Search Results (936)

In the present article, we study a nonlinear mathematical model for the steady-state non-isothermal flow of a dilute solution of flexible polymer chains between two infinite horizontal plates. Both plates are assumed to be at rest and impermeable, while the flow is driven by a constant pressure gradient. The fluid rheology model used is FENE-P type. The flow energy dissipation (mechanical-to-thermal energy conversion) is taken into account by using the Rayleigh function in the heat transfer equation. On the channel walls, we use one-parameter Navier’s conditions, which include a wide class of flow regimes at solid boundaries: from no-slip to perfect slip. Moreover, we consider the case of threshold-type slip boundary conditions, which state the slipping occurs only when the magnitude of the shear stresses overcomes a certain threshold value. Closed-form exact solutions to the corresponding boundary value problems are obtained. These solutions represent explicit formulas for the calculation of the velocity field, the temperature distribution, the pressure, the extra stresses, and the configuration tensor. The results of the work favor better understanding and more accurate description of complex dynamics and energy transfer processes in FENE-P fluid flows. Full article

A physics-informed neural network (PINN) framework is developed to model the large deformation and coupled electromechanical response of dielectric elastomer tubes for energy harvesting. The system integrates incompressible neo-Hookean elasticity with radial electric loading and compressible gas inflation, leading to nonlinear equilibrium equations with deformation-dependent boundary conditions. By embedding the governing equations and boundary conditions directly into its loss function, the PINN enables accurate, mesh-free solutions without requiring labeled data. It captures realistic pressure–volume interactions that are difficult to address analytically or through conventional numerical methods. The results show that internal volume increases by over 290% during inflation at higher reference pressures, with residual stretch after deflation reaching 9.6 times the undeformed volume. The axial force, initially tensile, becomes compressive at high voltages and pressures due to electromechanical loading and geometric constraints. Harvested energy increases strongly with pressure, while voltage contributes meaningfully only beyond a critical threshold. To ensure stable training across coupled stages, the network is optimized using the Optuna algorithm. Overall, the proposed framework offers a robust and flexible tool for predictive modeling and design of soft energy harvesters. Full article

This study explores the issue of fixed-time dynamic event-triggered consensus control for uncertain nonlinear multi-agent systems (MASs) within directed graph frameworks. In practical applications, the system encounters multiple constraints such as unknown time-varying parameters, unknown external disturbances, and input dead zones, which may increase the communication burden of the system. Therefore, achieving fixed-time consensus tracking control under the aforementioned conditions is challenging. To address these issues, an adaptive fixed-time consensus tracking control method based on boundary estimation and fuzzy logic systems (FLSs) is proposed to achieve online compensation for the input dead zone. Additionally, to optimize the utilization of communication resources, a periodic adaptive event-triggered control (PAETC) is designed. The mechanism dynamically adjusts the frequency at which the trigger is updated in real time, reducing communication resource usage by responding to changes in the control signal. Finally, the efficacy of the proposed approach is confirmed via theoretical evaluation and simulation. Full article

This research paper delves into the application of optimality results in orthogonal fuzzy metric spaces to demonstrate the existence and uniqueness of solutions of nonlinear differential equations with boundary conditions and nonlinear integral equations, emphasizing the importance of orthogonal fuzzy metric spaces in extending fixed-point theory. Through introducing this innovative concept, the study provides a theoretical framework for analyzing mappings in diverse scenarios. In this study, we introduce the concept of best proximity point (BPP) within the framework of orthogonal fuzzy metric spaces by employing orthogonal fuzzy proximal contractive mappings. Moreover, this research explores the implications of the established results, considering both self-mappings and non-self mappings that share the same parameter set. Additionally, some examples are provided to illustrate the practical relevance of the proven results and consequences in various mathematical contexts. The findings of this study can open up avenues for further exploration and application in solving real-world problems. Full article

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

In this work, we investigate the stability of solutions in a situation where the logarithmic source term competes with the viscoelastic dissipation under acoustic boundary conditions. We assume minimal conditions on the relaxation function g, namely, $g^{\prime }\left(t\right)\le -\xi \left(t\right)H\left(g\left(t\right)\right)$, where H is a strictly increasing and strictly convex function near the origin, and $\xi \left(t\right)$ is a non-increasing function. Under these general assumptions, we establish a general decay estimate for the solution. This result extends and improves some previous results. Full article

