Search Results (1,029)

This study introduces a Caputo fractional-order version of the SEIRS-V model to investigate the spreading dynamics of worms within wireless sensor networks. Traditional integer-order worm propagation models describe the instantaneous evolution of network states; however, they do not adequately account for memory and hereditary characteristics that may influence the transmission dynamics. Consequently, their ability to represent realistic network behavior can be limited in systems where past states affect current propagation patterns. The framework divides sensor nodes into susceptible, exposed, infectious, recovered, and vaccinated classes, while explicitly incorporating worm transmission rates, temporary loss of immunity, and the impact of preventive security measures under limited resource conditions. A detailed theoretical examination is performed, covering the existence, boundedness, and uniqueness of solutions of the fractional-order system. The coupled nonlinear fractional system is solved semi-analytically by means of the Fractional Reduced Differential Transform (FRDT) technique. To confirm accuracy and robustness, the identical system is also discretized and solved using the finite difference scheme (FDS). Unlike previous studies on worm propagation models in wireless sensor networks, which are mainly limited to equilibrium point analysis and qualitative investigations without deriving explicit solutions, the present work develops an approximate semi-analytical solution for the fractional-order SEIRS-V system using the FRDTM. Comparisons between the two solution sets demonstrate excellent agreement and high precision. Numerical outcomes are presented through a series of 2D graphical profiles that illustrate the time-dependent behavior of each compartment and reveal the sensitivity of worm propagation and suppression to variations in the fractional order and key model parameters. The integrated theoretical and computational findings underscore the strong protective role of vaccination in mitigating worm outbreaks and offer valuable guidelines for strengthening cybersecurity measures in wireless sensor networks. Full article

Analytical solutions serve as primary benchmarks for verifying model test design, provide rapid predictive tools for preliminary design, and offer fundamental physical understanding of complex structure interaction problems of the geological body. It is essential for ensuring the reliability of experimental results. For the study on slope stability under earthquakes, the seismic behavior of key inclined cracks in the slope is a hot topic, which is a crucial issue in rock mechanics and engineering geomechanics. This paper studies the dynamic propagation of the inclined crack under seismic conditions, proposes the analytical solution of fracture mechanics, and conducts a centrifuge shaking table test accordingly for monitoring and validation. The analytical solution results have been validated experimentally by a centrifuge shaking table test on the seismic behavior of an inclined crack. Results indicate that the amplitude of seismic waves significantly affects crack propagation: the greater the amplitude, the faster the propagation rate. Analysis of crack propagation and maximum surface displacement reveals hysteresis and sudden jumps of surface deformation caused by rock mass structure and locked segments, both in indoor tests and in strong earthquake regions. This paper combines a theoretical and experimental monitoring study, providing a good example of integrating analytical solutions and modeling validation for research on earthquake-induced landslide disasters. Full article

To systematically assess the regional impacts of new-energy base (NEB) development, this study proposes a comprehensive evaluation model integrating the Fuzzy Analytic Hierarchy Process (FAHP), Entropy Weight Method (EWM), and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). A 26-indicator framework across environmental, technological, economic, and social (ETES) dimensions was constructed. Empirical analysis of representative cases was carried out using game-theoretic integration of FAHP and EWM to derive indicator weights. Furthermore, an obstacle degree model was employed to identify key constraints. Three representative NEBs in Xinjiang Province were selected for analysis, including a medium-scale wind-PV hybrid base (Case A), a large-scale PV project with standalone storage (Case B), and a wind power expansion project (Case C). The results validate the scientific robustness of the ETES framework, with combined weighting indicating that economic criteria hold the highest priority. The case assessments reveal that Case B attained the highest relative closeness in the TOPSIS ranking, whereas Cases A and C performed less favorably due to significant deviations from ideal indicator values. Obstacle analysis further identified distinct limiting factors. These findings offer a theoretical basis and practical insights for analogous renewable energy initiatives, particularly in regions facing complex sustainability trade-offs. Full article

In this work, we investigate the spectral, information-theoretic, and thermodynamic properties of a fractal Schrödinger system with position-dependent mass subject to an effective semiconductor-like confinement. We employ a fractal momentum operator and a Von Roos Hamiltonian with BenDaniel–Duke ordering to obtain exact analytical solutions for the energy spectrum and wave functions. The interplay between the fractal parameter $\alpha$, the effective lattice scale $l_0$, and the harmonic confinement strength $\omega$ is explored. We perform a comprehensive analysis of the Shannon entropy, Fisher information, and Fisher–Shannon complexity in both coordinate and momentum spaces. Our results demonstrate that these parameters directly control the localization–delocalization transition and the informational architecture of the quantum states, while satisfying the entropic and Fisher uncertainty relations. Furthermore, we derive the exact partition function and the corresponding thermodynamic properties (free energy, internal energy, entropy, and specific heat) of the system. The analytical framework presented offers valuable insights into the spectral, information-theoretic, and thermodynamic behavior of quantum systems in fractal semiconductor-like environments. Full article

