Search Results (448)

Continuous introduction of advanced optimization algorithms promotes the development of electromagnetic (EM) technology in radar and communication systems. Wideband antenna design within a given space and wideband array pattern synthesis, especially in the scenario of strong mutual coupling, are two typical challenging electromagnetic problems. In this paper, a nature-inspired algorithm, i.e., the water cycle algorithm (WCA), is introduced to resolve the above two EM problems. Two typical wideband antennas, i.e., the dual-band E-shaped microstrip antenna and the typical magnetoelectric (ME) dipole antenna, are designed on the basis of the established WCA-based antenna design scheme. Compared with the well-known algorithms that have been introduced in antenna design, including the differential evolution (DE) algorithm and the gray wolf optimizer (GWO), better results can be achieved with WCA. In the sequel, a WCA-based low peak sidelobe level (PSLL) pattern synthesis is implemented based on a uniformly spaced 27-element folded fractal ME dipole array antenna with mutual coupling as high as −10 dB, the results of which further validate the superiority of WCA in array pattern synthesis and demonstrate the value of this application innovation. Full article

This study introduces a novel inertial-type iteration algorithm based on the Normal S iteration for the class of almost contraction mappings in Banach spaces. Traditional fixed point iterations often suffer from slow convergence and high computational cost; to address these limitations, the proposed framework incorporates an adaptive inertial-type parameter. We establish strong convergence of the algorithm and derive explicit a posteriori error estimates under weak contractive conditions. In addition, we demonstrate the asymptotic equivalence of the NS inertial-type trajectories with the classical Normal S iteration, provide a comprehensive weak $w^2$—stability analysis, and obtain sharp upper bounds for the data dependence problem. The practical performance of the algorithm is evaluated in two distinct computational domains: image deblurring via wavelet-based ${\mathrm{\ell }}_1$ regularization and the generation of complex fractal patterns, including Julia and Mandelbrot sets. Numerical results show that the proposed inertial-type iteration algorithm significantly outperforms existing methods—such as Picard, Mann, Ishikawa, and standard Normal S iterations—achieving faster convergence, higher PSNR values in image restoration, and more stable basins of attraction in fractal visualizations. These findings highlight the effectiveness and versatility of the NS inertial-type iteration algorithm approach for both theoretical analysis and real-world applications. Full article

Railways constitute a core component of China’s national comprehensive transportation network, and their spatial organization and temporal accessibility jointly shape transport integration and system efficiency. Identifying their evolution from the dual perspectives of spatial expansion and time compression is therefore of both theoretical and practical significance. Drawing on fractal theory, this study examines the structural characteristics, evolutionary trends, and driving factors of railway networks in China’s five major urban systems from 2014 to 2024 from a “space–time” dual perspective. The results show that railway networks exhibit a staged pattern of “spatial filling preceding temporal correlation”, with a lag of approximately 1–8 years—about 1 year in the Guangdong–Hong Kong–Macao Greater Bay Area (GBA), 5 years in the Middle Yangtze River (MYR) region and Beijing–Tianjin–Hebei (BTH), and up to 8 years in the Chengdu–Chongqing (CC) region. In addition, clear regional differences are observed: the Yangtze River Delta (YRD) is polycentric, with the greatest potential, projected to continue rapid spatial growth until 2027 and to remain in a fast-growth phase of temporal correlation; GBA is highly coordinated; BTH is developed but characterized by dual-core agglomeration; CC grows rapidly with lagging functionality; and MYR is corridor-dependent with limited potential. These findings indicate that network functionality does not emerge synchronously with infrastructure expansion, but depends on subsequent improvements in operational organization and service capacity. Compared with single-scale-based indicators, the “spatial distribution–temporal correlation” framework more effectively captures network performance and provides quantitative support for transport optimization and coordinated regional development. Full article

