Volume 21, Issue 1

The attachment oscillator, which plays an important role in the nanophysics such as nano/microelectromechanical systems, molecular devices, and nanofibers, is studied in this work. With the help of the semi-inverse method, the variational principle is established, and the Hamiltonian of the system is correspondingly constructed based on the obtained variational principle. Then, according to the principle of energy conservation, the energy balance theory is implemented to seek for the amplitude–frequency relationship. As predicted, the obtained solution has a good agreement with the existing results, which shows that the presented method is simple but effective, and is expected to provide a new idea for the study of the nonlinear oscillator arising in the nanophysics.

The article explores the three-dimensional stream of silver (Ag), magnesium oxide (MgO), and motile microorganism water-based hybrid nanofluids as independent of time through a circular cylinder with a sinusoidal radius. The goal of this research is to optimize the rate of energy and mass transfer through a circular cylinder having a periodic radius. The phenomena are simulated as a system of partial differential equations containing momentum, temperature, concentration, and the profile of motile microbes, which were then simplified to a dimensionless system of ordinal differential equations using the similarity technique. The problem is solved by using the parametric continuation method, which is a numerical methodology. From the analysis, it has been perceived that both the energy and velocity fields significantly enhance with the rising effect of hybrid nanoparticles (Ag–MgO). The effect of chemical reaction enhances the mass transition rate because chemical reaction parameter influence exercises the molecules inside the fluid. The motile microorganism outline is elevated with the increment of Lewis and Peclet number.

In this work, we propose the Ritz approximation approach with a satisfier function to solve fractal-fractional advection–diffusion–reaction equations. The approach reduces fractal-fractional advection–diffusion–reaction equations to a system of algebraic equations; hence, the system can be solved easily to obtain the numerical solution for fractal-fractional advection–diffusion–reaction equations. With only a few terms of two variables-shifted Legendre polynomials, this method is capable of providing high-accuracy solution for fractal-fractional advection–diffusion–reaction equations. Numerical examples show that this approach is comparable with the existing numerical method. The proposed approach can reduce the number of terms of polynomials needed for numerical simulation to obtain the solution for fractal-fractional advection–diffusion–reaction equations.

In this work, we numerically study the behaviour of the single-mode homogeneously broadened laser versus a large perturbation of the steady state. Periodic behaviour develops for suitable values of the ratio of the population decay rates ℘ \wp , which has been analytically predicted by the analytical approach developed in the previous works, and for a pumping parameter 2 C 2C situated below and above the instability threshold 2 C 2 th 2{C}_{2{\rm{th}}} . We here show that the adiabatic elimination of the polarisation with sinusoidal time-dependent perturbation of the cavity rate leads the single-mode homogenously broadened laser to exhibit chaotic emission, if the frequency ω \omega is equal to the natural frequency Δ P {\Delta }_{P} . Increasing the pumping parameter 2 C 2C , the laser undergoes a period-doubling sequence. This cascade of period doubling drives the laser towards chaos. We also propose a reformulation of our analytical procedure, which describes the self-pulsing regime of the single-mode homogeneously broadened laser. We here report that asymmetric aspect that appears in the time evolution of the electric field is due to phase effects between the electric field components.

A highly uniform nanostructured polypyrrole (PPy) film prepared by a simple, straightforward in situ route of chemical vapor oxidation has been demonstrated as a sensitive substrate for NH 3 gas sensing. The structure of PPy film was investigated by scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), and X-ray diffraction (XRD). The binding characteristics of the functional groups of the PPy film were examined by Fourier transform infrared and Raman spectroscopy. NH 3 sensing properties of the PPy film were evaluated by its resistive response to gas concentrations from 45 to 350 ppm at different temperatures ranging from 25 to 100°C. The sensing response maximum value was 142.6% when exposed to 350 ppm of NH 3 gas at room temperature (25°C). The sensing response of PPy film shows an excellent linear relationship and high selectivity toward NH 3 . The NH 3 sensing mechanism is due to the physisorption and chemisorption interactions of NH 3 molecules and the adsorptive sites of PPy (polaron and bipolaron charging carriers).

Flash detectors are mainly used to detect the brief light flashing when projectiles are launched or exploded in the air. They can output trigger pulse signals in real time to start a test instrument and carry out data collection. Because flash detectors cannot work reliably under strong background light radiation, this work studied the flash detector mechanism. The influence of background light radiance, lens aperture, and detection distance on the effective signal was analyzed, a mathematical model of detection sensitivity based on the background radiation brightness control was proposed, a mathematical formula of the detection distance of the flash detector was deduced, and the optimal working conditions were obtained. The researched model was verified by simulation analysis and actual test experiments, in the same external circumstances, the limit detection distance of the optimal aperture compared to the maximum aperture increased by 20%, and the effective signal voltage amplitude was twice the amplitude at the maximum aperture, and the results showed the correctness of the analysis. The proposed detection sensitivity model can be applied for a dynamic photoelectric detection instrument, which broadens its potential application in the engineering field.

Inspired by the work Zhong et al . (2018), we study the linear tensor perturbation of both the flat and bent thick branes with inner structure in two-field mimetic gravity. The master equations for the linear tensor perturbations are derived by taking the transverse and traceless gauges. For the Minkowski and Anti-de-Sitter brane, the brane systems are stable against the tensor perturbation. The effective potentials of the tensor perturbations of both the flat and bent thick branes are volcano-like, and this structure may potentially lead to the zero-mode and the resonant modes of the tensor perturbation. We further illustrate the results of massive resonant modes.

The present article aims to investigate the impacts of the thermal radiation and Lorentz force on the stagnation-point flow of third-grade liquid over a porous stretching sheet with suction. The governing equations are transformed using the similarity transformation. The resulting system of ordinary differential equations is solved using a “so-called” hybrid algorithm based on the finite difference method and the shooting method. The influence of the emerging parameters on the velocity and temperature profiles is analyzed. The results are shown in graphical and tabular forms. For the third-grade liquid flow, the velocity profile shows an inciting trend toward the Hartman number (magnetic parameter). The temperature profile shows a declining trend toward the Prandtl number and suction velocity, whereas an inciting trend towards the radiation parameter.

The weighted generalized cumulative residual entropy is a recently defined dispersion measure. This article introduces a new uncertainty measure as a generalization of the weighted generalized cumulative residual entropy, called it the weighted fractional generalized cumulative residual entropy of a nonnegative absolutely continuous random variable, which equates to the weighted fractional Shannon entropy. Several stochastic analyses and connections of this new measure to some famous stochastic orders are presented. As an application, we demonstrate this measure in random minima. The new measure can be used to study the coherent and mixed systems, risk measure, and image processing.

The addition of gyrotactic microbes in the nanoparticles is essential to embellish the thermal efficiency of many systems such as microbial fuel cells, bacteria-powered micro-mixers, micro-volumes like microfluidics devices, enzyme biosensor, and chip-shaped microdevices like bio-microsystems. This analysis investigates the second law analysis in the bioconvection flow of a Carreau nanoliquid through a convectively stretching surface. The heat transports characteristics encountered with Cattaneo–Christove heat flux and thermal radiation. The Buongiorno model is used for nanoliquid, which comprises the Brownian motion and thermophoretic. The appropriate transformation is invoked to change the system of the partial differential equation into ordinary differential equations. Afterward, these equations are classified analytically with the help of the homotopy analysis method. The influence of numerous physical variables is interpreted and elaborated via graphs. The tabular result shows the numerical consequences of different physical flow parameters. It is examined that a more significant Weissenber number We {\rm{We}} results in deprecation in the velocity field. It is appraised that the temperature profile reduces to augment the value of thermal relaxation time. Justification of the current work has existed through previous publishing results. The utilization of Carreau nanoparticles in the shear rate-dependent viscous fluid is of significant importance due to their potential to improve heat and mass transmission.

