Search Results (3,860)

Understanding the evolution of coal pore–fracture structures under coupled stress paths and creep deformation is critical for enhancing coalbed methane extraction and preventing coal and gas outbursts. In this study, coal samples from the Ningtiaota Mine were investigated using online Nuclear Magnetic Resonance (NMR) technology combined with triaxial loading–creep coupled experiments. The dynamic evolution of pore–fracture structures (PFSs) under different deviatoric stress levels was characterized and visualized in real time and across multiple scales. The results reveal a pronounced stress-dependent pore evolution during creep. Under low-stress conditions, seepage pores were compressed and gradually transformed into adsorption pores, whereas under high-stress conditions, seepage pores expanded and interconnected, dominating deformation and failure. Fractal theory was employed to quantify pore structure complexity, and repeated experiments demonstrated a significant positive correlation between the fractal dimension and the fractional order. Based on these findings, a fractal-dimension-based fractional creep model was developed by introducing a Riemann–Liouville fractional dashpot. The proposed model accurately captures the nonlinear creep behavior of coal and provides a microstructural interpretation of the fractional order. This study provides theoretical and experimental support for long-term stability assessment of deep coal–rock masses and prediction of coalbed methane migration. Full article

In this article, we present a new approximate solution for blood nanofluid having gold nanoparticles as it flows near a stretching porous cylinder in fractal space. A Casson non-Newtonian magneto-bio-nanofluid flowing through a porous medium is considered a potential application in chemotherapy for eradicating cancer cells. Without the need for the nonperturbative approach, the proposed solution uses an alternative approach to dealing with nonlinear problems. This approach transforms the nonlinear cubic jerk model resulting from the simplification of the governing fractional partial differential equations into an equivalent linear formula. This approach is known as highly efficient linear approximation (HELA) or non-perturbation technique (NPT), and this represents a significant advancement over traditional perturbation methods in the analysis of non-linear systems. As a robust mathematical approach, it excels at handling a wide range of coefficient values, particularly in cases of clear nonlinearity. This study also utilized the masking technique simultaneously with HELA, which played a crucial role, as they simplify the complex dynamics of the system, making it more amenable to analysis. The numerical solution by the Runge–Kutta fourth-order (RK-4) method integrated with a shooting technique compared favorably with graphs drawn for the analytical solution from the proposed strategy HELA. The current results show that an increase in the fractal factors enhances the resistance to fluid motion, leading to a suppression of the velocity field. Physically, this often relates to the complexity of the medium or the fractal nature of the transport process, where higher fractal dimensions or factors can lead to slower diffusion or flow rates, like the role of porous media. Therefore, the current study has significant implications in the promotion of nanotechnology fields in medicine, particularly the use of gold nanoparticles in chemotherapy for the eradication of cancerous cells. Full article

We report the fabrication and electrochemical characterization of TiO₂-based impedimetric sensors for the analysis of artificial sweat compositions. Two-electrode topologies were patterned on indium tin oxide (ITO) substrates: an interdigitated electrode (IDE) configuration and a Hilbert fractal electrode (HFE) geometry. TiO₂ thin films with thickness up to 350 nm were deposited by dip-coating and evaluated as photoactive sensing layers. The impedimetric response of the sensors was investigated by electrochemical impedance spectroscopy in artificial sweat with composition varied in terms of ionic content (0–100 mM Na⁺) and organic content (2.5–30 mM lactic acid and 5–50 mM urea). Regardless of TiO₂ thickness, the high-frequency response is predominantly governed by electrode topology, with the HFE design exhibiting up to 2.5-fold higher modulation compared to the IDE configuration. Under UV illumination, a low-frequency, photo-assisted response emerges, influenced by the TiO₂ layer thickness and primarily sensitive to the organic components of the solution, particularly lactic acid. These results suggest that frequency-resolved impedance measurements in TiO₂|ITO structures may enable partial differentiation between ionic conductivity and organic contributions in sweat, providing a promising basis for multi-parameter sweat analysis. Full article

