Search Results (1,468)

The Wulonggou gold district is located on the northern margin of the Qinghai–Tibet Plateau and represents the most promising area for mineral exploration within the East Kunlun mineralized belt in Qinghai Province. Previous studies on this gold district have lacked a comprehensive assessment of its metal mineralization potential. This paper conducts a comprehensive investigation of the distribution patterns of geochemical data in the Wulonggou gold district, employing multivariate statistical analysis to explore the distribution characteristics of different geochemical elements. Based on the analysis of geochemical anomaly patterns, the median + 2MAD method and fractal method were further introduced to delineate geochemical anomalies. For comparison, machine learning methods—including the radial basis function link network (RBFLN) model and the Bayesian-optimized random forest (BO-RF) model—were also applied to generate different geochemical anomaly maps. By comparing the results obtained from each method, we found that the BO-RF model performed best in predicting geochemical anomalies. Based on the above information, the BO-RF model was integrated with geological background information to delineate prospective areas. These findings provide important clues for mineral exploration and development in the Wulonggou area and can serve as a reference for other regions with similar geological backgrounds. Full article

This paper is devoted to the problem of identifying the mechanisms of hard excitation of oscillations in coupled systems of equilibrium neurons. In this study, a system of two coupled Chialvo neurons is used. For the deterministic model, we studied how increased coupling causes an abrupt transformation of the quiescent neurons into complex oscillations, both regular and chaotic. We show that even in the case when the deterministic system is in equilibrium, similar spike oscillations can be generated by noise. The important role of fractal basins of short and long deterministic transients is discussed. The potential of the principal directions and confidence domain methods for analyzing noise-induced excitation is demonstrated. The phenomena of coherence resonance and the global transition from order to chaos are explored. Full article

Urban heritage structures are most commonly understood as memorial artifacts, tourism assets, or redevelopment resources. While this common view acknowledges cultural and economic value, it overlooks a deeper function of heritage within the long evolution of human settlements. This paper advances a counter thesis: in addition to its historic contingencies and power relationships—which are real, but only part of the picture—urban heritage embodies valuable but often hidden intelligence that is highly relevant to contemporary urban challenges. Specifically, heritage environments encode useful structured information about spatial configurations that have gained adaptive value over time in a process known as stigmergy. Drawing on complexity science, network theory, the mathematics of symmetry, and theories of extended cognition, the paper argues that enduring urban forms persist not only for symbolic or historical reasons, but because they embed structural properties conducive to resilience, legibility, social interaction, climatic adaptation, and human well-being. Recurring characteristics include fine-grained network connectivity, fractal scaling hierarchies, organized symmetry, articulated thresholds, and biophilic integration. Evidence from environmental psychology, public health, and urban morphology suggests that such properties correlate with reduced stress, increased walkability, stronger social capital, and improved ecological performance. The paper proposes a methodological framework—what we call the Adaptive Patterns Model—for identifying, evaluating, and translating this embedded intelligence into contemporary regeneration practice. The Model is presented as a four-phase, conceptually synthesized framework—integrating insights from complexity science and stigmergy, urban morphological analysis, and pattern-language methodology—comprising documentation, pattern extraction, encoding, and performance correlation. It concludes by challenging a still-prevalent assumption that contemporary conditions invalidate accumulated spatial knowledge. Instead, urban heritage is understood as adaptive capital within an ongoing evolutionary process, offering a structurally grounded foundation for resilient urban transformation. Full article

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

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

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

Postural sway derived from center-of-pressure (CoP) trajectories is widely used to assess balance and fall risk in older adults, but conventional linear metrics mainly quantify sway magnitude and may overlook temporal organization. Guided by the loss-of-complexity hypothesis, we re-examined associations between fall history and linear and non-linear CoP metrics in an open-access dataset. Quiet-standing trials under eyes-open and eyes-closed conditions were analyzed in adults ≥60 years (fallers n = 19; non-fallers n = 57). To reduce confounding, propensity score matching was performed using age, sex, body mass index, activities of daily living level, illness status, number of medications, disability status, and orthosis/prosthesis use. Linear and non-linear indices, including recurrence quantification analysis, detrended fluctuation analysis, fractal dimension, multiscale entropy, stabilogram diffusion analysis, and sway density measures, were examined. After matching, no CoP metric differed significantly between groups. However, SHAP-based exploratory analysis suggested that non-linear features related to temporal structure and multiscale organization contributed more prominently to model output than conventional magnitude-based metrics. Given the limited sample size, these findings should be interpreted as exploratory and hypothesis-generating. Full article