Against the coordinated advancement of building a maritime power, high-quality development of marine tourism and ecological civilization construction, realizing positive interaction between marine resource conservation and tourism industrial development has emerged as a pivotal issue for high-quality growth in coastal regions. Taking 11 coastal provincial-level administrative regions in China spanning 2008 to 2024 as the research sample, this paper first establishes an evaluation indicator system covering marine resources and the tourism industry. It further adopts an integrated empirical framework encompassing the coupling coordination degree model, spatial Markov chain model, obstacle degree model, fixed-effect model and geographically and temporally weighted regression (GTWR) model to systematically unpack the spatiotemporal differentiation characteristics, internal restrictive obstacle factors and external driving determinants of the two-system coupling coordination. On this basis, a marine resource compensation mechanism for tourist destinations is formulated. Empirical results demonstrate four core findings: (1) In terms of temporal evolution, the overall coupling coordination level keeps rising and goes through three phases: initial development, rapid improvement and post-shock recovery. After a short-term decline triggered by the pandemic, the index rebounds markedly after 2023, showing that the two systems can recover and stabilize. (2) In terms of spatial layout, a persistent stratified spatial pattern featuring “higher coordination in southern coast versus lower coordination in northern coast with three-tier hierarchical differentiation” is identified; high-level neighboring regions exert prominent positive spatial spillover effects, whereas low-level adjacent areas are prone to fall into development lock-in traps. (3) For internal constraint obstacles, the marine resource subsystem is persistently restricted by resource exploitation limits and coastal spatial scarcity, while the dominant bottleneck of the tourism industrial subsystem shifts from insufficient market scale to inadequate human capital supply. (4) Regarding external driving forces, the proportion of tertiary industry and the digital infrastructure constitute core driving contributors, whereas marketization progress and opening-up degree act as primary restrictive factors, with pronounced spatial heterogeneity existing across all driving indicators. Finally, in line with the quasi-public-good attribute and ecological externality of marine resources, this study constructs a differentiated and synergistic marine resource compensation mechanism from three dimensions: stakeholder identification, compensation implementation pathways and institutional guarantee systems. The proposed framework provides theoretical references and practical policy options to facilitate high-level coupling and coordinated development between marine resource preservation and the coastal tourism industry. The marginal contribution of this research lies in integrating coupling coordination measurement, obstacle factor diagnosis, driving mechanism identification and compensation mechanism design into an integrated analytical framework, which delivers theoretical foundations and operable policy solutions for coastal marine resource protection, tourism industrial upgrading and differentiated compensation system construction. Full article

The Kelvin lattice is a fundamental model to study the dynamical properties of metamaterials. This paper is devoted to quantitatively characterizing a nanopteron solution, which is a superposition of a central solitary wave and trailing oscillations, in a Kelvin lattice. We have illustrated that each nanopteron solution possesses a Stokes curve. We have also shown that the appearance of trailing oscillations in nanopteron solutions is a result of Stokes phenomena, which emerges when the Stokes curve is crossed in the complex plane. By employing an exponential asymptotic analysis, we have obtained analytically the relation between the amplitude of the trailing oscillations and the system parameters. Our theoretical predictions show good agreement with numerical simulations for a wide range of system parameters. Full article

This study investigates the application of physics-informed neural networks (PINNs) to two-dimensional reaction–diffusion biological models with singular terms. Motivated by the classical prey–predator framework, we propose an improved model that incorporates human influence into the ecological environment. The stability of the reaction–diffusion system is analyzed, and an analytical solution is derived for a specific case to provide theoretical support for the numerical model. In addition, a PINN–Adam deep learning algorithm is developed to effectively handle the singular characteristics of the system. Unlike traditional finite element methods (FEMs), which rely on grid-based discretization, the proposed method utilizes random spatiotemporal sampling, leading to improved computational flexibility and prediction accuracy. The proposed approach is validated using real-world fish population data from coral reef ecosystems along the South Australian coast, demonstrating its effectiveness in modeling complex ecological dynamics. Full article

