Volume 23, Issue 1

A novel and highly promising Ag 2 S-P2MA nanoribbon photocathodes are synthesized using a single-step technique based on 2-mercaptoaniline oxidation with (NH 4 ) 2 S 2 O 8 and AgNO 3 . This process yields polymer composites with nanoribbon morphologies, typically 150 nm wide and ranging from 500 to 1,000 nm in length. These nanoribbons exhibit excellent absorbance across the entire optical spectrum up to 780 nm. The fabricated Ag 2 S/P2MA photocathode is designed for water splitting to generate hydrogen gas using two different electrolytes: natural Red Sea water and artificial seawater free from heavy metals. This variation allows observation of the impact of seawater’s heavy metals. Hydrogen gas production is studied using a three-electrode cell with linear sweep voltammetry at room temperature. In both electrolytes, the photocurrent is measured at 0.015 mA/cm 2 . However, both the current density in light ( J ph ) and dark ( J o ) values decrease in artificial seawater compared to natural seawater, with values of −0.033 and −0.017 mA/cm 2 in natural seawater and −0.027 and −0.012 mA/cm 2 in artificial seawater. The Ag 2 S-P2MA nanoribbon photocathodes exhibit stable behavior, producing hydrogen at a rate of 12 µmol/cm 2  h. Combined with their cost-effectiveness and potential for mass production, this positions them as viable candidates for commercial electrode applications in various industrial settings.

In this article, the (3+1)-dimensional Hirota–Satsuma–Ito-like equation is investigated by the modified direct method, from which some interaction solutions among lump, stripe solitons, and Jacobi elliptic function wave solutions are obtained, which are crucial in understanding complex behaviors in nonlinear systems where multiple wave types coexist and interact. The corresponding evolution and dynamics for the interaction solutions under different parameters are discussed. Such interactions are key to modeling realistic systems in which multiple phenomena coexist, such as fluid mechanics, plasma physics, and optical systems, where waves can exchange energy and form stable or unstable patterns. These results reported in this article can reveal the theoretical mechanisms of stability, energy transfer, and pattern formation in nonlinear media and may raise the possibility of related experiments and potential applications in nonlinear science fields, such as oceanography, nonlinear optics, and so on.

This article is intended to propose a novel gold and SiO 2 material based planar 5-element high half power beam-width (HPBW) end-fire antenna array for 300 GHz applications. The proposed radiating structure composes of a 5-element off-set feed rectangular patch antenna array fed by a tapered microstrip line to accomplish high HPBW. Off-set feeding and parasitic patch resonators are incorporated to access the end-fire radiation characteristics. This antenna operating frequency ranges from 277.5 to 315 GHz with a peak gain and HPBW of the antenna as 4.98 dBi and around 100°, respectively, at 300 GHz, making it a good radiator at the specified band. A gold material of thickness 5 μm is used as the metal, while the SiO 2 with a thickness of 60 μm is adopted for the substrate material. Design, parametric analysis, and lumped element circuit models are also explored in this work. End-fire pattern, high HPBW, and good performance make this antenna to be eligible to use in THz applications such as imaging, scanning, communication, and bio-medical.

The ( 2 + 1 ) \left(2+1) -dimensional modified Zakharov–Kuznetsov (mZK) partial differential equation is of importance as a model for phenomena in various physical fields such as discrete electrical lattices, electrical waves in cold plasmas, nonlinear optical waves, deep ocean-waves, and the propagation of solitary gravity waves. In this study, the main objective is to give a detailed analysis of exact traveling wave solutions of the mZK equation with truncated M-fractional spatial–temporal partial derivatives. Using an appropriate traveling wave transformation and the homogeneous balance rule, the mZK equation is converted into a corresponding ordinary differential equation (ODE). The ( G ′ ∕ G , 1 ∕ G ) \left(G^{\prime} /G,1/G) -expansion and Sardar subequation methods are then used to derive exact solutions of the ODE in the form of functions such as hyperbolic, trigonometric, and special generalized hyperbolic and trigonometric functions. The two methods give some novel solutions of the proposed model and are presented here for the first time. The fractional-order effects are studied through numerical simulations, including three-dimensional (3D), two-dimensional (2D), and contour plots. These numerical simulations clearly show physical interpretations of selected solutions. In particular, the generalized hyperbolic and trigonometric function solutions that have been derived by the Sardar subequation method are important as they provide examples of exact traveling wave solutions of various physical types. Furthermore, the results include examples of bifurcations and chaotic behaviors of the model through 2D and 3D plots when parameter values are varied. Finally, the methods of solution described in this study are reliable, powerful, and efficient and can be recommended to obtain traveling wave solutions of other nonlinear partial differential equations with truncated M-fractional derivatives.

Traditional laser thin film optical components are specially designed layered structures made of two or more materials. However, as the number of layers increases, the anti-laser damage ability of the optical elements is significantly reduced. In this study, a single-layer structured surface is designed to have better optical transmittance than its homogeneous substrate. It also shows potential advantages in laser damage resistance applications. The transmittance and laser damage morphology of periodic cylindrical surfaces and their uniform substrates using a combination of experimental and simulation methods are examined. According to ISO21254, the laser-induced damage threshold (LIDT) of the structured surface and the uniform substrate were measured on a 1-on-1 irradiation of a 1,064 nm laser with a pulse width of 10 ns. The measured LIDT values were (15.3 ± 1.15) J/cm 2 for the structured surface and (15.2 ± 1.09) J/cm 2 for the uniform substrate. The damaged morphology of the structured surface was analyzed using a polarizing microscope to study its periodic distribution. Additionally, the electric field distribution on the surface of the structure and its uniform substrate was simulated using the finite element method. The results indicate that the damage characteristics of the structured surface are influenced by the surface structure, and the presence of the structure influences the energy distribution of laser deposition. This study serves as a valuable reference for further research into the laser damage mechanism of structured surfaces.

To improve heat dissipation performance of panel-type radiator for transformers, this study investigated the flow and heat transfer characteristics in the air-side metal foam partially filled channels of the radiator. The porous thin-layer filled (PTLF) and porous fin filled (PFF) methods and the filling ratio ( V p ) were analyzed and compared. The result indicated that the permeability and interfacial turbulent kinetic energy in the porous region of PFF channel are higher. Increasing V p can promote flow mixing and heat transfer. For Re = 5,125–15,375, when V p = 11.1%, the performance evaluation criterion in PFF channel can increase by 12.0–30.8% as compared with PTLF channel. Then, the effects of metal foam material, porosity ( φ ), and pore density ( ω ) were explored. The results show that decreasing φ , increasing ω , and using copper metal foam are all beneficial for enhancing the heat transfer performance of the PFF channel within the range studied. Finally, when V p = 11.1%, the PFF channels filled with Cu-10-9.5 and Al-10-9.7 samples were selected for comparison with previous related studies, which demonstrated the feasibility of the metal foam partial filling method on the air side of the panel-type radiator.

This study computationally examines the water-based hybrid nanofluid flow with the impacts of carbon nanotubes on an elongating surface. The flow is influenced by velocity slip constraints, zero-mass flux conditions, and thermal convection. Magnetic effects are applied to the flow system in the normal direction. The activation energy and chemical reactivity effects are used in the concentration equation. The modeled equations have been evaluated numerically through the bvp4c technique after conversion to dimensionless form through a similarity transformation approach. It has been discovered in this work that with expansion in magnetic and porosity factors, the velocities declined. Augmentation in the ratio factor has declined the primary flow velocity while supporting the secondary flow velocity. Thermal profiles have intensified with progression in the Brownian motion factor, thermal Biot number thermophoresis factor, and exponential heat source and radiation factors. Concentration distribution has escalated with the activation energy factor and has declined with an upsurge in Schmidt number and chemical reaction factors. The impact of an upsurge in the thermophoresis factor enhances the concentration distribution, while the upsurge in the Brownian motion factor exhibits a reducing impact on concentration distribution. To ensure the validation of this work, a comparative study is conducted in this work with a fine agreement among the current and established datasets.

This work investigates the quadratic and quartic nonlinear diffusion–reaction equations with nonlinear convective flux terms, which are investigated analytically. Diffusion–reaction equations have a wide range of applications in several scientific areas, such as chemistry, biology, and population dynamics of the species. The new extended direct algebraic method is applied to obtain abundant families of solitary wave solutions. Different types of solitary wave solutions are obtained by applying this analytical method. This approach provides the solutions in the form of single and combined wave structures, which are observed in shock, complex solitary-shock, shock-singular, and periodic-singular forms. Some of the solutions are depicted graphically to illustrate the fact that they are, indeed, wave solutions of the mathematical model.

The prevalence and growth characteristics of glioma tumours in human tissues are often modelled by a parabolic partial differential equation. It is essential to analyse tumour growth factors to establish mathematical benchmarks in understanding cancer progression. In this tumour study, we consider factors such as the tumour proliferation rates and the anisotropy of the spatial diffusion tensor. We aim to solve the resulting model together with its initial condition, to provide realistic biological predictions into the mechanism of cancer invasion, metastasis and life expectancy after diagnosis. The solutions are inspired by transformations that we propose to convert the tumour model into a heat equation. A key component in understanding the physics of cancer phenomena, is through obtaining precise solutions. Lie symmetries provide the mechanism to obtain exact solutions.

A fiber-reinforced composite structure with carbon nanotubes-reinforced glass fiber panel (CNTs/GFP) clip and three-dimensional Kevlar fabric impregnated with shear thickening fluid (STF/3DKevlar) is proposed (CNTs/GFP-STF/3DKevlar). On this basis, the preparation, mechanical properties, and energy dissipation characteristics of CNTs/GFP, STF/3DKevlar, and their composite structures were studied. An experimental loading and testing system for a fragment penetration composite structure composed of a first-stage light gas gun, a high-speed camera, a dynamic strain gauge, and a PVDF piezoelectric sensor is constructed. According to the deformation process, the morphology of the target plate, and the results of industrial CT, it is concluded that the fabric structure and nanoparticle concentration play an active role in the mechanical and protective properties of the composite structure. Compared with the pure GFP-Kevlar composite structure, the energy dissipation of the reinforced composite structure is enhanced by the addition of CNTs, STF, and the 3D braided KEVLAR fabric, and the lowest kinetic energy consumption of bullets can be increased by 21.92% and the highest by 48.23%.

This work explores the influence of Hall current on the thermoelastic behavior of nanostructured (nonlocal) plates made of an elastic material, modeled under a double-temperature (two-temperature theory) framework, and subjected to ramp-type heating. The dual-temperature model accounts for the separate thermal dynamics, while the nonlocal elasticity theory incorporates long-range interactions within the material, making it particularly suitable for nanoscale materials. The governing equations are derived by integrating the effects of Hall current, and nonlocal elasticity into the coupled electro-thermo-mechanical equations according to the dual-phase lag model. The solution is obtained through the application of the normal mode analysis technique, allowing for the decoupling of the governing equations into solvable ordinary differential equations. Numerical simulations are performed, and results are presented graphically to compare the wave propagation characteristics of the basic physical fields such as temperature, displacement, acoustic pressure, and stress under the influence of Hall current and varying nonlocal parameters. The results reveal significant changes in wave propagation under varying boundary conditions, offering valuable insights into the interaction between magneto-electric fields, mechanical stresses, and thermal gradients. The study provides a novel framework for understanding wave propagation in nanostructured materials and paves the way for further research into their application in advanced thermoelectric-mechanical devices.

