magnetization and allows estimation of critical exponents. Additionally, variational autoencoders are implemented to study the phase transition through the loss function, which behaves as an order parameter. A correlation function between real and reconstructed data is defined and found to be universal at the critical point. Full article
(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics, Third Edition)
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13 pages, 6025 KB  
Article
The Magnetocaloric Properties and Critical Behavior of (Gd4Co3)100−xGex Rapidly Quenched Alloys
by Xichun Zhong, Yaxiang Wu, Haongya Yu and Zhongwu Liu
Metals 2025, 15(11), 1267; https://doi.org/10.3390/met15111267 - 19 Nov 2025
Viewed by 609
Abstract
Gd4Co3 is a promising magnetocaloric material with a high magnetic entropy value. However, it undergoes a first-order magnetic transition, which hinders practical applications. Hence, (Gd4Co3)100−xGex (x = 5, 10, 15) were studied to [...] Read more.
Gd4Co3 is a promising magnetocaloric material with a high magnetic entropy value. However, it undergoes a first-order magnetic transition, which hinders practical applications. Hence, (Gd4Co3)100−xGex (x = 5, 10, 15) were studied to obtain high magnetic entropy values and a second-order magnetic transition. To investigate the effects of Ge addition on the thermal stability, magnetocaloric properties, and critical behavior of Gd4Co3-based alloys, (Gd4Co3)100−xGex (x = 5, 10, 15) melt spun ribbons were prepared. Phase analysis showed these alloys are mainly amorphous, with a minority nanocrystalline phase. All alloys undergo a second-order ferromagnetic-to-paramagnetic transition. The Curie temperature (TC) increases linearly from 211 K (x = 5) to 217 K (x = 15) with increasing Ge content. Under a magnetic field variation of 5 T, the alloys with x = 5, 10, and 15 exhibit peak magnetic entropy change (−ΔSM) values of 7.15, 6.83, and 6.71 J/(kg·K), respectively, along with considerable refrigerant capacity (RC) in the range of 435–458 J/kg. These excellent magnetocaloric properties collectively demonstrate their great potential for magnetic refrigeration applications. Critical behavior analysis revealed critical exponents broadly consistent with mean-field theory (MFT, β = 0.5, γ = 1.0, δ = 3.0), indicating nanocrystals in the amorphous matrix induce long-range magnetic interactions. Full article
(This article belongs to the Special Issue Metallic Magnetic Materials: Manufacture, Properties and Applications)
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32 pages, 4892 KB  
Article
A Multivariate AI-Driven Generalized Framework for Structural Load Prediction of Monopile Used for Offshore Wind Turbines Under Non-Linear Wind and Wave Conditions
by Sajid Ali, Muhammad Hassaan Farooq Khan and Daeyong Lee
J. Mar. Sci. Eng. 2025, 13(11), 2154; https://doi.org/10.3390/jmse13112154 - 14 Nov 2025
Cited by 1 | Viewed by 379
Abstract
Predicting structural loads on offshore wind turbine support structures under varying environmental conditions is a complex yet critical task, particularly for large-capacity turbines such as the 15 MW offshore wind turbine. Current prediction methods often struggle with accuracy, especially for torsional moments, due [...] Read more.
Predicting structural loads on offshore wind turbine support structures under varying environmental conditions is a complex yet critical task, particularly for large-capacity turbines such as the 15 MW offshore wind turbine. Current prediction methods often struggle with accuracy, especially for torsional moments, due to the non-linear interactions between wind parameters and structural responses. To address this challenge, present study develops a generalized load estimation framework using multivariable polynomial regression, leveraging 10,000 numerical simulations. The framework accounts for four critical variables: Extreme Wind Speed (30 to 40 m/s), Turbulence Intensity (12% to 16%), Flow Inclination Angle (−8° to +8°), and Shear Exponent (0.1 to 0.3). The proposed equations predict six key moment components at the tower base, including the bending moments about the y-axis, torsional moments about the z-axis, bending moments in the x-y, x-z, and y-z planes, and the resultant combined moment. The framework was validated using 2000 testing data points, achieving high accuracy with R2 values exceeding 0.92 for all moments. Specifically, the prediction accuracy was highest for the resultant combined moment and y-z bending moment, with average absolute errors of 5.76% and 5.97%, respectively, while x-z bending moment had a slightly higher error of 13.91%, highlighting that torsional moments are inherently more challenging to predict. Heatmap and scatter plot analyses confirmed that the predicted moments align closely with the simulated values, particularly for the torsional moment about the z-axis and y-z bending moment, with standard deviation values as low as 4.85. By optimizing polynomial degrees between 2 and 4, the framework effectively balances prediction accuracy and computational efficiency. This approach provides engineers and scientists with a reliable tool for load estimation, facilitating improved design and analysis of offshore wind turbine support structures. Full article
(This article belongs to the Section Ocean Engineering)
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22 pages, 3753 KB  
Article
A High-Precision Hybrid Floating-Point Compute-in-Memory Architecture for Complex Deep Learning
by Zizhao Ma, Chunshan Wang, Qi Chen, Yifan Wang and Yufeng Xie
Electronics 2025, 14(22), 4414; https://doi.org/10.3390/electronics14224414 - 13 Nov 2025
Viewed by 1240
Abstract
As artificial intelligence (AI) advances, deep learning models are shifting from convolutional architectures to transformer-based structures, highlighting the importance of accurate floating-point (FP) calculations. Compute-in-memory (CIM) enhances matrix multiplication performance by breaking down the von Neumann architecture. However, many FPCIMs struggle to maintain [...] Read more.