Pumping station structures are widely employed to supply circulating cooling water systems in nuclear power plants (NPPs) throughout China. Investigating their seismic performance under complex heterogeneous site conditions and load scenarios is paramount to meeting nuclear safety design requirements. This study proposes and implements a novel, efficient, and accurate viscous-spring boundary methodology within the ANSYS 19.1 finite element software to assess the seismic safety of NPP pumping station structures. The Maximum Initial Time-step (MIT) method, based on Newmark’s integration scheme, is employed for nonlinear analysis under coupled static–dynamic excitation. To account for radiation damping in the infinite foundation, a Compact Viscous-Spring (CVs) element is developed. This element aggregates stiffness and damping contributions to interface nodes defined at the outer border of the soil domain. Implementation leverages of ANSYS User Programmable Features (UPFs), and a comprehensive static–dynamic coupled analysis toolkit is developed using APDL scripting and the GUI. Validation via two examples confirms the method’s accuracy and computational efficiency. Finally, a case study applies the technique to an NPP pumping station under actual complex Chinese site conditions. The results demonstrate the method’s capability to provide objective seismic response and stability indices, enabling a more reliable assessment of seismic safety during a Safety Shutdown Earthquake (SSE). Full article

Tailless unmanned aerial vehicles (UAVs) achieve high-agility maneuvers with flight control systems. The attainable moment set (AMS) provides critical theoretical foundations and constraints for their optimization. A computational method is proposed herein to address controllability limitations caused by nonlinear aerodynamic effectiveness. This method incorporates dual constraints on control surface angles and angular rates for the nonlinear AMS, aiming to meet the demands of attitude tracking dynamics in flight control systems. First, a quantitative model is established to correlate dual deflection constraints with aerodynamic moment amplitude and bandwidth limitations. Next, we construct a computational framework for the incremental attainable moment set (IAMS) based on differential inclusion theory. For monotonic nonlinear aerodynamic effectiveness, the vertices of the IAMS are updated using local interpolation, yielding the incremental nonlinear attainable moment set (INAMS). When non-monotonic nonlinearity occurs, stationary points are calculated to adjust the control effectiveness matrix and admissible control set, thereby reducing computational errors induced by non-monotonic characteristics. Furthermore, the effective actions set, derived from a time-varying incremental nonlinear attainable moment set, quantifies the residual moment envelope of tailless UAVs during maneuvers. Comparative simulations indicate that the proposed method achieves correct computation under nonlinear aerodynamic conditions while reliably determining safe flight boundaries during control failure. Full article

This study develops a vibration model for functionally graded material (FGM) plates with embedded planar cracks. Based on thin plate theory and von Kármán-type geometric nonlinear strain assumptions, the kinetic and potential energies of each region are derived. Displacement field trial functions are constructed according to boundary conditions, and the Ritz method is employed to determine natural frequencies and vibration modes under small deformation conditions. The investigation focuses on how crack parameters and material gradient coefficients affect vibration characteristics in exponentially graded FGM plates. The results show that natural frequencies decrease with increasing crack length, while crack presence alters nodal line patterns and mode symmetry. During free vibration, the upper and lower surfaces of the crack region exhibit relative displacement. Material gradient effects induce thickness–direction asymmetry, causing non-uniform displacements between the plate’s upper and lower sections. Full article

This study demonstrates the effectiveness of the differential transform method (DTM) in solving complex solid mechanics problems, focusing on static analysis of beams under various loads and boundary conditions. For cantilever beams (BSM1), DTM provided exact polynomial solutions for deflections and slopes: a cubic solution for concentrated end loads, a quadratic distribution for applied moments, and a fourth-degree polynomial for uniformly distributed loads, all matching established theoretical results. For simply supported beams (BSM2), DTM yielded solutions across two intervals for midspan concentrated forces, though required corrective terms for applied moments due to discontinuities. Under uniform loading, the method produced precise polynomial solutions with maximum deflection at midspan. Key advantages include DTM’s high-precision analytical solutions without additional approximations and its adaptability to diverse loading scenarios. However, for cases with pronounced discontinuities like concentrated moments, supplementary methods (e.g., Green’s functions) may be needed. The study highlights DTM’s potential for extension to nonlinear or dynamic problems, while software integration could broaden its engineering applications. This study demonstrates, for the first time, how DTM yields exact polynomial solutions for Euler–Bernoulli beams under discontinuous loads (e.g., concentrated moments), overcoming limitations of traditional numerical methods. The method’s analytical precision and avoidance of discretization errors are highlighted. Traditional methods like FEM require mesh refinement near discontinuities (e.g., concentrated moments), leading to computational inefficiencies. DTM overcomes this by providing exact polynomial solutions with corrective terms, achieving errors below 0.5% with only 4–5 series terms. Full article