The Belousov–Zhabotinsky (BZ) reaction–diffusion system is a well-known model of chemical self-organization that exhibits complex spatiotemporal patterns. The BZ reaction–diffusion system provides a useful tool for studying the behavior of waves in random and complex media. Its applications in this field are wide-ranging and have the potential to contribute to a better understanding of the behavior of waves in natural and engineered systems. In this article, we investigate the BZ system using both analytical and numerical methods. We first apply the Bernoulli sub-ordinary differential equation (ODE) technique to the BZ system to obtain a simplified system of ODEs. Then, we use the exponential cubic B-spline method and the trigonometric cubic B-spline method to solve the simplified system numerically. The results show that both methods are effective in capturing the essential features of the BZ system. We also compare the results obtained using the two numerical methods. Our findings analytically contribute to a better understanding of the BZ system through graphs of the soliton solutions.

The surface charge property plays a crucial role in the electrokinetic flow in silica nanochannel in which the surface charge is generated by surface chemical reaction and is dependent on the solution pH. In nanofluidic devices, many of the fluids belong to the viscoelastic fluid class. In this work, we develop theoretical analysis for the effects of the solution pH, background salt concentration, and electric field frequency on an alternating current (AC) electroosmotic flow (EOF) of Maxwell fluid. The results show that the velocity amplitude of AC EOF of Maxwell fluid decreases with the background salt concentration and increases with the relaxation time and the deviation of the solution pH from the isoelectric point (pH = 3.05). The velocity amplitude of Maxwell fluid is greater than that of Newtonian fluid. In particular, the velocity amplitude of Maxwell fluid increases with the electric field frequency, whereas the velocity amplitude of Newtonian fluid remains unaffected by the electric field frequency.

We revise the optical effects of the Sagnac type where the moving closed contour is traversed by a photon in the observable invariant time interval T T . Light propagation is described using relativistic transformations adopting an internal one-way synchronization procedure, not equivalent to the standard two-way Einstein synchronization. We show that for the reciprocal linear Sagnac effect, where the emitter–receiver C * C* is stationary and the contour is in motion, T T is no longer invariant for the standard Lorentz transforms, reflecting a weak form of the relativity principle. Instead, the relativity principle is fully preserved and T T is invariant for transforms based on conservation of simultaneity. We prove that in the standard linear Sagnac effect, if the local one-way speed along the optical fiber is assumed to be c c , the photon cannot cover the whole closed contour in the interval T T . The uncovered “missing” section reflects a breach in spacetime continuity related to the “time gap” of the transforms based on relative simultaneity. Our revision confirms the well-known result that the Lorentz transforms fail in interpreting these effects. Together with other examples, the results of the reciprocal linear effect invalidate the conventionalist claim that relative and absolute simultaneity are equivalent. The reciprocal effect can then be used for testing Lorentz and light speed invariance.

The establishment of secure global communication links is fundamentally dependent on the support of airborne platforms. However, the transmission of quantum signals from these platforms faces significant challenges related to boundary layer (BL) effects. This article presents an improved channel loss calculation model that effectively incorporates these BL effects in airborne environment. The model takes into account detailed variations in beam width, scintillation index, and transmission efficiency within the airborne environment. The results indicate that BL effects have an impact on the beam width and scintillation index, highlighting the need to maximize the receiver aperture within payload capacity constraints. In addition, the analysis shows that the supersonic BL results in greater losses and higher error rates compared to the transonic BL. Furthermore, atmospheric turbulence is identified as the primary factor that reduces transmission efficiency when transmitting over long distances in the airborne environment.

This research deals with the theoretical and numerical investigations of a memristor system with memductance function. Stability, dissipativity, and Lyapunov exponents are extensively investigated and the chaotic tendencies of the system are studied in depth. The memristor model, where a piecewise memductance function is incorporated, is modified with fractal–fractional derivatives with exponential decay, power law, and Mittag–Leffler kernels, which provide powerful tools for modeling complex systems with memory effects, long-range interactions, and fractal-like behavior. Employing the Krasnoselskii–Krein uniqueness theorem and the fixed point theorem, the existence and uniqueness of the solutions of the model including fractal–fractional derivatives with the Mittag–Leffler kernel are proven. The fractal–fractional derivative model is solved numerically using the Lagrange polynomial approach, and the chaotic tendencies of the system are exhibited through numerical simulations. The findings indicated that the memristor model with fractal–fractional derivatives was observed to exhibit chaotic behavior.

Controlling the physicochemical features of chromium sesquioxide α -Cr 2 O 3 (chromia) films is essential to widening their utilization. This work investigates the influence of heat treatment (HT) and La doping on the physical characteristics of chromia films spin-deposited on glass. X-ray diffraction/Fourier transform infrared spectroscopy and field-emission transmission electron microscopy techniques reveal that the crystallinity, size, and modes of vibration in chromia (eskolaite phase) can be tuned by HT and La doping. Energy-dispersive X-ray analysis confirms the presence of La in the hexagonal chromia films. All films display high transmittance (T%) and improved absorption indices in the UV and near-infrared regions. The films’ reflection and refractive indices are in the range of 6–15% and 1.77–1.97, respectively. The impact of HT and La content on the optical band gap, lattice dielectric constant, and electron-effective mass is reported. The current–voltage characteristic curves reveal the Ohmic resistance, and the films’ sheet resistance demonstrates sensitivity to HT and La content. The findings of this study illustrate the possible development of optoelectronic devices and chromia-based IR sensors.

To measure transient and extremely high temperatures of explosion processes, a high-speed multi-spectral temperature measurement system was developed. By measuring spectral radiant exitance corresponding to six wavelengths by six fast photodetectors, transient explosion temperature can be extracted in realtime through a linear correlation algorithm accelerated by the golden-section method. Real explosion experiments with the energetic material polymer-bonded explosive demonstrated that the method could rapidly and accurately determine explosion temperatures. Peak explosion temperature up to 3,560 K has been successfully extracted. The proposed method may find applications in explosive evaluations.

In this work, the main objective is to study the dynamic behavior of the generalized coupled fractional nonlinear Helmholtz equation with cubic–quintic term, which describes soliton propagation in nonlinear optics through the theory of dynamical system. First, the original equation is transformed into an integer-order coupled partial differential equation using Atangana’s fractional derivative. Then, considering traveling wave and linear transformations, a two-dimensional planar dynamical system is constructed. Through phase portraits, stability analysis, and parameter sensitivity analysis, the dynamical behavior of the system is studied. Next, considering the dynamic behavior of the system under triangular periodic perturbation and logarithmic perturbation respectively, the reasons for the evolution of the system behavior patterns under different initial conditions are analyzed. Through qualitative analysis, we have avoided the limitations and errors of precise solution methods, and obtained the stability of the system equilibrium point under parameter changes, as well as the dynamic behavior of the system, including periodic and chaotic behaviors. Finally, by investigating the modulation instability of the system, the conditions for maintaining stability of the system are obtained through the linear stability analysis method.

The precision of testing the damage threshold of thin film lasers has always been a limiting factor in the advancement of high-power laser systems. The conventional plasma flash method sometimes fails to differentiate between film and air plasma flashes, resulting in significant errors in determining the film damage threshold. By distinguishing between the different durations of thin film and air plasma flashes, misjudgment can be eliminated. The aim of this article is to determine both the calculated and experimental values of the duration of air plasma flash near the surface of thin films ( t c ) and to analyze the factors that influence it. First, a model is established to calculate the theoretical value of t c . For a sample consisting of a single-layer hafnium oxide film, we assume that the incident laser wavelength, focal spot diameter, energy, and pulse width are 1,064 nm, 0.08 cm, 57.21 mJ, and 10 ns, respectively. The focal length of the lens positioned in front of the film sample is set at 350 mm, with a distance of 5 mm between the film sample and this lens. Under these conditions, the theoretical value for t c is calculated to be 4.24 × 10 − 6 s 4.24\times {10}^{-6}\hspace{.25em}s . Second, the device was used to conduct eight experiments to obtain experimental values of t c . The results are as follows: (1) An increase in incident laser energy leads to an increase in t c . (2) The length of t c is solely dependent on the incident laser energy, regardless of the sample material or placement (even when the sample is not placed and the laser directly acts on air). (3) When substituting experiment parameters into the model for calculating t c , there is good agreement between theoretical and experimental values. Third, it was observed that t c increases with increasing incident laser energy, pulse width, and focal length of the lens, while decreasing with an increase in distance between the film sample and the lens.

In this article, we study the time-dependent two-dimensional system of Wu–Zhang equations of fractional order in terms of the Caputo operator, which describes long dispersive waves that minimize and analyze the damaging effects caused by these waves. This article centers on finding soliton solutions of a non-linear ( 2 + 1 2+1 )-dimensional time-fractional Wu–Zhang system, which has become a significant point of interest for its ability to describe the dynamics of long dispersive gravity water waves. The semi-analytical method called the q q -homotopy analysis method in amalgamation with the Laplace transform is applied to uncover an analytical solution for this system of equations. The outcomes obtained through the considered method are in the form of a series solution, and they converge swiftly. The results coincide with the exact solution are portrayed through graphs and carried out numerical simulations which shows minimum residual error. This analysis shows that the technique used here is a reliable and well organized, which enhances in analyzing the higher-dimensional non-linear fractional differential equations in various sectors of science and engineering.

The fluorescence spectrum of CO molecules in intense femtosecond laser fields was studied experimentally. Distinct spectral lines from excited atoms and molecules were identified. Different dependencies on gas pressure were observed for atomic and molecular spectral lines. Analysis indicated that these atomic spectral lines were induced by the TBR process, and those molecular spectral lines were induced by collision-induced excitation with tunneling electrons. This study paves the way for a better understanding of complex plasma processes.

This work is a major extension of our previous work in which we have solved a 2D nonconstant coefficient advection diffusion equation with nonconstant advection and constant diffusion terms on a square domain using the coefficient of dissipation D 1 = D 2 = 0.0004 {D}_{1}={D}_{2}=0.0004 using three finite difference methods, namely, Lax–Wendroff, Du Fort–Frankel and nonstandard finite difference methods. In this current work, the first novelty is that we solve a 2D nonconstant advection diffusion equation on an irregular domain with a more complicated initial profile and considered five combinations for values of D 1 {D}_{1} and D 2 {D}_{2} . Moreover, the second novelty is the study of numerical dispersion and dissipation of Lax Wendroff scheme for the five combinations of D 1 {D}_{1} and D 2 {D}_{2} . Third, we present some numerical profiles from the three methods for the five scenario at two times: T = 0.1 T=0.1 , 1. The fourth novelty is the plot of the modulus of the exact amplification factor, modulus of amplification factor, and relative phase error vs phase angle along x x direction vs phase angle along y y direction for the Lax–Wendroff scheme at x = y = 0.5 x=y=0.5 for the five scenarios.