Permian shale is the largest and most promising shale gas exploration target in southern China after Silurian shale. The fine evaluation of shale reservoirs is a prerequisite for large-scale exploration and development. Based on the fractal method, this study, through the combined technology of nuclear magnetic resonance cryoporometry (NMRC) and Image recognition software (Image-J), clarifies the pore size distribution of Permian shale in the HGG Basin. The purpose of this study is to characterize the macroscopic parameters of Permian shale and reveal the level of reservoir space development in Permian shale. The controlling factors of porosity and pore structure are demonstrated. It is suggested that Permian shales in the HGG Basin have organic carbon contents similar to marine shales. In the favorable interval of the Dalong Formation, the average organic carbon content is comparable to that of the LMX pay zone. The lower Longtan shales have the highest organic carbon and the greatest gas generation potential, followed by the Dalong shales. TOC is the primary control on porosity in the lower Longtan and Dalong formations, whereas clay minerals dominate the control in the upper Longtan. Abundant pores between grains and between layers within clay minerals account for most of the porosity in Upper Longtan shale. In the lower Longtan and Dalong formations, organic pores are pervasive, explaining the difference in the dominant controls on porosity between these intervals. Clay minerals are a key control on the development of Permian shale reservoirs. The fractal dimension of adsorption pores (D_A) has no clear relationship with the total clay content, is negatively correlated with the illite content, and shows no clear relationship with the chlorite content. In contrast, the fractal dimension of flow pores (D_S) shows a weak positive correlation with the total clay content, a clear positive correlation with the illite content, and a negative correlation with the chlorite content. When illite interacts with water, it tends to break down and plug pores, an effect that is especially pronounced in the smallest pores hosted by organic matter; this accounts for the negative correlation between D_A and the illite content. In larger, flow-bearing pores, disintegrated illite roughens otherwise smooth walls between and within grains, increasing structural complexity and raising D_S. By contrast, reactions between chlorite and pore fluids tend to smooth the walls of flow pores, reducing structural complexity and lowering D_S. Full article

An integrated analysis incorporating total organic carbon (TOC) content measurement, X-ray diffraction (XRD), scanning electron microscopy (SEM), and gas adsorption experiments was performed on core samples from Well FY1-4 of the upper-fourth Shahejie Formation (Es₄) in the Minfeng Sag. To address the lack of systematic research on the pore and fractal characteristics of organic-rich low-maturity shales in the Minfeng Sag (against the preponderance of studies on high-maturity shales), this study characterized the lithofacies, reservoir space and pore fractal features of the target low-maturity shale interval and clarified the sedimentary controls on lithofacies and key factors regulating pore fractal heterogeneity. The results reveal that the shale in the Es₄ of the study area exhibits low thermal maturity, with six distinct lithofacies identified. Organic-rich laminated calcareous shale lithofacies (RL-1) and organic-rich laminated calcareous/argillaceous mixed shale lithofacies (RL-2) represent the most favorable lithofacies, which are dominated by large mesopores and macropores. Their reservoir spaces were primarily composed of intergranular pores, intragranular pores, and organic pores, whereas the other lithofacies are dominated by small mesopores. The pore surface fractal dimension (D) was calculated using the Frenkel–Halsey–Hill (FHH) model based on low-temperature N₂ adsorption (LTNA) data. The meso-macropore system shows higher heterogeneity than the micropore system (D₂ > D₁). Both D₁ and D₂ exhibit a weak negative correlation with TOC and carbonate content and a positive correlation with clay content. In the initial depositional stage of the Es₄, the arid climate, weak terrigenous input, shallow lake depth, and high salinity resulted in the strongly reducing saline depositional environment with relatively low organic matter enrichment. As the climate became progressively humid in the middle and late stages, hydrodynamic conditions intensified, leading to a lithofacies transition from mixed shales to argillaceous calcareous shales. Increased TOC and carbonate contents reduce the pore fractal dimension of shale. Smaller fractal dimensions directly indicate a simple pore structure and regular pore surface in the shale oil reservoir of the Minfeng Sag, where reservoir space is dominated by large pores such as intercrystalline pores and dissolved pores. Such pore characteristics are more favorable for the enrichment of shale oil. Full article

