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Nanofluids, with their enhanced thermal properties, provide innovative solutions for improving heat transfer efficiency in renewable energy systems. This study investigates a numerical simulation of bioconvective flow and heat transfer in a Williamson nanofluid over a stretching wedge, incorporating the effects of chemical reactions and hydrogen diffusion. The system also includes motile microorganisms, which induce bioconvection, a phenomenon where microorganisms’ collective motion creates a convective flow that enhances mass and heat transport processes. This mechanism is crucial for improving the distribution of nanoparticles and maintaining the stability of the nanofluid. The unique rheological behavior of Williamson fluid, extensively utilized in hydrometallurgical and chemical processing industries, significantly influences thermal and mass transport characteristics. The governing nonlinear partial differential equations (PDEs), derived from conservation laws and boundary conditions, are converted into dimensionless ordinary differential equations (ODEs) using similarity transformations. MATLAB’s bvp4c solver is employed to numerically analyze these equations. The outcomes highlight the complex interplay between fluid parameters and flow characteristics. An increase in the Williamson nanofluid parameters leads to a reduction in fluid velocity, with solutions observed for the skin friction coefficient. Higher thermophoresis and Williamson nanofluid parameters elevate the fluid temperature, enhancing heat transfer efficiency. Conversely, a larger Schmidt number boosts fluid concentration, while stronger chemical reaction effects reduce it. These results are generated by fixing parametric values as $0.1<\varpi <1.5, 0.1<\mathit{Nr}<3.0, 0.2<\mathrm{Pr}<0.5, 0.1<\mathit{Sc}<0.4, \mathrm{and} 0.1<\mathit{Pe}<1.5.$ This work provides valuable insights into the dynamics of Williamson nanofluids and their potential for thermal management in renewable energy systems. The combined impact of bioconvection, chemical reactions, and advanced rheological properties underscores the suitability of these nanofluids for applications in solar thermal, geothermal, and other energy technologies requiring precise heat and mass transfer control. This paper is also focused on their applications in solar thermal collectors, geothermal systems, and thermal energy storage, highlighting advanced experimental and computational approaches to address key challenges in renewable energy technologies. Full article

In the process of energy harvesting, vibration energy harvesting still has several disadvantages, including a high-threshold excitation and a narrow working bandwidth. Therefore, a 2-degrees-of-freedom piezoelectric energy harvester is proposed. By introducing a nonlinear magnetic force to the system, the working bandwidth and the energy-harvesting efficiency of three magnetically coupled piezoelectric cantilever beams can be effectively improved. In this paper, a mathematical model consisting of three electrically coupled magnetically coupled piezoelectric cantilever beam systems is established, and the governing equations of electric coupling are solved numerically and verified experimentally. The dynamic characteristics under different excitations and frequencies are studied. The experiment shows that the working bandwidth can be increased by controlling the distance between three pairs of circular magnets and changing the excitation and frequency to induce resonance. Thus, the self-power requirement of micro-power devices can be realized. Overall, this study provides a promising solution for improving the performance of piezoelectric energy harvesters and offers theoretical insights for designing vibrating piezoelectric energy harvesters. Full article

An efficient linearization method for solving a system of nonlinear equations was developed, showing good stability and convergence properties. It uses an unconventional and simple strategy to improve the performance of classic methods by a full-rank update of the Jacobian approximates. It can be considered both as a discretized Newton’s method or as a quasi-Newton method with a full-rank update of the Jacobian approximates. A solution to the secant equation presented earlier was based on the Wolfe-Popper procedure. The secant equation was splitted into two equations by introducing an auxiliary variable. A simplified algorithm is given in this paper for the full-rank update procedure.It directly solves the secant equation with the pseudoinverse of the Jacobian approximate matrix. Numerical examples are shown for demonstration purposes. The convergence and efficiency of the suggested method are discussed and compared with the convergence and efficiency of classic linearization methods. Full article

In this article, we define a new class of noncommuting self mappings known as the S-operator pair. Also, we provide the existence and uniqueness of common fixed point results involving the S-operator pair satisfying the $(F,\phi ,\psi ,Z)$-contractive condition in m-metric spaces, which unifies and generalizes most of the existing relevant fixed point theorems. Furthermore, the variables in the m-metric space are symmetric, which is significant for solving nonlinear problems in operator theory. In addition, examples are provided in order to illustrate the concepts and results presented herein. It has been demonstrated that the results can be applied to prove the existence of a solution to a system of integral equations, a nonlinear fractional differential equation and an ordinary differential equation for damped forced oscillations. Also, in the end, the satellite web coupling problem is solved. Full article

