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The nonlinear stability of a plane interface separating two Bingham fluids and fully saturated in porous media is inspected in the existing work. The two fluids are compressed by a normal magnetic field. The two fluids have diverse viscoelasticity, densities, magnetic, and porosity medium, with the existence of surface tension at the interface. The motivation of applied physics and engineering relations has encouraged the discussion of the current paper. Because the mathematical behavior is rather complex, the viscoelasticity involvement is reproduced only at the surface of separation, which is well-known as the viscous potential theory. Thereby, the equations of movement are scrutinized in a linear form, whereas a set of nonlinear boundary conditions are supposed. This procedure produces a nonlinear expressive nonlinear partial differential equation of the interface displacement. The non-perturbative approach which is based on the He’s frequency formula is employed to transform the nonlinear distinguishing ordinary differential equation with complex coefficients into a linear one. A novel process relying on the non-perturbative approach is utilized to examine the nonlinear stability and scrutinize the interface presentation. A non-dimensional analysis produces several dimensionless physical numerals. To validate the new approach, a comparison between the non-perturbative approach and its corresponding linear ordinary differential equation via the Mathematica Software is described and interpreted through a set of diagrams. Additionally, the Polar graphs have been elucidated. It is found that the mechanism of the stability does not change in the cases of real and complex coefficients.

The nonlinear stability of two horizontal interfaces of three-layered stratified non-Newtonian fluids plays a pivotal role in advanced engineering applications. This phenomenon encompasses temperature management systems, microfluidic devices, and precise coating technologies. In an existing study, a multilayer system is considered wherein a central Casson liquid (CL) layer is bounded above and below by Powell–Eyring liquids (PELs). The impact of a uniform tangential electric field (EF) and surface tension is explored within a porous medium. To avoid the mathematical complexity, the viscous potential flow (VPF) is used to simplify the governing hydrodynamic formulations. The model involves Navier–Stokes and Maxwell equations under the quasi-static assumption. To obtain a nonlinear formulation, the linearized regulator equations are derived subject to appropriate nonlinear boundary conditions. The plan interfaces are presumed to propagate horizontally. To handle the nonlinear ordinary differential equations (ODEs) arising from the analysis, He’s frequency formula (HFF) is applied, transforming the problem into linear forms suitable for a non-perturbative approach (NPA). A non-dimensional analysis introduces key dimensionless collections, which help to characterize underlying fluid behavior and reduce system intricacy. A brief methodological summary of NPA is included to support reproducibility and clarity. The numerical calculations indicate that the stability can be evidently improved by the orientation of the tangential EF in relation to the horizontal wavenumber. PolarPlots are employed to imagine the influence of varying parameters, offering valuable insights into the mechanisms of the governing interfacial stability.

Nonlinear oscillators with two degrees of freedom (2DOF) serve as fundamental models for describing complex dynamical behavior in engineering and applied mechanics. Accurate prediction of their responses is crucial for stability enhancement, vibration suppression, and optimal design of coupled mechanical systems. In this study, three distinct 2DOF coupled oscillator models are examined, encompassing both linear and strongly nonlinear restoring forces that govern free and damped vibration regimes. These models provide realistic frameworks for analyzing nonlinear interactions, resonance phenomena, and stability boundaries in coupled dynamical systems. The primary objective is to develop and apply a robust non-perturbative approach (NPA) for deriving periodic solutions of conservative and damped coupled oscillators. The proposed approach, rooted in He’s Frequency Formula (HFF), fundamentally differs from classical perturbation techniques as it avoids Taylor-series expansions, linearization assumptions, and small-parameter constraints. Instead, the nonlinear governing equations are transformed into analytically tractable linear forms, enabling efficient treatment of strongly nonlinear performance. The analytical solutions are validated through comprehensive numerical simulations implemented in Mathematica Software (MS), and are systematically compared with direct numerical integrations, demonstrating excellent accuracy and computational efficiency. Furthermore, bifurcation diagrams and Poincaré maps (PMs) are employed to characterize the qualitative dynamical transitions and classify the complex response patterns exhibited by each coupled model.