In a high-power laser system, when the surface pressure of the optical film caused by laser plasma shock wave is greater than the adhesion per unit area of the film layer, the film will produce mechanical damage, and in serious cases, the whole system may not work. Therefore, studying the formation mechanism of optical film surface pressure and impulse caused by laser plasma shock wave is the key to ensure the normal operation of the high-power laser system. In this article, by studying the relaxation process of laser plasma shock wave on the surface pressure of optical film, and using the time accumulation effect of various pressures on the surface of the optical film, the calculation model of impulse on the optical film’s surface formed by laser plasma shock waves was established, and the variation rules of the impulse I st {I}_{\text{st}} and impulse coefficient j j on the unit area of single-layer Al 2 O 3 and HfO 2 optical films with different parameters were obtained. When the incident laser wavelength λ \lambda was 1,064 nm, the energy E E was 0.1 J 0.1\hspace{.1em}\text{J} , the pulse width t p {t}_{\text{p}} was 10 ns 10\hspace{.25em}\text{ns} , the focal length of the focusing lens f f was 350 mm 350\hspace{.25em}\text{mm} , the distance between the film surface and the focal plane of the focusing lens z 0 {z}_{0} was 5 mm 5\hspace{.5em}\text{mm} , and the film radius R R was 5 mm 5\hspace{.5em}\text{mm} , the calculation and simulation results show that the impulse I st {I}_{\text{st}} of the two films was 1 0 − 4 N s 1{0}^{-4}\hspace{.5em}\text{N}\hspace{.5em}\text{s} order of magnitude, the impulse coefficient j of the two films was 1 0 − 5 N s/J 1{0}^{-5}\hspace{.5em}\text{N}\hspace{.5em}\text{s/J} , the Al 2 O 3 film with small atomic number will obtain larger I st {I}_{\text{st}} and j j , I st {I}_{\text{st}} and j j of the two films increase with the increase of E E and f f , and I st {I}_{\text{st}} and j j of the two films decrease with the increase of z 0 {z}_{0} and t p {t}_{\text{p}} . In the total impulse transfer time ( t 0 {t}_{0} ), I st {I}_{\text{st}} and j j both increase with the increase of R R .

The heat transfer process of the sweeping jet and film composite cooling (SJF) structure of the turbine blade leading edge is complex. The current work divides the overall cooling effectiveness of the SJF into the impingement heat transfer effectiveness, the convection heat transfer effectiveness inside the film holes, and the external film cooling effectiveness by the decoupled method. Various cooling effectiveness proportions and trends are compared when the blowing ratios are 1.05, 2.07, and 4.11. There is an average ratio of 64.33% for impingement heat transfer effectiveness and 38.02% for convection heat transfer effectiveness. The ratio of external film cooling effectiveness gradually changes from positive to negative with the increase of the blowing ratio. Therefore, the proportion of external film cooling effectiveness and impingement heat transfer effectiveness should be considered when applying SJF. The convection heat transfer effectiveness cannot be ignored, especially when the design scheme of the shower head is used.

In this article, the influence of trapezoidal magnetization method on cogging torque of permanent magnet motor is studied. First, the structure is analyzed by analytical method to explain its mechanism of reducing cogging torque. Then, in order to verify the effectiveness of the formula, a six-slot four-pole motor is introduced for finite element analysis. Through comparison of the original structure motor, the magnet skew structure motor, and the trapezoidal magnetic pole structure motor, it demonstrates that the trapezoidal magnetic pole structure motor can effectively reduce the Cogging torque and does not produce additional axial electromagnetic force. Finally, a magnetizing fixture with a trapezoidal magnetic pole structure is made to magnetize the magnetic ring. The magnetized magnetic ring is installed on the motor, and the Cogging torque, Back EMF, etc. , are tested. The test results are in good agreement with the simulation results. This method can be used to optimize the cogging torque of the permanent magnet motor.

We propose to realize bipartite and tripartite entanglements transfer in a cavity magnomechanical system consisting of a microwave cavity with an yttrium iron garnet (YIG) sphere and a silicon-nitride membrane in it. The initial magnon–YIG phonon entanglement and photon-membrane phonon entanglement caused by the magnetostrictive interaction and the optomechanical interaction can be effectively transferred to magnon–membrane phonon entanglement and photon–YIG phonon entanglement. Photon–magnon–YIG phonon and photon–magnon–membrane phonon entanglements can also be realized in the system. These two types of tripartite entanglements can be easily transferred from one type to the other by adjusting the detuning or dissipation ratio. Moreover, the bipartite and tripartite entanglements and their transfer are all robust against temperature. Furthermore, by introducing supermodes formed by the photon and magnon modes, we find that the entanglement between the two mechanical modes can be obtained under the condition of an extremely low temperature. And the effective detuning region of the YIG phonon-membrane phonon entanglement is complementary to the detuning regions of other bipartite entanglements. Our results indicate that the combination of cavity magnomechanical and optomechanical systems could provide more flexible controllability of bipartite and tripartite entanglements and their transfer and could serve as a potential quantum interface among microwave, magnon, and mechanical systems.

The compounded Bell generalized class of distributions is proposed in this article as an alternative to the compounded Poisson generalized family of distributions. Some properties and actuarial measures are presented. The properties of a special model named Bell Weibull (BellW) are obtained such as the linear representation of density, r th moment, incomplete moment, moment generating function using Wright generalized hypergeometric function and Meijer’s G function, the p th moment of order statistics, reliability, stochastic ordering, and residual and reversed residual life. Moreover, some commonly used entropy measures, namely, Rényi, Havrda and Charvat, and Arimoto and Tsallis entropy are obtained for the special model. From the inferential side, parameters are estimated using maximum likelihood estimation. The simulation study is performed to highlight the behavior of estimates. Some actuarial measures including expected shortfall, value at risk, tail value at risk, tail variance, and tail variance premium for the BellW model are presented with the numerical illustration. The usefulness of the proposed family is evaluated using insurance claims and COVID-19 datasets. Convincing results are obtained.

Underwater plasma discharge is considered a nontoxic and effectual purification approach to control waterborne bacterial pathogens. In the present study, Vibrio cholerae contaminated drinking water was sterilized by using underwater capillary discharge generation via high voltage, oxygen ( O 2 {{\rm{O}}}_{2} ) injection, and hydrogen peroxide ( H 2 O 2 {{\rm{H}}}_{2}{{\rm{O}}}_{2} ) addition. The effects of oxidant species generated by plasma discharge on V. cholerae disinfection have been studied and reported. The electrical and optical analysis of capillary discharge revealed the generation of reactive oxygen species ( OH . {{\rm{OH}}}^{.} , H and O), which are highly useful for bacterial disinfection along with enhanced power and energy of discharge pulses. Complete elimination of V. cholerae (0 CFUs (colony forming units)) from the water after O 2 {{\rm{O}}}_{2} injected and H 2 O 2 {{\rm{H}}}_{2}{{\rm{O}}}_{2} added plasma discharge was achieved, and 100% inactivation of V. cholera from drinking water was proven. The retardant effect of the initial V. cholerae colonies with time variation was reported through optical density (OD 600   nm ) measurements. The time course study of bactericidal activity of plasma treatment on V. cholerae , observed every 12 h up to 36 h, revealed a high retardant effect on V. cholerae CFUs. Underwater capillary discharge is an efficient approach for the inactivation of V. cholerae from drinking water.

Numerous flow and heat transfer studies have relied on the construction of similarity transformations which map the nonlinear partial differential equations (PDEs) describing the flow and heat transfer, to ordinary differential equations (ODEs). For these reduced equations, one finds multiple analytic and approximate solution procedures as compared to the flow PDEs. Here, we aim at constructing multiple classes of similarity transformations that are different from those already existing in the literature. We adopt the Lie symmetry method to derive these new similarity transformations which reveal new classes of ODEs corresponding to flow equations when applied to them. With these multiple classes of similarity transformations, one finds multiple reductions in the flow PDEs to ODEs. On solving these ODEs analytically or numerically, we obtain different kinds of flow and heat transfer patterns that help in determining optimized solutions in accordance with the physical requirements of a problem. For the said purpose, we derive Lie point symmetries for the magnetohydrodynamic Casson fluid flow and heat transfer in a thin film on an unsteady stretching sheet with viscous dissipation. Linear combinations of these Lie symmetries that are again the Lie symmetries of the flow model are employed here to construct new similarity transformations. We derive multiple Lie similarity transformations through the proposed procedure which lead us to more than one class of reduced ODEs obtained by applying the deduced transformations. We analyze the flow and heat transfer by deriving analytic solutions for the obtained classes of systems of ODEs using the homotopy analysis method. Magnetic parameters and viscous dissipation influences on the flow and heat transports are investigated and presented in graphical and tabulated formats.

