Search Results (1,460)

Transmission tower guy wires are critical flexible tension members ensuring the stability and safe operation of overhead power transmission networks. However, these components are vulnerable to external impacts from falling rocks, ice masses, and other natural hazards, which can cause excessive deformation, anchorage loosening, and catastrophic failure. Current design standards primarily consider static loads, lacking comprehensive models for predicting dynamic impact responses. This study presents a theoretical model for predicting the peak impact response of guy wires by modeling the impact process as a point mass impacting a nonlinear spring system. Using an energy-based elastic potential method combined with cable theory, analytical solutions for axial force, displacement, and peak impact force are derived. Newton–Cotes numerical integration solves the implicit function to obtain closed-form solutions for efficient prediction. Validated through finite element simulations, deviations of peak displacement, peak impact force, and peak axial force between theoretical and numerical results are within ±4%, ±18%, and ±4%, respectively. Using the validated model, parametric studies show that increasing the inclination angle from 15° to 55° slightly reduces peak displacement by 2–4%, impact force by 1–13%, and axial force by 1–10%. Higher prestress (100–300 MPa) decreases displacement and impact force but increases axial force. Longer lengths (15–55 m) cause linear displacement growth and nonlinear force reduction. Impacts near anchorage points help control displacement risks, and impact velocity generally has a more significant influence on response characteristics than impactor mass. This model provides a scientific basis for impact-resistant design of power grid infrastructure and guidance for optimizing de-icing strategies, enhancing transmission system safety and reliability. Full article

We study a minimum-time (time-optimal) control problem for a nonlinear pendulum-type oscillator, in which the control input is the system’s natural frequency constrained to a prescribed interval. The objective is to transfer the oscillator from a given initial state to a prescribed terminal state in the shortest possible time. Our approach combines Pontryagin’s maximum principle with Bellman’s principle of optimality. First, we decompose the original problem into a sequence of auxiliary problems, each corresponding to a single semi-oscillation. For every such subproblem, we obtain a complete analytical solution by applying Pontryagin’s maximum principle. These results allow us to reduce the global problem of minimizing the transfer time between the prescribed states to a finite-dimensional optimization problem over a sequence of intermediate amplitudes, which is then solved numerically by dynamic programming. Numerical experiments reveal characteristic features of optimal trajectories in the nonlinear regime, including a non-periodic switching structure, non-uniform semi-oscillation durations, and significant deviations from the behavior of the corresponding linearized system. The proposed framework provides a basis for the synthesis of fast oscillatory regimes in systems with controllable frequency, such as pendulum and crane systems and robotic manipulators. Full article

The vibrations of the dynamical system play an important role in biological processes, electrical engineering, and mechanical structures. In this work, we focus on the behaviors of dynamical systems, such as periodical or damped oscillations and asymptotic behaviors. Theorems for explicitly integrability of the dynamical system are established. The effect of the physical parameters $0<a\le 1$, $d\ge 0$ is semi-analytically analyzed by means of the Optimal Parametric Iteration Method (OPIM). We pointed out some cases when the investigated system admits only one first integral or two first integrals. These cases are reduced to a second-order nonlinear differential equations, which are solved by OPIM. The OPIM solutions are highlighted qualitatively by figures and quantitatively by tables, respectively, and are in good agreement with corresponding numerical ones. The accuracy of the obtained results are emphasized by comparison with the iterative solutions, via the classical iterative method and new optimal iterative method, respectively. Other advantages of the applied method are pointed out. Full article