The study compares van der Pol and Rayleigh oscillators with time-delayed effects, providing insights into stability, bifurcations, and organization in nonlinear systems. It emphasizes unique dynamical properties and resonance conditions, strengthening the theoretical basis of the design of delay-controlled oscillatory systems. The aim is to adopt the non-perturbative approach, which transforms a weakly nonlinear oscillator of an ordinary differential equation into a linear one. Computed through a refined series approximation, the response manages both small and large oscillatory amplitudes without constraining assumptions, avoiding reliance on small parameter expansions. Validation outcomes reveal a strong agreement between parametric clarifications and the original nonlinear model, confirming the credibility of the proposed framework. Furthermore, a comprehensive assessment of the system’s stability is conducted in diverse situations. Two different instances of nonlinear Mathieu oscillators are inspected. A comprehensive stability analysis is performed for two nonlinear Mathieu-type oscillators with van der Pol and Rayleigh damping. Numerical simulations are carried out employing time histories, phase portraits, Poincaré maps, bifurcation diagrams, and Lyapunov exponents. These simulations ensure the accuracy and reliability of the analytical predictions. The outcomes expound distinct and contrasting stability performances for the van der Pol and Rayleigh oscillators. They demonstrate that nonlinear damping, excitation amplitude, natural frequency, and time delay play vital roles in governing the system’s dynamic response. It is observed that stability generally decreases with increasing natural and excitation frequencies, while it enhances with higher damping and excitation amplitudes. Moreover, the van der Pol and Rayleigh oscillators exhibit opposite impacts of nonlinear damping and natural frequency on stability. The novelty of this study lies in employing a non-perturbative approach to time-delayed Mathieu-type oscillators. The obtained findings provide valuable physical insight and practical guidance for the analysis and design of delay-controlled oscillatory systems in mechanical, structural, and engineering implementations.

Vessel vibrations have serious safety risks and must be effectively mitigated. This study investigates the reduction in ship pitch–roll vibrations modeled as a two degrees of freedom of nonlinear spring–pendulum system subjected to multi-parametric excitation, using proportional–derivative controller. The main objective is to develop a rapid and efficient analytical approach to nonlinear vibration analysis. A non-perturbative approach is employed to transform weakly nonlinear oscillators of ordinary differential equations into equivalent linear ones without using Taylor expansions. He’s frequency formula plays a central role in this transformation. The resulting parametric solutions are validated using Mathematica Software (v13) and show a strong agreement with the original nonlinear model. The effects of various parameters on stability are examined. Theoretical analysis is conducted using the multiple time scales method to identify worst resonance conditions and derive frequency response equations. Stability near simultaneous sub-harmonic resonance is assessed using Routh–Hurwitz criterion. Numerical simulations based on the fourth-order Runge–Kutta method confirm the effectiveness of proportional–derivative control. Excellent agreement between analytical and numerical results demonstrates the accuracy, efficiency, and practical applicability of the proposed method.

The current study investigates the peristaltic transport of an incompressible micropolar non—Newtonian nanofluid following the Sutterby model. The heat and mass transfer inside the two-dimensional symmetric vertical channel is considered. The system is affected by a strong magnetic field together with thermal radiation, couple stress, chemical reaction, Joule heating, heat generation, Dufour, Soret and Hall current effects. The governing equations of motion are analytically solved by utilizing the long wavelength and low Reynolds number approximations. Furthermore, the resulted boundary—value problem is solved by means of the Homotopy perturbation method (HPM). An illustration of the influence of the various physical parameters in the foreign distributions; such as Hall currents, magnetic field, Sutterby, couple stress, Brownian motion, thermophoresis and slip parameters is obtained throughout a set of graphs and tables. It is observed that the axial velocity enhances with the increase in the Sutterby parameter. Furthermore, the temperature decreases with the larger values of a heat transfer Biot number. While, the concentration enlarges with the increase in the values of mass transfer Biot numbers. Moreover, the trapping phenomenon is discussed throughout a set of figures. This depicts the variation of the streamlines under the impact of couple stress, amplitude ratio, and magnetic field parameters. It is noticed that the size of the trapped bolus increases with the increase in the foregoing three parameters.