The goal of this research is to consider the thermal impact on varied convection flow in hybrid nanofluids with heat generation over a two-dimensional heated flat around a stretchable sheet. The flow is considered steady and incompressible while the stretchable sheet is assumed an impermeable. Two distinctive nano-level particles are considered, namely copper (Cu) and silver (Ag) with ethylene glycol base fluid. The boundary layer was generated on a stretchable sheet surface by mixed convection flow in hybrid nanofluids. Ideally, the sink and source are thermal reservoirs of internal thermal capacities. This means you can extract or reject heat from them without changing their temperature. To make a study of thermodynamic systems like heat engines and refrigerator systems, the governing equations were solved numerically with Keller-box methodology depending on the implicit finite-difference technique. Research findings were worked with the parameters of mixed convection, Prandtl number, nanoparticle volume fraction, through various non-dimensional parameters, and heat generation. Especially for thermal generation enhancement, the fluidity and thermal dispersal get elevated. Even though the flowing behavior and the thermal dispersal of hybridity fluids with the combinations of Cu and Ag nanoparticles were similar, their values are distinct, which reflect in graphical displays. The hybrid nanofluidity gets improved with the volume variation of nanoparticles if the ϕ \phi value is 0.01 ≤ ϕ ≤ 0.05 0.01\le \phi \le 0.05 and if the flow profile value decreases ϕ h {\phi }_{{\rm{h}}} , where 0.01 ≤ ϕ h ≤ 0.05 0.01\le {\phi }_{{\rm{h}}}\le 0.05 as the dispersal of temperature enhances when the nanoparticle nanofluid constraint is improved.

This article presents a study on condition monitoring and predictive maintenance, highlighting the importance of tracking ball bearing condition to estimate their Remaining Useful Life (RUL). The study proposes a methodology that combines three algorithms, namely Variational Mode Decomposition (VMD), Decision Tree (DT), and Extreme Learning Machine (ELM), to extract pertinent features and estimate RUL using vibration signals. To improve the accuracy of the method, the VMD algorithm is used to reduce noise from the original vibration signals. The DT algorithm is then employed to extract relevant features, which are fed into the ELM algorithm to estimate the RUL of the ball bearings. The effectiveness of the proposed approach is evaluated using ball bearing data sets from the PRONOSTIA platform. Overall, the results demonstrate that the suggested methodology successfully tracks the ball bearing condition and estimates RUL using vibration signals. This study provides valuable insights into the development of predictive maintenance systems that can assist decision-makers in planning maintenance activities. Further research could explore the potential of this methodology in other industrial applications and under different operating conditions.

The inter-porosity transfer is one of the decisive factors for gas development in fractured-porous gas reservoirs. In this article, we establish an analytical solution for the inter-porosity transfer rate and producing degree of matrix. Then, we study the law of inter-porosity transfer based on the solution. Through the Stehfest inversion transform, the typical curves of inter-porosity transfer rate and producing degree of matrix are plotted. It is found that the producing degree of matrix is close to zero in the initial period. Then, the inter-porosity transfer rate begins to increase, and the producing degree of matrix becomes larger. In the late period, the producing degree of matrix remains constant. In addition, the differences between the quasi-steady state model and the three kinds of unsteady state models are compared. It is found that the inter-porosity transfer occurs earlier in unsteady models. However, when pressure propagates to the external boundary, the transfer rate is equal between quasi-steady and unsteady models. It is also found that the inter-porosity transfer rate is slightly different in the three unsteady models, whereas in the spherical model it is largest at the intermediate period. Next, we discuss the influence of key parameters. The results reveal that gas reservoir radius, storage ratio, and inter-porosity flow factor can play an essential role in inter-porosity transfer. The findings of this study can improve our understanding of gas flow between fractures and matrix. Besides, it helps field engineers better understand the variation law of gas productivity in fractured-porous gas reservoirs, which can provide the scientific basis for making a development scheme.

The existing models of the interstellar radiation field (ISRF) do not produce a Maxwell field. Here, the recent model of the ISRF as a Maxwell field is improved by considering separately the different frequencies at the stage of the fitting. Using this improved procedure: (i) It is checked in detail that the model does predict extremely high values of the spectral energy density (SED) on the axis of a galaxy, which however decreases very rapidly when ρ \rho , the distance to the axis, is increased from zero. (ii) The difference between the SED values (with ρ = 1 \rho =1 or 8 kpc 8\hspace{0.33em}{\rm{kpc}} ), as predicted either by this model or by a recent radiation transfer model, is reduced significantly. (iii) The slower decrease of the SED with increasing altitude z z , as compared with the radiation transfer model, is confirmed. We also calculate the evolutions of the SED at large ρ \rho . We interpret these evolutions by determining asymptotic expansions of the SED at large z z , and also ones at large ρ \rho .

Enhancement in thermal distribution of Williamson hybrid nanofluid flow is articulated in this research. Nichrome and TC4 nanoparticles are homogenously diffused in the water, which is the base fluid. An elongating surface holds the flow and thermal transition phenomenon in the existence of uniform sources of magnetic field and heat radiation. The boundary of wall obeys a suction and slip condition. The formulation for physical conservation laws is made as a system of partial differential equations. For the solution purpose, their boundary-value problem is transmuted into the ordinary differential form. Then, Matlab code involving Runge–Kutta procedure is run to compute the variation in velocity as well as temperature profiles under impacts of the controlling factors. The comparative computations are made for two cases: nanofluids ( TC 4 + water ) \left({\rm{TC}}4+{\rm{water}}) and hybrid nanofluids ( TC 4 , Nichrome + water ) \left({\rm{TC}}4,{\rm{Nichrome}}+{\rm{water}}) . The heat for that hybrid nanofluid case is larger than that for the nanofluids. The velocity curve is decreased against increasing magnetic field strength and Williamson parameter. Enhancement in thermal distribution is observed with increasing concentration ϕ 2 {\phi }_{2} of Nichrome.

A field is described as a region under the influence of some physical force, such as electricity, magnetism, or heat. It is a continuous distribution in the space of continuous quantities. The characteristics of the field are that the values vary continuously between neighboring points. However, because of the continuous nature of the field, it is possible to approximate a physical field of interpolation operations to reduce the cost of sampling and simplify the calculation. This article introduces the modeling of the parametric intensity of physical fields in a general form based on the interpolation shape function technique. Besides the node points with sample data, there are interpolation points, whose accuracy depends significantly on the type of interpolation function and the number of node points sampled. Therefore, a comparative analysis of theoretical shape functions (TSFs) and experimental shape functions (ESFs) is carried out to choose a more suitable type of shape function when interpolating. Specifically, the temperature field is the quantity selected to apply, analyze, and conduct experiments. Theoretical computations, experiments, and comparisons of results have been obtained for each type of shape function in the same physical model under the same experimental conditions. The results show that ESF has an accuracy (error of 0.66%) much better than TSF (error of 10.34%). Moreover, the field model surveyed by a generalized reduced gradient algorithm allows for identifying points with the required parameter values presented in detail. The illustrated calculations on temperature field control in the article show that the solution for both forward and reverse problems can be determined very quickly with high accuracy and stability. Therefore, this technique is expected to be entirely feasible when applied to thermal control processes such as drying in paint technology, kilns, and heat dissipation in practice.

Using mathematical modeling and computational analysis, this study aims to examine the peristaltic blood flow of a non-Newtonian material in a tapered channel with radiative heat flux and response mechanisms. By utilizing a long-wavelength approximation, ignoring the wave number, and performing under conditions of low Reynolds number, closed form solutions for the velocity, temperature, and concentration fields are achieved. Several governing parameters and their effects on the system were analyzed, and relevant diagrams were provided. Increasing the Biot number, Jeffrey material, and thermal radiation parameter of the heat and mass transfer mechanism increases the velocity profile. When the heat source/sink parameter and the heat transfer Biot number increase, the temperature profile improves. The resultant concentration distributions are enhanced when mass transfer Biot number, heat radiation, and chemical processes are all raised. We observe that the pressure rate decreases in all three pumping zones when the heat transfer Grashof number and heat transfer Biot number rise. This is because the pressure rate is affected by the Grashof number and Biot number of heat transmission. The increase in thermal radiation parameter and heat transfer Biot number results in a slower rate of heat transfer than when Prandtl number and heat source/sink parameter increases. When the Soret number, Schmidt number, Biot number, and heat source/sink parameter are all raised, the mass transfer coefficient also rises. This rate, however, decreases as the heat radiation and chemical reaction parameters rise. The findings presented in this study have interesting implications for other aspects of human physiology. The preponderance of organs are permeable. Furthermore, fluids render the location of natural boundaries uncertain. The presented mathematical model can be used to derive predictions about the behavior of various systems. For the study of cancer treatment in biological systems, a mathematical model that includes nanoparticles, viscosity dissipation, and rotation holds much promise. Model development incorporated Soret–Dufour effects and thermal analysis of the digestive system.