This research focuses on the dynamic analysis of an oscillating conveyor mechanism using numerical methods to solve nonlinear differential equations that govern its motion. The system under study is modeled by a second-order differential equation of the form $R\left(t\right){\displaystyle \frac{d{\omega }_1}{dt}}+Q\left(t\right){\omega }_1^2\left(t\right)=W\left(t\right)$, where R(t), Q(t), and W(t) are time-dependent functions representing system parameters such as resistance, damping, and external driving forces. To solve these equations, we employed a numerical approach based on Euler’s method, which discretizes the time domain into small steps h and approximates the derivatives of angular velocity and angular displacement. The angular velocity ${\omega }_{k+1}$ and angular displacement ${\phi }_{k+1}$ are updated iteratively using the formulas ${\omega }_{k+1}={\omega }_k+h\left({\displaystyle \frac{W_k}{R_k}}-{\displaystyle \frac{Q_k}{R_k}}{\omega }_k^2\right)$ and ${\phi }_{k+1}={\phi }_k+h{\omega }_k$, respectively. Initial conditions, with ${\omega }_0=0$ and ${\phi }_0=0$, were specified, and the system was simulated over a specified time range divided into N time steps. In the simulation, key parameters such as $A\left(t\right)$, B(t), D(t), E(t), F(t), $H\left(t\right)$, N(t), M(t), $Q\left(t\right)$, $R\left(t\right)$, and $W\left(t\right)$ were evaluated at each time step based on the system’s geometry and the angular displacements. Due to the complexity of the system, analytical solutions were impractical, so the Runge–Kutta method was employed for higher accuracy in the integration process. The results from the numerical simulations were validated by comparing them with theoretical expectations, and the system’s dynamic behavior was visualized using time-series and 3D plots. The simulation demonstrated that the system’s stability and accuracy were highly dependent on the time step h, with smaller values providing more precise results at the cost of increased computational time. The research confirms the applicability of numerical methods in solving complex nonlinear differential equations for dynamic systems and provides insights into the system’s behavior under various operating conditions. Full article

Data on the diffusion and migration characteristics of rare earth metal ions in fluoride molten salt systems are crucial for optimizing the electrolytic preparation of rare earth metals and alloys. This study investigated the solubility, conductivity, and density of the (LiF-CaF₂)_eut. system saturated with Nd₂O₃ using the isothermal saturation method, conductivity cell constant variation, and the Archimedes method, respectively. Employing the Hittorf method’s principles, a three-compartment electrolyzer was designed to determine the mobility number of dissolved Nd* (III) ions in the saturated (LiF-CaF₂)_eut.-Nd₂O₃ system. The radial distribution function was computed via ab initio molecular dynamics, and the self-diffusion coefficient of ions in the system was analyzed. Utilizing the Nernst–Einstein equation, the diffusion coefficient of Nd* (III) ions was calculated. The solubility, conductivity, and density of the saturated (LiF-CaF₂)_eut.-Nd₂O₃ system exhibit linear variation within 1173–1473 K. The mobility number of solvated Nd* (III) ions increases linearly with temperature, displaying nonlinear variation with potential within 3.5–4.5 V, and gradually decreases after reaching a maximum of 4.0–4.25 V. The radial distribution function reveals the highest diffusion and mobility barriers for Nd* (III) ions, with solvated O* (II) ions presenting the most significant hindrance. The Nd* (III) ion diffusion coefficients linearly increase with temperature (1123–1373 K) under specific potential conditions (3.5–4.5 V) but exhibit nonlinear changes with potential (3.5–4.5 V) under fixed temperature conditions (1123–1373 K), then decrease after peaking within 4.0–4.5 V. The diffusion coefficients of Nd* (III) ions are sensitive to potential changes. Full article

A family of strongly nonlinear nonstationary equations of mathematical physics with three independent variables is investigated, which contain an arbitrary degree of the first derivative with respect to time and a quadratic combination of second derivatives with respect to spatial variables of the Monge–Ampère type. Individual PDEs of this family are encountered, for example, in electron magnetohydrodynamics and differential geometry. The symmetries of the considered parabolic Monge–Ampère equations are investigated by group analysis methods. Formulas are obtained that make it possible to construct multiparameter families of solutions based on simpler solutions. Two-dimensional and one-dimensional symmetry and non-symmetry reductions are considered, which lead to the original equation to simpler partial differential equations with two independent variables or ordinary differential equations or systems of such equations. Self-similar and other invariant solutions are described. A number of new exact solutions are constructed by methods of generalized and functional separation of variables, many of which are expressed in elementary functions or in quadratures. To obtain exact solutions, the principle of the structural analogy of solutions was also used, as well as various combinations of all the above-mentioned methods. In addition, some solutions are constructed by auxiliary intermediate-point or contact transformations. The obtained exact solutions can be used as test problems intended to check the adequacy and assess the accuracy of numerical and approximate analytical methods for solving problems described by highly nonlinear equations of mathematical physics. Full article