As artificial intelligence (AI) advances, deep learning models are shifting from convolutional architectures to transformer-based structures, highlighting the importance of accurate floating-point (FP) calculations. Compute-in-memory (CIM) enhances matrix multiplication performance by breaking down the von Neumann architecture. However, many FPCIMs struggle to maintain high precision while achieving efficiency. This work proposes a high-precision hybrid floating-point compute-in-memory (Hy-FPCIM) architecture for Vision Transformer (ViT) through post-alignment with two different CIM macros: Bit-wise Exponent Macro (BEM) and Booth Mantissa Macro (BMM). The high-parallelism BEM efficiently implements exponent calculations in-memory with the Bit-Separated Exponent Summation Unit (BSESU) and the routing-efficient Bit-wise Max Finder (BMF). The high-precision BMM achieves nearly lossless mantissa computation in-memory with efficient Booth 4 encoding and the sensitivity-amplifier-free Flying Mantissa Lookup Table based on 12T Triple Port SRAM. The proposed Hy-FPCIM architecture achieves 23.7 TFLOPS/W energy efficiency and 0.754 TFLOPS/mm2 area efficiency, with 617 Kb/mm2 memory density in 28 nm technology. With almost lossless architectures, the proposed Hy-FPCIM achieves an accuracy of 81.04% in recognition tasks on the ImageNet dataset using ViT, representing a 0.03% decrease compared to the software baseline. This research presents significant advantages in both accuracy and energy efficiency, providing critical technology for complex deep learning applications. Full article
(This article belongs to the Special Issue Emerging Computing Paradigms for Efficient Edge AI Acceleration)
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36 pages, 12082 KB  
Article
Comparative Study of Oscillator Dynamics Under Deterministic and Stochastic Influences with Soliton Robustness Darboux Transformations and Chaos Transition
by Maham Munawar, Adil Jhangeer and Mudassar Imran
Computation 2025, 13(11), 263; https://doi.org/10.3390/computation13110263 - 7 Nov 2025
Cited by 1 | Viewed by 555
Abstract
This paper presents a comprehensive study of nonlinear wave and oscillator dynamics under both deterministic and stochastic influences. By comparing soliton-like and dispersive waveforms, we employ spectral solvers, Darboux transformations, and nonlinear diagnostics, including Lyapunov exponents, power spectral analysis, and multidimensional phase-space reconstructions, [...] Read more.
This paper presents a comprehensive study of nonlinear wave and oscillator dynamics under both deterministic and stochastic influences. By comparing soliton-like and dispersive waveforms, we employ spectral solvers, Darboux transformations, and nonlinear diagnostics, including Lyapunov exponents, power spectral analysis, and multidimensional phase-space reconstructions, to examine transitions from quasiperiodic motion to chaotic and stochastic regimes. The results highlight the robustness of soliton solutions in preserving energy and structure, in contrast to the degradation observed in dispersive waves under noise and damping. We also show that spectral broadening, entropy growth, and ergodic phase-space patterns are caused by the critical influence of initial conditions and noise intensity on system behavior. Incorporating control strategies such as OGY chaos control, this work provides a flexible framework for analyzing, modeling, and stabilizing nonlinear systems. Applications span nonlinear optics, fluid flows, and electrical lattices, offering insight into the interplay of nonlinearity and noise with implications for both theoretical understanding and practical system design. Full article
(This article belongs to the Section Computational Engineering)
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37 pages, 25662 KB  
Article
A Hyperspectral Remote Sensing Image Encryption Algorithm Based on a Novel Two-Dimensional Hyperchaotic Map
by Zongyue Bai, Qingzhan Zhao, Wenzhong Tian, Xuewen Wang, Jingyang Li and Yuzhen Wu
Entropy 2025, 27(11), 1117; https://doi.org/10.3390/e27111117 - 30 Oct 2025
Viewed by 574
Abstract
With the rapid advancement of hyperspectral remote sensing technology, the security of hyperspectral images (HSIs) has become a critical concern. However, traditional image encryption methods—designed primarily for grayscale or RGB images—fail to address the high dimensionality, large data volume, and spectral-domain characteristics inherent [...] Read more.
