Search Results (143)

Not all particle-size fractions in widely graded granular materials contribute equally to compaction densification. For non-ideal particle-size distributions (PSDs) with local deviations or fine-end disturbances, the full-range fractal index may be influenced by particle-size fractions that contribute weakly to densification and, therefore, may not consistently represent the maximum dry density response. To address this problem, this study proposes a response-constrained truncation framework to identify a more effective PSD fitting range for fractal characterization. First, 20 concave and S-shaped PSDs from previous experiments were re-analyzed to compare full-range and truncated indices. Then, 21 progressively truncated specimens derived from three standard fractal PSDs were tested by relative density experiments. A unit-mass densification contribution coefficient, η_j, was defined from adjacent maximum dry density differences and particle-fraction mass contents. The η_j-d responses exhibited unimodal patterns, and the transition diameter d_c shifted with PSD coarseness. For the two material sources, replacing the full-range index with the truncated index increased the R² values between the fractal index and maximum dry density from 0.195 to 0.886 and from 0.191 to 0.856, respectively. A continuous percentile search showed that the optimal characteristic scale was concentrated near q ≈ 30, with a robust common optimum of q = 30.53. Sensitivity analysis for β = 0.85–0.95 indicated that 0.225d₃₀ falls within the transition region from highly effective filling to reduced densification efficiency. Accordingly, d_L = 0.225d₃₀ is proposed as a preliminary engineering estimate of the lower fitting limit for non-ideal PSDs. The framework is intended for widely graded materials whose full-range fractal parameters are inconsistent with compaction response. Full article

Population-based metaheuristic algorithms are widely used for multi-objective city evacuation planning, yet their opaque internal dynamics limit practitioner trust in safety-critical contexts. This study introduces, to the best of our knowledge, the first unified coupling of fractional calculus and fractal analysis with the EvoMapX process-level explainability framework in the context of evacuation optimization. In contrast with classical integer-order EvoMapX paired with exponential moving averages of operator credit, the proposed formulation embeds long-range memory directly into the explainability pipeline through Caputo and Grünwald–Letnikov derivatives. The Operator Attribution Matrix (OAM), Population Evolution Graph (PEG), and Convergence Driver Score (CDS) are extended with fractional-order formulations employing Caputo and Grünwald-Letnikov fractional derivatives with adaptive memory parameters, alongside Mittag–Leffler urgency escalation dynamics. A Fractional-Order PSO variant (FO-EPSO) with segment-specific fractional velocity updates and a fractal fitness landscape analysis module for adaptive parameter tuning are introduced. The framework incorporates nine evacuation-specific operators, a spatial OAM for zone-level attribution, and a multi-stakeholder explanation pipeline. Experiments across 520 disaster scenarios demonstrate that explainability and optimization performance are not mutually exclusive: the EvoMapX-integrated NSGA-II achieved a mean hypervolume of 0.731 versus 0.728 for the standard variant, with less than 5% computational overhead. The OAM revealed disaster-type-specific operator patterns invisible to conventional analysis. Real-world validations on Beijing Chaoyang District and Kigali, Rwanda, confirmed these findings. From an operational standpoint, the most consequential outcome of this work concerns its impact on human decision-makers: a controlled study with 45 emergency-management professionals showed that incorporating EvoMapX explanations cut the time required to commit to an evacuation plan by 24.9%, raised reported decision confidence by 20.3%, and lifted self-assessed algorithm understanding from 18.1% to 78.9% (all p < 0.001). Equally important for real-time disaster response, this entire layer of process-level transparency is delivered with a runtime penalty of under 5% relative to the non-explainable baselines, which we view as a key practical advantage for field deployment. This work establishes fractional-order process-level transparency as a feasible and beneficial paradigm for interpretable optimization in safety-critical domains. Full article

Resistivity is a key parameter in shale reservoir characterization. Diverse micro-pore types and complex conduction mechanisms in shale result in poor accuracy when applying existed conductivity models. Establishing a high-precision conductivity response model requires comprehensive consideration of the pore structure and clay-bound water conduction. The primary novelty of this work lies in replacing macroscopic empirical fitting parameters with a mechanistic, multi-dimensional fractal framework. We develop a novel conductivity response characterization model that explicitly couples multi-dimensional fractal pore structure theory with clay-bound water conduction. Experimental data verification demonstrates the new model’s superior characterization accuracy. Results indicate three distinct zones in the shale conductivity-pore water conductivity relationship: a nonlinear zone, a transition zone, and a linear zone. A higher cation exchange rate on clay surfaces leads to an increase in the nonlinear characteristics of the conductivity for both the shale and the pore water in low-salinity regions. An increase in the values of the conduction path fractal dimension, pore morphology fractal dimension, and pore fractal dimension all contribute to reduced shale conductivity. While sharing clay-induced conductivity terms with conventional dual-water and shale volume models, the new model offers advantages in operational simplicity and parameter accessibility. This research provides a physically rigorous and highly accessible approach for conductivity-based reservoir parameter calculation, offering new technical perspectives for complex shale oil/gas evaluation. Full article