Moderate thermal exposure can significantly influence the mechanical behavior of volcanic rocks by inducing microcrack development and altering crack network characteristics. However, quantifying such damage processes remains challenging when relying solely on conventional mechanical parameters. In this study, the evolution of crack network complexity in andesite and andesitic–basaltic rocks subjected to moderate thermal exposure (200 °C) is investigated using fractal analysis integrated with mechanical and mineralogical observations. Six core specimens were tested under uniaxial compression, including three natural specimens and three specimens thermally treated at 200 °C prior to loading. After failure, crack surfaces were digitized and fractal dimensions (D) were calculated using the box-counting method. Petrographic observations and X-ray powder diffraction (XRPD) analyses were conducted to characterize the mineralogical composition and microstructural features controlling crack development. The results indicate that thermal exposure primarily reduces rock stiffness rather than peak strength. While the uniaxial compressive strength (UCS) of two specimens remains nearly unchanged after heating, the elastic modulus (E) decreases in all thermally treated specimens. Mineralogical observations reveal a heterogeneous volcanic fabric dominated by plagioclase and pyroxene within a fine-grained groundmass, with secondary calcite phases occurring in veins and pocket fillings. Fractal analysis shows generally lower D values in thermally treated specimens, suggesting crack redistribution and coalescence rather than increased network complexity, consistent with the observed reduction in stiffness and a tendency toward more ductile deformation behavior. Full article

Assouad-type dimensions primarily describe the local structure of sets and have attracted significant attention in recent years within the field of fractal geometry. In this paper, we derive a formula for the Assouad dimension and establish an upper bound for the lower dimension for homogeneous Moran sets under the condition ${sup}_{k\ge 1}\left\{n_k\right\}<+\infty$. We also present formulas for the Assouad spectrum and the lower spectrum of Cantor-like sets. Our results generalize some results in the references. Full article

With the rapid growth of digital image transmission, ensuring data security has become increasingly important. However, existing chaos-based image encryption algorithms often suffer from insufficient chaotic randomness and weak integration between chaotic dynamics and encryption mechanisms. To address these issues, a novel image encryption scheme based on a two-dimensional hyperbolic–exponential Sine–Logistic map (2D-HESLM) is proposed. A Sierpiński carpet-inspired scrambling strategy and a cascaded diffusion mechanism are designed to enhance permutation and diffusion performance based on the 2D-HESLM. The experimental results show that the information entropy value is 7.9980, while NPCR and UACI are approximately averaged 99.6147% and 33.4672%, respectively, with correlation coefficients close to zero. These results demonstrate the effectiveness and security of the proposed scheme. Full article

Vitamin D plays an important role in bone metabolism and may influence postoperative healing processes. This study evaluated the association between preoperative serum vitamin D levels and recovery after mandibular third molar extraction. This secondary exploratory analysis included 122 healthy patients undergoing surgical extraction of an impacted mandibular third molar, of whom 98 had complete datasets for clinical and radiographic evaluation. Postoperative outcomes included pain intensity, facial swelling, trismus, early soft tissue healing assessed with the Wachtel Early Healing Index, and bone regeneration evaluated four months after surgery using CBCT-based fractal dimension analysis. Serum vitamin D levels were not significantly associated with postoperative pain, trismus, or early soft tissue healing. A weak correlation was observed between lower vitamin D levels and greater swelling along the tragus–pogonion line on postoperative day 1 (ρ = −0.21, p = 0.035), with no significant associations at later time points. Fractal dimension analysis did not demonstrate significant differences between groups. Within the limitations of this secondary exploratory analysis, vitamin D levels showed limited and inconsistent associations with postoperative outcomes, and their clinical relevance remains uncertain. Full article

The present study proposes a fractal-inspired multiscale framework to interpret the structural, thermal, mechanical and dielectric properties of polylactic acid (PLA). Experimental investigations were performed using tensile testing, TG-DTA thermal analysis, X-ray diffraction (XRD) and dielectric spectroscopy. The structural organization was analyzed using XRD data, where a scaling tendency compatible with power-law behavior was identified over a limited $\mathrm{q}$-range. The thermal degradation exhibited a sharp transition, while the mechanical and dielectric responses reflected the heterogenous behavior typical of semicrystalline polymers. Rather than claiming a fully validated fractal model, the present work introduces a conceptual multiscale interpretation, supported by experimental observations, and proposes a fractal integrity index (FII) as an exploratory descriptor integrating structural, thermal and mechanical information. The results suggest that fractal-based descriptors may provide a useful complementary framework for interpreting complex polymer behavior, although further validation across multiple materials and experimental conditions is required. Full article