With the rapid advancement of hyperspectral remote sensing technology, the security of hyperspectral images (HSIs) has become a critical concern. However, traditional image encryption methods—designed primarily for grayscale or RGB images—fail to address the high dimensionality, large data volume, and spectral-domain characteristics inherent to HSIs. Existing chaotic encryption schemes often suffer from limited chaotic performance, narrow parameter ranges, and inadequate spectral protection, leaving HSIs vulnerable to spectral feature extraction and statistical attacks. To overcome these limitations, this paper proposes a novel hyperspectral image encryption algorithm based on a newly designed two-dimensional cross-coupled hyperchaotic map (2D-CSCM), which synergistically integrates Cubic, Sinusoidal, and Chebyshev maps. The 2D-CSCM exhibits superior hyperchaotic behavior, including a wider hyperchaotic parameter range, enhanced randomness, and higher complexity, as validated by Lyapunov exponents, sample entropy, and NIST tests. Building on this, a layered encryption framework is introduced: spectral-band scrambling to conceal spectral curves while preserving spatial structure, spatial pixel permutation to disrupt correlation, and a bit-level diffusion mechanism based on dynamic DNA encoding, specifically designed to secure high bit-depth digital number (DN) values (typically >8 bits). Experimental results on multiple HSI datasets demonstrate that the proposed algorithm achieves near-ideal information entropy (up to 15.8107 for 16-bit data), negligible adjacent-pixel correlation (below 0.01), and strong resistance to statistical, cropping, and differential attacks (NPCR ≈ 99.998%, UACI ≈ 33.30%). The algorithm not only ensures comprehensive encryption of both spectral and spatial information but also supports lossless decryption, offering a robust and practical solution for secure storage and transmission of hyperspectral remote sensing imagery. Full article
(This article belongs to the Section Signal and Data Analysis)
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15 pages, 2809 KB  
Article
La3+/Bi3+ Co-Doping in BaTiO3 Ceramics: Structural Evolution and Enhanced Dielectric Properties
by María Inés Valenzuela-Carrillo, Miguel Pérez-Labra, Francisco Raúl Barrientos-Hernandez, Antonio Romero-Serrano, Irma Mendoza-Sanchez, Alejandro Cruz-Ramírez, Mizraim U. Flores, Martín Reyes-Pérez and Julio C. Juárez-Tapia
Processes 2025, 13(11), 3426; https://doi.org/10.3390/pr13113426 - 25 Oct 2025
Viewed by 949
Abstract
La3+/Bi3+ co-doped BaTiO3 ceramics were synthesized via ball milling followed by heat treatment at 1200 °C according to the Ba1−3xLa2xTi1−3xBi4xO3 formula, with dopant levels ranging from x = 0.0 to [...] Read more.