Energy deficiency is one of the most challenging issues of the present world due to its increasing demand in industrial and technological processes. To address this issue, energy efficiency improvement is essential. Hybrid nanofluids have significant applications in the industrial and engineering sectors because of their higher thermal conductivity compared to conventional nanofluids. Keeping these important applications in mind, this work investigates the two-dimensional magnetohydrodynamic hybrid nanofluid flow on shrinking/stretching sheets under the impact of the Cattaneo–Christov model, suction/injection, thermal radiation, and slip effects. The hybrid nanofluid is formed by mixing nanoparticles of copper and alumina with a base fluid. The main equations are converted to a dimensionless form using appropriate variables. The model is evaluated by using the bvp4c built-in code in MATLAB. As main outcomes of the work, it is revealed that the increasing magnetic parameter enhances the skin friction of hybrid nanofluids; however, a reverse influence is noticed in the velocity curve. An upsurge in thermal radiation and Eckert number causes a substantial augmentation in the heat transfer rate, and a similar influence is observed in the temperature profile. The mass transfer rate shows a decreasing behavior through growth in chemical reactions and the Schmidt number. This investigation offers comprehensive insights into optimizing heat transfer and fluid flow in various engineering and industrial applications, such as thermal management, manufacturing processes, chemical reactors, and microfluidic devices.

In the current research, the influence of a sinusoidal heat flux and a heated rectangular cavity in a partially porous Casson hybrid nanofluid-filled square enclosure being affected by a constant magnetic field imposed in the x -direction having magnitude B 0 , on natural convection were investigated numerically. A rectangular heated cavity having width H /5 and height H /2 was positioned in the middle of the square enclosure. The sinusoidal heat flux of length H /2 is positioned centrally at the enclosure’s bottom wall, although the top wall is at a lower temperature, say T c, and the rest of the enclosure was insulated. The finite-difference method, combined with the successive over relaxation, successive under relaxation, and Gauss–Siedel techniques, is employed to address the challenge of solving the nonlinear coupled governing partial differential equations of motion and energy. Numerical calculations were carried out using the values of the relevant parameters in the range 0 ≤ \le Ha ≤ \le 15, 10 4 ≤ \le \hspace{1em} Ra ≤ \le 10 6 , 0.00 ≤ ϕ hnf ≤ 0.04 0.00\le {{\rm{\phi }}}_{{\rm{hnf}}}\le 0.04 , 10 −5 ≤ Da \le {\rm{Da}} ≤ \le 10 −3 , 0.1 ≤ \le γ \gamma ≤ \le 1, 4 ≤ \le N ≤ \le 12. The Kirpichev heat number ( K i = 1 {K}_{i}=1 ) and Prandtl number (Pr = 6.26) are fixed throughout the study. Contour plots for isotherms and streamlines were plotted to ascertain the impacts of distinct factors on them. The results of this investigation suggest that the heat transfer rate rises as ϕ hnf {{\rm{\phi }}}_{{\rm{hnf}}} , Ra, and γ \gamma rise and reduce as the Ha and N rises. Finally, it has been observed that decreasing the heated rectangular cavity’s aspect ratio leads to a substantial enhancement in heat transfer from both the heat flux and the heated rectangular cavity.

Slit die extrusion depends highly on fluid temperature and flow properties, which play a crucial role in determining material quality. This research aims to enhance product quality in extrusion processes by deriving a mathematical model from the extrusion process, ensuring practical relevance to industrial applications. The study focuses on the stability analysis of unsteady ternary nanofluid flow past a stretching/shrinking wedge, incorporating viscous dissipation and Joule heating. A key novelty of this work lies in identifying the critical values for the existence of dual solutions and conducting a comprehensive stability analysis. The findings reveal that the first solution is stable, whereas the second is unstable. Critical values are determined using the boundary value problem solver using 4th-order collocation method function in Matlab, and the effects of key parameters – such as the wedge parameter, Eckert number, suction/injection parameter ( S S ), and hybridity – are analyzed through graphical representations. Results show that for a shrinking wedge, the skin friction coefficient and Nusselt number increase with higher values of the unsteadiness parameter, nanoparticle volume fraction, and S S . When λ > − 3.23 \lambda \gt -3.23 (shrinking wedge), the ternary nanofluid demonstrates superior thermal transfer compared to binary and mono nanofluids. This study provides a critical foundation for validating advanced models and optimizing heat transfer performance in industrial processes, paving the way for enhanced applications in extrusion and thermal management systems.

This study employs the Hirota bilinear transformation method to investigate solitary and soliton solutions resulting from different symmetry wave functions associated with nonlinear atom chain models. These models are complex dynamic systems that have an impact on a variety of scientific areas. In this work, we derive exact solutions for several symmetry wave functions. Our results reveal a wide range of wave structures, including anti-kink waves (resulting from the interaction of exponential wave functions), M-shaped waves with single and double kinks (generated by combining M-shaped and kink wave functions), and periodic multiple lump waves (produced by the interaction of multi-lump and periodic wave functions). Solitary waves and numerous periodic lump waves have also been reported as a result of various multi-wave function combinations. In the present report, we also derive periodic bright lump waves, periodic cross-kink waves, and dark lump strip waves caused by interactions between exponential, trigonometric, and hyperbolic functions. Additional solutions include solitary waves from mixed wave functions and bright breather waves obtained from homoclinic breather functions. For illustration purposes, we provide three-dimensional visualizations of these solutions as well as accompanying contour plots.

This article investigates a significant mathematical model for multiwave interactions. For the first time, the bilinear form of the (3+1)-dimensional negative-order Korteweg–de Vries (KdV)-Calogero–Bogoyavlenskii–Schiff (CBS) equation is derived using binary Bell polynomials, and 1, 2, and 3-soliton solutions are obtained through this bilinear form. These solutions are further visualized via 3D and 2D plots representations. This study fills a research gap in this direction and demonstrates that the results can significantly enhance the efficiency of obtaining diverse solutions for the (3+1)-dimensional negative-order KdV-CBS equation. It is anticipated that these solutions will not only deepen our understanding of the physical phenomena associated with the equation but also reveal more complex physical behaviors, thereby advancing analytical studies on solutions to other nonlinear partial differential equations.

This study investigates the variable coefficient cubic–quintic nonlinear Schrödinger equation, which models the propagation of ultrashort femtosecond pulses in optical fibers and three-body recombination losses in Bose–Einstein condensates. Using a mapping technique combined with an extended chirp wave transformation, 20 chirp wave solutions were derived, including bright and dark solitons, kink waves, periodic and singular waves. These solutions encompass previously reported results and introduce novel ones. Three-dimensional plots illustrate the soliton and kink chirp wave solutions for both constant and exponentially varying group velocity dispersion (GVD) and Raman effect parameters. Analysis reveals that the sign of the Raman effect parameter influences the soliton type, yielding bright solitons for positive values and dark solitons for negative values. Furthermore, both GVD and Raman effect significantly impact the wave shape, inducing oscillations in the case of exponentially distributed fiber. The stability of the soliton wave solution is also analyzed. These diverse wave profiles have potential applications in nonlinear optics and plasma physics.

This research examines the impact of varying thermal conductivity within the framework of generalized photo-thermoelastic theory in a thermo-hydrodynamic semiconductor material. The changes in thermal conductivity are presented to evaluate the wave distributions of temperature, carrier density, excess pore water pressure, stress, and displacement in a poroelastic (poro-silicon, PSi) material. The integrated model of thermoelasticity, hydro-mechanics, and plasma waves is examined. The normal mode analysis is employed to provide the analytical solution of the distribution of the researched fields as components of this phenomenon. The findings are demonstrated about the effects of the thermal conductivity parameter as the heat source decays. A comparison of the numerical results with prior analytical studies is conducted, excluding the new parameter, and the behaviors of physical quantities in the numerical solutions are analyzed to validate the accuracy of the proposed technique. All physical quantities are influenced by changing thermal conductivity.

The optimization of dissipative disorder in fluid dynamics is a critical aspect of enhancing heat and mass transport efficiency in advanced thermal applications. In this study, we investigate the radiative thin film flow of a partially ionized non-Newtonian hybrid nanofluid (HNF) under the influence of a second-order slip condition. The HNF comprises magnesium oxide (MgO) and zinc oxide (ZnO) nanoparticles (NPs) suspended in water, which enhances its thermophysical properties, including thermal conductivity and heat absorption capacity. HNFs exhibit superior thermal transport capabilities compared to conventional fluids; however, their flow behavior is highly complex, especially in the presence of ionization effects, radiative heat transfer, and interfacial slip dynamics. The second-order slip condition accounts for microscale effects, which are crucial for accurately modeling thin film flows in high-performance cooling and coating applications. The governing equations, incorporating the effects of viscoelasticity, solar radiation, Brownian motion, slip, unsteadiness, and magnetic field interactions, are formulated and solved using collocation weighted residual. The results indicate that incorporating MgO and ZnO NPs into the water base fluid enhances thermal conductivity, leading to improved heat transfer efficiency. The solar radiation parameter significantly increases the fluid temperature, leading to a stronger thermal boundary layer. The findings provide insight into minimizing dissipative losses while enhancing energy transport in industrial and aerospace systems. This study contributes to the advancement of HNF-based technologies by optimizing flow and heat transfer characteristics under complex physical conditions.

This article investigates the traveling wave solution of the fractional (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili model by using the complete discriminant system method. These solutions not only include rational function solutions, trigonometric function solutions, but also Jacobian function solutions. In order to illustrate the propagation of these solutions in the field of nonlinear optics and water wave models, some three-dimensional, two-dimensional, and contour maps are drawn. Meanwhile, the phase portrait of two-dimensional dynamical systems and its perturbation systems are studied using the planar dynamical system analysis method. By drawing phase diagrams, it is easy to observe the stability, periodicity, and chaotic behavior of two-dimensional dynamical systems through geometric visualization, which can also provide strong basis for researchers to design corresponding control systems.

To comprehend nonlinear dynamics, one must have access to soliton solutions, which faithfully portray the actions of numerous physical systems and nonlinear equations. Notable nonlinear equations in relativistic physics, quantum field theory, nonlinear optics, dispersive wave phenomena, contemporary industrial applications, and plasma physics include the Klein–Gordon and Sharma–Tasso–Olver equations, which shed light on wave behavior and interactions. This study introduces a powerful approach to uncovering some novel soliton solutions for these equations, namely, the new generalized ( G ′ / G ) ({G}^{^{\prime} }\left/G) -expansion method. The derived soliton solutions are articulated in terms of rational, trigonometric, and hyperbolic functions, each embodying the physical implications of the equations through meticulously specified parameters. The resulting solutions encompass several waveforms, including sharp solitons, singular periodic solitons, flat kink solitons, and singular kink solitons. The results indicate that the employed method is both robust and very effective for the analysis of nonlinear evolution equations (NLEEs). It is compatible with computer algebra systems, facilitating the generation of more generalized wave solutions. The strength and versatility of the new generalized ( G ′ / G ) ({G}^{^{\prime} }\left/G) -expansion method suggest its potential for further research, particularly in exploring exact solutions for other NLEEs. The approach represents a significant expansion in the methodologies available for handling nonlinear wave equations, opening new avenues for theoretical and applied investigations in nonlinear science. Furthermore, the bifurcation analysis is carried out, which reveals the comprehension and precise representation of the dynamics of these two nonlinear partial differential equations. It offers the information required to build a comprehensive and significant phase portrait, including insights into solution behaviors, stability changes, and parameter dependencies.