Motivated by the generic dynamical property of most quadratic Lorenz-type systems that the unstable manifolds of the origin tending to the stable manifold of nontrivial symmetrical equilibria forms a pair of heteroclinic orbits, this technical note reports a new 3D sub-quadratic Lorenz-like system: x ˙ = a ( y − x ) \dot{x}=a(y-x) , y ˙ = c x 3 + d y − x 3 z \dot{y}=c\sqrt[3]{x}+{\rm{d}}y-\sqrt[3]{x}z and z ˙ = − b z + x 3 y \dot{z}=-bz+\sqrt[3]{x}y . Instead, the unstable manifolds of nontrivial symmetrical equilibria tending to the stable manifold of the origin creates a pair of heteroclinic orbits. This drives one to further investigate it and reveal its other hidden dynamics: Hopf bifurcation, invariant algebraic surfaces, ultimate bound sets, globally exponentially attractive sets, existence of homoclinic and heteroclinic orbits, singularly degenerate heteroclinic cycles, and so on. The main contributions of this work are summarized as follows: First, the ultimate boundedness of that system yields the globally exponentially attractive sets of it. Second, the existence of another heteroclinic orbits is also proved by utilizing two different Lyapunov functions. Finally, on the invariant algebraic surface z = 3 4 a x 4 3 z=\frac{3}{4a}\sqrt[3]{{x}^{4}} , the existence of a pair of homoclinic orbits to the origin, and two pairs of heteroclinic orbits to two pairs of nontrivial symmetrical equilibria is also proved by utilizing a Hamiltonian function. In addition, the correctness of the theoretical results is illustrated via numerical examples.

In this article, the modulation instability (MI) of open Bose–Bose mixtures with helicoidal spin–orbit coupling (SOC) was studied. Unlike previous spin–orbit (SO)-coupled Bose–Einstein condensate system with helicoidal gauge potential, the purpose of this article to study the input of the helicoidal SOC in the emergence of MI in open Bose–Bose mixtures by taking into account the Lee–Huang–Yang corrections to the coupled Gross–Pitaevskii equations. We present the detailed analyses of system parameters on the characteristics of MI and analytically conclude the parameter conditions for MI occurrence. Our results provide a potential way to manipulate the MI in the helicoidal SO-coupled open Bose–Bose mixtures.

To solve the problem of feature extraction in electronic circuits due to the nonstationary and nonlinear characteristics of fault signals, a fault feature extraction method for electronic circuits is proposed, which combines wavelet packet analysis and an improved landmark ISOMAP mapping algorithm. The wavelet packet technology is used to decompose and reconstruct the fault feature signals at multiple levels. The extracted wavelet entropy is used to construct the feature vector matrix. The density-based spatial clustering of applications with noise (DBSCAN) clustering algorithm is used to calculate and screen the landmark points. The improved landmark ISOMAP is used to embed the high-dimensional fault feature parameter set into the low-dimensional eigenspace, extract the low-dimensional and sensitive fault feature subset, and apply the support vector machine to identify the fault. The fault diagnosis experiment of the three-phase VIENNA rectifier shows that compared with the principal component analysis method, the traditional ISOMAP method, and the landmark ISOMAP method, the landmark ISOMAP method based on DBSCAN clustering algorithm extracts the fault signal characteristics of electronic equipment more easily.

Using the finite difference time domain (FDTD) method based on the eight-element Dirac equation, we found that a stable Dirac field wave packet with low velocity can be created without explicit consideration of Zitterbewegung (the rapid oscillatory motion of elementary particles), which is difficult in one-dimensional simulations. Furthermore, we successfully simulated the formation process of atomic orbitals for the first time without any physical approximations by calculating the eight-element Dirac field propagation in the central electric force potential. Initially, a small unstable orbital appears, which rapidly grows and results in a large stable orbital with a radius equal to the Bohr radius divided by the atomic number, as given by the solution of the Schrödinger equation. The FDTD calculation based on the conventional four-element Dirac equation cannot produce such reasonable orbitals owing to the spatial asymmetry of the 4 × 4 4\times 4 Dirac matrices. This method has the potential to be used for transient analyses of not only atomic or molecular orbitals but also interactions among elementary particles.

Models of various physical, biological, and artificial phenomena follow a power law over multiple magnitudes. This article presents a modified Pareto model with an upside-down shape and an adjustable right tail. The moments, quantiles, failure rate, mean residual life, and quantile residual life functions are examined. In addition, some stochastic ordering characteristics of the proposed model are investigated. The estimation of the parameters using the maximum likelihood estimator, the mean square error, and the Anderson–Darling estimator is explored, and a simulation study is conducted to analyze their behavior. Finally, we compare the proposed model with alternative methods for describing a dataset on the strength of carbon fiber and a dataset on customer waiting times in a bank.

The dynamic cumulative residual (DCR) entropy is a helpful randomness metric that may be used in survival analysis. A challenging issue in statistics and machine learning is the estimation of entropy measures. This article uses progressive censored type II (PCT-II) samples to estimate the DCR Tsallis entropy (DCRTE) for the moment exponential distribution. The non-Bayesian and Bayesian approaches are the recommended estimating strategies. We obtain the DCRTE Bayesian estimator using the gamma and uniform priors via symmetric and asymmetric (linear exponential and general entropy) loss functions (LoFs). The Metropolis–Hastings algorithm is employed to generate Markov chain Monte Carlo samples from the posterior distribution. The accuracy of different estimates for various sample sizes, is implemented via Monte Carlo simulations. Generally, we note based on the simulation study that, in the majority of cases, the DCRTE Bayesian estimates under general entropy followed by linear exponential LoFs are preferable to the others. The accuracy measure of DCRTE Bayesian estimates using a gamma prior has smaller values than the others using a uniform prior. As sample sizes grow, the Bayesian estimates of the DCRTE are closer to the true value. Finally, analysis of the leukemia data confirmed the proposed estimators.

Homogeneous and heterogeneous reactions play a decisive role in biological procedures such as burning, polymer creation, ceramic construction, distillation, and catalysis. The magnetic properties of hemoglobin molecules are organic. Magnetic resonance imaging (MRI) and electronic components with an electromagnetic field are now readily available, allowing for the explanation of fundamental biological processes. These ideas form the foundation of an ongoing study that attempts to look into the impact of both homogeneous and heterogeneous reactivity on the peristaltic transport of magnetohydrodynamics Oldroyd-B fluid. When convective and partial sliding conditions are present, the configuration changes to a non-uniform vertical channel. The fundamental partial differential equations are resolved utilizing the Homotopy Analysis Method. Entropy optimization has been carried out. The primary limits entering the problem are investigated, and then a graph is used to show the influences of temperature, velocity, skin fraction, Nusselt number, and pressure increase against mean circulation, trapping phenomena, homogeneous reactions, and heterogeneous way to respond. When magnetic parameter rises, the velocity of Oldroyd-B fluid and Bejan number decrease, while temperature, entropy generation, and pressure gradient increase. The tables show that the skin friction coefficient rises for accumulative values of the Grashof number and magnetic parameter, while the skin friction coefficient drops for rising values of the velocity slip parameter and Reynolds number. The Nusselt number increases for large values of Eckert, Grashof numbers, and magnetic parameters.

Today, the use of artificial intelligence in electron optics, as in many other fields, has begun to increase. In this scope, we present a machine learning framework to predict experimental cross-section data. Our framework includes 8 deep learning models and 13 different machine learning algorithms that learn the fundamental structure of the data. This article aims to develop a machine learning framework to accurately predict double-differential cross-section values. This approach combines multiple models such as convolutional neural networks, machine learning algorithms, and autoencoders to create a more robust prediction system. The data for training the models are obtained from experimental data for different atomic and molecular targets. We developed a methodology for learning tasks, mainly using rigorous prediction error limits. Prediction results show that the machine learning framework can predict the scattering angle and energy of scattering electrons with high accuracy, with an R -squared score of up to 99% and a mean squared error of <0.7. This performance result demonstrates that the proposed machine learning framework can be used to predict electron scattering events, which could be useful for applications such as medical physics.