Currently, China boasts abundant shale gas resources. However, in the process of flowing production, there remain significant discrepancies in our understanding of the flow patterns of gas and water, and many challenges persist in gas–water measurement. Given the dense pore structure and complex micro-features of shale gas reservoirs, this study proposes a method to estimate the fractal dimension by utilizing shale mercury injection curves based on experimentally determined relative permeability curves, thereby enabling a more accurate fitting of these curves. Experimental results show that the two-phase co-infiltration zone in the shale is narrow overall, with bound water saturation exceeding 50%. The findings indicate that the experimentally measured relative permeability curves closely match those fitted using the fractal dimension approach. Moreover, the lower the permeability, the more the equal-permeability points of the fitted curves shift toward the lower-right quadrant. Overall, the fitting performance is satisfactory, providing additional research directions and insights for determining relative permeability curves of gas and water in shale gas reservoirs. Full article

The efficient recovery of coalbed methane (CBM) is critically constrained by the inherent low permeability of coal reservoirs, a challenge predominantly attributed to mineral blockages within the pore-fracture structure. In this study, the deashing efficacy of several acid solutions (HCl, HNO₃, HF, and CH₃COOH) on bituminous coals from the Yushuwan (YSW) and Jiangna (JN) mines was initially assessed to determine the optimal acidizing system. Subsequently, the multi-scale evolution of pore-fracture structures and the fractal characteristics of coal samples treated with the optimized acids were systematically investigated. A multi-analytical approach, integrating scanning electron microscopy (SEM), X-ray diffraction (XRD) with microcrystalline peak-fitting, and low-temperature nitrogen gas adsorption (LT-N₂GA), was employed to quantitatively elucidate the underlying transformation mechanisms. The experimental results indicate that HCl and HNO₃ emerged as the most effective agents for the YSW and JN coals, respectively. Optimized acidification achieved significant reductions in ash content (specifically, an ash removal efficiency of 83.99% for HCl-treated YSW coal) through the selective dissolution of carbonate and clay minerals, thereby facilitating the exposure of the organic matrix and the induction of extensive dissolution pits and secondary fractures. Although the dissolution-induced collapse of mineral-supported fine pores led to a reduction in both total pore volume and BET specific surface area, the average pore diameter undergoes a substantial increase (e.g., nearly doubling from 9.0068 nm to 16.5126 nm for the JN coal). Furthermore, the reduction in Frenkel–Halsey–Hill (FHH) fractal dimensions (D₁ and D₂) indicates a decrease in pore-surface complexity and structural heterogeneity. These findings reveal that optimized acidification induces significant alterations in pore structure and mineral composition. The treatment facilitates the conversion of isolated pores into interconnected networks, accompanied by an increase in pore volume and a shift in pore size distribution toward larger dimensions. This research elucidates the mechanisms of mineral dissolution and pore expansion, providing a fundamental characterization of the microstructural evolution of coal in response to acid treatment. Full article