La3+/Bi3+ co-doped BaTiO3 ceramics were synthesized via ball milling followed by heat treatment at 1200 °C according to the Ba1−3xLa2xTi1−3xBi4xO3 formula, with dopant levels ranging from x = 0.0 to 0.006. X-ray diffraction and Rietveld refinement confirmed a ferroelectric tetragonal phase for all compositions, with the highest tetragonality (c/a = 1.009) observed for x = 0.001 exceeding that of pure BaTiO3 (1.0083). High-resolution electron microscopy analysis revealed faceted particles with mean sizes between 362.5 nm and 488.3 nm. Low-doped samples (x = 0.001 and 0.002) exhibited higher permittivity than undoped BaTiO3, with the maximum dielectric constant (εr = 2469.0 at room temperature and 7499.7 at the Curie temperature) recorded for x = 0.001 at 1 kHz. At x = 0.006, minimal permittivity variation indicated a stable dielectric response. A decrease in the Curie temperature was observed with increasing doping levels, indicating a progressive tendency toward the cubic phase. Critical exponent γ values (0.94–1.56) indicated a sharp phase transition for low-doped samples and a diffuse transition for highly doped BaTiO3. These results showed that La3+/Bi3+ co-doping effectively tunes the structural and dielectric properties of BaTiO3 ceramics. Full article
(This article belongs to the Special Issue Microstructure Properties and Characterization of Metallic Material)
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21 pages, 6725 KB  
Article
Microstructure-Dependent Creep Mechanisms in Heat-Treated CZ1 Zr Alloy at 380 °C
by Haoyu Shi, Jianqiang Wang, Meiqing Chen, Pengliang Liu, Zhixuan Xia, Chenyang Lu, Rui Gao, Weiyang Li, Yujie Zhang, Zhengxiong Su and Jing Hu
Nanomaterials 2025, 15(21), 1624; https://doi.org/10.3390/nano15211624 - 24 Oct 2025
Viewed by 620
Abstract
This study investigates the stress-dependent creep behavior of a CZ1 Zr alloy exhibiting two distinct microstructural states induced by different annealing treatments. Creep tests were conducted at 380 °C under applied stresses of 140 MPa and 260 MPa. CZ1-2 (fully recrystallized), characterized by [...] Read more.
This study investigates the stress-dependent creep behavior of a CZ1 Zr alloy exhibiting two distinct microstructural states induced by different annealing treatments. Creep tests were conducted at 380 °C under applied stresses of 140 MPa and 260 MPa. CZ1-2 (fully recrystallized), characterized by coarse grains and low dislocation density, demonstrated superior creep resistance under low stress due to suppressed dislocation activity and diffusion-dominated deformation. Stress exponent analysis revealed n = 5 for CZ1-1 (partially recrystallized) and n = 10 for CZ1-2, confirming a mechanism transition from steady-state dislocation climb to power-law breakdown. TEM characterization provided direct evidence of evolving dislocation networks, stacking faults, and second-phase particle redistribution. These findings underscore the critical role of microstructural conditioning in governing creep pathways and provide a mechanistic basis for tailoring Zr alloys to stress-specific service environments in advanced nuclear applications. Full article
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23 pages, 3512 KB  
Review
Advances in the Application of Fractal Theory to Oil and Gas Resource Assessment
by Baolei Liu, Xueling Zhang, Cunyou Zou, Lingfeng Zhao and Hong He
Fractal Fract. 2025, 9(10), 676; https://doi.org/10.3390/fractalfract9100676 - 20 Oct 2025
Viewed by 841
Abstract
In response to the growing complexity of global exploration targets, traditional Euclidean geometric and linear statistical methods reveal inherent theoretical limitations in characterizing hydrocarbon reservoirs as complex geological bodies that exhibit simultaneous local disorder and global order. Fractal theory, with its core parameter [...] Read more.
In response to the growing complexity of global exploration targets, traditional Euclidean geometric and linear statistical methods reveal inherent theoretical limitations in characterizing hydrocarbon reservoirs as complex geological bodies that exhibit simultaneous local disorder and global order. Fractal theory, with its core parameter systems such as fractal dimension and scaling exponents, provides an innovative mathematical–physics toolkit for quantifying spatial heterogeneity and resolving the multi-scale characteristics of reservoirs. This review systematically consolidates recent advancements in the application of fractal theory to oil and gas resource assessment, with the aim of elucidating its transition from a theoretical concept to a practical tool. We conclusively demonstrate that fractal theory has driven fundamental methodological progress across four critical dimensions: (1) In reservoir classification and evaluation, fractal dimension has emerged as a robust quantitative metric for heterogeneity and facies discrimination. (2) In pore structure characterization, the theory has successfully uncovered structural self-similarity across scales, from nanopores to macroscopic vugs, enabling precise modeling of complex pore networks. (3) In seepage behavior analysis, fractal-based models have significantly enhanced the predictive capacity for non-Darcy flow and preferential migration pathways. (4) In fracture network modeling, fractal geometry is proven pivotal for accurately characterizing the spatial distribution and connectivity of natural fractures. Despite significant progress, current research faces challenges, including insufficient correlation with dynamic geological processes and a scarcity of data for model validation. Future research should focus on the following directions: developing fractal parameter inversion methods integrated with artificial intelligence, constructing dynamic fractal–seepage coupling models based on digital twins, establishing a unified fractal theoretical framework from pore to basin scale, and expanding its application in low-carbon energy fields such as carbon dioxide sequestration and natural gas hydrate development. Through interdisciplinary integration and methodological innovation, fractal theory is expected to advance hydrocarbon resource assessment toward intelligent, precise, and systematic development, providing scientific support for the efficient exploitation of complex reservoirs and the transition to green, low-carbon energy. Full article
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23 pages, 1965 KB  
Article
Multifractality and Its Sources in the Digital Currency Market
by Stanisław Drożdż, Robert Kluszczyński, Jarosław Kwapień and Marcin Wątorek
Future Internet 2025, 17(10), 470; https://doi.org/10.3390/fi17100470 - 13 Oct 2025
Cited by 1 | Viewed by 743
Abstract
Multifractality in time series analysis characterizes the presence of multiple scaling exponents, indicating heterogeneous temporal structures and complex dynamical behaviors beyond simple monofractal models. In the context of digital currency markets, multifractal properties arise due to the interplay of long-range temporal correlations and [...] Read more.