The key for improving the mixing efficiency of pseudoplastic fluids is to enhance the chaotic degree in the flow field. The xanthan gum solution was used to study the chaotic characteristics and mixing performance in a stirred tank with the impeller of perturbed six-bent-bladed turbine. Based on the velocity time series collected by the experiment of particle image velocimetry (PIV), the distributions of the largest Lyapunov exponent (LLE) and Kolmogorov entropy (K entropy) of the system were obtained through the programming calculation using the software MATLAB (R2016a) for characterizing the chaotic degree. The mixing performance of the fluid was numerically investigated using the Computational Fluid Dynamics package, and the velocity distributions were compared with the results obtained by the experiment of PIV. The relevance between the chaotic degree and the mixing performance was clarified. Results showed that the numerical results of velocity distributions agreed well with the experimental data which validated the Computational Fluid Dynamics model established. When the speed reached 600 rpm, the LLE and K entropy climbed the maximal values at the same time, which meant the greatest degree of chaos, and the mixing energy per unit volume was minimal at that moment, which was corresponding to the highest mixing efficiency. As the speed increased further, the LLE and K entropy decreased instead, which meant the chaos reduction, and the corresponding mixing energy per unit volume increased with the low mixing efficiency.

The fundamental objective of this work is focused to achieve a class of advanced and impressive exact estimations to the Zoomeron equation and the time-fraction biological population model through contrivance by a couple of important and magnificent techniques, namely, the modified extended tanh-function method which depend on the balance theory and the Ricatti–Bernoulli sub-ODE method which is independent of the balancing principle. The suggested model is one of the major concerns for studying population distribution dynamics as well as the quantum field theory which is an important discipline for the description of interactions between light and electrons. The two suggested reliable, effective techniques are considered famous among ths ansatz methods that have various visions to realize the exact solutions to the non linear partial differential equation that reduce the volume of calculations examined before and usually give good results. It is solicited for this contrivance finding new exact solutions for two models in terms of some variable. The models are significant in quantum field theory, description of interactions between light and electron, quantum electrodynamics, demographic model, important to bring it into line with the reasonable distribution of wealth, resources, income, etc . The achieved results predict many types of solutions as trigonometric functions, hyperbolic functions, perfect periodic soliton solutions, singular periodic soliton solutions, and other rational solitons solutions. The efficiency of the techniques is demonstrated by the satisfactory results obtained through the derivation of closed-form soliton solutions from the exact solution by assigning definite values to the variables present in it.

The ultra-stable optical reference cavity (USORC) is a key element for a variety of applications. In this work, based on the orthogonal experimental design method, we study the vibration sensitivity optimization of a classical USORC with a 100 mm length. According to a test of 4 levels and 3 factors, the L 16 (4 3 ) orthogonal table is established to design orthogonal experiments. The vibration sensitivities under different parameters are simulated and analyzed. The vibration sensitivities in three directions of the USORC are used as three single-object values, and the normalized sum of the three vibration sensitivities is selected as comprehensive object values. Through the range analysis of the object values, the influence degrees of the parameters on the three single objects and the comprehensive object are determined. The optimal parameter combination schemes are obtained by using the comprehensive balance method and the comprehensive evaluation method, respectively. Based on the corresponding fractional frequency stability of ultra-stable lasers, the final optimal parameter combination scheme A1B3C3 is determined and verified. This work is the first to use an orthogonal experimental design method to optimize vibration sensitivities, providing an approach to vibration sensitivities optimization and is also beneficial for the vibration sensitivity design of a transportable USORC.

In a variety of applications using ionizing radiation, it is essential to ensure the safety of both individuals and equipment. To this end, excellent radiation shielding materials, including glasses and rare earth elements, such as Dy 2 O 3 , are currently being researched. The goal of this study is to explore the effect of Dy 2 O 3 on the radiation-shielding properties of the SiO 2 –PbO–B 2 O 3 –Dy 2 O 3 glass system; for clarity, it is abbreviated as Dy-X. Dy 2 O 3 is a good choice for use as a modifier in radiation shielding glasses since it has high density. Additionally, Dy 2 O 3 has good thermal stability and can be added to glass matrices without substantially affecting their physical features. The influence of increasing the amount of Dy 2 O 3 present in the glasses from 0 to 5 mol% on the linear attenuation coefficient (LAC) and effective atomic number ( Z eff ) was studied using glasses with five distinct compositions and densities. In order to achieve this, the Phy-X program was utilized. The results demonstrate that Dy5 (with a composition of 55B 2 O 3 –25PbO–20SiO 2 –5Dy 2 O 3 ) has the highest LAC value of the prepared glasses, while Dy0 has the lowest. We investigated the influence of Dy 2 O 3 on Z eff at 0.284 MeV. The results show that the Z eff values increase with increasing Dy 2 O 3 content. The Z eff values were found to be 27.35, 27.94, 28.52, 29.09, 29.65, and 30.20 for Dy0, Dy1, Dy2, Dy3, Dy4, and Dy5, respectively. From the Z eff results, we observed that increasing the Dy 2 O 3 content in the samples leads to an improvement in the shielding ability of the glass system. We compared the LAC of the Dy-X glasses with six glass systems at 0.662 MeV. All Dy0–Dy3 glasses have lower LAC values than all the TeO 2 –Li 2 O–ZnO glasses, but Dy4 has an LAC value greater than those of three of these glasses.

This article investigates the long-wave anti-plane shear motion in a symmetric three-layered laminate composed of pre-stressed compressible elastic layers. The layers of the laminate are perfectly bonded, while traction-free and fixed boundary conditions are considered on the outer faces of the laminate. In both cases, the dispersion relation is obtained in terms of symmetric and anti-symmetric decompositions. Numerical results and an asymptotic long-wave analysis are presented, corresponding to the three possible vibration modes. It is revealed that a low-frequency mode only exists in respect of symmetric motion with free-faces, while all other cases pose a series of non-zero cut-off frequencies. Comparisons between the exact and approximate asymptotic results are presented, and excellent agreement is observed.

In this article, through the Hirota bilinear method and long wave limit method, based on the N-solitons, we construct the multiple lump solutions of the generalized (3+1)-dimensional Hirota–Satsuma–Ito equation. Furthermore, to enhance our understanding of the solutions obtained, we further elucidate the physical implications of these solutions with three-dimensional and two-dimensional graphs. The solutions obtained might have practical applications in elucidating the dynamic behaviors of higher-dimensional systems, particularly in the study area of waves in shallow water and the study of nonlinear optics.

In electrodynamics, it has been long believed that when the electrostatic equilibrium is reached the electrostatic field outside a metal is always perpendicular to the metal surface. However, the tangential electrostatic field (TEF) may be discovered at the metal surface through the mechanical-electric coupling in the work. The TEF can lead to new knowledge and more accurate modification on electrostatics of metals including the electrostatic equilibrium conditions, uniqueness theorem, method of image charges, electrostatic shielding, Thompson’s theorem, and Green’s reciprocation theorem. The TEF and the mechanical-electric coupling can also indicate that an intrinsically intensive electrostatic field may exist at the nanoparticle surface. Thereby a unified model could be constructed for the surface-enhanced Raman scattering (SERS) which has been a long-standing problem in physics and chemistry in recent several decades. Furthermore, when the micro-electro-mechanical systems (MEMS) work, the deformation of the metal plate can induce an additional electrostatic field and a newly attractive electrostatic force between the metal plates. They may be important for the design and fabrication of high-performance MEMS devices. Overall, the revealed TEF may update the physical knowledge of the electrostatics of metals in electrodynamics and may acquire widespread applications in the areas of SERS, MEMS, and so on. Graphical abstract

Interest in the thermal effects of nanofluid (NF) has increased recently due to the use of nanocomposites to magnify the thermal conductivity of conventional liquids and so boost the heat transit phenomena. Based on this fundamental concept, the current study inspects the thermal advanced third-grade fluid flow with nanocomposites with an extended surface and the inclusion of stratification, non-Fourier heat flux, mass flux, and radiation. Buongiorno’s NF model is employed to observe the thermophoresis and Brownian motion properties. The gyrotactic microorganisms, which are connected to the bioconvection phenomenon that intrigues most, are also considered to be present in the nanoparticles. The governing models are composed of partial differential equations; thereafter, the relevant transformations are applied to these equations to convert the structure into an ordinary differential model. These resultant models are solved by implementing the homotopy analysis method. It is explained in detail how the pertinent parameters are affecting the motion, temperature of fluid, nanocomposite volume, dynamic microbe density, skin friction rates, local Nusselt, and local Sherwood numbers. Applications for the flow of nanoparticles carrying gyrotactic microorganisms include enzyme biosensors, microfluidic devices, microbial fuel cells, and biotechnology.