An HVDC-GIL system with a conical spacer in a radioactive environment is studied in this work using simulated data on COMSOL^® Multiphysics. Electromagnetic simulations on a 2D model were performed with varying ion-pair generation rates and potential applied to the system. This article explores machine learning methods to derive time to steady state, dark current, gas conductivity, and surface charge density expressions. The focus was on constructing symbolic representations, which could be interpretable and less prone to overfitting, using the symbolic regression (SR) and sparse identification of nonlinear dynamics (SINDy) algorithms. The study successfully derived the intended expressions, demonstrating the power of symbolic regression. Predictions of dark currents in the gas–ground electrode interface reported an absolute error and mean absolute percentage error (MAPE) of 1.04 × ${10}^{-4}$ pA and 0.01%, respectively. The solid–ground electrode interface reported an error of 8.99 × ${10}^{-5}$ pA and MAPE of 0.04%, showing strong agreement with simulation data. Expressions for time to steady state had a test error of approximately 110 h with MAPE of around 3%. Steady-state gas conductivity expression achieved an absolute error of 0.55 log(S/m) and MAPE of 1%. An interpretable equation was created with SINDy to model the time evolution of surface charge density, achieving a root mean squared error of 1.12 nC/m²/s across time-series data. These results demonstrate the capability of SR and SINDy to provide interpretable and computationally efficient alternatives to time-consuming numerical simulations of HVDC systems under radiation conditions. While the model provides useful insights, performance and practical applications of the expressions can improve with more diverse datasets, which might include experimental data in the future. Full article

The study is dedicated to the statistical optimization of radar imaging of surfaces with the synthetic aperture radar (SAR) technique, assuming a static surface area and applying the ability to move a sensor along a nonlinear trajectory via developing a new method and validating its operability for remote sensing and non-destructive testing. The developed models address the sensing geometry for signals reflected from a surface along with the observation signal–noise equation, including correlation properties. Moreover, the optimal procedures for coherent radar imaging of surfaces with the static SAR technology are synthesized according to the maximum likelihood estimation (MLE). The features of the synthesized algorithm are the decoherence of the received oscillations, the matched filtering of the received signals, and the possibility of using continuous signal coherence. Furthermore, the developed optimal and quasi-optimal algorithms derived from the proposed MLE have been investigated. The novel framework for radio imaging has demonstrated good overall operability and efficiency during simulation modeling (using the MATLAB environment) for real sensing scenes. The developed algorithms of spatio–temporal signal processing in systems with a synthesized antenna with nonlinear carrier trajectories open a promising direction for creating new methods of high-precision radio imaging from UAVs and helicopters. Full article

This paper presents a novel Graphics Processing Unit (GPU) accelerated implementation of a modified Particle Swarm Optimization (PSO) algorithm specifically designed to solve large-scale Systems of Nonlinear Equations (SNEs). The proposed GPU-based parallel version of the PSO algorithm uses the inherent parallelism of modern hardware architectures. Its performance is compared against both sequential and multithreaded Central Processing Unit (CPU) implementations. The primary objective is to evaluate the efficiency and scalability of PSO across different hardware platforms with a focus on solving large-scale SNEs involving thousands of equations and variables. The GPU-parallelized and multithreaded versions of the algorithm were implemented in the Julia programming language. Performance analyses were conducted on an NVIDIA A100 GPU and an AMD EPYC 7643 CPU. The tests utilized a set of challenging, scalable SNEs with dimensions ranging from 1000 to 5000. Results demonstrate that the GPU accelerated modified PSO substantially outperforms its CPU counterparts, achieving substantial speedups and consistently surpassing the highly optimized multithreaded CPU implementation in terms of computation time and scalability as the problem size increases. Therefore, this work evaluates the trade-offs between different hardware platforms and underscores the potential of GPU-based parallelism for accelerating SNE solvers. Full article

The issue of inventory balance in supply chain management represents a classic problem within the realms of management and logistics. It can be modeled using a mixture of equality and inequality constraints, encompassing specific considerations such as production, transportation, and inventory limitations. A Zeroing Neural Network (ZNN) model for time-varying linear equations and inequality systems is presented in this manuscript. In order to convert these systems into a mixed nonlinear framework, the method entails adding a non-negative slack variable. The ZNN model uses an exponential decay formula to obtain the desired solution and is built on the specification of an indefinite error function. The suggested ZNN model’s convergence is shown by the theoretical results. The results of the simulation confirm how well the ZNN handles inventory balance issues in limited circumstances. Full article