We present a comprehensive mathematical analysis of a within-host dual-target HIV dynamics model, which explicitly incorporates the virus’s interactions with its two primary cellular targets: CD4${}^{+}$ T cells and macrophages. The model is formulated as a system of five nonlinear delay differential equations, integrating three distinct discrete time delays to account for critical intracellular processes such as the development of productively infected cells and the maturation of new virions. We first establish the model’s biological well-posedness by proving the non-negativity and boundedness of solutions, ensuring all trajectories remain within a feasible region. The basic reproduction number, ${\mathcal{R}}_0^d$, is derived using the next-generation matrix method and serves as a sharp threshold for disease dynamics. Analytical results demonstrate that the infection-free equilibrium is globally asymptotically stable (GAS) when ${\mathcal{R}}_0^d\le 1$, guaranteeing viral eradication from any initial state. Conversely, when ${\mathcal{R}}_0^d>1$, a unique endemic equilibrium emerges and is proven to be GAS, representing a state of chronic infection. These global stability properties are rigorously established for both the non-delayed and delayed systems using carefully constructed Lyapunov functions and functionals, coupled with LaSalle’s invariance principle. A sensitivity analysis identifies viral production rates ($p_1,p_2$) and infection rates (${\beta }_1,{\beta }_2$) as the most influential parameters on ${\mathcal{R}}_0^d$, while the viral clearance rate (m) and maturation delay (${\tau }_3$) have a suppressive effect. The model is extended to evaluate antiretroviral therapy (ART), revealing a critical treatment efficacy threshold ${ϵ}^{cr}$ required to suppress the virus. Numerical simulations validate all theoretical findings and further investigate the dynamics under varying treatment efficacies and maturation delays, highlighting how these factors can shift the system from persistence to clearance. This study provides a rigorous mathematical framework for understanding HIV dynamics, with actionable insights for designing targeted treatment protocols aimed at achieving viral suppression. Full article

This paper presents a theoretical framework modeling space-time as a quantized elastic medium. This elastic model is not intended to replace general relativity, but to offer a complementary mechanical interpretation in the approximation of the weak gravitational field. The goal is not to redefine gravity, but to explore whether this elastic formalism can simplify certain aspects of space-time dynamics, provide new insights, and generate falsifiable predictions—particularly in contexts where analytical solutions in general relativity are difficult to obtain. As originally envisaged by A. Sakharov, who associated general relativity with the concept of space-time behaving like an elastic medium, this paper introduces the notion of the “elasther” and reinterprets gravitational effects, time dilation, and phenomena commonly attributed to dark energy and dark matter through analogies with established mechanical principles such as Hooke’s law, thermal expansion, and creep. Full article

The exact analytical solutions of a new combined Kairat-II-X differential equation are presented. The related model is investigated by combining the enhanced modified extended tanh function method and the modified $tan(\varphi /2)$-expansion method. Then, a wide range of solitary wave solutions with unknown coefficients are extracted in a variety of shapes, including dark, bright, bell-shaped, kink-type, combine, and complex solitons, exponential, hyperbolic, and trigonometric function solutions. To offer physical insight, some of the identified solutions are presented in figures. Also, 3D, 2D, and 2D density profiles of the obtained outcomes are illustrated in order to examine their dynamics with the choices of parameters involved. Based on the obtained findings, we can assert that the suggested computational approaches are efficient, dynamic, well-structured, and valuable for tackling complex nonlinear problems in several fields, including symbolic computations. The bifurcation analysis and sensitivity analysis are employed to comprehend the dynamical system. We assume that our findings will be very beneficial in improving our understanding of the waves that manifest in solids. Full article

A theoretical model of the interaction between a following current and a semi-infinite floating ice sheet under compressive stress near a vertical impermeable wall is developed, within the scope of linear water wave theory, to study the hydroelastic behavior. The conceptual framework defining the buoyant ice structure incorporates the tenets of elastic beam theory. The associated fluid dynamics are governed by strict adherence to the potential flow paradigm. To resolve the undetermined parameters appearing in the Fourier series decomposition of the potential functions, investigators systematically apply higher-order criteria detailing the coupling relationships between modes. The current results are compared with a specific case of results available in the literature, and the convergence analysis of the analytical solution is made for computational accuracy. Further, the free edge conditions are applied at the edge of the floating ice sheet, and the effects of current speed, compressive stress, the thickness of the ice sheet, flexural rigidity, water depth on the strain, displacements, reflection wave amplitude, and the horizontal force on the rigid vertical wall are analyzed in detail. It is found that the higher values of the following current heighten the strain, displacements, reflection amplitude, and force on the wall. The study’s outcomes are considered to benefit not just cold region design applications but also the engineering of resilient floating structures for oceanic and offshore environments, and to the design of marine structures. Full article

