Search Results (250)

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 ${\ell }_1$ 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

The building façade serves as the primary interface between the built environment and external climate, marking the transition from static regulation to dynamic response in climate-adaptive design. While existing research predominantly addresses periodic climatic elements such as temperature and solar radiation, the highly stochastic wind environment and its potential for internal acoustic problems remain systematically unexplored. This study investigates the acoustic modulation mechanism of building façades under dynamic wind conditions through a simulation-based methodology. The primary aim is to demonstrate the use of active control to mitigate the influence of fluctuating wind on the internal acoustic environment of buildings with open windows or semi-open boundaries, focusing on the coupling between stochastic wind fields and architectural acoustics in humid subtropical climates. We propose a wind-responsive adaptive acoustic façade system employing fractal geometry and configurable delay strategies, and develop a high-fidelity simulation framework to quantify how façade geometry and activation logic regulate acoustic parameters under varying wind conditions (1–8 m/s). Results indicate that: (1) support vector regression-based mapping of wind speed to delay strategies maintains key sound-field parameters (Lateral Fraction (LF), Speech Clarity (C₅₀), and Early Decay Time to Reverberation Time ratio (EDT/RT₃₀)) within 10% fluctuation across wind regimes; (2) fractal configurations achieve balanced wide-band (125 Hz–8 kHz) performance, with SPL fluctuation <3 dB, spectral tilt (+0.3 dB), and reverberation time slope <0.3; (3) configurational switching between column (high LF) and row (high C₅₀) arrangements enables dynamic trade-off between spatial impression and speech clarity. This work establishes an integrated framework coupling wind dynamics, façade morphology, and acoustic modulation to regulate objective indoor acoustic parameters. Based on the simulated omnidirectional point-source model, the results show that key acoustic indicators remain stable across varying wind conditions, providing a theoretical and quantifiable basis for climate-responsive acoustic envelope design. Future work will include empirical prototype testing and listening tests to determine whether these simulated acoustic parameters translate into improved comfort and well-being for occupants. Full article

Characterizing multiscale fracture networks in shale gas reservoirs remains challenging, while the limited applicability of conventional continuum-based models and insufficient multi-objective coordination often lead to low efficiency in development optimization. To address these issues, this study proposes a production history matching and multi-objective collaborative optimization framework for shale gas horizontal wells based on an equivalent fractal fracture (EFF) model. By integrating fractal theory with intelligent optimization techniques, a multiscale equivalent fractal permeability tensor is constructed, forming a hybrid machine-learning framework that combines physics-based fractal constraints with data-driven learning for efficient representation of complex fracture networks. Microseismic event clouds were converted into continuous fracture-density and fractal-geometry descriptors through denoising, temporal alignment, and spatial interpolation, and these descriptors were mapped to the equivalent fractal fracture model to dynamically update key flow parameters for history matching and parameter inversion. On this basis, a multi-objective collaborative optimization strategy is developed to achieve simultaneous time-varying fracture characterization and dynamic regulation of development parameters. Comparative results indicate that the EFF-based approach yields a production prediction error of 6.8%, slightly higher than the 4.2% obtained using discrete fracture network (DFN) models, while requiring only one-eighteenth of the computational time. Using the net present value (NPV) as the unified objective function, constraints are imposed on bottom-hole flowing pressure, flowback rate and system switching time for optimization. With the optimized pressure drop being more uniform and the gas saturation distribution being more balanced, it is verified that “EFF + NPV” can achieve the coordinated optimization of “production capacity—decline—cost” and enhance the development efficiency. Full article

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

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

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

This study offers a computational framework that analyzes the escape characteristics of transcendental complex maps by utilizing the AK iteration scheme. The well-known polynomial map of the form $z^n+c$ is generalized to the form $z^n+\sin \left(z\right)+\log \left(c^m\right)$, with $m\ge 1$ and $c\in \mathbb{C}\backslash \left\{0\right\}$, allowing the creation of complex fractal structures. A precise escape criterion is developed for the AK iteration scheme, ensuring the numerical stability of the scheme when applied to the construction of the Mandelbrot set and the Julia set. In order to validate the effectiveness of the developed framework, a comparative analysis is performed between the AK iteration scheme and the CR iteration scheme, focusing on the first parametric case of the Mandelbrot set and the Julia set. The average escape time, average number of iterations, non-escaping area index, and fractal dimension are analyzed with respect to the two iteration schemes. The numerical results indicate that the fractal structure obtained by the AK iteration scheme is different from the fractal structure obtained by the CR iteration scheme, showing the effectiveness of the AK iteration scheme as a powerful tool in the study of complex systems. 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

