Search Results (243)

We are especially interested in the general framework and ability of a semi-analytic method (SAM) to use the trigonometric basis function (TBF) in different domains. Moreover, the stabilizing effect of increasing boundary nodes on the convergence of the method when a level of noise is added to the boundary data of the inverse boundary value problem for the nonlinear Rayleigh–Stokes (R-S) equation is investigated. The solution of the ill-conditioned Rayleigh–Stokes equation which the equation is reduced to the linear system $\Im \left[\mathcal{C}\right]=♭$ with corrupted boundary data by quasilinearization technical on nonlinear source terms relies on TBFs and radial basis functions (RBFs). Finally, the implementation of the scheme is supported by the numerical experiments. Full article

Developing improved mathematical and numerical models of groundwater flow is crucial for monitoring and forecasting water resources. Most existing models are linear and fail to capture the complex physical processes involved in groundwater dynamics. This study aims to develop a nonlinear mathematical model for observing and forecasting changes in groundwater levels influenced by water intake wells, evaporation, and precipitation. The proposed mathematical model is formulated as a nonlinear differential equation. To solve this model, it was reduced to a dimensionless form, and the quasi-linearization method was employed to simplify the calculations. The finite difference method was then used to obtain a numerical solution. An algorithm and software were developed to demonstrate the results of the calculations. Numerical calculations performed using the developed software provide insights into the effects of water intake wells, surface evaporation, and precipitation on groundwater levels. The findings of this study hold practical significance for optimizing the sustainable use of water resources and highlighting how the location and flow rate of water intake wells impact groundwater levels. Full article

This study presents a hyperbolic three-dimensional telegraph interface model with regular interfaces, numerically solved using a hybrid scheme that integrates Haar wavelets and the finite difference method. Spatial derivatives are approximated via a truncated Haar wavelet series, while temporal derivatives are discretized using the finite difference method. For linear problems, the resulting algebraic system is solved using Gauss elimination; for nonlinear problems, Newton’s quasi-linearization technique is applied. The method’s accuracy and stability are evaluated through key performance metrics, including the maximum absolute error, root mean square error, and the computational convergence rate $R_c\left(M\right)$, across various collocation point configurations. The numerical results confirm the proposed method’s efficiency, robustness, and capability to resolve sharp gradients and discontinuities with high precision. Full article

Continuous SiC fiber-reinforced SiC matrix composites (SiC/SiC), as structural heat protection integrated materials, are often used in parts for large-area heat protection and sharp leading edges, and there are a variety of low-velocity impact events in their service. In this paper, a drop hammer impact test was conducted using narrow strip samples to simulate the low-velocity impact damage process of sharp-edged components. During the test, different impact energies and impact times were set to focus on investigating the low-velocity impact damage characteristics of 2.5D SiC/SiC composites. To further analyze the damage mechanism, computed tomography (CT) was used to observe the crack propagation paths and distribution states of the composites before and after impact, while scanning electron microscopy (SEM) was employed to characterize the differences in the micro-morphology of their fracture surfaces. The results show that the in-plane impact behavior of a 2.5D needled SiC/SiC composite strip samples differs from the conventional three-stage pattern. In addition to the three stages observed in the energy–time curve—namely in the quasi-linear elastic region, the severe load drop region, and the rebound stage after peak impact energy—a plateau stage appears when the impact energy is 1 J. During the impact process, interlayer load transfer is achieved through the connection of needled fibers, which continuously provide significant structural support, with obvious fiber pull-out and debonding phenomena. When the samples are subjected to two impacts, damage accumulation occurs inside the material. Under conditions with the same total energy, multiple impacts cause more severe damage to the material compared to a single impact. Full article