This paper develops a mathematical approach to the analysis of the stability of economic equilibria in nonsmooth models. The $\lambda$-Hölder apparatus of subdifferentials is used, which extends the class of systems under study beyond traditional smooth optimization and linear approximations. Stability conditions are obtained for solutions to intertemporal choice problems and capital accumulation models in the presence of nonsmooth dependencies, threshold effects, and discontinuities in elasticities. For $\lambda$-Hölder production and utility functions, estimates of the sensitivity of equilibria to parameters are obtained, and indicators of the convergence rate of trajectories to the stationary state are derived for $\lambda >1$. The methodology is tested on a multisectoral model of economic growth with technological shocks and stochastic disturbances in capital dynamics. Numerical experiments confirm the theoretical results: a power-law dependence of equilibrium sensitivity on the magnitude of parametric disturbances is revealed, as well as consistency between the analytical $\lambda$-Hölder convergence rate and the results of numerical integration. Stochastic disturbances of small variance do not violate stability. The results obtained provide a rigorous mathematical foundation for the analysis of complex economic systems with nonsmooth structures, which are increasingly used in macroeconomics, decision theory, and regulation models. Full article

This paper explores the integrability of the Akbota equation with various types of solitary wave solutions. This equation belongs to a class of Heisenberg ferromagnet-type models. The model captures the dynamics of interactions between atomic magnetic moments, as governed by Heisenberg ferromagnetism. To reveal its further physical importance, we calculate more solutions with the applications of the logarithmic transformation, the M-shaped rational solution method, the periodic cross-rational solution technique, and the periodic cross-kink wave solution approach. These methods allow us to derive new analytical families of soliton solutions, highlighting the interplay of discrete and continuous symmetries that govern soliton formation and stability in Heisenberg-type systems. In contrast to earlier studies, our findings present notable advancements. These results hold potential significance for further exploration of similar frameworks in addressing nonlinear problems across applied sciences. The results highlight the intrinsic role of symmetry in the underlying nonlinear structure of the Akbota equation, where integrability and soliton formation are governed by continuous and discrete symmetry transformations. The derived solutions provide original insights into how symmetry-breaking parameters control soliton dynamics, and their novelty is verified through analytical and computational checks. The interplay between these symmetries and the magnetic spin dynamics of the Heisenberg ferromagnet demonstrates how symmetry-breaking parameters control the diversity and stability of optical solitons. Additionally, the outcomes contribute to a deeper understanding of fluid propagation and incompressible fluid behavior. The solutions obtained for the Akbota equation are original and, to the best of our knowledge, have not been previously reported. Several of these solutions are illustrated through 3-D, contour, and 2-D plots by using Mathematica software. The validity and accuracy of all solutions we present here are thoroughly verified. Full article

Based on existing models, this paper incorporates some key ecological factors, thereby obtaining a class of eco-epidemiological models that can more objectively reflect natural phenomena. This model simultaneously integrates disease dynamics within the prey population and the Beddington–DeAngelis functional response, thus achieving an organic combination of ecological dynamics, epidemic transmission, and spatial movement under time-varying environmental conditions. The proposed framework significantly enhances ecological realism by simultaneously accounting for spatial dispersal, predator–prey interactions, disease transmission within prey species, and seasonal or temporal variations, providing a comprehensive mathematical tool for analyzing complex eco-epidemiological systems. The theoretical results obtained from this study can be summarized as follows: Firstly, the existence and uniqueness of globally positive solutions for any positive initial data are rigorously established, ensuring the well-posedness and biological feasibility of the model over extended temporal scales. Secondly, analytically tractable sufficient conditions for uniform population persistence are derived, which elucidate the mechanisms of species coexistence and biodiversity preservation even under sustained epidemiological pressure. Thirdly, by employing innovative applications of differential inequalities and fixed point theory, the existence and uniqueness of a positive spatially homogeneous periodic solution in the presence of time-periodic coefficients are conclusively demonstrated, capturing essential rhythmicities inherent in natural systems. Fourthly, through a sophisticated combination of the upper and lower solution method for parabolic partial differential equations and Lyapunov stability theory, the global asymptotic stability of this periodic solution is rigorously established, offering a powerful analytical guarantee for long-term predictive modeling. Beyond theoretical contributions, these research findings provide actionable insights and quantitative analytical tools to tackle pressing ecological and public health challenges. They facilitate the prediction of thresholds for maintaining ecosystem stability using real-world data, enable the analysis and assessment of disease persistence in spatially structured environments, and offer robust theoretical support for the planning and design of wildlife management and conservation strategies. The derived criteria support evidence-based decision-making in areas such as controlling zoonotic disease outbreaks, maintaining ecosystem stability, and mitigating anthropogenic impacts on ecological communities. A representative numerical case study has been integrated into the analysis to verify all of the theoretical findings. In doing so, it effectively highlights the model’s substantial theoretical value in informing policy-making and advancing sustainable ecosystem management practices. Full article