Surface topography characterization is essential for evaluating the effects of texturing processes and for describing surface-dependent phenomena. Assessing the relationships between manufacturing, surface geometries, and functional properties requires, firstly, a detailed characterization of surfaces. Conventional parameters defined in ISO 25178-2 describe the statistical distribution of surface heights relative to the mean plane, as well as the arrangement, spacing, and directionality of surface features. They also include height and spatial descriptors, functional properties derived from the Abbott–Firestone curve, and characteristics of individual topographic features, such as peaks and valleys, including their shape, volume, and distribution. While these parameters provide a valuable description of the surface, they are not intrinsically multiscale and provide only a single aggregated descriptor of the surface. Therefore, multiscale parameters complement this description by capturing relative areas and area-scale fractal-like complexity across geometrically decomposed surface features over a range of scales from the nano and micro to the macro scale. The main objective of this study is to evaluate correlations between conventional and multiscale topographic parameters, based on surfaces produced by electrical discharge machining (EDM). The novelty of this study lies in the integrated analysis of correlations between conventional and multiscale parameters, enabling a more comprehensive framework for surface characterization. Full article

The harmonic equivalent method is a non-perturbative approach to nonlinear vibration issues, aiming to create linearly coupled systems from coupled vibrations. However, there is still much to be discovered about managing interconnected nonlinear components. This paper examines the nonlinear components of a fractal-connected system and offers suggestions. This paper explores insights into the principles and uses of nonlinear systems in science and engineering by investigating the dynamic behavior of a connected cubic–quintic damping fractal system analytically using an innovative approach to analytical examination. A two-scale transformation and reformulation of the system into fractal form simplify its governing equations for dynamic and stability analysis. Two analytical scopes are presented: one decouples nonlinear systems using weighted averaging functions, and the other converts even nonlinearities into odd terms using El-Dib’s frequency formulas for linear representation, enabling an equivalent linear representation of the system. The resilience of the decoupled system is verified by numerical simulations using Mathematica, which shows high agreement and minimal relative errors. It also accurately reflects dynamic behavior. Additionally, the work uses the bridging techniques of El-Dib and Elgazery to convert a linear damping fractal coupled system into a classical continuous-space form. A scaling fractal factor is made possible by re-expressing the fractal structure using pseudo-dimensional parameters. The linearly linked damping system has an exact analytical solution. The paper provides valuable insights into the design and control of coupled nonlinear oscillatory systems by validating analytical solutions through numerical simulations using Mathematica. 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

This study details the design and development of an ultra-sensitive microwave sensor for non-invasive blood glucose monitoring, achieved by analyzing variations in the response of a split-ring resonator (SRR) through advanced engineering methodologies. There were three design phases in the development process. In the first phase, a standard SRR design was used. It had a resonant frequency of 2.975 GHz in S₂₁ and a sensitivity of only 0.0032 dB/(mg/dL). In the second phase, an interdigital capacitor (IDC) was added to the SRR structure. This made it work better and made it more sensitive, with a sensitivity of 0.015 dB/(mg/dL) at 4.1 GHz. The third phase was to use a fourth-order Moore fractal geometry to improve the resonance properties of the design a lot. From the obtained S₁₁, the maximum sensitivity was 0.042 dB/(mg/dL), which was a huge improvement in sensing efficiency compared to earlier designs. Several resonant frequencies were recorded between 4.84 and 7.56 GHz. The addition of the fractal structure made the electromagnetic field stronger in the resonant space and made the waves interact more with small changes in the biological medium, all without changing the sensor’s size (80 mm × 40 mm). These results show that fractal architecture is a promising way to create non-invasive, accurate, and easily integrated sensors in biological systems that can continuously measure blood glucose levels. Full article