Along with the increase in demand for electricity, dependability requirements for the power supply system also increase. Transformers are the backbone of the electrical system; thus, they must function reliably and safely. In this study, a method based on Fourier-transform infrared spectroscopy technology is proposed for assessing the ageing level of insulating oils. Copper-catalysed thermal ageing is applied to four distinct insulating oils at a temperature of 12 0 ° C 12{0}^{^\circ }{\rm{C}} . The insulating oil ageing peaks are promptly measured using infrared spectroscopy, and the peak area ratios are associated with the interfacial tension and dielectric loss factor. It is observed that the peak area ratio of the ageing peaks and interfacial tension are significantly correlated, and this relationship can be used to determine the ageing condition of the insulating oil. The findings of this study can be used to design sensors for online monitoring of insulating oil quality.

The effect of cationic surfactants on the growth of gypsum was evaluated under conditions of a simulated production process of gypsum desulfurization. We used a laser particle size analyzer and a microscope to determine the particle size and morphology. The growth rate of gypsum was determined by the equation for the rate of chemical reaction of CaSO 4 ·2H 2 O. The results showed that the growth rate at a supersaturation ratio of 2.4 increased by 50% with 30 mg/L of a dodecyldimethylbenzylammonium chloride. The gypsum morphology changed from needle-like in the absence of additives to tabular in the presence of cationic surfactants, indicating that relatively thicker and larger crystals were formed. Finally, the investigated cationic surfactants were beneficial to the normal operation of the desulfurization process.

The KCl/PHPA waste drilling fluid is produced during drilling operations in Bohai Oilfield, China, which cannot be directly used or discharged, it needs to be flocculated. In order to know the aggregation mechanism of colloidal particles in KCl/PHPA drilling fluid, the calculation method of zeta potential and the relationship between the stability of waste fluid and zeta potential are discussed in detail in this article. The process of decreasing the zeta potential of waste fluid due to the addition of cationic polyacrylamide is called instability. The process in which unstable particles aggregate into larger particles is called coagulation, and the process in which unstable particles aggregate into large flocs is called flocculation. According to the types of treatment agents in KCl/PHPA waste drilling fluid, the structure and energy changes formed between low-viscosity polyanionic cellulose, partially hydrolyzed polyacrylamide, xanthan gum, starch, and water molecules are constructed. The energy of the four treatment agent systems decreased by 21.4–67.5% after the cationic polyacrylamide was added. The reduction of system energy reduced the repulsive force between colloidal particles in the waste fluid and promoted the agglomeration of colloidal particles. The agglomeration mechanism of waste liquid particles was obtained.

This manuscript attempts to construct diverse exact traveling wave solutions for an important model called the (3+1)-dimensional Kadomtsev–Petviashvili equation. In order to achieve that, the Jacobi elliptic function technique and the Kudryashov technique are chosen in favor of their noticeable efficacy in dealing with nonlinear dynamical models. As expected, the used approaches lead to a variety of traveling wave solutions of different types. Finally, we have graphically illustrated some of the obtained wave solutions to further make sense of their representation. Also, we provide an overview of the main results at the end.

In the present work, a novel compact and highly sensitive microwave antenna sensor at 2.45 GHz is proposed for evaluating glucose concentration in blood. The antenna is printed on an FR-4 substrate of compact dimensions 35 mm × 13.5 mm × 1.6 mm. A human finger phantom model is constructed in the EM simulation high frequency structure simulator environment consisting of skin, blood, fat, and bone layers. In the study, finger models with various shapes like rectangular, cylindrical, and ellipsoid are considered, and the results are compared. The glucose concentration is changed from 0 to 500 mg/dL, and the corresponding shift is evaluated by keeping the finger phantom at different locations near the antenna. The frequency shifts obtained in the designed experiment are used to evaluate glucose concentration in blood samples. In this work, a minimum and a maximum frequency shift of around 1.25 and 5 MHz, respectively, are observed when the finger phantom is placed at the top of the radiating element. Simulated antenna results are found to be in good agreement with the measured results. The developed method is validated with a two-antenna model by calculating time delay and isolation for different glucose concentrations. An experiment of placing a real human finger around a fabricated antenna presents good correspondence with the simulation results.

The main aim of this study is to analyse the electrically conductive flow of compressible liquids by two infinitely permeable surfaces. The distance between the two surfaces is h h . Thermal relation consists of viscous dissipation. The entropy features along with magnetic force and dissipation are taken into account. The x -axis extends in the flow path along the bottom stationary plate, whereas the y -axis is orthogonal to the surfaces. The channel plates are subjected to a consistent transverse magnetic field that is implemented perpendicularly. Herein, two scenarios are investigated: the first is the Couette flow, and in the second scenario, both porous surfaces are parallel and fixed at a distance of 2 h , and the motion is a Poiseuille flow controlled by pressure. The flow across the x x -axis is supposed to be generated and dependent on y y exclusively. The governed system is solved using analytical solutions. It is found that the entropy formation is higher near the cloud porous plate in comparison to the hot porous plate and the increasing values of the suction/injection parameter increase the fluid temperature. The increase in the magnetic field parameter decreases the momentum boundary layer thickness. The Brinkman number improves the thermal boundary thickness. The magnetic field parameter, suction/injection, and the Brinkman number accelerate the entropy formation in both cases.

This article investigates the potential Kadomtsev–Petviashvili (pKP) equation, which describes the evolution of small-amplitude nonlinear long waves with slow transverse coordinate dependence. For the first time, we employ Lie symmetry methods to calculate the Lie point symmetries of the equation, which are then utilized to derive exact solutions through symmetry reductions and with the help of Kudryashov’s method. The solutions obtained include exponential, hyperbolic, elliptic, and rational functions. Furthermore, we provide one-parameter group of transformations for the pKP equation. To gain a better understanding of the nature of each solution, we present 3D, 2D, and density plots. These obtained solutions, along with their associated physical characteristics, offer valuable insights into the propagation of small yet finite amplitude waves in shallow water.In addition, the pKP equation conserved vectors are derived by utilizing the multiplier method and the theorems by Noether and Ibragimov.

The Sagnac effect can be demonstrated with light propagating either along a circular contour or, as done by Wang et al ., back and forth along a linear contour. In the linear Sagnac effect, the emitter–receiver device is in motion relative to the contour where light propagates. In the reciprocal linear Sagnac effect (RLSE), the device is stationary and the contour is in motion. When the contour changes direction of motion, some special features of the linear Sagnac effect are not fully reciprocal to the RLSE, which foresees variations of the first order in v ⁄ c v/c in the round-trip time taken by a light signal to cover the contour. The RLSE can be tested with present technology and, if confirmed experimentally, it might have interesting technological applications. Presently, it can be important for testing light-speed invariance, simultaneity, and the relativity principle.

The problem of optimization of interatomic potentials is formulated and solved by means of generalization of the Morse, Kaxiras–Pandey, and Rydberg potentials. The interatomic potentials are treated as solutions of some second-order ordinary differential equations which will be classified and analyzed. The most appropriate analytic form of the understudied potentials will be proposed based on a one-dimensional search for the parameter, γ \gamma , which is the power of the interatomic distance, r r . The optimal analytic form will also be proposed for metals such as gold, copper, aluminium, titanium, and the silver–copper alloy. The method of least squares will be used to estimate the potential parameters. Phenomenological potentials such as the classical Rydberg, classical Morse, generalized Morse, Kaxiras–Pandey, and classical Lennard–Jones will be studied, and new potentials based on the combination of some of the aforementioned potentials will also be proposed. Metrics such as the goal function values, will be used to identify which optimal value of the parameter, γ \gamma , is most appropriate to introduce into the preferred interatomic potential for interaction between atoms.