We investigate dynamic weighted fractional information-theoretic measures for linear stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (1/2,1)$. Motivated by recent constructions of fractional Deng entropy and building upon explicit Gaussian solutions and closed-form fractional moments derived in previous work, we establish fully analytical expressions for the Shannon entropy, Rényi entropy, Tsallis entropy, extropy, and a continuous weighted fractional entropy $\mathbb{E}\left[X_t^p(-\log p_{X_t}\left(X_t\right))\right]$ for $p\ge 0$, expressed directly in terms of known fractional moments without density estimation. All derived measures share a universal asymptotic scaling law growing as $H\log t$, establishing a precise quantitative link between long-memory effects and information dynamics. The weighted fractional entropy further reveals remarkable structural properties as a function of the weighting order p, exposing a dual role of long memory on the system’s informational content. As a concrete application, we characterize anomalous diffusion in aging soft materials through an explicit critical time linking maximal uncertainty to the memory exponent H and the macroscopic aging rate. All results are validated through extensive Monte-Carlo simulations, demonstrating excellent agreement with the closed-form expressions across a wide range of Hurst exponents H and weighting orders p. Full article

The conflict between individual rationality and collective rationality, as revealed by the tragedy of the commons, constitutes the core dilemma of collective action in ecological and environmental governance. The key to resolving this dilemma lies in systematically diagnosing the social–ecological system and identifying the crucial factors that hinder cooperation. However, existing diagnostic frameworks have largely focused on identifying the conditions for collective action formation. Thus, those frameworks establish a diagnostic logic centered on conditional principles, but they neglect the capture of the formation process of collective action. To address this gap, this paper further introduces a procedural principle centered on “squeeze-out → transformation → return” into the traditional diagnostic framework. This is achieved by constructing an integrated analytical framework that combines procedural and conditional principles. This study takes the ecological and environmental governance of the Dawangtan Reservoir in Nanning, Guangxi Zhuang Autonomous Region, China, as a case study. The limitations of the traditional framework in diagnosing complex social–ecological systems are also examined. Further, this study demonstrates how the proposed integrated diagnostic framework enables problem identification and dilemma resolution by capturing the formation process of collective action. This research not only enriches the theoretical understanding of the formation process of collective action in complex contexts, but also helps practitioners more efficiently identify context-specific solutions to collective action problems. Full article

In this paper, we investigate the existence and positivity of solutions for a class of twelfth-order nonlinear boundary value problems that naturally arise in the mathematical modeling of elastic and micro-mechanical systems. The considered model incorporates higher-order derivatives to account for nonlocal and gradient effects that commonly appear in the analysis of micro- and nano-scale elastic structures. By employing the Leray–Schauder nonlinear alternative and fixed point theorems, we establish sufficient conditions for the existence of at least one positive solution. The analysis relies on the explicit construction and properties of the associated Green’s function, which plays a fundamental role in deriving upper and lower bounds for the nonlinear term. The obtained results extend and generalize earlier works on sixth, eighth and tenth-order problems to the twelfth-order case. Finally, numerical examples are presented to illustrate the applicability and accuracy of the theoretical findings. The results provide a rigorous analytical foundation for the study of high-order elastic models and micro-scale structural stability. Full article

This paper investigates a discrete diffusion carbon emission-absorption model with periodic boundary conditions derived via the piecewise constant argument scheme. The existence of equilibrium points is established, and sufficient conditions for the local asymptotic stability of the positive equilibrium are derived through eigenvalue analysis. Then, uniform boundedness of positive solutions is proved, and the global asymptotic stability of the interior equilibrium is established by an iterative method and the comparison principle for difference equations. Furthermore, the model is shown to undergo a flip bifurcation when a critical parameter threshold is reached, leading to period-doubling dynamics and chaotic behavior. The influence of spatial diffusion is examined through a Turing instability analysis, yielding conditions for diffusion-driven instability and spatial pattern formation. Finally, Decision Tree and Random Forest classifiers are used as proof-of-concept tools to efficiently approximate the analytically derived stability regions using Monte Carlo-generated data. Both classifiers successfully reproduce the analytical stability structure, while the Random Forest classifier provides higher accuracy and smoother stability boundaries. Numerical simulations support the theoretical results and illustrate the stability and bifurcation phenomena exhibited by the model. These findings indicate that the proposed framework is useful for analyzing carbon emission-absorption dynamics and that machine learning can serve as an efficient computational surrogate for identifying stability regions in nonlinear dynamical systems. Full article