Granular deposition and grading strongly influence pore-space topology and hence hydraulic conductivity in natural and engineered porous media, yet quantitative links between deposition sequence, particle-scale morphology, pore-network descriptors, and permeability anisotropy remain incomplete. Here, we develop a process-based digital porous-media framework that couples discrete element method (DEM) deposition with pore-network characterization and Darcy-scale permeability evaluation. Two deposition sequences—normal grading (coarse-to-fine) and reverse grading (fine-to-coarse)—are simulated using bi-disperse particle sets with controlled size ratios. To further isolate the role of particle morphology, particle irregularity is parameterized by a Perlin-noise-based shape perturbation factor and incorporated into the DEM-generated packings. For each packing, pore networks are extracted and quantified in terms of pore/throat size distributions and connectivity, while pore-space complexity is measured via box-counting fractal dimension. Single-phase flow is solved under imposed pressure gradient, and intrinsic permeability is computed along three orthogonal directions to evaluate anisotropy. Results show that increasing size contrast reduces porosity, shifts pore and throat distributions toward smaller characteristic radii, increases pore-space fractal dimension, and yields a monotonic permeability reduction. For identical size ratios, reverse grading consistently yields higher permeability than normal grading, suggesting that deposition sequence exerts a strong control on the continuity and efficiency of effective flow pathways at the sample scale. Increasing particle irregularity decreases permeability and systematically modifies permeability anisotropy, transitioning from weak horizontal anisotropy toward near-isotropy and, at strong irregularity, toward preferential vertical permeability. The proposed framework provides a reproducible route to relate depositional history and particle morphology to pore-network structure and directional permeability, offering implications for filtration, packed-bed design, and sedimentary reservoir characterization. Full article

Accurate estimation of soil hydraulic parameters under drip irrigation is essential for improving water flow simulations and optimizing irrigation management; however, field measurements in aeolian sandy soils are often expensive and time-consuming. This study focused on typical aeolian sandy soils in the Kubuqi Desert. Field drip irrigation experiments were conducted to obtain temporal variations in soil water content and wetting front advancement, which were used to inversely estimate and calibrate hydraulic parameters for different soil layers. Soil pore space characteristics were quantified using nitrogen adsorption, and their relationships with hydraulic parameters were analyzed through correlation and redundancy analyses. On this basis, the combined effects of particle-size distribution and pore space structure on parameter prediction were evaluated, and soil water movement under drip irrigation was simulated and validated using HYDRUS-2D/3D. The results indicated pronounced spatial variability in soil hydraulic parameters. Residual water content, saturated hydraulic conductivity, and pore-size distribution index were significantly correlated with specific surface area, total pore volume, mean pore diameter, micropore volume fraction, and pore fractal dimension. Compared with approaches based solely on particle-size distribution, incorporating pore space structure effectively reduced the prediction errors of both hydraulic parameters and wetting front migration, thereby improving simulation accuracy. These findings demonstrate that integrating particle-size distribution and pore space characteristics provides a feasible approach for the rapid estimation of hydraulic parameters and the analysis of water movement in aeolian sandy soils under drip irrigation. Full article

Classical contact mechanics typically relies on simplifying assumptions such as linear elasticity and frictionless interfaces. A notable example is the Westergaard model, a rigorous theoretical solution for the contact between a rigid sinusoidal surface and an elastic half-space with a flat surface. This configuration captures the features of surface roughness at a single characteristic scale. Such modeling is particularly relevant since most natural and engineered surfaces exhibit roughness, significantly influencing their contact behavior. In this work, we present a nonlinear analytical contact model, which overcomes the main limitations of the Westergaard solution. Specifically, we formulate the contact problem within a finite elasticity framework and include interfacial friction. The analytical model is derived from the results of dedicated finite element simulations and subsequently validated against experimental data from the literature, demonstrating improved predictive accuracy in estimating the contact area as a function of the applied mean pressure. This work lays the foundation for the development of weakly nonlinear multiscale models, where solutions for single-scale roughness can be superimposed to approximate the behavior of more complex, fractal surface geometries. Such an approach holds promise for applications in areas such as tactile human–device interactions, soft robotics, and the design of bioinspired surfaces. Full article

This study introduces a modified computational scheme for handling linear and nonlinear fractal time-dependent partial differential equations. The method is constructed using three different stages that provide third-order accuracy in the fractal time variable. The stability of the approach is examined using scalar fractal models and Fourier analysis, while convergence is established for coupled convection–diffusion systems. The numerical algorithm is applied to analyze the mixed convective flow of a Carreau–Yasuda non-Newtonian fluid over stationary and oscillating plates under the influence of viscous dissipation and magnetic field effects. For spatial discretization, the incompressible continuity equation is handled by a first-order difference scheme, whereas higher-order compact schemes are implemented for the momentum, thermal, and concentration equations. The numerical findings show that increasing the Weissenberg number and magnetic field inclination reduces the velocity distribution. An accuracy assessment against existing numerical techniques demonstrates that the present method yields smaller computational errors, particularly when central difference schemes are used in space. In addition, a surrogate machine learning model is developed to predict the skin friction coefficient and local Nusselt number using Reynolds, Weissenberg, Prandtl, and Eckert numbers as input features. The predictive capability of the model is validated through Parity plots, bar charts for sensitivity analysis, scatter visualization, and Taylor Diagrams, confirming strong agreement with the numerical results. Full article