The generalized (2+1)-dimensional stochastic Calogero–Bogoyavlenskii Schiff equation (SCBSE) driven by a multiplicative Brownian motion is taken into consideration. The Riccati equation mapping and He’s semi-inverse methods are utilized to obtain the rational function, hyperbolic function, and trigonometric function for SCBSE. We expand some solution from previous studies. The acquired solutions of SCBSE may explain many exciting physical phenomena because it is widely used in plasma physics and fluid dynamics. Also, it explains the relationship between the Riemann y -axis propagating wave and the long x -axis propagating wave. Using a variety of 2D and 3D graphs, we illustrate how the Brownian motion influences the exact solutions of SCBSE.

As an advanced optical precision ranging method, FMCW (frequency-modulated continuous-wave) laser interferometric ranging technology can achieve a large-scale and high-precision absolute distance measurement, so it has high research and application value in the field of coordinate measurement in large space. How to improve the resolution and stability of laser interferometry is a research difficulty in this technology. Based on FMCW laser interferometry relative distance technology, a method for achieving absolute distance measurement through phase comparison after repeated sampling is proposed. Using the FMCW laser distance measuring system, two interference optical paths of measuring interferometer and auxiliary interferometer are constructed, respectively. Synchronous sampling is performed on two interference signals, and the phase ratio of the two interference signals is obtained through the extracted frequency information. The optical path difference of the unknown measurement interferometer is derived from the known auxiliary interferometer information. This method uses a triangular wave modulation laser to reduce the influence of Doppler frequency shift and eliminate quantization errors. By using the fixed-point repeated sampling, the optical path difference information is quickly extracted, and the nonlinear error of laser interference frequency modulation is effectively reduced.

To enhance the sensitivity of detecting Cu and Zn in aluminum alloys, we incorporated a spark discharge unit into the femtosecond laser-induced breakdown spectroscopy (fs-LIBS) system, forming a femtosecond laser ablation spark-induced breakdown spectroscopy (fs-LA-SIBS) system. We utilized both fs-LA-SIBS and fs-LIBS techniques to detect Cu and Zn in various aluminum alloy samples with different contents. Our results reveal that the spark discharge extends the duration of laser-induced plasma atomic radiation and amplifies the peak intensity of atomic radiation, thereby significantly increasing the time-integrated signal intensity of laser-induced plasma. Under the present experimental conditions, the limits of detection (LoDs) of Cu and Zn in aluminum alloy by fs-LA-SIBS are 16 and 12 ppm, respectively. In contrast, the LoDs of Cu and Zn by fs-LIBS technique under the same laser pulse energy are 96 and 84 ppm, respectively. Hence, for Cu, the LoDs by the fs-LA-SIBS technique are 1/6 of those by the fs-LIBS technique, and for Zn, the LoDs by the fs-LA-SIBS technique are 1/7 of those by the fs-LIBS technique. Our findings demonstrate that the fs-LA-SIBS technique is more sensitive than the fs-LIBS technique in the quantitative analysis of elements and may be a practical approach for elemental analysis in alloys.

Using the classical ensemble model, we investigate the effect of laser wavelength on the electron dynamics process of nonsequential double ionization (NSDI) for linear triatomic molecules driven by a counter-rotating two-color circularly polarized laser field. Based on the delay time between recollision and final double ionization, two particular ionization channels are separated: recollision-impact ionization (RII) and recollision-induced excitation with subsequent ionization (RESI). Numerical results show that with the increase of the laser wavelength, the triangle structure of the ion momentum distribution becomes more obvious, which indicates that the electron–electron correlation of NSDI is enhanced. In addition, we find that the ratio of the RESI channel gradually decreases with the increase of the laser wavelength, while the ratio of the RII channel is opposite. However, the dominant channel is still RESI. It means that the two ionization channels can be controlled effectively by changing the laser wavelength.

In this study, we use a dual technique that combines the Laplace residual power series method (LRPSM) and the new iteration method, both of which are combined with the Caputo operator. Our primary goal is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional Fisher’s equation. These equations, which are crucial in modeling complex processes, confront analytical complications, owing to their fractional derivatives and nonlinear behavior. We develop exact and efficient solutions by merging these unique methodologies, which are supported by thorough figures and tables that demonstrate the precision and trustworthiness of our methodology. We not only shed light on the solutions to these equations, but also demonstrate the prowess of the LRPSM and the new iteration method as powerful tools for grappling with complex mathematical and physical models, significantly contributing to advancements in various scientific domains.

The Marangoni convective phenomena have a unique impact on industries and medical tools. These phenomena are more prominent in the presence of dual nanoparticles (NPs) over base fluids such as blood that are surrounded by a thin interfacial nanolayer, an important feature to control the physical and thermal properties of the NP. In this problem, we have analysed the thermo-solutal Marangoni convective Darcy-Forchheimer flow of nanomaterials with the impact of the interfacial nanolayer. The results of the system of an exponential heat source, non-linear radiation, joule heating, and activation energy are discussed. An appropriate transition is applied to rationalise the substantially paired and nonlinear governing equations and then processed by the Galerkin finite element method (G-FEM). The impression of different governing parameters on the governing systems in conjunction with entropy and Bejan number is demonstrated through graphical and tabular form. Graphs are drawn with an evaluation of general and hybrid nanofluids (HNFs) and different nanolayer thicknesses of NPs. Activation energy and chemical reaction parameters restrict the Sherwood number, and the same is observed for the Nusselt number with an increase in the Brinkman and Eckert numbers. The thickness of the interfacial nanolayer of the NPs restricts the entropy generation of the system, while the entropy is higher for the HNF than the nanofluid. An opposite feature was observed for the Bejan number.

Air compressors are widely used in factories to power automation systems and store energy. Several studies have been conducted on the performance of reciprocating and screw compressors. Advancements in design and manufacturing techniques, such as generative design and topology optimization, are leading to improved performance and turbomachinery growth. This work presents a methodology to design and manufacture air compressor pistons using topology optimization and metal additive manufacturing. The existing piston is converted to 3D CAD data and topology optimization is conducted to reduce material in stress concentration regions. Thermal and mechanical loads are considered in boundary conditions. The results show reduced material and improved efficiency, which is validated using ANSYS fluent. The optimized 3D model of the piston is too complex for conventional subtractive manufacturing, so laser sintering 3D printing is proposed. Honeycomb pattern infill patterns are used in 3D printing. This investigation is a step toward researching similar methods in other reciprocating compressor components such as cylinder, cylinder head, piston pins, crankshaft, and connecting rods, which will ultimately lead to improved compressor efficiency.

Breast cancer diagnosis relies on breast ultrasound (BUS) and the early breast cancer screening saves lives. Computer-aided design (CAD) tools diagnose tumours via BUS tumour segmentation. Thus, breast cancer analysis automation may aid radiologists. Early detection of breast cancer might help the patients to survive and in context with this many approaches have been demonstrated by different researches, however, some of the works are weak in the segmentation of breast cancer images. to tackle these issues, this study propose a novel Hybrid Attendseg based gravitational clustering optimization (HA-GC) method which is utilized to segment breast cancer as normal malignant, and benign. For this we have taken the dataset known as breast ultrasound (BUS) images. This method constructively segments the breast cancer images. Prior to the segmentation, pre-processing is carried out which can be used to normalize the images incorporated with the removal of unwanted noises and format the images Optimization selects the best qualities. An experiment is conducted and compared the results with the parameters such as Dice coefficient, Jacquard, Precision, and Recall and attained over 90% and ensures the usage of present work in the segmentation of breast cancer images.

This investigation explores two numerical approaches: the optimal auxiliary function method (OAFM) and the new iterative method (NIM). These techniques address the physical fractional-order Klein-Gordon equations (FOKGEs), a class of partial differential equations (PDEs) that model various physical phenomena in engineering and diverse plasma models. The OAFM is a recently introduced method capable of efficiently solving several nonlinear differential equations (DEs), whereas the NIM is a well-established method specifically designed for solving fractional DEs. Both approaches are utilized to analyze different variations in FOKGE. By conducting numerous numerical experiments on the FOKGE, we compare the accuracy, efficiency, and convergence of these two proposed methods. This study is expected to yield significant findings that will help researchers study various nonlinear phenomena in fluids and plasma physics.