Nanofluids (NFs) have been implemented in several areas to increase heat transfer efficiency. Thus, efficiency for heat energy can be achieved. In this study, the effect of nanoparticle (NP) type, volume fraction, and Re number on the heat transfer efficiency of NFs were analyzed numerically, statistically, and theoretically. Heat transfer coefficient, number of transfer units, wall shear stress, and friction factor were selected as the heat transfer efficiency of NFs. ANSYS Fluent software was utilized to carry out computational fluid dynamics analyses. The numerical calculation scheme was implemented by employing the Taguchi L9 orthogonal array with three decisive factors. NP type, volume fraction, and Re number were assumed as decisive factors with three levels. Signal-to-noise ratio analysis was utilized to determine the direction of impact and ideal levels of each decisive factor on the heat transfer efficiency of NFs. Significance levels and contribution rates of the decisive factors on the heat transfer efficiency were calculated with Analysis of Variance. According to the mathematical responses, the most effective NPs on h and τ w were identified as Gr, Al 2 O 3 , and Cu, respectively, whereas the most effective NPs on number of transfer units are found to be Cu, Al 2 O 3 , and Gr, respectively. In addition, the increase in Re number from 6,000 to 8,000 causes an increase in h and τ w and a decrease in NTU and f . The data achieved from the mathematical research may be utilized to be a guide paper in experimental analyses.

In light of the subtle connection between the strange attractors and the degree of dynamical systems, in this study, we propose a new simple asymmetric Lorenz-like system and report the finding of single-wing Lorenz-like attractors, which can also be created by the collapse of asymmetric singularly degenerate heteroclinic cycles. Moreover, we prove the existence of a single heteroclinic orbit to the origin and the nontrivial equilibrium point. Besides, numerical simulations also verify the theoretical analysis.

In this study, we use the powerful and strong method to obtain a solution of the Sasa–Satsuma equation as ( ℋ + G ′ G 2 ) \left({\mathcal{ {\mathcal H} }}+\frac{{{\mathcal{G}}}^{^{\prime} }}{{{\mathcal{G}}}^{2}}) -expansion method. This method plays a considerable role in solving nonlinear partial differential equations (NPDEs). We investigate the modulation instability in higher-order NPDEs. Modulation instability is a phenomenon observed in certain types of nonlinear systems, such as optical fiber or plasma waves. Modulation instability is a key process in generating optical solitons, rogue waves, and interest in various fields such as nonlinear optics and plasma physics. Using a linearizing technique, we establish the modulation instability and show the influence of a higher nonlinear component in modulation instability. We examine the bifurcation analysis of the Sasa–Satsuma equation. The time histories and Poincare mapping are used to scrutinize the chaotic behaviors of the dynamical system of the Sasa–Satsuma equation excited by a parametric excitation force. To control the vibrating system, use proportional feedback control (P-Controller). Two-dimensional and three-dimensional figures are presented for singular, dark, and bright optical soliton solutions related to optical fiber. These graphs are very important and useful in describing the behavior of solutions.

In the ongoing work, the ( n + 1 n+1 )-dimensional modified Zakharov–Kuznetsov equation is discussed, which characterizes the dispersive and ion acoustic wave propagation in plasma physics. The main research content is to analyze the chaotic dynamics of the equation and provide some new traveling wave solutions. The studied equation is transformed into an ordinary differential equation by using traveling wave transformation. The bifurcation theory, Lyapunov exponent, and sensitivity of initial value condition are employed to analyze the chaotic behavior and stability of the equation. Furthermore, by utilizing the integral form of the equation and complete discrimination system for polynomial method, some new exact solutions are given, including rational, trigonometric, hyperbolic, and Jacobi elliptic function solutions. To examine the properties and shapes of the solutions, some two- and three-dimensional graphs are given with the aid of MATLAB software under appropriate parameters intuitively.

The present study constructs and investigates solitonic phenomena in the complex structured (3+1)-dimensional conformable Heisenberg ferromagnetic spin chain equation (CHFSCE). This model explains the behavior of ferromagnetic spin chains and is an extension of the integer-order Heisenberg equation in nonlinear physics that controls the magnetization of the ferromagnetic solid. We present a new array of soliton solutions in the form exponential, rational, hyperbolic, and rational-hyperbolic functions, using the Riccati modified extended simple equation method (RMESEM). The proposed anstaz uses a complex structured wave transformation to convert CHFSCE into a more manageable nonlinear ordinary differential equation (NODE) and constraint conditions. The resulting NODE is assumed to have a close form solution that further converts it into a system of nonlinear algebraic equations via substitution in order to identify fresh plethora of optical soliton solutions. Moreover, the fundamental characteristics and theory of the employed conformable derivative, specifically, the chain rule, have been described. We demonstrate the existence of quasi-periodic solitons, including smooth-, multiple-, and periodic-periodic solitons, in the context of CHFSCE using a range of 3D, 2D, and contour visual representations. The obtained quasi-periodic solitons prominently result in the development of fractal structures while their squared norms result in the development of hump, peakon, and parabolic solitons. Additionally, we investigate bifurcating and chaotic behavior, detecting its existence in the perturbed dynamical system and finding advantageous results that suggest quasi-periodicity and fractal behavior in the model. According to the results we obtained, the suggested strategy is a powerful method for detecting novel soliton phenomena in such types of nonlinear settings.

The single-step fabrication of the Mn( iv ) oxide-Mn( ii ) sulfide/Poly-2-mercaptoaniline porous network nanocomposite (MnO 2 -MnS/P2MA) involves incorporating the Mn source into the P2MA polymer during polymerization. XPS analysis confirms the presence of peaks corresponding to Mn( iv ) and Mn( ii ), while XRD analysis highlights the formation of pronounced crystalline peaks, indicative of excellent semiconductive properties, with a crystalline size of 42 nm. The nanocomposite serves as the main electrode for electrochemically assessing its charge storage capabilities. Optimal energy density ( E ) values are achieved at lower current densities, with 9.7 and 7.0 W h/kg at 0.6 and 1.0 A/g, respectively. Similarly, the specific capacitance ( C S ) reaches peak values of 120 and 86 F/g within the same current density range. The electrochemical impedance spectroscopy (EIS) behavior is notable, with an R s value of 7.3 Ω and an impressive cycle retention of 99.2% over 1,000 cycles. The combination of simple one-pot fabrication, excellent charge storage performance, and high stability underscores the potential of these materials for charge storage applications. The MnO 2 -MnS/P2MA nanocomposite’s superior EIS behavior, optimal energy and capacitance values, and remarkable cycle stability make it a promising candidate for efficient and reliable charge storage solutions.

In this study, we delve into the exploration of the new (2+1)-dimensional KdV model, a mathematical model essential to the understanding of various nonlinear phenomena such as ion acoustic waves and harmonic crystals. The primary objective of this study is to conduct a comprehensive symmetry analysis of the model, a method that has not been previously applied to the model. This approach aims to uncover new exact solutions, which will not only enrich the existing literature but also provide valuable insights for researchers specializing in symmetry analysis and the broader scientific community. To achieve this goal, we employ a comprehensive analytical methodology that combines Lie symmetry analysis technique with Kudryashov’s method, the simplest equation technique, direct integration, Jacobi elliptic expansion technique, and the power series method. Through the utilization of these diverse analytical approaches, we successfully derive solutions for the model in various functional forms, including exponential, trigonometric, hyperbolic, Jacobi elliptic, and rational functions. These solutions exhibit broad applicability across diverse disciplines within nonlinear science and engineering. To provide a deeper understanding of the obtained solutions, we present our findings through visual representations, utilizing three-dimensional, two-dimensional, and density plots. By selecting appropriate ranges for the involved arbitrary constants, we effectively illustrate the dynamical wave behaviours inherent in the solutions. Notably, our visual representations reveal discernible patterns characterized by periodic and kink-shaped structures, shedding light on the intricate dynamics encapsulated within the solutions. Furthermore, we endeavour to identify conserved vectors associated with the model under investigation. To achieve this, we employ the multiplier method and Ibragimov’s theorem. The results are expected to enhance our understanding of the model’s physical implications and contribute to advancing the field.

In this work, we introduce a model for a two-atom (T–A) system interacting with a field mode initially prepared in a coherent state of a Para Bose–field (P–F). The T–As are initially represented by a Bell state, and we present the quantum framework for the whole system by solving the dynamical equations. We investigate the time-dependent behavior of essential quantum resources relevant to various tasks in quantum optics and information science, including atomic population inversion, T–As entanglement, T–As-P–F entanglement, and the statistical properties of the P–F as they relate to the model parameters. Our analysis reveals how these quantum resources are affected by different parameters in the T–As-P–F model. Finally, we illustrate the evolving interdependencies among these quantum resources within the system.

Practical fields, including materials processing, space technology, ocean technology, and many mechanical machineries, play a major part in advancing the modern world. Lack of energy production and energy reduction have been noticed as one of the main challenges in recent decades. To properly address this, one should need to modify the thermal characteristics of traditional materials with different surface dynamics involvement. The present investigation examines the heat transfer performance and pumping power of destructive flow patterns of rheological materials caused by viscous stress is significant due to physical aspects. One key objective is to demonstrate the conversion of kinetic energy into internal energy, highlighting its applications across various fields of engineering, science, and technology. The current study is about to address the impacts of viscous stress, stagnation point, gravity, slip flow, and thermal slip in the typical swirling motion of Cross liquid. The main problem that arises from these physical aspects is presented in the form of dimensionless mathematical equations. The flow problem configured in this study is based on the higher viscous forces and lower inertial forces. The leading dimensionless equations are formulated by using the Lie symmetry analysis. A well-known modified collocation formula is used to examine the higher radial flow speed of the material with the parallel variation in the Richardson number, and the other components decline with the same variation. The temperature of the dissipated materials is enhanced by considering the higher values of the Eckert number. Time relaxation caused a reduction in the resistance forces in the r -direction and is noticed with the opposite trend in the case of θ -direction which is more prominent. An excellent agreement is observed by introducing a comparison with the existing works.

This research provides a machine learning (ML) method to predict the optical density of photovoltaic (PV) polymers. The results show that extra gradient boosting regressor and random forest regressor are the best-performing models among all the tested ML models, whose good R -squared ( R 2 ) values reveal their prediction accuracy. Furthermore, their SHapley Additive exPlanations analysis demonstrates that the polar surface area is the most impactful feature to influence its model outputs for highlighting its essential role in their design process. The results also reveal that the evaluated models exhibit consistent performance across different K values, with their mean squared error values spanning from 0.001 to 0.009 and R 2 values of 0.96–0.98. In addition, their synthetic accessibility likelihood index scores show a value as high as 15 for the top polymers to imply favorable conditions for their practical synthesis. The current study not only expands the understanding of polymer design but also furthers the field of PVs by establishing a good framework to design efficient solar energy materials.