Noise contamination is a common challenge in the analysis of time series data, where stochastic perturbations can obscure deterministic dynamics and complicate the interpretation of signals from chaotic and physiological systems. Reliable identification of noise regimes and their intensity is therefore essential for robust analysis of dynamical and biomedical signals, where incorrect attribution of stochastic perturbations can lead to misleading interpretations of system behavior. For this reason, the present study examines the role of complexity-based descriptors for identifying stochastic perturbations in time series and analyzes how these metrics respond to different noise regimes across heterogeneous dynamical systems. A supervised learning approach based on complexity descriptors was developed to analyze controlled perturbations in multiple signal types. Gaussian, pink, and low-frequency noise disturbances were injected at predefined intensity levels into the Rössler and Lorenz chaotic systems, the Hénon map, and synthetic electrocardiogram signals, while AR(1) processes were used for validation on inherently stochastic signals. From these systems, eighteen entropy-based, fractal, statistical, and singular value decomposition-based complexity metrics were extracted from either raw signals or reconstructed phase spaces. These features were used to perform three classification tasks that capture different aspects of noise characterization, including detecting the presence of noise, identifying the perturbation type, and discriminating between different noise intensities. In addition to predictive modeling, the study evaluates the complexity profiles and feature relevance of the metrics under varying perturbation regimes. The results show that no single complexity metric consistently discriminates noise regimes across all systems. Instead, system-specific relevance patterns emerge. Under given experimental constraints (data partitioning, machine learning algorithm, etc.), Approximate Entropy provides the strongest discrimination for the Lorenz system and the Hénon map, the Coefficient of Variation, Sample and Permutation Entropy dominate classification for ECG signals, and the Condition Number and Variance of first derivative together with Fisher Information are most informative for the Rössler system. Across all datasets, the proposed framework achieves an average accuracy of 99% for noise presence detection, 98.4% for noise type classification, and 98.5% for noise intensity classification. These findings demonstrate that complexity metrics capture structural and statistical signatures of stochastic perturbations across a diverse set of dynamic systems. Full article

Sleep disorders are prevalent in the world, and they lead to severe health issues such as cardiovascular disease and cognitive disabilities. Conventional polysomnography-based diagnosis is based on manual EEG analysis under the supervision of trained specialists, which is time-consuming and may have inter-rater variability. Although the predictions of deep learning (DL) models on the task of sleep classification of EEG have been promising, they, in many cases, do not explain the multiscale, temporal dynamics that physiological signals are characterized by. In this work, a hybrid model that is a combination of CNN and multifractal detrended fluctuation analysis (MF-DFA) was proposed to detect localized temporal features and long-term fractal-based dynamics of single-channel EEG recordings. The performance of the suggested model was tested using two separate polysomnographic datasets: the CAP Sleep Dataset of five-class sleep disorder classification (Healthy, Insomnia, Narcolepsy, PLM, and RBD) and the ISRUC Sleep Dataset on the three-class subject-independent validation. In the CAP dataset, the framework had an accuracy of 86.38%. Cross-dataset transfer to the ISRUC Sleep Dataset, where only the classification head was fine-tuned on a small labeled subset while all feature-extraction layers remained frozen from CAP training, achieved 87.50% accuracy, demonstrating that the learned representations generalize across differing recording protocols, sampling rates, and diagnostic label spaces. The experiments of ablation proved the paramount importance of the MF-DFA features, and the lack of them led to low classification rates. The findings demonstrate the clinical feasibility of applying fractal analysis in conjunction with DL to detect sleep disorders in an automated, generalizable manner, suitable for use in large-scale monitoring and resource-starved clinical environments. Full article