Tight sandstone reservoirs are characterized by highly heterogeneous pore structures, in which multiscale pore–throat systems jointly control the shapes of capillary pressure curves and relative permeability, thereby exerting a fundamental influence on water production behavior and the overall development performance of gas reservoirs. The Ordos Basin is generally characterized by the development of tight sandstone. The tight sandstones exhibit porosities of 2–13% and permeabilities of 0.01–10 × 10⁻³ μm². To quantitatively elucidate the controlling mechanisms of multiscale pore structure on capillary pressure curve morphology and relative permeability, this study systematically investigates the fractal and multifractal characteristics of pore structures in tight sandstones based on high-pressure mercury intrusion (MICP) and nuclear magnetic resonance (NMR) experimental data, and establishes a quantitative relationship between fractal parameters and the capillary pressure curve shape parameter λ. First, capillary pressure curves were fitted using the Brooks–Corey model within the effective saturation interval to extract the shape parameter λ, which characterizes the concentration degree of pore-size distribution and the drainage behavior. Subsequently, based on NMR T₂ spectra, the small-pore fractal dimension D₁, large-pore fractal dimension D₂, and the multifractal singularity spectrum width Δα were extracted to quantitatively describe the geometric complexity of pore structures at different scales. On this basis, the correlations between λ and D₁, D₂, and Δα were systematically analyzed, and the predictive performance of λ under different parameter combinations was compared. The results indicate that: (1) the pore structures of tight sandstones exhibit pronounced fractal and multifractal characteristics at the NMR T₂ scale, with significant differences among samples; (2) λ shows an overall negative correlation with fractal parameters, among which the correlations with the large-pore fractal dimension D₂ and the multifractal spectrum width Δα are the most significant; (3) compared with models using a single fractal dimension, the multiparameter model incorporating Δα provides a more comprehensive characterization of multiscale pore heterogeneity, leading to a substantial improvement in the accuracy and stability of λ prediction; and (4) λ exerts a clear control on the shape of relative permeability curves, where a larger λ corresponds to earlier initiation and forward-shifted rising segments of water-phase flow, while a smaller λ results in overall flatter relative permeability curves. From the perspectives of fractal and multifractal theory, this study establishes an intrinsic linkage among pore structure, capillary pressure curve shape parameters, and relative permeability, providing a novel quantitative framework for constraining relative permeability curve morphology in tight sandstones under conditions where systematic relative permeability experiments are unavailable. Full article

In this study, CT scanning technology was combined with ImageJ 1.54r and Avizo 3D 2022 professional image analysis software to quantify porosity. The aim was to reveal the intrinsic correlation between the pore structure characteristics and the macroscopic properties of vegetated concrete. A combination of 3D reconstruction, fractal analysis and multi-parameter regression modelling techniques was utilised to quantify the association between pore parameters and material properties. The mechanistic role of pore structure in regulating the strength–permeability trade-off relationship was elucidated. The results show that: (1) aggregate particle size and porosity are significantly negatively correlated with the compressive strength of vegetated concrete and strongly positively correlated with the water permeability coefficient, while the effects of both of them on the pH value of the material are negligible; (2) the porosity obtained by the image analysis method meets the design requirements of the target porosity, and the deviation between the computed 3D porosity from CT scanning and the 2D sliced porosity is less than 1%. The image analysis porosity is slightly lower than the measured value, a deviation within a reasonable range. (3) There is a robust positive correlation between the fractal dimension of the vegetated concrete structural surface and porosity. With increasing aggregate size, porosity gradually increases, pore network connectivity is significantly enhanced, and the fractal dimension increases correspondingly. (4) Function fitting analysis confirms that the correlation between the connected porosity and the compressive strength and permeability coefficient is more significant than that of the cross-sectional porosity. Specifically, compressive strength is significantly negatively correlated with equivalent pore size and fractal dimension, and the water permeability coefficient is strongly positively correlated with these two parameters. This study can provide important theoretical support and engineering reference for the optimization of the mix proportion and performance control of vegetated concrete. Full article

Characterizing full-scale pore-throat systems constitutes a critical challenge in the investigation of hydrocarbon-bearing spaces within tight unconventional reservoirs. Given the intricate nature of micro–nano-scale pore throats, individual characterization techniques are insufficient to achieve a comprehensive and precise description. In response, this study develops a Gaussian Mixture Model (GMM)-oriented methodology for full-scale pore-throat analysis integrating multi-source data, which encompasses five successive procedures: data optimization, optimal cluster number determination, model analysis, data fusion, and data reconstruction. Taking tight mixed-lithology samples from Block D of the Qaidam Basin as the research object, effective pore-throat thresholds were defined based on lithology-dependent breakdown pressures to facilitate cluster analysis of multi-source datasets. Following the screening of representative pore-throat clusters and data fusion via Gaussian Mixture functions, the full-scale pore-throat distribution was ultimately derived. Comparative analysis demonstrates that Nuclear Magnetic Resonance (NMR) and High-Pressure Mercury Intrusion (HPMI) data exhibit satisfactory fitting consistency at major cluster peaks, with NMR being more effective in resolving nanopores and HPMI excelling in characterizing medium to large pores. Comprehensive evaluation results validate that the proposed methodology enables efficient integration of multi-technical data, uncovers hidden pore-throat systems, and realizes innovative fractal dimension analysis of full-scale pore-throat structures by taking pore-throat clusters as the basic analytical unit. Consequently, this work offers a novel methodological framework for the quantitative characterization of full-scale pore-throats using multi-source data. Full article