The compressive capacity of helical anchors constitutes a pivotal performance parameter in geotechnical design. To precisely predict the compressive bearing behavior of helical anchors in aeolian sand, this study integrates in situ testing with finite element numerical analysis to systematically elucidate the non-linear evolution of its load-bearing mechanisms. The XGBoost algorithm enabled the rigorous quantification of the governing geometric features of compressive capacity, culminating in a computational framework for the bearing capacity factor (N_q) and lateral earth pressure coefficient (K_u). The research findings demonstrate the following: (1) Compressive capacity exhibits significant enhancement with increasing helix diameter yet displays limited sensitivity to helix number. (2) Load–displacement curves progress through three distinct phases—initial quasi-linear, intermediate non-linear, and terminal quasi-linear stages—under escalating pressure. (3) At embedment depths of H < 5D, tensile capacity diminishes by approximately 80% relative to compressive capacity, manifesting as characteristic shallow anchor failure patterns. (4) When H ≥ 5D, stress redistribution transitions from bowl-shaped to elliptical contours, with ≤10% divergence between uplift/compressive capacities, establishing 5D as the critical threshold defining shallow versus deep anchor behavior. (5) The helix spacing ratio (S/D) governs the failure mode transition, where cylindrical shear (CS) dominates at S/D ≤ 4, while individual bearing (IB) prevails at S/D > 4. (6) XGBoost feature importance analysis confirms internal friction angle, helix diameter, and embedment depth as the three parameters exerting the most pronounced influence on capacity. (7) The proposed computational models for N_q and K_u demonstrate exceptional concordance with numerical simulations (mean deviation = 1.03, variance = 0.012). These outcomes provide both theoretical foundations and practical methodologies for helical anchor engineering in aeolian sand environments. Full article

Silty clay is extensively distributed in northern China. Numerous seismic events have demonstrated that underground structures embedded in silty clay strata are prone to severe damage during earthquakes. This study employs dynamic cyclic triaxial tests on undisturbed and remolded specimens (50–300 kPa confining pressures) to pioneer the quantification of pressure-amplified structural superiority. The experimental results reveal that: (1) Undisturbed soils exhibit 20–30% higher maximum shear stress (τ_dmax) and shear modulus (G_dmax) than remolded counterparts at 300 kPa, far exceeding the <5% deviation at 50 kPa due to enhanced particle-cementation synergy under pressure. (2) The normalized shear modulus ratio (G_d/G_dmax) exhibits low sensitivity to confining pressure, with G_d/G_dmax–γ_d relationship curves predominantly confined within a narrow band range. A triphasic evolutionary characteristic is manifested in the progressive reduction of G_d/G_dmax with increasing shear strain (γ_d), and quasi-linear attenuation is observed within the shear strain range of 1 × 10⁻⁴ ≤ γ_d ≤ 1 × 10⁻². (3) Remolded and undisturbed specimens demonstrate close correspondence in damping ratio (λ_d) across consolidation pressures. Under identical γ_d conditions, undisturbed specimens consistently exhibit lower λ_d values than remolded counterparts, attributable to enhanced energy dissipation resulting from structural homogenization in remolded soils, with λ_dmax magnitudes ranging between 0.2 and 0.3. The research provides mechanistic insights for seismic design of underground structures in silty clay terrains, particularly regarding disturbance sensitivity under deep burial conditions. Full article

In recent decades, the deployment of quadcopters has significantly expanded, particularly in outdoor applications such as parcel delivery. These missions require highly stable aerial platforms capable of maintaining balance under diverse environmental conditions, ensuring the safe operation of both the drone and its payload. This paper focuses on the stabilization of a quadcopter designed for outdoor use. A detailed dynamic model of a compact vertical takeoff and landing (VTOL) drone forms the basis for a non-linear control strategy targeting stability during the critical takeoff phase. The control law is designed using a quasi-linear parameter-varying (quasi-LPV) model that captures the system’s non-linear dynamics. Lyapunov theory and linear matrix inequalities (LMIs) are employed to validate the stability and design the controller. Numerical simulations demonstrate the controller’s effectiveness, and a comparative study is conducted to benchmark its performance against a reference quadrotor model. Full article