Different methodologies have been developed for the analysis and study of dynamical systems, including both theoretical models and natural systems. Examples span a wide range of applications, such as astronomy, financial and economic time series, biophysical systems, physiological phenomena, and Earth sciences, including seismicity and climatic processes. The study of these complex systems is commonly based on the analysis of the signals they generate, using mathematical tools to extract relevant information. A broad spectrum of mathematical disciplines converges in this context, including stochastic, probability and statistical theory, entropic and informational measures, fractal and multifractal analysis, natural time analysis, modeling of non-linearity and recurrence methods, generalized entropies, non-extensive systems, machine learning, and high-dimensional and multivariate complexity. Research in this area is largely focused on the characterization of complex systems, providing indicators of determinism or stochasticity, distinguishing between regularity, chaos, and noise, and identifying topological as well as disorder-regularity features. In addition, short- and long-term forecasting, together with the identification of short- and long-range correlations, play a central role in such characterization. To address these objectives, numerous mathematical tools have been developed for the analysis of time series and point processes, each designed to capture specific signal properties. In this work, many of the most important tools used in time series analysis are compiled and reviewed, highlighting their main characteristics and the different types of complex systems to which they have been applied. Full article

Power system blackouts represent typical manifestations of instability in complex systems, whose evolution often exhibits non-stationarity, long-range correlations, and nonlinear scaling behavior. Most reliability assessment methods widely used in engineering practice are built on the core assumptions of event independence and light-tailed distribution, which will inevitably lead to systematic underestimation of extreme tail risks when blackouts actually present long-range memory and power-law heavy-tailed characteristics. Based on long-cycle historical blackout records of China’s power grid spanning 1981–2025, this paper develops an integrated framework combining Self-Organized Criticality (SOC) theory, Hurst exponent analysis, symbolic time-series methods, and Multifractal Detrended Fluctuation Analysis (MFDFA). This study systematically characterizes the evolution law and inherent dependence structure of blackout events from four dimensions: statistical scaling, temporal correlation, nonlinear structure, and multi-scale fractal spectrum. The results show that both the load-loss magnitudes and inter-event intervals of blackouts follow strict power-law distributions, with the system exhibiting scaling behavior consistent with SOC theory. The blackout event sequence presents significant long-range positive correlation and self-similarity, confirming a persistent long-term memory effect in the system evolution. Symbolic analysis further reveals the nonlinear fluctuation patterns and burst clustering behavior of the blackout process, reflecting the intermittency and complexity of blackout risks. MFDFA results verify that the blackout sequence has a broad-spectrum multifractal structure across different temporal scales, and Monte Carlo shuffle tests demonstrate that this multifractality mainly arises from intrinsic long-range temporal correlations, rather than being driven solely by heavy-tailed distribution. This study confirms that blackouts in China’s power grid are not random independent events, but present fractal statistical characteristics consistent with the self-organized critical mechanism. The findings provide a novel fractal perspective and quantitative framework for the statistical characterization, operational security assessment, and multi-scale early-warning modeling of blackout risks in China’s large-scale power systems. Full article

While parameters such as slope and aspect are routinely considered in solar radiation modelling, the role of terrain or surface roughness remains underexplored, with no universally accepted method for its calculation. This study compares several approaches to quantifying terrain or surface roughness in several geographical information system (GIS) environments (ArcGIS, QGIS, WhiteboxTools, and SAGA GIS) and introduces local fractal dimension, computed using a custom Python script, as an additional metric. The aim is to evaluate the influence of surface roughness on potential solar radiation modelling and to examine its relationship with other terrain parameters. The analysis is based on case studies from both a rugged alpine environment in the Tatra Mountains (Tichá and Kôprová dolina (valleys), Kriváň peak; 944–2467 m a.s.l.) and an urban environment (the city of Poprad, near the High Tatras, Slovakia). The results demonstrate that surface roughness can significantly affect potential solar radiation modelling in areas with high surface variability. The findings are applicable not only to solar radiation studies, but also to other fields of spatial modelling, where incorporating surface roughness can improve the accuracy and robustness of spatial analyses and predictions. Full article