High-alkali coal can cause slagging and fouling and impact the operational lifespan of the boilers. Traditional single-indicator methods often yield inconsistent results when evaluating the slagging risk of high-alkali coal. In this study, six coal samples were selected and systematically analyzed for their slagging characteristics using scanning electron microscopy (SEM), X-ray fluorescence (XRF), X-ray diffraction (XRD), and ash morphology analysis. Furthermore, a comprehensive evaluation model was constructed by integrating the technique for order preference by similarity to ideal solution (TOPSIS) with the entropy weight method. Additionally, based on images of ash morphology, the fractal dimension (D) was introduced as a quantitative indicator to predict slagging tendency through crack characteristics. The results show that TF, ZD, and KB samples, which are rich in alkaline oxides (CaO, Fe₂O₃, Na₂O, K₂O), form low-melting-point eutectic silicates during combustion, resulting in significant melting and agglomeration with wide cracks between aggregates, indicating a strong slagging tendency. Their fractal dimensions (D) range from 1.81 to 1.92. In contrast, HM and WQ samples, dominated by SiO₂ and Al₂O₃, form high-melting-point mullite and quartz, showing loose ash morphology with uniformly distributed cracks and a weak slagging tendency, with D values of 1.68 and 1.75, respectively. A significant negative correlation was observed between D and the E-TOPSIS model (y = 3.54 − 1.72x). Therefore, fractal analysis allows for rapid assessment of slagging risk without the need for complex chemical testing. This study provides valuable insights for predicting the slagging tendency of high-alkali coal during combustion. Full article

Accurate tail risk forecasting in emerging markets is frequently compromised by the nonlinear dynamics and time-varying long memory of high-frequency volatility. In this study, we employ multifractal detrended fluctuation analysis (MF-DFA) to decode the complex market behavior, revealing pronounced multifractality and strong persistence that defy the static assumptions of classical linear models. The multifractal analysis is only used for research motivation and model design, not as input features for the model. To bridge the gap between fractal diagnostics and predictive modeling, we propose an attention-based dynamically reweighted SA-HAR-J-Net framework. This architecture uniquely integrates HAR-style multi-horizon inputs with a bidirectional LSTM (BiLSTM) encoder and a temporal self-attention mechanism. Crucially, the attention module functions as a dynamic reweighting system, allowing the model to adaptively emphasize historical patterns that receive higher attention weights under changing market conditions, thereby mimicking the time-varying correlations inherent in multifractal processes. Furthermore, we incorporate jump proxies and realized higher moments to enhance the capture of extreme tail dynamics. Utilizing a strict expanding-window out-of-sample protocol, the proposed method achieves significantly lower quantile loss and superior calibration relative to established econometric and machine learning benchmarks for Value-at-Risk (VaR) forecasting. This work provides a robust framework for tail risk monitoring by effectively aligning deep learning architectures with the stylized facts of multifractal markets. Full article

Accurate regional ocean forecasting requires models that are both computationally efficient and capable of representing predictive uncertainty. This work investigates ensemble learning strategies for sea surface temperature (SST) forecasting using Graph Neural Networks (GNNs), with a focus on how input perturbation design affects forecast skill and uncertainty representation. We adapt a GNN architecture to the Canary Islands region in the North Atlantic and implement a homogeneous ensemble approach inspired by bagging, where diversity is introduced during inference by perturbing initial ocean states rather than retraining multiple models. Several noise-based ensemble generation strategies are evaluated, including Gaussian noise, Perlin noise, and fractal Perlin noise, with systematic variation of noise intensity and spatial structure. Ensemble forecasts are assessed over a 15-day horizon using deterministic metrics (RMSE and bias) and probabilistic metrics, including the Continuous Ranked Probability Score (CRPS) and the Spread–skill ratio. The results show that, while deterministic skill remains comparable to the single-model forecast, the type and structure of input perturbations influence uncertainty representation, particularly at longer lead times. Ensembles generated with spatially coherent perturbations, such as low-resolution Perlin noise, achieve improved calibration and lower CRPS compared to purely random Gaussian perturbations. These findings highlight the role of noise structure and scale in ensemble GNN design, indicating that specifically structured input perturbations can improve ensemble diversity and calibration without additional training cost. These results provide a methodological contribution toward the study of ensemble-based GNN approaches for regional ocean forecasting. Full article