We investigate the behavior of solutions of second-order elliptic Dirichlet problems for a convex domain by using a “gliding hump” technique and prove that there are no contour limits at a specified point of the boundary of the domain. Then we consider two-dimensional domains which have a reentrant (i.e., nonconvex) corner at a point P of the boundary of the domain. Assuming certain comparison functions exist, we prove that for any solution of an appropriate Dirichlet problem on the domain whose graph has finite area, there are infinitely many curves of finite length in the domain ending at P along which the solution has a limit at P. We then prove that such behavior occurs for quasilinear operations with positive genre. Full article

Cross-Track Interferometric Synthetic Aperture Radar (XTI-SAR) can utilize variations in interferometric phase to measure sea surface velocity along radar radial direction and sea surface height, which can be used for ocean wave parameter inversion. However, research on the imaging mechanisms of XTI-SAR systems for ocean waves remains understudied, and there are still some problems in its perception. To further study the imaging mechanism of XTI-SAR measurement systems for ocean waves, this paper describes research based on the nonlinear integral transform model and the quasi-linear integral transform model derived by Bao in 1999, which relate the XTI-SAR ocean wave spectrum to the phase spectrum. Firstly, this work derived another quasi-linear integral transform model based on the nonlinear integral transform model, and also optimized the quasi-linear integral transform model derived by Bao. The optimized quasi-linear integral transform model eliminates the need for complex calculations of cross-correlation functions between sea surface height and radar radial orbital velocity components of ocean waves, as well as the radar line-of-sight velocity transfer function, while maintaining high integral transform accuracy. Secondly, based on two-dimensional sea surface simulations, we analyzed the differences between the quasi-linear integral transform models and the nonlinear integral transform model corresponding to different XTI-SAR system configurations and different sea states. The numerical simulation results show that, for the XTI-SAR system, in general, the difference between the quasi-linear integral transform model derived in this work and the nonlinear integral transform model is greater than that of the quasi-linear integral transform model derived by Bao. However, the difference between the optimized quasi-linear integral transform model and the nonlinear integral transform model in this study is smaller, and it is more convenient when transforming the ocean wave spectrum to the phase spectrum. Full article

The accurate prediction of space target trajectories is critical for aerospace defense and space situational awareness, yet it remains challenging due to complex nonlinear dynamics, measurement noise, and environmental uncertainties. This study proposes a confidence-based dual-model fusion framework that separately processes linear and nonlinear trajectory components to enhance prediction accuracy and robustness. The Attention-Based Convolutional Long Short-Term Memory (AC-LSTM) network is designed to capture nonlinear motion patterns by leveraging temporal attention mechanisms and convolutional layers while also estimating confidence levels via a signal-to-noise ratio (SNR)-based multitask learning approach. In parallel, the Kalman Filter (KF) efficiently models quasi-linear motion components, dynamically estimating its confidence through real-time residual monitoring. A confidence-weighted fusion mechanism adaptively integrates the predictions from both models, significantly improving overall prediction performance. Experimental results on simulated radar-based noisy trajectory data demonstrate that the proposed method outperforms conventional algorithms, offering superior precision and robustness. This approach holds great potential for applications in pace situational awareness, orbital object tracking, and space trajectory prediction. Full article

In this article, the validity of the comparison principle (CP) for weakly coupled quasi-linear cooperative systems with delays is proven. This is a powerful tool for studying the qualitative properties of the solutions. The CP is crucial in the proofs of the existence and uniqueness of weak solutions to cooperative reaction–diffusion systems presented here. Other direct consequences of the CP are the stability of the solution, the attenuation of long time periods, etc. An example model is given by spatial SEIR models with delays. They are suitable for modeling disease spread in space and time and can be described using a weakly coupled cooperative reaction–diffusion system. In this paper, spatial SEIR models with delays are considered in a continuous space. The emphasis is on the qualitative properties of the solutions, which are important for providing a mathematical basis for the model. Full article