Low-maturity shale is a prime target for in situ conversion (ICP), yet heating window selection remains largely empirical because pore evolution and hydrocarbon generation are rarely quantified in tandem. Nenjiang Formation shale from the Songliao Basin (TOC = 8.91%; R_o,max = 0.54%) was subjected to closed-system pyrolysis at 300–500 °C (20 °C h⁻¹; 72 h per step). Released oil and gas and residual chloroform-extractable bitumen (“A”) were quantified, and pore evolution was characterized using 2D low-field NMR, SEM, micro-CT, and low-pressure N₂ adsorption. Fractal dimensions (D_s and D_p) were derived from Frenkel–Halsey–Hill (FHH) fitting. Oil yield and bitumen “A” increased sharply above 350 °C and peaked at 375 °C, whereas gas generation accelerated above 400 °C and continued to increase to 500 °C. NMR indicates a temperature-dependent shift in retained hydrocarbons toward weaker confinement and higher mobility, with enhanced expulsion/mobility signals near 375 °C. At 375 °C, BJH pore volume and average pore diameter reached maxima (0.0675 cm³ g⁻¹ and 15.36 nm), while D_s and D_p reached minima (2.343 and 2.444). The coincidence of peak oil expulsion with minimum fractal complexity suggests that FHH-based fractal indices provide a quantitative metric for comparing ICP heating windows in low-maturity shale. Full article

Rock pore–fracture systems exhibit inherent fractal characteristics, which exert a significant influence on fluid transport. In this study, coal rock is selected as the representative medium. Based on fractional calculus in physical fractal space, and by integrating operator algebra with the force–electric analogy method, a fractional order control equation is derived. To validate the proposed model, porosity measurements of coal and limestone were performed using the two-compartment Boyle’s law method and compared with conventional porosity calculation approaches. The results demonstrate that the fractional order model achieves a coefficient of determination (R²) of up to 0.99 for porosity and 0.98 for pressure, representing an improvement of approximately 0.07 over the exponential model. Moreover, the root mean square error (RMSE) of porosity is as low as 0.0008, while the RMSE of pressure is 0.0715, both significantly lower than those obtained using the exponential model. These results indicate that the fractional order model more effectively captures the non-Darcy flow behavior and the temporal evolution of porosity, providing substantially improved fitting accuracy. Further analysis reveals that the porosity–time relationship is jointly governed by fluid compressibility and pore compressibility under effective stress conditions. Comparative results across different lithologies reveal that the pore compressibility coefficient increases with porosity; for the same rock type, a higher coefficient implies a more complex pore structure and a longer equilibration time. Overall, the proposed fractional order framework provides a more accurate description of the fractal pore structures in rocks, establishing a clear link between microscale fractal geometry and macroscale fractional order response. Full article

This paper uses the theory of self-affine fractal functions to model the dynamic flight graphs of starling flocks, integrating the fractional calculus of self-affine fractal functions to quantitatively characterize the intrinsic nonlinear dynamics and memory effects within the system, employing statistical inference methods to find the fractal fit for the images. The changes in box dimensions over time could characterize the phase transition process of the starling flight flocks. By analyzing the rate of change of fractal dimensions, we identify critical points corresponding to phase transitions during collective flight behavior. During the flight of the starling flocks, a real-time phase transition process for evading attacks and effective advancement has been identified. Experimental data confirms the effectiveness of controlling the phase transition. Full article

Nowadays, renewable energy sources are gaining importance, yet global energy demand is primarily met by burning fossil fuels. Fluctuations in fossil fuel availability, driven by geopolitical tensions, supply–demand changes, and natural disasters, can lead to sudden energy price spikes or supply shortages, adversely affecting the global economy. Despite its negative impact on carbon emissions and climate change, Heating Oil (HO) offers advantages over other fossil fuels in efficiency, reliability, and availability. Accurate time series prediction models for HO are crucial for stakeholders. This study proposes a novel hybrid model, integrating the Chaotic Adaptive Fitness-Distance Balance-based Stochastic Fractal Search (AFDB-SFS) algorithm with a Bidirectional Long-Short Term Memory (Bi-LSTM) network, for HO close price prediction. The dataset comprises daily observations of five financial time series (close, open, high, low, and volume) over 4260 trading days, yielding a total of 21,300 data points (4260 days × 5 variables). During the feature extraction stage, financial signal processing methods such as Demand Concentration Curve (DCC) and traditional technical indicators are utilized. A total of 189 features are extracted at appropriate intervals for each indicator. Due to the large number of features, the AFDB-SFS algorithm then efficiently identifies the most compatible feature subsets, optimizing the Bi-LSTM model based on three criteria: maximizing R², minimizing RMSE, and minimizing feature count. Experimental results demonstrate the proposed hybrid model’s superior performance, achieving high accuracy (R² of 0.9959 and RMSE of 0.0364), outperforming contemporary models in the literature. Furthermore, the model is successfully implemented on the Jetson Orin Nano Developer Platform, enabling real-time, high-frequency HO price predictions with ultra-low latency (1.01 ms for Bi-LSTM), showcasing its practical utility for edge computing applications in commodity markets. Full article