Mean and slowly varying wave loads on floating offshore wind turbines (FOWTs) need to be estimated accurately for the design of mooring systems. The low-frequency drift forces are underestimated by potential flow theory, especially in steep waves. Viscous forces on columns is an important contributor which could be included by adding the quadratic drag of Morison formulation to the potential flow solution. The drag coefficients in Morison equation can be determined based on an empirical formula, CFD study, or model testing. In the WINDMOOR project, a FOWT support structure, composed of three columns joined at the bottom by pontoons and at the top by deck beams, is studied using CFD. In order to extract the KC-dependent drag coefficients, a series of simulations for the fixed structure in regular waves is performed with the CFD code STAR-CCM+. In this study, the forces along each column of the FOWT are analyzed using the results of CFD as well as potential flow simulations. The hydrodynamic interactions between the columns are addressed. A methodology is proposed to process the CFD results of forces on the columns and extract the contribution of viscous effects. Limitations of the Morison drag model to represent extracted viscous forces in steep waves are investigated. The obtained drag coefficients are compared with the available data in the literature. It is shown that accounting for potential flow interactions and nonlinear flow kinematics could, to a large degree, explain the previously reported differences between drag coefficients for a column in waves. Moreover, it is shown that the proposed model can capture the contribution of viscous effects to mean drift forces for fixed columns in waves. Full article

In this paper, we study nonlinear systems of fractional differential equations with a Caputo fractional derivative with respect to another function (CFDF) and we define the strict stability of the zero solution of the considered nonlinear system. As an auxiliary system, we consider a system of two scalar fractional equations with CFDF and define a strict stability in the couple. We illustrate both definitions with several examples and, in these examples, we show that the applied function in the fractional derivative has a huge influence on the stability properties of the solutions. In addition, we use Lyapunov functions and their CFDF to obtain several sufficient conditions for strict stability. Full article

Reductions in the vibration of a continuum system via a nonlinear energy sink have been widely investigated. It is usually assumed that weight effects can be ignored if the vibration is measured from the static equilibrium configuration. The present investigation reveals the dynamic effects of weight on the vertical transverse vibrations of a Euler–Bernoulli beam coupled with a nonlinear energy sink. The governing equations considering and neglecting weights were derived. The equations were discretized with some numerical support. The discretized equations were analytically solved via the harmonic balance method. The harmonic balance solutions were compared with the numerical solution via the Runge–Kutta method. Finite element simulations were performed via ANSYS software (version number: 2.2.1). Free and forced vibrations, predicted by equations considering or neglecting the weights, were compared with the finite element solutions. For the forced vibrations, the amplitude–frequency responses determined by the harmonic balance method agree well with those calculated by the Runge–Kutta method. The free and forced vibration responses predicted by the equations considering the weights are closer to those computed by the finite element method than the responses predicted by the equation neglecting the weights. The assumption that weights can be balanced by static deflections leads to errors in the analysis of the vertical transverse vibrations of a Euler–Bernoulli beam with a nonlinear energy sink. Full article

Background/Objectives: Cancer is a dynamic and complex disease that remains largely untreated despite major advances in oncology and treatment. In this context, we aimed here to investigate optimal control techniques in the management of tumor growth inhibition, with a particular focus on cancer chemotherapy treatment strategies. Methods: Using both linear autoregressive with exogenous inputs (ARX) and advanced non-linear tumor growth inhibition (TGI) modeling approaches, we investigated various single-agent treatment protocols, including continuous, periodic, and intermittent chemotherapy schedules. By integrating advanced mathematical modeling with optimal control theory and methods, namely the Linear Quadratic Regulator (LQR) and the “pseudo-linear” state-space equivalent representation and suboptimal control of a non-linear dynamic system known as the State-Dependent Riccati Equation (SDRE) approach, this work explores and evaluates successfully, more effective chemotherapy treatment strategies at the computer simulation level, using real preclinical data which increases the expectation to be applied in the clinical practice of oncology. Results: The integration of these methods provides insights into how different drug administration schedules may affect tumor response at the preclinical level. This work uses mathematical modeling to evaluate the efficacy of various periodic and intermittent chemotherapy treatment strategies, with a focus on optimizing drug doses while minimizing the potential side effects of chemotherapy due to the administration of less effective chemotherapeutic doses. Conclusions: The treatment scenarios tested in this study could effectively stop tumor growth or even lead to tumor regression to a negligible or near-zero size. This approach highlights the importance of computational tools for more effective treatment strategies in chemotherapy and offers a promising direction for future research and more efficient clinical applications in oncology as part of a more individualized approach. Full article