This study investigates the existence and multiplicity of weak solutions for a class of degenerate weighted quasilinear elliptic equations that incorporate nonlocal nonlinearities, a double Hardy term, and variable exponents. The problem encompasses a degenerate nonlinear operator characterized by variable exponent growth, along with a nonlocal interaction term and specific constraints on the nonlinearity. By employing critical point theory, we establish the existence of at least three weak solutions under sufficiently general assumptions. Full article

In the framework of lightweight aircraft preliminary design and optimisation, different computational approaches are formulated and assessed for the large-amplitude static aeroelastic response of very-flexible slender thin wings in subsonic incompressible flow at low speed. Starting from either a continuous or a discrete model, either numerical or semi-analytical solutions are derived and compared for several combinations of flow speed and angle of attack. Exploiting the Euler–Bernoulli beam idealisation for the wing structure and its local deformation, non-linear and quasi-linear models are presented where the elastic axis is inextensible and its global displacement is geometrically nonlinear; to this purpose, Hencky’s model is also adopted. Employing modified strip theory for the airload, reduced-order conceptual assessments and parametric evaluations are possible, and the results are shown for the Pazy wing which exhibit excellent agreement with nonlinear higher-fidelity simulations in the literature. Both closed-loop and open-loop solutions are then provided, with the latter being readily resumed from the former in the low-speed limit far away from static aeroelastic divergence. In conclusion, the novel approaches hereby explored demonstrate overall consistency while offering both theoretical insights and practical recommendations for their trust region, especially in terms of the impact and importance of the linear and nonlinear features as well as their effects. Full article

There are three principal novelties in the present investigation. It is the first time Cohen–Grossberg-type neural networks are considered with the most general delay and advanced piecewise constant arguments. The model is alpha unpredictable in the sense of electrical inputs and is researched under the conditions of alpha unpredictable and Poisson stable outputs. Thus, the phenomenon of ultra Poincaré chaos, which can be indicated through the analysis of a single motion, is now confirmed for a most sophisticated neural network. Moreover, finally, the approach of pseudo-quasilinear reduction, in its most effective form is now expanded for strong nonlinearities with time switching. The complexity of the discussed model makes it universal and useful for various specific cases. Appropriate examples with simulations that support the theoretical results are provided. Full article

In this study, our aim is to diagnose how two quasi-linear convective systems (QLCS) are organized so one can determine the possible role of the city of Chicago, IL, USA, in modifying convective precipitation systems. In this Part I of a two-part study, we employ large-scale analyses, radiosonde soundings, surface observations, and Doppler radar data to diagnose the precursor atmospheric circulations that organize the evolution of two mesoscale convective systems and compare those circulations to radar and precipitation. Several multi-scale processes are found that organize and modify convection over the Chicago metroplex. Two sequential quasi-linear convective systems (QLCS #1 and #2) were organized that propagated over Chicago, IL, USA, during an eight-hour period on 5–6 July 2018. The first squall line (QLCS #1) built from the southwest to the northeast while strengthening as it propagated over the city, and the second (QLCS #2) propagated southeastwards and weakened as it passed over the city in association with a polar cold front. The weak upper-level divergence associated with a diffluent flow poleward of an expansive ridge built over and strengthened a low-level trough and confluence zone, triggering QLCS #1. Convective downdrafts from QLCS #1 produced a cold pool that interacted with multiple confluent low-level jets surrounding and focused on the metroplex urban heat island, thus advecting the convection poleward over the metroplex. The heaviest precipitation occurred just south-southeast of Midway Airport, Chicago. Subsequently, a polar cold front propagated into the metroplex, which triggered QLCS #2. However, the descending air above it under the polar jet and residual cold pool from QLCS #1 rapidly dissipated the cold frontal convection. This represents a case study where very active convection built over the metroplex and was likely modified by it, as evidenced in numerical simulations to be described in Part II. Full article