Smart museums increasingly rely on digital media, interactive installations, artificial intelligence, augmented reality, and virtual reality to support cultural communication and visitor engagement. However, existing studies have mainly examined specific technologies, usability, or visitor satisfaction, while a systematic and quantitative framework for comparing interactive experience across different smart museums remains limited. To address this gap, this study proposes a hybrid multi-criteria decision-making framework for evaluating smart museum interactive experience. Based on the Strategic Experiential Modules, an evaluation system consisting of five dimensions—Sense, Feel, Think, Act, and Relate—and sixteen indicators was constructed. The Analytic Hierarchy Process was used to determine subjective weights from expert judgments, the entropy method was applied to capture the data-driven dispersion characteristics of expert evaluation data, and a game-theoretic combination weighting strategy was used to integrate the two weighting results. Subsequently, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was employed to compare five representative smart museum cases. The results show that Zhejiang Provincial Museum achieved the highest relative closeness value (C_i = 0.9891), followed by Shanghai Museum (C_i = 0.8457) and Hunan Museum (C_i = 0.5326). Robustness analysis further showed that the ranking order remained consistent under entropy weights, AHP weights, average weights, and game-theoretic combined weights. The Friedman test indicated no significant difference in the relative closeness coefficients across weighting schemes (χ² = 1.200, p = 0.753). These findings indicate that the proposed framework can effectively identify relative strengths and weaknesses in smart museum interactive experience and provide a replicable decision-support tool for experience-oriented museum design and optimization. Full article

This research explores the existence of solutions for a class of random fractional differential equations characterized by bounded delay, specifically within the context of Fréchet spaces. Random fractional differential equations serve as powerful mathematical tools for modeling complex phenomena subjected to stochastic perturbations and hereditary effects. Despite their significance, establishing solution existence in infinite-dimensional spaces remains a challenging task. By integrating the properties of the noncompactness measures with a generalized Darbo fixed point approach, we establish new existence results for the associated Darboux-type problem under milder compactness conditions. To illustrate the practical utility of these analytical results and demonstrate the validity of our theoretical framework, a representative example is provided. Full article

This study presents an integrated framework for enhancing the safety and operational efficiency of robotic arms in laparoscopic surgery by addressing minimum distance estimation between multi-arm manipulators and the associated collision-aware warning. By combining analytical modeling, real time simulation, and machine learning, the framework offers a robust solution for ensuring safe robotic operations. An analytical model was developed to estimate the minimum distances between robotic arms based on their joint configurations, offering theoretical calculations that serve as both a validation tool and a benchmark. To complement this, a 3D simulation environment was created to model two 7 DOF Kinova robotic arms (Kinova Inc., Boisbriand, QC, Canada), generating a diverse dataset of configurations for distance estimation and collision warning. Using these insights, a deep residual neural network model was trained with joint configurations as inputs. On the held out validation set, the model achieves $R^2=0.940$, RMSE $=42.0$ mm, MAE $=28.7$ mm, and a near zero mean bias, demonstrating strong predictive accuracy and consistent generalization across the workspace. The framework is intended as an early collision warning layer, where a warning is triggered when the predicted inter-arm distance falls below a 0.2 m threshold, which corresponds to a surface to surface clearance of approximately 50 mm given the Kinova Gen3 (Kinova Inc., Boisbriand, QC, Canada) cross sectional radius. This work demonstrates the effectiveness of combining analytical modeling with machine learning to enhance the precision and reliability of multi-arm robotic systems. Full article

In this paper, analytical and numerical analyses of the mechanical response of an ultra-large-diameter shield tunnel with a nonuniform convergence of axial symmetry are conducted. A nonuniform convergence of axial symmetry around the tunnel boundary is adopted. The bending moment and axial force of the tunnel liner with different diameters from 6 to 18 m are obtained and compared in detail. The theoretical analysis results show that at the same buried depth of the tunnel crown, both the maximum absolute bending moment and axial force of the shield tunnel liner grow as the diameter of the tunnel increases. Moreover, the distributions of the bending moments of the tunnel liner along the tunnel boundary present a “8” shape and are axially symmetric along the vertical axis, where the upper and lower parts are positive and the left and right sides are negative. The maximum absolute bending moment of the tunnel liner is at the axis of 280°. Furthermore, the axial force of the shield tunnel liner is always negative, and the maximum absolute axial forces of the tunnel liner are at the axis of 0° and 180°. Finally, it is worth pointing out that the maximum bending moment and axial force increase 26.99 times and 8.99 times, respectively, when the diameter increases only three times from 6 m to 18 m, which is of great guiding significance for the rational design of ultra-large-diameter shield tunnels. The results of the analytical solution are verified by a numerical analysis, which shows that the analytical solution has a higher computational efficiency than the numerical simulation while ensuring accuracy. Full article