Search Results (3,526)

Due to the diverse origins of shale reservoirs, the coal measure shales of the Wuxiang block, Qinshui Basin typically exhibit fractal pore structures, which significantly influence shale gas occurrence and migration. Clarifying the fractal nature of pore structures is significant for the efficient development and utilization of shale gas. In this study, mercury intrusion porosimetry and liquid nitrogen adsorption experiments were conducted to develop a method that integrates pore compressibility correction and nitrogen adsorption for pore structure characterization. On this basis, this study analyzed the fractal characteristics of coal measure shale pore structures across multiple scales. The results reveal that coal measure shale pores exhibit a three-stage fractal pattern, consisting of three regions with pore diameters >65 nm (seepage pores), 6–65 nm (transition pores), and <6 nm (micropores). Samples with fractal dimensions of seepage pores ($D_{\mathrm{a}}$) exceeding 2.9 and transition pores ($D_1$) exceeding 2.5 tend to have larger specific surface areas and more complex pore structures; this is indicated by the increased surface roughness of large-scale pores, which hinders gas seepage. Samples with lower fractal dimension of micropores ($D_2$)—in the range of 2.2–2.8—exhibit higher micropore development, larger specific surface area, and simpler pore structures, as demonstrated by a greater number of micropores and a more uniform pore distribution, which promotes gas adsorption. Full article

Various structures that exist worldwide are three-dimensional. Consequently, evaluating only two-dimensional cross-sectional structures is insufficient for analysing all worldwide structures. In this study, we interpreted the generalised fractal-dimensional formula of two-dimensional multifractal analysis and proposed three computational extension methods that consider the structure of three-dimensional slices. The proposed methods were verified using Monte Carlo and Gray–Scott simulations; the pixel-existence probability (PEP)-averaging method, which averages the pixel-existence probability in the slice direction, was confirmed to be the most suitable for analysing three-dimensional structures in two dimensions. This method enables a stable quantitative evaluation, regardless of the direction from which the three-dimensional structure is observed. Full article

This study introduces a new class of coupled differential systems described by fractal–fractional Caputo derivatives with both constant and state-dependent delays. In contrast to traditional delay differential equations, the proposed framework integrates memory effects and geometric complexity while capturing adaptive feedback delays that vary with the system’s state. Such a formulation provides a closer representation of biological and physical processes in which delays are not fixed but evolve dynamically. Sufficient conditions for the existence and uniqueness of solutions are established using fixed-point theory, while the stability of the solution is investigated via the Hyers–Ulam (HU) stability approach. To demonstrate applicability, the approach is applied to two illustrative examples, including a predator–prey interaction model. The findings advance the theory of fractional-order systems with mixed delays and offer a rigorous foundation for developing realistic, application-driven dynamical models. Full article

We introduce a class of triply coupled systems of differential equations with fractal–fractional Caputo derivatives and time-dependent delays. This framework captures long-memory effects and complex structural patterns while allowing delays to evolve over time, offering greater realism than constant-delay models. The existence and uniqueness of solutions are established using fixed point theory, and Hyers–Ulam stability is analyzed. A numerical scheme based on the Adams–Bashforth method is implemented to approximate solutions. The approach is illustrated through a numerical example and applied to a three-species food-chain model, comparing scenarios with and without time-dependent delays to demonstrate their impact on system dynamics. Full article

The immiscibility of most polymers leads to poor interfacial adhesion in blends, a critical challenge that often limits the mechanical performance of polymer composites. This research introduces shape-forming elements (SFEs), a novel class of coextrusion dies designed to create additional geometric complexity and control over interfacial architecture. Specifically inspired by Julia Set and T-Square fractals, SFEs were simulated, prototyped, and found to be effective in coextrusion of different-colored polymer clays. The SFEs were employed to coextrude architected composites consisting of a liquid crystalline polymer (Vectra A950) and a cycloaliphatic polyamide (Trogamid CX7323). Mechanical testing revealed a strong positive correlation between the draw ratio and both the tensile modulus (adjusted R² = 0.94) and tensile stress at break (adjusted R² = 0.84). However, experimental cross-sections significantly differed from simulation results. These discrepancies were attributed to interfacial instabilities caused by material incompatibility between the two polymers and potential moisture-induced defects. This finding highlights critical challenges that arise during practical processing, emphasizing the importance of addressing polymer compatibility and moisture management to realize the full potential of SFEs in designing advanced polymer composites with targeted properties. Full article