We construct a family of self-adjoint operators on the prime numbers whose entries depend on pairwise arithmetic divergences, replacing geometric distance with number-theoretic dissimilarity. The resulting spectra encode how coherence propagates through the prime sequence and define an emergent arithmetic geometry. From these spectra we extract observables such as the heat trace, entropy, and eigenvalue growth, which reveal persistent spectral compression): eigenvalues grow sublinearly, entropy scales slowly, and the inferred dimension remains strictly below one. This rigidity appears across logarithmic, entropic, and fractal-type kernels, reflecting intrinsic arithmetic constraints. Analytically, we show that for the unnormalized Laplacian, the continuum limit of its squared Hamiltonian corresponds to the one-dimensional bi-Laplacian, whose heat trace follows a short-time scaling proportional to $t^{-1/4}$. Under the spectral dimension convention $d_s=-2d\log \Theta /d\log t$, this result produces $d_s=1/2$ directly from first principles, without fitting or external hypotheses. This value signifies maximal spectral compression and the absence of classical diffusion, indicating that arithmetic sparsity enforces a coherence-limited, non-Euclidean geometry linking spectral and number-theoretic structure. Full article

In this study, the exhaust particulates of a diesel engine burning methanol/F-T diesel blends were collected. The nanostructure and oxidation reactivity of the particulates were explored using the Brunauer–Emmett–Teller (BET) method, high-resolution transmission electron microscope (HRTEM), and thermogravimetric analysis (TGA), and the relationship between them was assessed via the partial least squares (PLS) and variable importance in the projection (PLS-VIP). The results showed that particulates from methanol/F-T diesel combustion were aggregates composed of several primary particles, and the distribution range of particulate half pore width ($R$) was 8~76 nm. As the methanol mixture ratio increased, the mean $R$ of particulates decreased, and the particulates′ total pore volume ($V_p$), specific surface area ($S_{BET}$), and the fractal dimension ($D_f$) increased. Compared with F-T diesel, methanol/F-T diesel blends particulates showed more disordered structure with a smaller diameter ($d_p$) of primary particles, a shorter fringe length ($L_a$), a wider separation distance ($d$), and a larger tortuosity ($T_f$). With increasing the methanol mixture ratio, it was also found that the amount of soluble organic fraction (SOF) of particulates increased, while oxidation characteristic temperature and the apparent activation energy ($E_a$) reduced. The correlation coefficients of $E_a$ with $T_f$ and $D_f$ were 0.99 and 0.98, respectively, by the linear fitting, illustrating that they showed the strongest linear relationship with the reactivity among the discussed nanostructure parameters. The VIP values of $D_f$, $T_f$, $V_p$, and d, with $E_a$ obtained by the PLS and PLS-VIP, were greater than 1, indicating that they were the chief factors influencing particulate reactivity. Full article

The accurate determination of the soil-water characteristic curve (SWCC) and unsaturated hydraulic conductivity is vital across multiple disciplines, including hydrogeology, soil science and geotechnical engineering. Nevertheless, conventional techniques for measuring these unsaturated soil parameters are often laborious and time-consuming, posing significant practical challenges. This research presents a new technique for estimating SWCC and unsaturated hydraulic conductivity by employing fractal theory and utilizing a three-dimensional fractal dimension (D_s). The results revealed that all three soils exhibited fractal characteristics in their particle surfaces, with D_s values of 2.611 for Malan loess, 2.688 for paleosol, and 2.771 for remolded loess. The complexity of the pore structure was in the order of remolded loess > paleosol > Malan loess. The test results of the soil-water characteristic curve indicate that the water storage capacity of the three soils was in the order of paleosol > remolded loess > Malan loess. Compared with the Brooks-Correy fitting curve, the fractal model is feasible in predicting the soil-water characteristic curve. Two models were used to predict the unsaturated hydraulic conductivities of three types of soil, and the results were compared with the measured values. By comparing the R² and RMSE values of the fractal model and the Brooks-Corey model, it was found that the fractal model proposed in this paper can effectively predict the unsaturated hydraulic properties of these three types of soil. This study provides a simple and effective alternative for predicting the SWCC and unsaturated hydraulic conductivity of unsaturated soils, with potential applications in various earth science fields. Full article