We investigate the robustness of Einstein–Podolsky–Rosen (EPR) steering, nonlocality, and quantum coherence in a bipartite atomic system coupled to cavity fields under the influence of decoherence. The system consists of two non-interacting atoms, where each atom is confined within a cavity that interacts with another cavity field, which plays a crucial role in governing the dynamical evolution of two atoms. Through a combination of analytical and numerical investigations, we demonstrate that quantum steering, Bell nonlocality, and coherence can be not only preserved but also enhanced by appropriately tuning the cavity–cavity interaction strength, effectively mitigating environmental decoherence and extending the coherence lifetime of the system. Our results reveal that, under optimal conditions, steering, nonlocality, and coherence remain resilient against decoherence over extended timescales. These findings offer valuable insights into the controlled manipulation of quantum resources in open quantum systems and have significant implications for quantum information processing and secure communication technologies.

Coating techniques are broadly used in the production of sticky tapes, plastic films, books, wallpapers and magazines, adhesive tapes, as well as the textile and metal preservation, packaging, material protection, and X-ray films. The rheology of the magneto-hydrodynamic (MHD) hybrid nanomaterial on the final coating thickness is studied by using the reverse roll coating technique. In the coating industry, the application of nanomaterials over the sheet/substrate has better non-Newtonian like rheological features as opposed to the ordinary fluid. The dimensionless governing equations are reduced using lubrication approximation theory, and the exact solutions for velocity and pressure gradient are obtained. To find the transition point, coating thickness, and other mechanical quantities, a numerical technique is utilized. Graphs and tables are used to study the impacts of hybrid nanoparticles and magnetic fields on the flow and engineering quantities in detail. The flow rate, transition point, and coating thickness decrease due to an increase in the nanoparticle volume fraction and MHD. Controlling these relevant parameters helps in engineering applications, including attaining an efficient coating process, protecting and prolonging the substrate life. Graphical abstract

This article presents a new chaotic hyperjerk system by adding nonlinear term to an existing model. The dissipativity and invariance, equilibrium points, and their stability conditions, as well as the conditions for the existence of Hopf bifurcations at the equilibrium points, are analyzed. Meanwhile, we investigate the rich dynamical phenomena of the hyperjerk system, and the results show that the system exhibits chaos over a wide range of parameter variations and demonstrates complex dynamical characteristics such as periodic orbits, multi-periodic orbits, and quasi-periodic orbits under different parameter conditions. Furthermore, the chaotic synchronization, and circuit implementation of the hyperjerk system are also studied. Finally, the application of the hyperjerk system in chaotic encryption and decryption is discussed.

In this study, we have applied the intrinsic decoherence (ID) model of the Milburn equation to investigate the temporal evolution of various quantum resources (steerability, entanglement, and coherence) in the generated dipole-coupled two-qubit states. Einstein–Podolsky–Rosen steering, EOF, and Jensen–Shannon divergence are used to analyze these quantum resources. We consider two dipole-coupled qubit interacting with two spatially separated cavities with nonlinear photonic transitions, filled with a superposition of generalized Barut–Girardello coherent fields. The exploration of steerability, entanglement, and coherence has been carried out by considering the nonlinearity of qubit–cavity interactions, the nonclassicality of the superposition of Barut–Girardello coherent fields, the dipole–dipole coupling, and the ID of qubit–cavity interactions. Our results show that the nonlinearity of qubit–cavity interactions, the initial generalized Barut–Girardello coherent states, and the qubit–cavity detuning significantly enhance the generation of quantum steerability, entanglement, and coherence. The dynamics of entanglement and steerability are consistent with the hierarchy principle. The ID effect reduces the amplitudes and frequencies of the generated quantum resources to their stationary values. It is found that the phenomena of sudden steerability arising and sudden annihilation of entanglement are influenced by the initial non-classicality, dipole coupling, and intrinsic qubit–cavity decoherence. Moreover, the strong decoherence and dipole coupling significantly enhance the steady-state values of steerability, entanglement, and coherence.

This study numerically investigates turbulent convective heat transfer (HT) in a rectangular channel enhanced with fins and grooves using the finite element method and the standard k – ε turbulence model. The novelty lies in the combined evaluation of rectangular, trapezoidal, and triangular grooves by varying the b / c ratio from 1.0 to 0, along with a systematic optimization of plus (+) and flat fin heights. Among six groove configurations, the b / c = 0.75 trapezoidal groove produced the highest temperature increase (Δ T = T out − T inlet ) of 16.54% improvement over the baseline ungrooved channel. Through additional optimization, raising both fin types to 1.50 h was found to provide the optimal thermal performance with an outlet temperature of 51.17°C and a 146.88% improvement in Δ T compared to the baseline. These results highlight the large synergistic effect of groove geometry and fin height optimization, yielding an effective design strategy for enhancing HT in solar heat exchanger devices.

This work employs the one-dimensional quantum hydrodynamic model to investigate the nonlinear propagation of modulated ion-acoustic waves (IAWs) in unmagnetized quantum plasma with ion beams. A reductive perturbation technique (RPT) is carried out to reduce the set of fluid equations to a cubic nonlinear Schrödinger equation (NLSE), which governs the propagation of the modulational instability (MI) and its associated modulated structures (envelope solitons). It is demonstrated that plasma configurational parameters, such as ion beam density, quantum diffraction parameter, and ion beam temperature, significantly affect MI and the related nonlinear structures. We also examined the impact of these pertinent physical parameters on the critical wavenumber and the growth rates related to MI. The critical wavenumber and MI growth rate were found to decrease with growing values of quantum diffraction parameters and ion beam temperature while falling with ion beam density. Furthermore, the modulated nonlinear localized structures that appear as bright and dark envelope solitons are discussed in detail. Our results are expected to reveal the mystery of the behavior of the modulated nonlinear phenomena that may arise and propagate in such a type of quantum plasma with ion beams. Moreover, the results can be used to understand the behavior of many modulated nonlinear phenomena and then devote them to various applications.

Accelerated life tests (ALTs) involve subjecting units to more extreme conditions than normal to reduce the duration of testing. These tests, whether fully accelerated or partially accelerated, are crucial in life testing research as they help save both time and money. When results from ALT cannot be extrapolated to normal circumstances, partial ALTs are performed. This study introduces a constant-stress partial ALT, which relies on a generalized Type-II hybrid censoring scheme and assumes that the lifetimes of units under the specified conditions follow the Burr III distribution. The estimates of parameters and accelerated factor of the Burr III distribution are obtained under normal use settings by applying the maximum likelihood and Bayesian techniques. Bayesian estimators are generated using symmetric and asymmetric loss functions through the Monte Carlo Markov Chain approach. Additionally, credible intervals and asymptotic confidence intervals are constructed. Simulation research is carried out using different censoring techniques and sample sizes in order to compare the suggested methodologies. Next, two data sets are analyzed to show the value of the proposed approaches. The study’s conclusion contains a summary of its main conclusions.

Studies of 1D hydrogenic atoms or ions reveal interesting physics and could be relevant to the following experimental situations: (1) hydrogenic atoms in very strong magnetic fields where the electron is effectively confined in a finite-radius cylinder surrounding a field line; (2) an electron constrained to the surface of a nanotube in the field of an ion; (3) excitons in research of semiconductors, superconductivity, and polymers; (4) electron at the surface of liquid helium. In the present theoretical paper, we revisited the 1D Dirac–Coulomb problem. We employed a model where the Coulomb potential is truncated by a constant value at some relatively small but finite distance R from the origin, thus allowing for the finite size of the nucleus of charge Z . We derived analytically the wave functions in the exterior and interior regions. We showed that for nonzero energies, the wave functions in the exterior and interior regions and their derivatives cannot be matched at the boundary, so that the corresponding mathematical solutions are not physically acceptable. For zero energy, we determined the value of R ( Z ), at which the interior and exterior wave functions and their derivatives can be matched at the boundary. We demonstrated that for the electronic hydrogenic atoms or ions, the matching value of R ( Z ) is greater than the corresponding nuclear sizes by at least two orders of magnitude. However, for the muonic hydrogenic atoms or ions, the matching value of R ( Z ) turned out to be approximately equal to the nuclear size R 0 ( Z ) (within the accuracy of the expressions for R 0 ( Z )) for the range of the nuclear charges 14 ≤ Z ≤ 25 ( i.e. , from Si to Mn), the best match of R and R 0 being for Z = 18 (Ar) and Z = 19 (K).

This study aims to investigate thin film flow with the effects of a magnetic field in association with Cu and CuO nanoparticles past an inclined plate. The second law of thermodynamics is used to optimize the production of entropy and to reduce the fluid’s friction. The leading equations have been solved through the homotopy analysis method in dimensionless form. It is observed that fluid motion is slowed down as the thickness factor, volumetric fraction of nanoparticles, and unsteadiness parameter increase, while it intensifies with higher values of mass and thermal Grashof numbers. The thermal distribution has augmented with an upsurge in volumetric fraction, magnetic factor, Eckert number, and unsteadiness factor. Bejan number as well as the rate of entropy production are opposed by Brinkman number and are supported by growth in magnetic factor. For nanoparticle volume fractions ranging from 0.01 to 0.03, the Nusselt number shows significant improvement, particularly for hybrid nanoparticles, where it increases from 4.3207 to 6.6983%, demonstrating their superiority over traditional nanoparticles. Validation of work has been ensured through comparative analysis between current results and published works.

A new four-dimensional hyperchaotic model (4-DHM) with eight parameters is examined in this work. Depending on how two of these parameters are chosen, this model may contain equilibrium points or not. Therefore, we may choose a value that will make the corresponding attractor either hidden or self-excited. In this model, we consider the two scenarios and analyze the dynamics of the two instances. The numerical simulation of the novel 4-DHM is shown together with bifurcation diagrams, the Lyapunov exponent, and an examination of equilibrium and stability. The novel 4-DHM may be used in many science and engineering applications, such as electronic circuits and image encryption. A physical implementation is added to the electronic circuit’s MATLAB Simulink to confirm that the new 4-DHM can be built. The results of the numerical analysis and electronic circuit simulation of our model were in a good agreement. The color image’s encryption, decryption, histogram analysis, information entropy, correlation coefficient, number of pixels change rate, and unified average changing intensity are examined using the proposed model.