In this paper, we investigate the (1 + 1)-dimensional nonlinear truncated M-fractional FitzHugh–Nagumo model. The main objective is to analyze the dynamical behavior and obtain exact solutions for the model. First, a fractional transformation is applied to convert the governing partial differential equation into an ordinary differential equation. Subsequently, a Galilean transformation is employed to reduce the resulting equation to a dynamical system. The bifurcation structure and chaotic dynamics of the model are then examined. The presence of chaos is further confirmed through the phase portrait, basin of attraction, return map, Lyapunov exponent, permutation entropy, Poincaré map, power spectrum, attractor, fractal dimension, multistability, time analysis, and recurrence plot. In addition, the sensitivity of the system to the initial conditions is analyzed. Finally, exact solutions for the model are constructed using the unified Riccati equation expansion method. The obtained results are illustrated using two-dimensional, three-dimensional, and contour plots. Full article

Clarifying the relationship between landscape patterns and runoff coefficient, along with identifying key influencing pathways, is crucial for formulating sustainable water resource management strategies. Since the launch of the Grain-for-Green (GfG) project in 1999, the landscape pattern of the Loess Plateau has been profoundly reshaped, altering regional rainfall-runoff processes. Assessment across 27 catchments selected in the central Loess Plateau demonstrated forest and grassland areas expanded by 738.8 km² and 480.4 km², respectively, paralleled by a 20.1% enhancement in vegetation coverage. Correspondingly, surface runoff decreased by 28.1–90.6% in the 2000s and 12.8–95.5% in the 2010s compared to the 1960s, with a similar decline in runoff coefficient. This study further developed a novel landscape unit mapping method, integrating vegetation coverage, land use, slope, and soil type to compute landscape metrics. Partial least squares regression (PLSR) and piecewise structural equation modeling (piecewiseSEM) were constructed to systematically analyze the linkage between landscape patterns and surface runoff. The constructed landscape metrics explained 64.6% of the variance in the runoff coefficient, with perimeter area fractal dimension (PAFRAC), mean perimeter-area ratio (PARA_MN), and aggregation index (AI) exerting significant influence. The findings provide a scientific basis for water resource management in regions with similar environmental characteristics. Full article

Despite its importance in modeling subdiffusion in fractal and heterogeneous media, a rigorous and computational scheme for solving the fractional diffusion equation on generalized comb structures over unbounded domains has remained elusive, mainly due to the nonlocal memory effect and slow spatial decay of solutions. To the best of our knowledge, we address this long-standing gap by presenting a fully integrated framework that simultaneously resolves both challenges. We derive the governing equation from constitutive relations and establish exact absorbing boundary conditions (ABCs) for the multi-skeleton comb model, a result absent in prior work. A transparent Dirichlet-to-Neumann (DtN) map, constructed via Laplace analysis, rigorously handles skeletal Dirac delta singularities and eliminates spurious reflections without empirical parameters. Furthermore, we propose a novel structure-preserving finite difference scheme that applies the sum-of-exponentials (SOE) approximation not only to the interior Caputo derivative but also to the convolution kernels arising from the ABCs. This yields a dramatic reduction in computational complexity, from quadratic $O\left(N_t^2\right)$ to quasi-linear $O(N_{t}log{N}_t)$, while preserving the physics of anomalous transport. We prove the well-posedness, unconditional stability, and convergence of the method. Numerical results confirm theoretical error estimates and show excellent agreement between simulated particle distributions, mean square displacement profiles, and exact asymptotics, validating both accuracy and robustness. The speedup (CPU time ratio Direct/Fast) is about $1.00\times$–$1.23\times$ for $N_t=5000$ in our tests. Our approach sets a new benchmark for simulating anomalous dynamics in fractal-inspired media. Full article

The development of fractal set theory has been strongly driven by the introduction of new classes of fractal sets, among which the attractors of iterated function systems (IFSs) play a central role. In this work, we study a generalization of the classical IFS framework leading to the construction of fractal interpolation functions (FIFs) in which the standard linear ordinate scaling is replaced by a nonlinear contraction. This modification gives rise to a new family of FIFs associated with contractions of the general integral type, offering a flexible and robust approach for the approximation of experimental and irregular data. Furthermore, we introduce a class of generalized iterated function systems defined by mappings acting on product spaces of the form $f:{\mathbb{X}}^m\to \mathbb{X}$, with $m\in {\mathbb{N}}^{*}$. We prove the existence and uniqueness of the corresponding attractor, thereby extending several classical results from the theory of IFS and fractal interpolation. Full article