Hot-filament chemical vapor deposition (HFCVD) facilitates the realization of industrial mass production owing to its simple synthesis device, facile control of process conditions, and low preparation cost. Reactive pressure is one of the deposition parameters that exert a profound influence on the growth of HFCVD diamond films on polycrystalline diamond (PCD) substrates, primarily affecting the growth rate and grain size of the deposited diamond coating. A univariate experimental approach was employed to investigate the effects of reactive pressure (2 kPa, 3 kPa, 4 kPa, 5 kPa) on the properties of as-deposited diamond films. The results show that with the increase in reactive pressure, the growth rate increased first and then decreased, peaking at 5.366 μm/h at 3 kPa. The fractal dimension and grain size follow a similar variation trend, both decreasing first and then increasing. The grain size drops to 15.8 nm when the reactive pressure is 3 kPa, at which point the adhesive strength of the film is maximized. This phenomenon can be attributed to the fact that excessively low reactive pressure extends the mean free path of particles and active species, endowing them with higher kinetic energy and reducing collision-induced energy loss. This in turn significantly promotes diamond nucleation, secondary nucleation and grain refinement, thus facilitating the growth of nanocrystalline diamond. In contrast, an excessively high pressure yields the opposite effect, inhibiting nucleation and promoting grain coarsening. Full article

The complex surface architecture of natural oyster reefs is widely considered to promote biological attachment, yet the underlying mechanisms and the relevance to the design of artificial reefs are not fully understood. Here, we combined field experiments, 3D surface characterization, and numerical modelling to quantify how reef-like roughness regulates biofouling development and near-wall flow around artificial substrates. Surface morphological characteristics of natural oyster reefs were first obtained by 3D scanning and used to fabricate concrete panels with simulated rough textures, while traditional smooth concrete panels served as controls. The two types of panels were simultaneously deployed in the target sea area for a hanging-panel experiment. Samples were collected after 3, 6, 9, and 12 months to track changes in biofouling communities. At each sampling time, the panel surfaces were quantified by canopy roughness ($R_C$), surface heterogeneity ($\sigma$), and fractal dimension ($D$), and these metrics were integrated into numerical simulations combined to resolve the flow field, turbulence kinetic, and near-wall shear stress around the colonized panels. The research results show that, after 12-month immersion, the mean thickness of the biofouling layer on rough and control panels reached 6.39 mm and 5.91 mm, respectively. Rough panels exhibited consistently higher $R_C$ and $\mathsf{\sigma }$ than controls, and these two parameters are strongly linearly correlated ($R^2=0.891)$. Numerical simulations reveal that increased $R_C$ enlarges the oyster settlement shear-stress window (OSSW), indicating more favorable hydrodynamic conditions for oyster settlement and growth on rough panels. Nevertheless, the hydrodynamic differences between the initial rough panels and control panels gradually diminish over time, suggesting that biological growth can progressively naturalize initially smooth substrates. These findings advance the mechanistic understanding of how small-scale roughness and biofouling co-evolve to shape oyster habitat quality and provide a quantitative basis for the eco-engineering design of artificial oyster reefs. Full article

This study addresses a two-dimensional anomalous solute transport process within a two-zone fractal porous medium. A mathematical formulation is developed to characterise transport phenomena in a non-homogeneous porous domain. The medium consists of two interacting regions: one containing mobile fluid and the other containing immobile fluid, between which mass transfer occurs. In the mobile-fluid region, solute transport is governed by the convection–diffusion equation. In contrast, the immobile-fluid region is described using a first-order kinetic model. The problem of solute injection through a designated boundary point is formulated and numerically implemented. The effects of anomalous transport behaviour on solute migration and filtration characteristics are examined. The study further evaluates the pressure field, filtration velocity distribution, and solute concentration in both zones. Full article

In this paper, we study the dynamical analysis and solutions of the fractional Benjamin–Bona–Mahony–Burger equation. We demonstrate various derived solutions using different definitions of fractional derivatives, namely the $\beta$-derivative, conformable derivative, and M-truncated derivative, to examine their kinetic characteristics. Firstly, we find the solution of the fractional Benjamin–Bona–Mahony–Burger equation using two different approaches. We then discuss the effects of the fractional derivative on the solutions using 3D graphical discussion. Finally, we discuss the dynamical analysis using sensitivity and chaos analysis. We also discuss the chaos analysis using permutation entropy, 2D and 3D phase portrait, fractal dimension, time analysis, return map, Lyapunov exponent, and multistability through Poincare map and basins of attraction. To explore a diverse range of phenomena across the fields of physical science and engineering, this study highlights the computational strength and flexibility of the proposed method. Full article