This study aims to address the research gap in the digital analysis of traditional patterns by proposing an image-processing-driven parametric modeling method that combines graphic primitive function modeling with topological reconstruction. The image is processed using a dual-channel image processing algorithm (Canny edge detection and grayscale mapping) to extract and vectorize graphic primitives. These primitives are uniformly represented using B-spline curves, with variations generated through parametric control. A topological reconstruction approach is introduced, incorporating mapped geometric parameters, topological combination rules, and geometric adjustments to output topological configurations. The generated patterns are evaluated using fractal dimension analysis for complexity quantification and applied in cultural heritage imaging practice. The proposed image processing pipeline enables flexible parametric control and continuous structural integration of the graphic primitives and demonstrates high reproducibility and expandability. This study establishes a novel computational framework for traditional patterns, offering a replicable technical pathway that integrates image processing, parametric modeling, and topological reconstruction for digital expression, stylistic innovation, and heritage conservation. Full article

Complex fractal dimensions, defined as poles of appropriate fractal zeta functions, describe the geometric oscillations in fractal sets. In this work, we show that the same possible complex dimensions in the geometric setting also govern the asymptotics of the heat content on self-similar fractals. We consider the Dirichlet problem for the heat equation on bounded open regions whose boundaries are self-similar fractals. The class of self-similar domains we consider allows for non-disjoint overlap of the self-similar copies, provided some control over the separation. The possible complex dimensions, determined strictly by the similitudes that define the self-similar domain, control the scaling exponents of the asymptotic expansion for the heat content. We illustrate our method in the case of generalized von Koch snowflakes and, in particular, extend known results for these fractals with arithmetic scaling ratios to the generic (in the topological sense), non-arithmetic setting. Full article

With the continuous advancement of 3D perception technology, point cloud data has found increasingly widespread application. However, the presence of holes in point cloud data caused by device limitations and environmental interference severely restricts algorithmic performance, making point cloud completion a research topic of high interest. This study observes that most existing mainstream point cloud completion methods primarily focus on capturing global features, while often underrepresenting local structural details. Moreover, the generation process of complete point clouds lacks effective control over fine-grained features, leading to insufficient detail in the completed outputs and reduced data integrity. To address these issues, we propose a Set Combination Multi-Layer Perceptron (SCMP) module that enables the simultaneous extraction of both local and global features, thereby reducing the loss of local detail information. In addition, we introduce the Squeeze Excitation Pooling Network (SEP-Net) module, an informative channel attention mechanism capable of adaptively identifying and enhancing critical channel features, thus improving the overall feature representation capability. Based on these modules, we further design a novel Feature Fusion Point Fractal Network (FFPF-Net), which fuses multi-dimensional point cloud features to enhance representation capacity and progressively refines the missing regions to generate a more complete point cloud. Extensive experiments conducted on the ShapeNet-Part and MVP datasets compared to L-GAN and PCN showed average prediction error improvements of 1.3 and 1.4, respectively. The average completion errors on the ShapeNet-Part and MVP datasets are 0.783 and 0.824, highlighting the improved fine-detail reconstruction capability of our network. These results indicate that the proposed method effectively enhances point cloud completion performance and can further promote the practical application of point cloud data in various real-world scenarios. Full article