Accurately modelling non-Newtonian fluid flow through porous media is vital in several industrial and engineering processes, particularly where inertial effects and temperature-dependent properties are critical. This study aims to develop a high-order numerical scheme for simulating Darcy–Forchheimer flow of Williamson fluids with temperature-dependent thermal conductivity. The proposed methodology combines a second-order exponential time integrator with a sixth-order compact finite difference scheme for spatial discretization. A modified predictor–corrector structure is formulated, and its conditional stability is verified through Fourier (von Neumann) analysis. The method avoids linearization and iterative solvers, enhancing computational efficiency. Quantitative validation demonstrates that the scheme achieves second-order accuracy in time and sixth-order convergence in space, with a reduction in error norm of up to 18% compared to the classical second-order Runge–Kutta method. Parametric studies confirm the strong influence of Weissenberg number, Forchheimer number, and non-linear conductivity on velocity, temperature, and concentration fields, validating the robustness and applicability of the scheme in complex transport phenomena. All computations were carried out using MATLAB R2023a, where the proposed scheme was implemented and validated against benchmark solutions to confirm its numerical accuracy and computational efficiency.

In this study, we investigate the fractional regularized long-wave (FRLW) equation using the Aboodh transform iteration method (ATIM), a semi-analytical technique that effectively combines the Aboodh integral transform with iterative schemes to handle fractional differential equations. The FRLW equation, a nonlinear model arising in ion-acoustic wave propagation in plasma, is extended to the fractional domain to better capture the temporal nonlocal behavior. The proposed method provides approximate analytical solutions in a straightforward and computationally efficient manner. Graphical results are presented to demonstrate the impact of the fractional-order parameter on wave dynamics, including dispersion and stability. The results confirm that ATIM is a powerful and accurate approach for solving nonlinear fractional partial differential equations and enriches the analytical understanding of fractional plasma wave models.

This study presents the innovative design and development of a bismuth( iii ) oxyiodide/intercalated iodide-poly(1 H -pyrrole) rough spherical nanocomposite (Bi( iii )OI/I-P1HP RS-nanocomposite) as a next-generation photocathode for sustainable hydrogen production directly from seawater. The material features a unique rough-surfaced spherical morphology, composed of finely distributed nanoparticles averaging 15 nm in diameter, which enhances the surface area and light interaction. The strategic incorporation of iodide components significantly boosts photon absorption, while the optimal bandgap of 2.45 eV enables efficient light harvesting from the ultraviolet to mid-visible spectral range – ideal for real-world solar-driven applications. Hydrogen evolution experiments conducted using both natural Red Sea seawater and a synthetically formulated laboratory electrolyte demonstrated consistent and efficient performance, with current densities ( J ph ) in light of −0.20 and −0.19 mA cm⁻ 2 , respectively. These values correspond to an impressive hydrogen production rate of 5.0 µmol h −1  cm −2 . The photocathode exhibited remarkable operational stability and reproducibility under chopped illumination, confirming its robustness under dynamic light conditions. Furthermore, spectral response studies across various wavelengths revealed adaptable behavior based on photon energy, underscoring its versatility in different lighting environments. With its compelling combination of high photoelectrochemical efficiency, structural stability, and economic viability, the Bi( iii )OI/I-P1HP RS-nanocomposite emerges as a promising candidate for scalable, eco-friendly hydrogen generation. This work lays the foundation for future industrial applications in renewable energy, offering a practical and sustainable route toward clean fuel production directly from seawater.

Thermal transport in ternary nanofluid is a topic of interest in different engineering systems. These fluids have higher thermal conductivity than traditional nanofluids. Hence, the present study aims to develop a new ternary nanofluid model for a cylindrical working domain. For this, thermophysical properties of ternary nanoliquids and appropriate transformations are used. The problem is then investigated through a numerical approach and the comparative results are obtained. The ternary nanofluid shows an optimum decrease in the velocity due to the involvement of three types of nanoparticles. Suction of the fluid with strength α = 0.1 , 0.9 , 1.7 , 2.5 \alpha =0.1,\hspace{.5em}0.9,\hspace{.5em}1.7,\hspace{.5em}2.5 and Reynolds effects Re = 1.0 , 1.5 , 2.0 , 2.5 \text{Re}=1.0,\hspace{.5em}1.5,\hspace{.5em}2.0,\hspace{.5em}2.5 significantly control the motion and dominant behaviour is examined for a simple nanofluid. The thermal capability of the nanofluids is enhanced against the concentration factor ϕ 1 = 0.01 , 0.0.3 , 0.05 , 0.07 {\phi }_{1}=0.01,\mathrm{0.0.3},0.05,0.07 while suction phenomena resist the temperature. Inclusion of radiations ( Rd = 0.1 , 0.5 , 0.9 , 1.3 ) (\text{Rd}\hspace{.25em}=\hspace{.25em}0.1,0.5,0.9,1.3) and convective transport ( B i = 0.01 , 0.02 , 0.03 , 0.04 {B}_{i}=0.01,0.02,0.03,0.04 ) contribute dominantly for thermal applications in nanofluids. The shear drag magnitude changes from 107.4995 to 162.287% (TNF), 113.427 to 170.666% (HNF), and 120.886 to 180.704% (SNF) for varying ϕ 1 {\phi }_{1} from 1.0 to 7.0%. Further, the efficiency of TNF, HNF, and SNF showed a prominent increase from 42.0126 to 68.8055% (TNF), 40.6019 to 66.6076% (HNF), and 39.8879 to 65.5324% (SNF), for stronger Biot effects from 0.5 to 2.0. Hence, the study’s outcomes would help to address the heat transfer issues from multiple aspects.

This study explores the dynamics of a two two-level atomic system interacting with a parity-deformed field, modeled as a coherent state. By varying the parity deformation parameter and incorporating the effects of intensity-dependent coupling, we examine the time evolution of key quantum phenomena. These include atomic population inversion, von Neumann entropy, concurrence, quantum Fisher information, and the Mandel parameter, where each serves as a critical indicator. Our analysis reveals how the interplay between the deformation parameter and coupling effects governs the quantum dynamics, influencing entanglement, parameter estimation, and statistical properties of the field. These insights contribute to a more comprehensive understanding of how to control and optimize quantum phenomena, highlighting the model’s relevance for quantum information processing technologies.

This article introduces a novel modified G ′ G 2 \left(\phantom{\rule[-0.75em]{}{0ex}},\frac{G^{\prime} }{{G}^{2}}\right) expansion method, combined with Maple software, for solving the exact solutions of the generalized hyperelastic-rod wave equation (GHRWE). The GHRWE has extensive applications in various fields, including the study of dark soliton molecules in nonlinear optics, the propagation of longitudinal waves in fractional derivative viscoelastic materials, and the investigation of the local well-posedness and dispersive limit behavior of the generalized hyperelastic rod wave equation. Through this method, we have obtained a variety of solutions, including U-shaped dark solitons, inverted U-shaped solitons, single W-shaped solitons, and bright-dark alternating solitons. These solutions not only enrich the solution set of GHRWE but also provide a theoretical basis for understanding and predicting behaviors in nonlinear dynamical systems. Our research delves into the impact of fractional order variations on soliton solution characteristics, such as shape and amplitude, and analyzes the effects of different fractional derivative selections on soliton properties. In addition, a significant contribution of this study is the construction of the Hamiltonian system for GHRWE using the trial equation method, revealing complex bifurcations and chaotic dynamics that have eluded previous research. Ultimately, we employed the Chebyshev method, renowned for its exceptional accuracy and numerical stability, to rigorously validate our analytical solutions, ensuring minimal error margins. Through these efforts, we have not only advanced the understanding of GHRWE but also provided new perspectives and tools for research in related fields.

One of the earliest attempts to make special relativity and quantum mechanics compatible was the Klein–Gordon equation (KGE). In the 1920s, Oskar Klein and Walter Gordon independently proposed it. This equation plays a very significant role in the fields of quantum mechanics and quantum field theory. This equation has been solved using a variety of techniques. The current work presents a numerical approach that uses cubic B-spline (CBS) functions to solve the KGE involving Atangana–Baleanu fractional derivative. The fractional derivative in time is discretized using a finite difference scheme in the proposed technique, while the space direction is discretized using a θ \theta -weighted scheme based on CBS functions. The Fourier approach is used to prove that the proposed scheme is unconditionally stable. A second-order convergence in the temporal and spatial directions has been proved theoretically and numerically. Finally, four applications of the KGE show the efficiency and accuracy of the proposed method than other methods.

In this study, the breather solutions and interaction solutions for the (3+1)-dimensional conformable fractional potential Yu-Toda-Sasa-Fukuyama-like model are conducted. The fractional derivative is described using the conformable derivative. By using certain commutative methods, we derived the breather solutions and the interaction solutions of breathers and lumps in terms of Gramian. Solutions of these forms have never been studied. The features of the solutions were examined. Each interval of the breather has one and only one peak as well as trough, and the interaction between the breather wave and the breather wave or the lump wave is elastic. In addition, the effect of a fractional order change on the shape of the breathers is discussed through 3-dimensional images, and this change is able to be reduced to integer order and different fractional order.

In response to the problem that traditional hydraulic fracturing technology is difficult to describe the specific situation of ground fissures, this study proposes to introduce a mechanics model of fracturing disappearance and optimize the model in order to achieve accurate description of the distribution of ground fissures after hydraulic fracturing. The model is validated and analyzed through case studies, and it is found that stress sensitivity, invasion factor, and retention factor all have varying degrees of influence on the tracing process. In addition, the model can accurately infer the fractures of hydraulic fracturing wells, with a variance of 148.9, a coefficient of determination of 0.81, and a root mean square error of 1.87. In terms of production, the oil production reaches 104.2 m 3 , accounting for 20.4% of the total oil production, and the water production reaches 47.6 m 3 , accounting for 15.8% of the total water production. In the examination of economic and environmental benefits, it is found that the model proposed by the research reduces labor expenditure costs to 292,000 yuan, equipment costs to 392,000 yuan, chemical supplies costs to 217,000 yuan, and maintenance costs to 98,000 yuan, but the revenue increases to 1.34 million yuan, and environmental satisfaction reaches 81.4%. The comprehensive results indicate that the model can be well applied in the tracing technology of hydraulic fracturing radioactive sources.

The non-Newtonian (NN) hybrid nanofluids (HNF) flow over a porous stretching or shrinking Riga sheet is calculated. The HNF is produced by the scattering of cerium oxide (CeO 2 ) and aluminum oxide (Al 2 O 3 ) nanoparticles. NN HNF offers a wide variety of uses. For instance, enhanced heat transportation, cooling, maintenance, and reliability in mechanically powered delivery of medicines, increased efficacy in microfluidic devices, advanced material synthesis, and energy-related applications such as storing energy and solar power generation systems are a few of them. For this purpose, the flow phenomena are modeled in the form of nonlinear partial differential equations (PDEs), which are reduced into the dimension-free form through the similarity conversion. The solution is obtained by using the numerical approach parametric continuation method. The stability analysis has also been performed to check which solution is stable and reliable in practice. The results are compared to the numerical outcomes of the published studies. The present findings have shown the best correlation with the previous published studies. The relative error between the published and present study at Pr = 10 (Prandtl number) is 0.00046%, which is gradually reduced up to 0.00202% with the variation of Pr = 0.7. Furthermore, the impact of a viscoelastic factor enhances the velocity field of HNF (Al 2 O 3 and CeO 2 /SA) for both types of NN fluids (second-grade fluid & Walter’s B fluid) in the case of stretching Riga sheet.