This paper presents a traffic-driven scaling framework for a digital twin proxy pool (DTPP) in vehicular edge computing (VEC), designed to eliminate the latency and synchronization issues inherent in conventional digital twin (DT) migration approaches. The core innovation lies in replacing the migration of vehicle DTs between edge servers (ESs) with instantaneous switching within a pre-allocated pool of DT proxies, thereby achieving zero migration latency and continuous synchronization. The proposed architecture differentiates between short-term DTs (SDTs) hosted in edge-side in-memory databases for real-time, low-latency services, and long-term DTs (LDTs) in the cloud for historical data aggregation. A queuing-theoretic model formulates the DTPP as an M/M/c system, deriving a closed-form lower bound for the minimum number of proxies required to satisfy a predefined queuing-delay constraint, thus transforming quality-of-service targets into analytically computable resource allocations. The scaling mechanism operates on a cloud–edge collaborative principle: a cloud-based predictor, employing a TCN-Transformer fusion model, forecasts hourly traffic arrival rates to set a baseline proxy count, while edge-side managers perform monotonic, 5 min scale-ups based on real-time monitoring to absorb sudden traffic bursts without causing service jitter. Extensive evaluations were conducted using the PeMS dataset. The TCN-Transformer predictor significantly outperforms single-model baselines, achieving a mean absolute percentage error (MAPE) of 17.83%. More importantly, dynamic scaling at the ES reduces delay violation rates substantially—for instance, from 13.57% under static provisioning to just 1.35% when the minimum proxy count is 2—confirming the system’s ability to maintain service quality under highly dynamic conditions. These findings shows that the DTPP framework provides a robust solution for resource-efficient and latency-guaranteed DT services in VEC. Full article

The accurate and rapid determination of olefin content in gasoline is crucial for fuel quality control. While near-infrared spectroscopy (NIR) offers a rapid analytical solution, multiple parameters in the conventional partial least squares regression (PLSR) modeling process rely on the modeler’s subjective judgment. Consequently, the quantitative accuracy of the model is often influenced by the modeler’s experience. To address this limitation, this study developed an integrated adaptive PLSR framework. The methodology incorporates four core adaptive components: automated selection of latent variables based on the rate of decrease in PRESS values, dynamic formation of calibration subsets using Spectral Angle Distance and sample number thresholds, optimization of informative wavelength regions via correlation coefficients, and systematic database cleaning through iterative residual analysis. Applied to 248 gasoline samples, this strategy dramatically enhanced model performance, increasing the coefficient of determination (R²) from 0.7391 to 0.9102 and reducing the root mean square error (RMSE) from 1.51% to 0.866% compared to the global PLSR model. This work demonstrates that the adaptive PLSR framework effectively mitigates spectral nonlinearity and improves predictive robustness, thereby providing a reliable and practical solution for the on-site, rapid monitoring of gasoline quality using handheld NIR spectrometers. Full article