In the current paper, the peristaltic transport of a non-Newtonian fluid obeying a Casson model with heat and mass transfer inside a vertical circular cylinder is studied. The considered system is affected by a strong horizontal uniform magnetic field together with the heat radiation and the Hall current. The problem is modulated mathematically by a system of PDE that describe the basic behavior of the fluid motion. The boundary value problem is analytically solved with the appropriate boundary conditions in accordance with the special case, in the absence of the Eckert number. The solutions are obtained in terms of the modified Bessel function of the first kind. Again, in the general case, the system is solved by means of the homotopy perturbation and then numerically through the Runge-Kutta Merson with a shooting technique. A comparison is done between these two methods. Therefore, the velocity, temperature and concentration distributions are obtained. A set of diagrams are plotted to illustrate the influence of the various physical parameters in the forgoing distributions. Finally, the trapping phenomenon is also discussed. nema

In this work, a novel isatin-Schiff base L2 had been synthesized through a simple reaction between isatin and 2-amino-5-methylthio-1,3,4-thiadiazole. The produced Schiff base L2 was then subjected to a hydrothermal reaction with cerium chloride to produce the cerium (III)-Schiff base complex C2. Several spectroscopic methods, including mass spectra, FT-IR, elemental analysis, UV–vis, 13 C-NMR, 1 H-NMR, Thermogravimetric Analysis, HR-TEM, and FE-SEM/EDX, were used to completely characterize the produced L2 and C2. A computer simulation was performed using the MOE software program to find out the probable biological resistance of studied compounds against the proteins in some types of bacteria or fungi. To investigate the interaction between the ligand and its complex, we conducted molecular docking simulations using the molecular operating environment (MOE). The docking simulation findings revealed that the complex displayed greater efficacy and demonstrated a stronger affinity for Avr2 effector protein from the fungal plant pathogen Fusarium oxysporum (code 5OD4) than the original ligand. The antibacterial activity of the ligand and its Ce 3+ complex were applied in vitro tests against different microorganism. The study showed that the complex was found to be more effective than the ligand.

In the context of climate change and the circular economy, biochar has recently found many applications in various sectors as a versatile and recycled material. Here, we review application of biochar-based for carbon sink, covering agronomy, animal farming, anaerobic digestion, composting, environmental remediation, construction, and energy storage. The ultimate storage reservoirs for biochar are soils, civil infrastructure, and landfills. Biochar-based fertilisers, which combine traditional fertilisers with biochar as a nutrient carrier, are promising in agronomy. The use of biochar as a feed additive for animals shows benefits in terms of animal growth, gut microbiota, reduced enteric methane production, egg yield, and endo-toxicant mitigation. Biochar enhances anaerobic digestion operations, primarily for biogas generation and upgrading, performance and sustainability, and the mitigation of inhibitory impurities. In composts, biochar controls the release of greenhouse gases and enhances microbial activity. Co-composted biochar improves soil properties and enhances crop productivity. Pristine and engineered biochar can also be employed for water and soil remediation to remove pollutants. In construction, biochar can be added to cement or asphalt, thus conferring structural and functional advantages. Incorporating biochar in biocomposites improves insulation, electromagnetic radiation protection and moisture control. Finally, synthesising biochar-based materials for energy storage applications requires additional functionalisation.

Parkinson’s disease (PD), one of whose symptoms is dysphonia, is a prevalent neurodegenerative disease. The use of outdated diagnosis techniques, which yield inaccurate and unreliable results, continues to represent an obstacle in early-stage detection and diagnosis for clinical professionals in the medical field. To solve this issue, the study proposes using machine learning and deep learning models to analyze processed speech signals of patients’ voice recordings. Datasets of these processed speech signals were obtained and experimented on by random forest and logistic regression classifiers. Results were highly successful, with 90% accuracy produced by the random forest classifier and 81.5% by the logistic regression classifier. Furthermore, a deep neural network was implemented to investigate if such variation in method could add to the findings. It proved to be effective, as the neural network yielded an accuracy of nearly 92%. Such results suggest that it is possible to accurately diagnose early-stage PD through merely testing patients’ voices. This research calls for a revolutionary diagnostic approach in decision support systems, and is the first step in a market-wide implementation of healthcare software dedicated to the aid of clinicians in early diagnosis of PD.