With the increasing demands for autonomy and coverage efficiency in tasks such as security patrol and post-disaster exploration using mobile robots, achieving random, efficient, and complete coverage path planning has become a critical challenge. Traditional chaotic path planning methods, while capable of generating unpredictable trajectories, still have limitations in terms of randomness strength, traversal uniformity, and convergence coverage. To address this, this study proposes a complete-coverage random path planning method based on a novel four-dimensional fractal-fractional multi-scroll chaotic system. The main contributions of this research are as follows: First, by introducing additional state variables and fractal-fractional operators into the classical Chen system, a fractal-fractional chaotic system with a multi-scroll attractor structure is constructed. The output of this system is then mapped into robot angular velocity commands to achieve area coverage in unknown environments. Key findings include: the novel chaotic system possesses two positive Lyapunov exponents; Spectral Entropy (SE) and Complexity (CO) analyses indicate that when parameter B is fixed and the fractional order α increases, the dynamic complexity of the system significantly rises; in a 50 × 50 grid environment, the robot driven by this system achieved a coverage rate of 98.88% within 10,000 iterations, outperforming methods based on Lorenz, Chua systems, and random walks; ablation experiments further demonstrate that the combined effects of the fractal order β, fractional order α, and multi-scroll nonlinear terms are key to enhancing system complexity and coverage performance. The significance of this study lies in that it not only provides new ideas for constructing complex chaotic systems but also offers a reliable theoretical foundation and practical solution for mobile robots to perform efficient, random, and high-coverage autonomous inspection tasks in unknown regions. Full article

Marine concrete is often exposed to multiple aggressive ions, so mechanical deterioration cannot be reliably interpreted using single-ion durability concepts. This study investigates ocean-oriented concretes incorporating high contents of mineral admixtures under coupled sulfate/chloride/carbonate/magnesium actions and develops a pore-structure-based D–P dual-parameter framework linking microstructural descriptors to macroscopic peak stress and peak strain. Three binder systems were designed: ordinary Portland cement concrete (OPC), cement–silica fume concrete (CSC, 20% silica fume), and cement–silica fume–fly ash concrete (CSFC, 20% silica fume + 50% fly ash). Specimens were immersed for 12 and 24 months in four representative binary-salt solutions. Porosity evolution and pore-size-class distributions were quantified by low-field NMR, while pore complexity was characterized using multi-scale fractal dimensions. The results show that mineral admixtures generally refine the pore system and improve the integrity of fine pores; CSFC exhibits the most robust microstructural stability across the tested environments, whereas CSC shows a pronounced degradation of fine-pore structure under CE4. A second-order response surface model built on Z-score normalized fractal dimension (D) and porosity (P) achieves reliable predictability for peak strain (R² = 0.85) and peak stress (R² = 0.79). Global Sobol sensitivity analysis reveals distinct controlling mechanisms: peak strain is predominantly governed by porosity (S_P = 85.9%), whereas peak stress is controlled by the combined effects of porosity, pore complexity, and their interaction (S_P = 42.4%, S_D = 19.8%, S_{D × P} = 37.8%). Local sensitivity mapping further identifies high-sensitivity regimes at extreme pore states, providing mechanistic guidance for mixture optimization. Overall, the proposed D–P framework quantitatively bridges pore volume/geometry evolution and mechanical degradation, offering a practical predictive tool for durability-oriented design of marine concretes under multi-ionic attack. Full article

We present an analytical solution for the complex spectrum of a Creutz ladder subject to an imaginary Stark potential. By mapping the system to a momentum-space differential equation, we derive the closed-form solution for the momentum-space wavefunctions. We identify a distinct cross-shaped spectrum consisting of discrete localized sectors and a continuous branch of asymptotically real states. Our derivation reveals that the discrete sectors arise from a global phase winding condition, whereas the asymptotically real branch emerges when the energy magnitude is smaller than the inter-cell hopping strength, a regime in which the momentum-space wavefunction develops singularities. We demonstrate that these singularities prevent standard quantization; instead, the open boundary conditions are satisfied via a size-dependent imaginary energy component that regulates the wavefunction decay. To investigate the properties of this branch in the thermodynamic limit, we perform large-scale finite-size scaling analysis up to system sizes $L\sim {10}^9$. The numerical results confirm the power-law decay of the residual imaginary energy, supporting the asymptotic reality of these states. Furthermore, scaling of the inverse participation ratio and fractal dimension indicates that these states, while exhibiting size-dependent localization in finite systems, evolve into an extended phase in the thermodynamic limit. Our results establish a theoretical framework for understanding spectral transitions in systems with imaginary Stark potentials, with potential realizations in photonic frequency synthetic dimensions. Full article