This work focuses on the impact of a magnetic field and viscous dissipation on the mixed convective flow of a couple stress nanofluid over a sheet that is stretching linearly. The research focuses on how these variables impact the model’s overall heat transfer characteristics and the fluid’s behavior. The sheet’s stretching causes the fluid to move as it extends, which is what causes the flow. When considering a heating procedure at the prescribed surface temperature, the heat transmission problem has been examined. The modified Adomian decomposition method (ADM) is a computational method that simplifies the complex governing equations of the model under study and finds their numerical solutions. This technique uses the Mohand transform in conjunction with the ADM, which ensures a high degree of convergence, producing a series solution that closely resembles the exact solution to the problem. In addition, we evaluate the residual error function to satisfy the effectiveness and accuracy of the introduced technique. When the current findings were compared with other methods for particular flow scenarios, they demonstrated strong agreement, confirming the accuracy of the solution. A complete examination of the effects of the different parameters has been provided, including graphic and tabular illustrations of the effects. Additionally, a comparison chart illustrating the agreement between the two sets of data has been given to show the coherence between the present numerical outcomes and previously published findings.

This article investigates fluid flow in a dynamic system using the coupled Boussinesq–Burgers equation to precisely narrate the propagation of shallow water waves. This work proposes a novel approach to using the quintic B-spline technique to obtain an approximate solution to the nonlinear fractional coupled Boussinesq–Burgers equation. For discretizing time, the Caputo fractional derivative is used to handle the fractional derivative effectively, while the quintic B-spline function is used to interpolate the spatial derivative. We provide two numerical examples to show the level of accuracy and practicality of the current scheme in solving the fractional coupled Boussinesq–Burgers problem and see how observe the effect of the fractional-order on wave propagation. In addition, we conduct a stability analyzis and numerically determine the order of convergence. We compute the error norms to assess the accuracy of the proposed method.

Hybrid nanofluids, an advanced class of working fluids, gained significant attention due to their superior thermal performance and heat transfer characteristics. These fluids consist of two types of nanoparticles suspended in a base fluid, offering enhanced thermal performance, making them crucial in engineering applications. In many industrial processes, magnetohydrodynamic (MHD) hybrid nanofluid flow plays a vital role in controlling mass and heat transfer in systems involving precipitation and chemical processing. The interaction between thermal radiation, chemical reactions, Joule heating, and heat sources significantly affects the efficiency of such systems, necessitating an in-depth analysis of their combined effects. This study focuses on the heat and mass transfer in hybrid nanofluid flow over various geometries, which is crucial for thermal management in electronic devices, precipitation, and filtration processes. Practical applications of a hybrid nanofluid flow around cones and wedges include spacecraft design, nuclear reactors, solar power collectors, etc. Therefore, this research examines the MHD hybrid nanofluid flow over a cone and wedge, using a suspension of SWCNTs and MWCNTs as nanomaterials in H 2 O as the base fluid. The study also considers the impact of Joule heating, an exponential space-based heat source in the temperature equation with thermal and mass convective conditions over two geometries (cone and wedge). Additionally, chemical reactions play a significant role in various natural and industrial processes. With this initiation, this research explores the effect of the activation energy and binary chemical reaction on the MHD hybrid nanofluid flow. The hybrid nanofluid model over two different geometries is governed by partial differential equations and converted to ordinary differential equations using similarity variables. The bvp4c method in MATLAB was employed to solve these equations numerically. The effects of the sundry flow parameter on the velocity, temperature, and concentration distributions were determined and discussed briefly. The study’s findings show that the improvement in both the thermal and mass Grashof numbers results in an increase in the velocity profile, supporting the effectiveness of hybrid nanofluids in cooling technologies for electronic devices. The increasing impression of the activation energy and mass Biot number on the concentration profile is progressive for wedges compared to cones. Furthermore, the results reveal that the presence of a nonlinear heat source tends to intensify the thermal profiles for wedges more significantly than the flow over cones, which is also related to the application of solar power collectors. The rate of heat transfer for the flow over a cone case is higher for the growing estimation of radiation, and the Biot number is particularly relevant to high-temperature applications such as nuclear reactors and spacecraft. The increasing impact of the Schmidt number, chemical reaction, and mass Biot number on the mass transfer rate is higher for cones as compared to wedges, while the activation energy has an opposite behavior for both flow cases. The observed trends in the mass transfer rate also support filtration and separation technologies, optimizing their efficiency based on fluid and material properties.

Exact solutions of (1+1)-dimensional M-fractional Kairat-II equation are obtained via proposed three extended mathematical methods with the help of the computational software Mathematica. This model has many applications in optical fibers, which is used to describe the trajectory of optical pulses in optical fibers. The derived solutions are novel and newer existing in any kind of literature. The constructed solutions are in distinct form, such as trigonometric, hyperbolic, exponential, and rational functions. For the physical phenomena of concern fractional model, some obtained solutions are plotted in two-dimensional and three-dimensional by assigning the specific values to the parameters under the constrain conditions. Moreover, the proposed methods are enormously superbly mathematical tools to review wave solutions of several fractional models in nonlinear science.

This study investigates thermally radiative nanofluid flows on an elongating surface using porous media. The flow dynamics are affected by the combined impacts of exponential and thermally dependent heat sources. Additionally, magnetic effects are introduced to the flow system while it is inclined. Copper (Cu) and copper oxide (CuO) nanoparticles are mixed in water (H 2 O) to fabricate nanofluid flows. Different shapes of Cu and CuO nanoparticles, including column, sphere, hexahedron, tetrahedron, and lamina, were studied in this analysis. The system flow is triggered by the stretching properties of the sheet. The textured surface of the stretching sheet facilitates the exploration of the slip velocity phenomenon. The modeled equations are evaluated using the bvp4c approach in a dimensionless form. The present study is validated by comparing its findings with established datasets available in the literature. The results of this analysis show that the velocity distributions decline with increasing values of the porosity factor, velocity slip factor, and magnetic factor. The reduction in velocity profiles is quite significant in the case of Cu–water nanofluid, in contrast to the CuO–water nanofluid due to more dominance of resistive constraints in the case of the Cu–water nanofluid. The thermal distribution increases with an increase in the magnetic factor, radiation factor, Eckert number, thermal-dependent heat source, and space-based heat source, and declines with an increase in the inclination angle and thermal slip factor. The Nusselt number augments for both types of nanofluids with an increase in various emerging factors in the scenarios of thermal slip and no-slip, where an increase in the Nusselt number is maximum for the scenario where there is no thermal slip. A higher thermal distribution and heat transfer rate are determined for the lamina-shaped Cu–water and CuO–water nanofluid flows for both slip and no-slip thermal conditions. On the basis of the current findings, this study aims to design efficient cooling systems for microelectronics, improve solar thermal collectors, enhance drug delivery via heat-sensitive nanoparticles, optimize industrial heat exchangers, and advance smart textile technologies requiring controlled thermal regulation using shape-engineered Cu and CuO nanofluids.

The present study investigates the heat transfer for the unsteady, incompressible, two-dimensional mixed convective copper–water nanofluid flow in a lid-driven square cavity in the presence of the magnetic field. The lid-driven square cavity’s top and bottom walls are assumed to be adiabatic. The nanofluid model is developed in ANSYS-FLUENT using Boussinesq approximation. A pressure-based solver with a Semi-Implicit Method for Pressure-Linked Equations algorithm is used to simulate the governing equations of the model. The results obtained from the developed fluid model are examined for the different influential physical parameters to enhance heat transfer from the cavity to the flowing fluid. Qualitative and quantitative results for nanofluid concentration, magnetic field parameter, and Reynolds number are analyzed. A noteworthy observation is that the velocity of the nanofluid reduces with improvement in the magnetic field strength. The findings of the attempt provide the capability of nanofluids in heat transfer, which aids in creating innovative geometries with improved and regulated heat transfer due to applied magnetic fields. This attempt holds potential applications in solar collectors, electrical devices, and the medical field manageable due to the slower fluid flow (nanofluid).

This analysis examined the convective heat transport influence of stagnant point bioconvection movement of a Darcy–Forchheimer flow past a rotating disk with entropy generation analysis. The energy expression is contributed by the effect of thermal radiation and the heat generation/absorption rate. The second law analysis also accounted for the given study’s inspection of the irreversible analysis. The Buongiorno nanoscale model simulates the Brownian movement and thermophoretic effect. Also, the Maxwell fluid model is used for non-Newtonian rheological characteristics, and a Darcy–Forchheimer flow model is used for the porous medium. The nonlinear model equations are transformed into dimensionless equations through an appropriate transformation. Further, the converted expressions were computed using the homotopic procedure. Moreover, the graphs illustrate the consequences of flow variables on microorganism profile density, concentration distributions, thermal, velocity, entropy, and the Bejan number. The inertia coefficient and non-Newtonian fluid variable reveal the significance of axial and radial velocity decrease. An enhancement in the thermal field is noted for the higher values of the radiation parameter and the Biot number. The larger magnitude of the Brinkman number escalates the rate of entropy and the Bejan number. The drag force decreased from 7.95 to 7.13% for the values of the inertia coefficient. Heat transport is enhanced by 22% as the larger magnitude of thermal radiation parameter ( Rd {\rm{Rd}} ) rises. Mass transfer is further enhanced by bioconvection, which increases nanoparticle dispersion by up to 18%.

Non-Newtonian fluids, particularly those with high viscosity and complex flow behavior, present unique challenges in manufacturing processes. The modeling of their flow dynamics is crucial to achieve the desired outcomes in industrial applications. This study aims to theoretically model and analyze the flow dynamics of the Eyring–Powell fluid under varying temperature conditions using lubrication approximation theory and perturbation method. To simplify the mathematical formulation of fluid flow motion, lubrication approximation theory is applied. Using a perturbation method, the dimensionless governing equations are solved to derive expressions for velocity, pressure gradient, and pressure distributions. Numerical integration is then used to calculate critical engineering parameters, such as power input and roll-separating force, offering practical insights for optimizing the manufacturing process. Additionally, using the response surface method, Nusselt number ( Nu ) (\text{Nu}) , sheet thickness H H 0 \left(\phantom{\rule[-0.75em]{}{0ex}},\frac{H}{{H}_{0}}\right) , and shear stress ( S x y ) ({S}_{xy}) , simulations were carried out to investigate the influence of variable viscoelastic parameters on the response functions ( Nu \text{Nu} , H H 0 \frac{H}{{H}_{0}} , and S x y {S}_{xy} ). The virtuousness of appropriate of the empirical model is obvious based on the coefficient of determination ( R 2 ) ({R}^{2}) obtained from the analysis of variance. The findings reveal that the Weissenberg number, viscosity parameter, and Brinckmann number significantly influence velocity distribution, pressure profiles, power input, and roll-separating force, which are critical factors in the calendering process. Furthermore, the heat transfer rate shows an increase of approximately 5% with the rising values of the involved parameters, highlighting their significant influence on thermal performance. The coefficients of determination ( R 2 ) ({R}^{2}) rise by about 99% for all response parameters, indicating the empirical model’s goodness of fit. These results provide valuable insights for engineers and researchers working on the calendering process of non-Newtonian fluids with complex rheological behavior, enabling better optimization of manufacturing processes and improved industrial outcomes.