Multifractality in time series analysis characterizes the presence of multiple scaling exponents, indicating heterogeneous temporal structures and complex dynamical behaviors beyond simple monofractal models. In the context of digital currency markets, multifractal properties arise due to the interplay of long-range temporal correlations and heavy-tailed distributions of returns, reflecting intricate market microstructure and trader interactions. Incorporating multifractal analysis into the modeling of cryptocurrency price dynamics enhances the understanding of market inefficiencies. It may also improve volatility forecasting and facilitate the detection of critical transitions or regime shifts. Based on the multifractal cross-correlation analysis (MFCCA) whose spacial case is the multifractal detrended fluctuation analysis (MFDFA), as the most commonly used practical tools for quantifying multifractality, we applied a recently proposed method of disentangling sources of multifractality in time series to the most representative instruments from the digital market. They include Bitcoin (BTC), Ethereum (ETH), decentralized exchanges (DEX) and non-fungible tokens (NFT). The results indicate the significant role of heavy tails in generating a broad multifractal spectrum. However, they also clearly demonstrate that the primary source of multifractality encompasses the temporal correlations in the series, and without them, multifractality fades out. It appears characteristic that these temporal correlations, to a large extent, do not depend on the thickness of the tails of the fluctuation distribution. These observations, made here in the context of the digital currency market, provide a further strong argument for the validity of the proposed methodology of disentangling sources of multifractality in time series. Full article
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22 pages, 3290 KB  
Article
Influence of Surface Complexity and Atmospheric Stability on Wind Shear and Turbulence in a Peri-Urban Wind Energy Site
by Wei Zhang, Elliott Walker and Corey D. Markfort
Energies 2025, 18(19), 5211; https://doi.org/10.3390/en18195211 - 30 Sep 2025
Viewed by 837
Abstract
The large-scale deployment of wind energy underscores the critical need for accurate resource characterization to reduce uncertainty in power estimates and to enable the installation of wind farms in increasingly complex terrains. Accurate wind resource assessment in peri-urban and moderately complex terrains remains [...] Read more.
The large-scale deployment of wind energy underscores the critical need for accurate resource characterization to reduce uncertainty in power estimates and to enable the installation of wind farms in increasingly complex terrains. Accurate wind resource assessment in peri-urban and moderately complex terrains remains a significant challenge due to spatial heterogeneity in surface terrain features and atmospheric thermal stability. This study investigates the influence of surface complexity and atmospheric stratification on vertical wind profiles at a utility-scale wind turbine site in Cedar Rapids, Iowa. One year of multi-level wind data from a 106-meter-tall meteorological tower were analyzed to quantify variations in the wind shear exponent α, wind direction veer, and horizontal turbulence intensity (TI) across open-field and complex-surface wind sectors and four thermal stability classes, defined by the bulk Richardson number Rib. The results show that the wind shear exponent α increases systematically with atmospheric stability. Over the open-field terrain, α ranges from 0.11 in unstable conditions to 0.45 in strongly stable conditions, compared to 0.17 and 0.40 over the complex surface. A pronounced diurnal variation in α was observed, particularly during the summer months. Wind veer was greatest and exceeded 30° under strongly stable conditions over open terrain. Elevated TI values peaked at 32 m in height due to flow separation and wake turbulence from nearby vegetation and sloping terrain. These findings highlight the importance of incorporating terrain-induced and thermally driven variability into wind resource assessments to improve power prediction and turbine siting in complex heterogeneous terrain environments. Full article
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