Cryptocurrencies such as Bitcoin can be classified as commodities under the Commodity Exchange Act (CEA), giving the Commodity Futures Trading Commission (CFTC) jurisdiction over those cryptocurrencies deemed commodities, particularly in the context of futures trading. This paper presents a method for predicting both long- and short-term trends in selected cryptocurrencies based on the Fractal Market Hypothesis (FMH). The FMH applies the self-affine properties of fractal stochastic fields to model financial time series. After introducing the underlying theory and mathematical framework, a fundamental analysis of Bitcoin and Ethereum exchange rates against the U.S. dollar is conducted. The analysis focuses on changes in the polarity of the ‘Beta-to-Volatility’ and ‘Lyapunov-to-Volatility’ ratios as indicators of impending shifts in Bitcoin/Ethereum price trends. These signals are used to recommend long, short, or hold trading positions, with corresponding algorithms (implemented in Matlab R2023b) developed and back-tested. An optimisation of these algorithms identifies ideal parameter ranges that maximise both accuracy and profitability, thereby ensuring high confidence in the predictions. The resulting trading strategy provides actionable guidance for cryptocurrency investment and quantifies the likelihood of bull or bear market dominance. Under stable market conditions, machine learning (using the ‘TuringBot’ platform) is shown to produce reliable short-horizon estimates of future price movements and fluctuations. This reduces trading delays caused by data filtering and increases returns by identifying optimal positions within rapid ‘micro-trends’ that would otherwise remain undetected—yielding gains of up to approximately 10%. Empirical results confirm that Bitcoin and Ethereum exchanges behave as self-affine (fractal) stochastic fields with Lévy distributions, exhibiting a Hurst exponent of roughly 0.32, a fractal dimension of about 1.68, and a Lévy index near 1.22. These findings demonstrate that the Fractal Market Hypothesis and its associated indices provide a robust market model capable of generating investment returns that consistently outperform standard Buy-and-Hold strategies. Full article

This paper investigates the channel performance through a high-gain, circularly polarized microstrip patch antenna that is developed for contemporary wireless communication systems. The proposed antenna creates two orthogonal modes for circular propagation with slightly varying resonance frequencies by using a cross line and truncations to circulate surface currents. Compactness, reduced surface wave losses, and enhanced impedance bandwidth are made possible by the coaxial probe feed, periodic electromagnetic gap (EBG) slots, and fractal patch geometry. For in-phase reflection and beam focusing, a specially designed single-layer metasurface (MTS) reflector with an 11 × 11 circular aperture array is placed 20 mm behind the antenna. A log-normal shadowing model was used to test the antenna in real-world scenarios, and the results showed a strong correlation between the model predictions and actual data. At up to 250 m, the polarization-agile, high-gain antenna demonstrated reliable performance across a variety of channel conditions, enabling accurate characterization of the Channel Quality Indicator (CQI), Signal-to-Noise Ratio (SNR), and Reference Signal Received Power (RSRP). By combining cutting-edge antenna architecture with an empirical channel performance study, this research presents a compact, affordable, and fabrication-friendly solution for increased wireless coverage and efficiency. Full article

The quasisymmetric minimality for fractal sets is a hot research topic for scholars focused on the fractal geometry and quasisymmetric mappings. In this paper, we study the quasisymmetric minimality on packing dimension for homogeneous perfect sets. By using some mathematical tools such as the mass distribution principle, we find that a special class of homogeneous perfect sets with packing dimension 1 is quasisymmetrically packing minimal. Our result generalizes the results in the references. Full article

As a key target area in China’s new round of strategic mineral exploration initiatives, Tibet possesses favorable metallogenic conditions shaped by its unique geological evolution and tectonic setting. In this paper, the Saga region of Tibet is the research object, and Level-2A Sentinel-2 imagery is utilized. By applying mixed pixel decomposition, interfering endmembers were identified, and spectral unmixing and reconstruction were performed, effectively avoiding the drawback of traditional methods that tend to remove mineral alteration signals and masking interference. Combined with band ratio analysis and principal component analysis (PCA), various types of remote sensing alteration anomalies in the region were extracted. Furthermore, the fractal box-counting method was employed to quantify the fractal dimensions of the different alteration anomalies, thereby delineating their spatial distribution and fractal structural characteristics. Based on these results, two prospective mineralization zones were identified. The results indicate the following: (1) In areas of Tibet with low vegetation cover, applying spectral mixture analysis (SMA) effectively removes substantial background interference, thereby enabling the extraction of subtle remote sensing alteration anomalies. (2) The fractal dimensions of various remote sensing alteration anomalies were calculated using the fractal box-counting method over a spatial scale range of 0.765 to 6.123 km. These values quantitatively characterize the spatial fractal properties of the anomalies, and the differences in fractal dimensions among alteration types reflect the spatiotemporal heterogeneity of the mineralization system. (3) The high-potential mineralization zones identified in the composite contour map of fractal dimensions of alteration anomalies show strong spatial agreement with known mineralization sites. Additionally, two new prospective mineralization zones were delineated in their periphery, providing theoretical support and exploration targets for future prospecting in the study area. Full article