This work examined solitary wave solutions to the nonlinear damped Korteweg–de Vries equation by employing the new auxiliary equation approach. The physical structure to the secured solutions visualized in dark solitons, bright solitons, periodic solitons, kink and anti-kink wave solitons, peakon bright and dark solitons, and dispersive solitary waves. The physical interpretation of constructed solutions is visually portrayed using two-dimensional, three-dimensional, and contour plots on the basis of numerical simulation, which help comprehend the physical features of nonlinear behaviour for the solitary waves. The explored solutions will be play important role in Mathematical physics, ion-acoustic waves, dust-acoustic waves, and plasma physics. This study has demonstrated that our suggested method is more beneficial, successful, strong and effective for studying analytically various nonlinear partial differential equations (NLPDEs) that arise in mathematical physics, engineering, plasma physics, and many other scientific fields.

This article provides a concise comparative examination of how heat generation affects the flow of a magnetized micropolar blood-based hybrid nanofluid (HNF) via a stenotic artery. The effects of Joule heating and viscous dissipation are considered. The purpose of this model is to evaluate and contrast the efficiency of HNF models. Our objective is to comprehend the complex process of hybridization by studying the behavior of titanium dioxide (TiO 2 ) and gold (Au) nanoparticles scattered in blood. The mathematical model has been converted into a dimensionless form by applying similarity transformations. This modified model is then efficiently solved using numerical methods, specifically bvp4c, which is a built-in command in MATLAB for solving boundary value problems, and facilitates the efficient handling of nonlinear ordinary differential equations with high accuracy and stability. The cylindrical surface is employed for the computation of flow measures, and the results are visually depicted using tables and graphs. This study makes a substantial contribution by uncovering previously unidentified flow characteristics. The use of Au nanoparticles demonstrates efficacy in improving the blood flow and offers a promising approach for addressing arterial disorders, as opposed to aluminum oxide nanoparticles. Moreover, an inquiry is carried out to examine the skin friction and heat transfer related to the dynamics of blood flow. The results demonstrate that the inclusion of Au and TiO 2 nanoparticles enhances heat transfer compared to single-component nanofluids (NFs) while effectively moderating the velocity and temperature profiles under varying conditions. Also, the HNF shows a reduction in temperature rise compared to NFs with only Au nanoparticles, under specific parameter settings.

The goal of the current study is to discover the impact of cross diffusion effects, activation energy, thermal radiation, and convective heating on three-dimensional doubly diffusive convective nanoliquid flow over a rotating surface in a Darcy–Forchheimer porous domain with heat generation. The governing model (partial differential equations) are solved numerically after being converted by similarity transformation into a nonlinear ordinary differential system. The numerical solutions are obtained for various combinations of effects involved in the physical model. The skin friction and mass and heat transferral rates are also computed. The activation energy is more pronounced on solutal transport than that of on thermal transport. The heat transfer is suppressed by strengthening the values of the inertia parameter and the rotational parameter.

The role of generalized nanoparticles was observed to be significant while increasing the surface area interaction between the base materials and the solid surface. The conductivity of such materials with the occurrence of similar and nonsimilar reactants has been observed to be very effective. Particularly, the processing of many rheological materials in industries is considered one of the significant applications. However, this study explored the unique features of the melting heat approach while considering the spinning motion of nanocomposite shear-thinning materials. The rheological material model was tested in the presence of autocatalytic reactions during its transparent conversion to a liquid state. Furthermore, the flow, temperature distribution, and nanoparticle concentration of the materials were represented by the conservation of momentum, concentration, and energy concepts. The leading problem is then presented using dimensionless local similar equations. The same equations are then numerically approximated by adopting one of the improved building three-stage formulas. The results were presented in terms of physical velocity, concentration, pressure, temperature, resistive forces, mass, and heat flow rates. The material dynamics are significantly reduced by plugging the higher relaxation time, and a reverse conduct is determined in the case of thermal analysis of the same materials. The melting heating factor and Brownian motion variation enhanced the flow speed and material temperature. On the other hand, a remarkable reduction in the material concentration was observed while uplifting similar and non-similar reaction factors. The method’s accuracy is confirmed through a well-matched comparison with the literature.

Four samples of natural sand and clay materials from the Adrar region in southern Algeria were studied for their shielding parameters at three chosen energies in this work (0.662, 1.172,1.333 MeV). There was only a small difference between the outcomes demonstrated by Géant 4 and WinXcom. Due to the nearly equal density of the materials examined, the shielding coefficients were likewise similar. But the green clay was the best, as the value of the linear attenuation coefficient (LAC) is equal to 0.117 cm −1 at photon energy was 1.172 MeV and it required a small thickness half-value layer equal to 5.903 cm. Subsequently, sand, red clay, and white clay follow green clay in a sequential manner.

The discrepancy in the measured value of neutron lifetime has significance in big-bang nucleosynthesis and testing the accuracy of the standard model. A discrepancy of approximately 10 s still persists between the average value of the neutron lifetime obtained by storing ultracold neutrons in traps and the most accurate method of using neutrons in beams. This discrepancy is thought to be due to an unknown systematic uncertainty in these experiments or the existence of new physics. This article discusses a possible explanation for this discrepancy in neutron lifetime. This neutron lifetime anomaly is likely attributed to an increase in the decay probability caused by multiple elastic collisions between neutrons and between neutrons and trap walls. Graphical abstract

Mine cooling and refrigeration system to deal with the heat hazard is well developed, but the mine air cooler which serves as the most important terminal equipment is relatively backward. The severe heat hazard and urgent cooling demand in deep underground mines necessitate further improvement of cooling capacity and effectiveness under strict requirements such as being compact, portable, nontoxic, and no-pollution. The thermoelectric (TE) energy conversion technology has great potential in cooling and miniaturization applications, which can meet the strict requirements of the underground mine cooling devices. Yet, a research gap exists in integrating TE energy conversion technology with the traditional air-cooling heat exchanger to the best of our knowledge. In this work, a hybrid utilization of TE and the helically coiled tube heat exchanger (HCEX) is proposed for air cooling at the working face of underground mine. The advantage of the TE-integrated HCEX lies in the combination of the heat transfer enhancement effect by secondary flow induced inside the helically coiled tube and the solid-state Peltier cooling effect by the TE module positioned on the external shell wall of the heat exchanger, which can potentially improve the air-cooling capacity without occupying large space. A numerical simulation of the fluid-thermal-electric multiphysics field is performed to investigate the cooling rate and the effectiveness of the TE-integrated HCEX. Results show that additional cooling power can be effectively provided by TE. As the filling ratio (FR) of TE module on the external shell wall increases from 50 to 100%, the air-cooling capacity continuously increases, performing better than that of the conventional HCEX. The effect of air inlet temperature and inlet velocity on the cooling performance is investigated for the best design of the TE-integrated HCEX with FR of 100%. When the inlet temperature of air increases from 303.15 to 313.15 K under constant inlet velocity, the cooling rate increases and cooling effectiveness decreases. Also, the cooling rate increases and the cooling effectiveness decreases when the inlet velocity of air increases from 10 to 25 m s −1 under constant inlet temperature. Within the simulated range of air inlet conditions in this work, the maximum total cooling rate Q c,total at optimal current of 6 A for the TE-integrated HCEX results in an enhancement of 49.8 to 35.0% compared to the conventional HCEX. The maximum cooling effectiveness at optimal current of 6 A is 21.73–26.49% for the TE-integrated HCEX, which is higher than the effectiveness of the conventional HCEX of 15.74–18.24%.

The isothermal gas sphere model may be beneficial for understanding certain features of astrophysical objects like stars, but it has severe limits when used for compact stars. This study expands the Tolman–Oppenheimer–Volkoff (TOV) equation of the fractional relativistic gas sphere to contain fractional derivatives, resulting in a more general fractional TOV equation (FTOVI). The analytical solution of the FTOVI equation is tackled using an accelerated series expansion. We computed models for various relativistic ( σ ) and fractional ( α ) parameters. Models with α = 1 are retained to the relativistic integer models calculated by the integer version of the TOV equation. We examine the effects of the relativistic and fractional parameters on the Emden function, mass function, and the first derivative of the Emden function and the impact of these quantities on the pressure, density, and mass-radius relation. Investigating the central density-mass relation as an analog to neutron stars indicates that a maximum mass of the sphere exists, which further increases central density, resulting in instability and collapse. The observed mass and radius of three neutron stars and those predicted from the FTOVI models agreed well. The results of high-density fractional models demonstrate that fractional derivatives might drastically modify the expected mass and radius of neutron stars compared to integer models, indicating a possible need to reinterpret observational data of neutron stars via the lens of fractional calculus.

The present study investigates different types of wave symmetries in the ( 3 + 1 ) \left(3+1) -dimensional Chafee–Infante equation via the Hirota bilinear transformation technique. In this work, we derived exact solutions that include bright and dark solitons, periodic cross kink, multiple waves, mixed waves, homoclinic breathers, M-shaped related waves and periodic lump waves. These solutions exhibit stability, energy confinement, and dynamic interactions. It is observed that the Hirota method captures the highly nonlinear complex phenomena that result from the balance between the nonlinearity and the dispersion. These factors lead to a stability and coherent formation of wave forms. We employed Mathematica 11.1 software to obtain 3D, contour, and 2D graphs of our solution. The graphs present the spatial and temporal evolution of these solutions. The periodic structures, oscillatory solitons, and cross-kink configurations have dynamic interaction while maintaining fundamental properties of waves. Breather and homoclinic breather solutions present the basis of oscillatory local dynamics, which stress on energy transfer and phase modulation. The novelty of this article is in the use of the Hirota bilinear technique to the Chafee–Infante equation in ( 3 + 1 ) \left(3+1) -dimensional dimension, which allows the derivation of a wide variety of exact multidimensional wave solutions, including intricate hybrid solutions previously unreported for the equation. This provides great value by extending the analytical theory and improving the understanding of nonlinear wave behaviors in high-dimensional environments. It is worth noting that all the solutions have been verified and found to satisfy the governing equation.

This research introduces a numerical approach that employs the midpoint technique successively to solve differential equations that contain Atangana–Baleanu and Caputo fractional derivatives. The stability and consistency of the proposed approach has been demonstrated through the application of the technique suggested for solving the perturbed problem. Furthermore, the error analysis has been carried out for a nonlinear equation with Caputo derivatives. The effectiveness of this method is illustrated by examining various examples incorporating nonlocal kernels. Finally, by the use of an example, the well-known Fitzhugh–Nagumo model with Atangana–Baleanu fractional derivatives is simulated by using the proposed scheme. The method exhibits improved accuracy, consistency, and stability compared to the classical midpoint method, with particularly good performance for the Atangana–Baleanu and Caputo cases due to a specially designed predictor component. The novelty of the work lies in extending the method to fractional operators with non-local and non-singular kernels, offering a more robust approach than existing techniques in the literature.