The fractal extension of the time-dependent Ginzburg–Landau (TDGL) equation, formulated within the framework of Scale Relativity, generalizes superconducting dynamics to non-differentiable space–time. Although analytically well established, its numerical solution remains difficult because of the strong coupling between amplitude and phase curvature. Here we develop two complementary deep learning solvers for the fractal TDGL (FTDGL) system. The Fractal Physics-Informed Neural Network (F-PINN) embeds the Scale-Relativity covariant derivative through automatic differentiation on continuous fields, whereas the Fractal Graph Neural Network (F-GNN) represents the same dynamics on a sparse spatial graph and learns local gauge-covariant interactions via message passing. Both models are trained against finite-difference reference data, and a parametric study over the dimensionless fractality parameter $\mathcal{D}$ quantifies its influence on the coherence length, penetration depth, and peak magnetic field. Across multivortex benchmarks, the F-GNN reduces the relative L₂ error on ${\left|\psi \right|}^2$ from 0.190 to 0.046 and on B_z from approximately 0.62 to 0.36 (averaged over three seeds). This ≈4× improvement in condensate-density accuracy corresponds to a substantial enhancement in vortex-core localization—from tens of pixels of uncertainty to sub-pixel precision—and yields a cleaner reconstruction of the 2π phase winding around each vortex, improving the extraction of experimentally relevant observables such as ξ_eff, λ_eff, and local B_z peaks. The model also preserves flux quantization and remains robust under 2–5% Gaussian noise, demonstrating stable learning under experimentally realistic perturbations. The $\mathcal{D}$—scan reveals broader vortex cores, a non-monotonic variation in the penetration depth, and moderate modulation of the peak magnetic field, while preserving topological structure. These results show that graph-based learning provides a superior inductive bias for modeling non-differentiable, gauge-coupled systems. The proposed F-PINN and F-GNN architectures therefore offer accurate, data-efficient solvers for fractal superconductivity and open pathways toward data-driven inference of fractal parameters from magneto-optical or Hall-probe imaging experiments. Full article

This paper presents a new approach to the dimensional synthesis of a robotic limb mechanism for a wheel-legged robot. The proposed kinematic structure enables independent control of wheel motions relative to the robot platform, allowing each drive to perform a distinct movement. The selection of the mechanism’s common dimensions simplifies platform levelling to a single-drive actuation. The hybrid limb design, which combines features of driving and walking systems, enhances platform stability on uneven terrain and is suitable for rescue, exploration, and inspection robots. The synthesis method defines the desired trajectory of the wheel centre and applies a genetic algorithm to determine mechanism dimensions that reproduce this motion. The stochastic optimisation process yields multiple feasible solutions, enabling the introduction of additional design criteria for optimal configuration selection. Analytical kinematic relations were developed for workspace and trajectory evaluation, solving both direct and inverse kinematic problems. The results confirm the effectiveness of evolutionary optimisation in synthesising complex kinematic mechanisms. The proposed approach can be adapted to other mobile robot structures. Future work will address dynamic modelling, adaptive control for real-time platform levelling, and comparative studies with other synthesis methods. Full article

In this research article, we propose a fuzzy fractional-order SEI$R_i{U}_i$HR model to describe the transmission dynamics of COVID-19, comprising susceptible, exposed, infected, reported, unreported, hospitalized, and recovered compartments. The uncertainty in initial conditions is represented using fuzzy numbers, and the fuzzy Laplace transform combined with the Adomian decomposition method is employed to solve nonlinear differential equations and also to derive approximate analytical series of solutions. In addition to fuzzy lower and upper bound solutions, a model is introduced to provide a representative trajectory under uncertainty. A key feature of the proposed model is its inherent symmetry in compartmental transitions and structural formulation, which show the difference in reported and unreported cases. Numerical experiments are conducted to compare fuzzy and normal (non-fuzzy) solutions, supported by 3D visualizations. The results reveal the influence of fractional-order and fuzzy parameters on epidemic progression, demonstrating the model’s capability to capture realistic variability and to provide a flexible framework for analyzing infectious disease dynamics. Full article