This work investigates the intricate dynamics of the Carreau hybrid nanofluid’s inclined magnetohydrodynamic (MHD) flow, exploring both active and passive control modes. The study incorporates critical factors, including Arrhenius activation energy across a stretched sheet, chemical interactions, and nonlinear thermal radiation. The formulation of the boundary conditions and governing equations is inherently influenced by symmetric considerations in the physical geometry and flow assumptions. Such symmetry-inspired modeling facilitates dimensional reduction and numerical tractability. The analysis employs realistic boundary conditions, including convective heat transfer and control of nanoparticle concentration, which are solved numerically using MATLAB’s bvp5c solver. Findings indicate that an increase in activation energy results in a steeper concentration boundary layer under active control, while it flattens in passive scenarios. An increase in the Biot number ($Bi$) and relaxation parameter ($\mathsf{\Gamma }$) enhances heat transfer and thermal response, leading to a rise in temperature distribution in both cases. Additionally, the 3D surface plot illustrates elevation variations from the surface at low inclination angles, narrowing as the angle increases. The Nusselt number demonstrates a contrasting trend, with thermal boundary layer thickness increasing with higher radiation parameters. A graphical illustration of the average values of skin friction, Nusselt number, and Sherwood number for both active and passive scenarios highlights the impact of each case. Under active control, the Brownian motion’s effect diminishes, whereas it intensifies in passive control. Passive techniques, such as zero-flux conditions, offer effective and low-maintenance solutions for systems without external regulation, while active controls, like wall heating and setting a nanoparticle concentration, maximize heat and mass transfer in shear-thinning Carreau fluids. Full article

The control of many industrial processes, such as superheated steam temperature control, exhibits poor robustness and degraded accuracy in the presence of model parameter uncertainties. This paper addresses this issue by developing a novel interval power integration-based nonlinear suppression scheme for a class of uncertain nonlinear systems with unknown but bounded parameters. The efficacy of this approach is specifically demonstrated for the superheated steam temperature control in thermal power plants. By integrating Lyapunov stability theory and homogeneous system theory, this method extends the traditional homogeneous degree theory to the interval domain, establishes interval boundary conditions for time-varying parameters, and constructs a Lyapunov function with interval numbers to recursively design the controller. Furthermore, the interval monotonic homogeneous degree and an admissibility index are introduced to ensure system stability under parameter uncertainties. The effectiveness of the proposed method is verified through numerical simulations of superheated steam temperature control. Simulation results demonstrate that the method effectively suppresses nonlinearities and achieves robust asymptotic stability, even when model parameters vary within bounded intervals. In the varying-exponent scenario, the proposed controller achieved an Integral of Absolute Error (IAE) of 70.78 and a convergence time of 37s for the superheated steam temperature control. This represents a performance improvement of 42.79% in IAE and 53.16% in convergence time compared to a conventional PID controller, offering a promising solution for complex thermal processes with inherent uncertainties. Full article

In this manuscript, we study a class of nabla fractional difference equations with summation boundary conditions that depend on a parameter. We construct the Green’s function related to the linear problem and we deduce some of its properties. First, we obtain an upper bound of the sum of it, and use this property to give an existence result for the considered problem based on the Leray–Shauder nonlinear alternative. Then, we establish some bounds on the parameter in which the Green’s function is positive, and by using Krasnoselski–Zabreiko fixed-point theorem, we deduce another existence result. Finally, we give some particular examples in order to demonstrate our primary findings. Full article

This study investigates the dynamics of dust acoustic periodic waves in a three-component, unmagnetized dusty plasma system using generalized $(r^{\star },q^{\star })$ distributions. First, boundary conditions are applied to reduce the model to a second-order nonlinear ordinary differential equation. The Galilean transformation is subsequently applied to reformulate the second-order ordinary differential equation into an unperturbed dynamical system. Next, phase portraits of the system are examined under all possible conditions of the discriminant of the associated cubic polynomial, identifying regions of stability and instability. The Runge–Kutta method is employed to construct the phase portraits of the system. The Hamiltonian function of the unperturbed system is subsequently derived and used to analyze energy levels and verify the phase portraits. Under the influence of an external periodic perturbation, the quasi-periodic and chaotic dynamics of dust ion acoustic waves are explored. Chaos detection tools confirm the presence of quasi-periodic and chaotic patterns using Basin of attraction, Lyapunov exponents, Fractal Dimension, Bifurcation diagram, Poincaré map, Time analysis, Multi-stability analysis, Chaotic attractor, Return map, Power spectrum, and 3D and 2D phase portraits. In addition, the model’s response to different initial conditions was examined through sensitivity analysis. Full article

In this paper, we propose the MUSWENO scheme, a novel mapped weighted essentially non-oscillatory (WENO) method that employs unequal-sized stencils, for solving nonlinear degenerate parabolic equations. The new mapping function and nonlinear weights are proposed to reduce the difference between the linear weights and nonlinear weights. Smaller numerical errors and fifth-order accuracy are obtained. Compared with traditional WENO schemes, this new scheme offers the advantage that linear weights can be any positive numbers on the condition that their summation is one, eliminating the need to handle cases with negative linear weights. Another advantage is that we can reconstruct a polynomial over the large stencil, while many classical high-order WENO reconstructions only reconstruct the values at the boundary points or discrete quadrature points. Extensive examples have verified the good representations of this scheme. Full article