Wet–dry cycles are a key factor aggravating the durability degradation of foam concrete. To address this issue, this study prepared bentonite slurry–steel slag foam concrete (with steel slag and cement as main raw materials, and bentonite slurry as admixture) using the physical foaming method. Based on 7-day unconfined compressive strength tests with different mix proportions, the optimal mix proportion was determined as follows: mass ratio of bentonite to water 1:15, steel slag content 10%, and mass fraction of bentonite slurry 5%. Based on this optimal mix proportion, dry–wet cycle tests were carried out in both water and salt solution environments to systematically analyze the improvement effect of steel slag and bentonite slurry on the durability of foam concrete. The results show the following: steel slag can act as fine aggregate to play a skeleton role; after fully mixing with cement paste, it wraps the outer wall of foam, which not only reduces foam breakage but also inhibits the formation of large pores inside the specimen; bentonite slurry can densify the interface transition zone, improve the toughness of foam concrete, and inhibit the initiation and propagation of matrix cracks during the dry–wet cycle process; the composite addition of the two can significantly enhance the water erosion resistance and salt solution erosion resistance of foam concrete. The dry–wet cycle in the salt solution environment causes more severe erosion damage to foam concrete. The main reason is that, after chloride ions invade the cement matrix, they erode hydration products and generate expansive substances, thereby aggravating the matrix damage. Scanning Electron Microscopy (SEM) analysis shows that, whether in water environment or salt solution environment, the fractal dimension of foam concrete decreased slightly with an increasing number of wet–dry cycle times. Based on fractal theory, this study established a compressive strength–porosity prediction model and a dense concrete compressive strength–dry–wet cycle times prediction model, and both models were validated against experimental data from other researchers. The research results can provide technical support for the development of durable foam concrete in harsh environments and the high-value utilization of steel slag solid waste, and are applicable to civil engineering lightweight porous material application scenarios requiring resistance to dry–wet cycle erosion, such as wall bodies and subgrade filling. Full article

Cement-based materials are essential construction components, yet their complex microstructures critically govern mechanical performance and durability. This study investigates the micro-textural characteristics and mechanical properties of cement paste modified with grinding aids (triethanolamine, TEA; maleic acid triethanolamine ester, MGA) and polycarboxylate-based superplasticizer (PCA). Moving beyond qualitative SEM limitations, we employ advanced image-based quantitative techniques: grayscale-based texture analysis for statistical evaluation and fractal dimension analysis for geometric quantification of microstructural irregularity. Results demonstrate that grinding aids enhance particle dispersion and reduce agglomeration, resulting in a more uniform micro-texture characterized by lower grayscale variability and reduced fractal dimensions. PCA superplasticizers further significantly enhance fluidity and compressive strength. The optimal formulation (MGA + PCA) achieved a 20% increase in 28-day compressive strength compared to control samples. The fractal dimension D_B exhibits a positive correlation with compressive strength, while energy and correlation values show a negative correlation; in contrast, entropy and contrast values demonstrate a positive correlation. This research advances quantitative microstructure characterization in cementitious materials, offering insights for tailored additive formulations to enhance sustainability and efficiency in concrete production. Full article

This work analyzes the behavior of the boundary layer subjected to stresses by obstacles using hourly measurements, in the form of time series, of meteorological variables (temperature (T), relative humidity (RH), and magnitude of the wind speed (WS)) in a given period. The study region is Santiago, the capital of Chile. The measurement location is in a rugged basin geography with a nearly pristine atmospheric environment. The time series are analyzed through chaos theory, demonstrating that they are chaotic through the calculation of the parameters Lyapunov exponent (λ > 0), correlation dimension (D_C < 5), Kolmogorov entropy (S_K > 0), Hurst exponent (0.5 < H < 1), and Lempel–Ziv complexity (LZ > 0). These series are simultaneous measurements of the variables of interest, before and after, of three different volumetric geometries arranged as obstacles: a parallelepiped, a cylinder, and a miniature mountain. The three geometries are subject to the influence of the wind and present the same cross-sectional area facing the measuring instruments oriented in the same way. The entropies calculated for each variable in each geometry are compared. It is demonstrated, in a first approximation, that volumetric geometry impacts the magnitude of the entropic fluxes associated with the measured variables, which can affect micrometeorology and, by extension, the climate in general. Furthermore, the study examines which geometry favors greater information loss or greater fractality in the measured variables. Full article