Momentum and heat transmission influence the coated physical characteristics of wire product. As a result, understanding the polymeric movement and heat mass distribution is crucial. An increase in thermal efficiency is necessary for the wire covering technology. So, the aim of this work is to investigate the influence of nanomaterials on the heat and mass transport processes in wire coating analyses. A thin film nanofluid is used to investigate heat and mass transfer in three dimensions over a rotating inclined disc. Both the suction and injection effects of nanofluids and the thermal radiation of their fluxes are taken into account. By employing similarity variables, the set of governing equations can be transformed into a differential equation system. The necessary differential equation system is solved using the Haar wavelet collocation method. Plots and observations of the velocity distribution, concentration, and thermal fields within the boundary layer across an inclining, steadily rotating plane are made. Flow characteristics change as a result of varying embedded factors such as S , Sc , N b , Pr , S,{\rm{Sc}},{N}_{{\rm{b}}},\Pr , and thermophoretic parameters. Evidence suggests that as the number of rotation parameters grows, the thermal boundary layer weakens.

The extreme environment formed during bubble collapse can cause a series of chemical reactions inside the bubble, and multiple products ( i.e ., ˙OH, H˙, O, H 2 , and HO 2 ˙, etc .) are produced, which is called sonochemistry. In this study, a new model is used to predict the sonochemistry characteristics inside an oxygen bubble oscillating in water. The influences of static pressure, ultrasonic frequency, and the equilibrium radius on the temperature inside the bubble and the yields of chemical products are analyzed. The numerical calculation results are obtained during bubble oscillations under a steady state, which is different from the previous studies that focus on the sonochemical characteristics at the bubble collapse. Numerical studies show that with the change in the equilibrium radius, the maximum bubble temperature fluctuates drastically, and the maximum yields of H 2 and ˙OH show a Gaussian curve trend. The cavitation activity corresponding to the equilibrium radius depends on the combination of static pressure and ultrasonic frequency.

The optimal auxiliary function method (OAFM) is introduced and used in the analysis of a nonlinear system containing coupled Schrödinger–KdV equations, all within the framework of the Caputo operator. The OAFM, known for its efficiency in solving nonlinear issues, is used to obtain approximate solutions for the coupled equations’ complicated dynamics. Numerical and graphical assessments prove the suggested method’s correctness and efficiency. This study contributes to the understanding and analysis of coupled Schrödinger–KdV equations and their many applications by providing insights into the behavior of nonlinear systems within mathematical physics.

In this study, the steady 2D flow of micropolar fluid via a vertical surface is taken into account. The magnetohydrodynamics applied normally to the flow direction at a vertical surface in the presence of temperature-dependent attributes. The effect of the chemical reaction under the generalized Fourier–Fick law is considered to investigate the heat transference rate at the vertical sheet. Under the flow assumptions, the boundary layer approximations were applied to the nonlinear differential equations and partial differential equations were obtained. The use of similarity modifications allows for a reduction in the number of partial differential equations. The resulting ordinary differential equations are then resolved numerically using a technique known as the homotopy analysis method. The results reveal that microparticle suspensions have a significant impact on the flowing domain when varied fluid characteristics are utilized. The effect of potential factors on flow, micro-rotation velocities, temperature, drag force factor, and heat transport rate is investigated. The obtained results show that the velocity profile and micropolar function increase for larger values of micropolar parameters. Drag force effects are also seen, and required outcomes are observed to be in outstanding accord with the available literature. Significant results of this work were toward the velocity function, which gets reduced with increasing magnetic field parameter values, but the velocity function enhances for higher values of β \beta and λ \lambda . On temperature distribution, it decreased for higher values of ϵ 1 {{\epsilon }}_{1} and temperature profile declines due to higher values of Pr \text{Pr} , γ 2 {\gamma }_{2} and γ 1 {\gamma }_{1} or both cases of δ > 0 \delta \gt 0 and δ < 0 \delta \lt 0 . The higher values of Sc \text{Sc} resist declining the temperature function at the surface.

The Mott problem is a simpler version of the quantum measurement problem that asks: Is there a microscopic physical mechanism – based (explicitly or implicitly) only on Schroedinger’s equation – that explains why a single alpha particle emitted in a single spherically symmetric s-wave nuclear decay produces a manifestly nonspherically symmetric single track in a cloud chamber? I attempt here to generalize earlier work that formulated such a mechanism. The key ingredient there was identification of sites at which the cross section for ionization by a passing charged particle is near singular at ionization threshold. This near singularity arose from a Penning-like process involving molecular polarization in subcritical vapor clusters. Here, I argue that the same Mott problem question should be asked about Geiger counters. I then define a simple experiment to determine if ionization physics similar to the cloud chamber case takes place in the mica window of a Geiger counter and explains the collimation of wavefunctions that are spherically symmetric outside the counter into linear ion tracks inside. The experiment measures the count rate from a radioactive point source as a function of source-window separation. I have performed a proof of concept of this experiment; results are reported here and support the near-singular-ionization picture. These results are significant in their own right, and they may shed light on physical mechanisms underlying instances of the full quantum measurement problem. I illustrate this for the Stern–Gerlach experiment and a particular realization of superconducting qubits. I conclude by detailing further work required to flesh out these results more rigorously.

In this article, we investigated the Landau–Ginzburg–Higgs (LGH) equation, focusing on the analysis of isolated soliton solutions and their stability. To compute the isolated soliton solutions, we used the advanced auxiliary equation (AAE) approach, which has proven to be a powerful and efficient method for extracting soliton solutions in various nonlinear partial differential equations (NLPDEs). We provided a detailed explanation, both graphically and physically, of the obtained soliton solutions in this article. Furthermore, we used the linear stability technique to conduct a stability analysis of the LGH equation. Additionally, we studied the bifurcation and stability of the equilibria and performed phase plane analysis of the model. We also provided a discussion on the comparisons between the AAE method and two other well-known approaches: the generalized Kudryashov method and the improved Bernoulli sub-equation function method. The application of the AAE approach in this study demonstrates its effectiveness and capability in analysing and extracting soliton solutions in NLPDEs.

The objective of this study is to assess the flow behavior of the peristalsis mechanism of a couple stress fluid in incorporating a porous material. In addition, reaction mechanism and Ohmic heating are also taken into consideration with slip boundary conditions. For the purposes of mathematical simulation, we assume a long-wavelength approximation, ignoring the wave number and taking a low Reynolds number into account. The obtained outcome is shown in a graphical manner and then analyzed. The results of this investigation reveal that when the Hartmann number improves, the pattern of velocity noticeably decelerates. The Lorentz forces have a retarding impact on the velocity of the fluid from a physical standpoint. As the couple stress variable rises, so does the velocity of the fluid. As the couple stress component increases, the skin friction coefficient increases in one region of the fluid channel and falls in another region, between x = 0.5 and x = 1. As the thermal slip variable rises, more heat is transferred through the surface to the fluid, resulting in a rise in the temperature profile. When the couple stress variable is raised, the Nusselt number rises, while the thermal radiation factor causes the Nusselt number to decline. The results showed a positive relationship between the Sherwood number and the reaction mechanism parameter. This study demonstrates the potential use of this research in the fields of a career in engineering, namely, in enhancing hydraulic systems, as well as in medicine, particularly in optimizing gastrointestinal processes. The process of dissection facilitates the unimpeded circulation of blood and lymph inside the vascular system of the body, enabling the delivery of oxygen to tissues and the elimination of waste materials.

Accelerated or partially accelerated life tests are particularly significant in life testing experiments since they save time and cost. Partially accelerated life tests are carried out when the data from accelerated life testing cannot be extrapolated to usual conditions. The constant-stress partially accelerated life test is proposed in this study based on a Type-II censoring scheme and supposing that the lifetimes of units at usual conditions follow the inverted Topp–Leone distribution. The Bayes and E-Bayes estimators of the distribution parameter and the acceleration factor are derived. The balanced squared error loss function, which is a symmetric loss function, and the balanced linear exponential loss function, which is an asymmetric loss function, are considered for obtaining the Bayes and E-Bayes estimators. Based on informative gamma priors and uniform hyper-prior distributions, the estimators are obtained. Finally, the performance of the proposed Bayes and E-Bayes estimates is evaluated through a simulation study and an application using real datasets.

Soliton solutions of the Konopelchenko–Dubrovsky (KD) equation using four analytical methods are established. The KD system is used to study the portrays in physics with weak dispersion. The investigated results are obtained in different forms such as trigonometric, hyperbolic, and exponential functions. For the physical behavior of the concerned nonlinear system, some solutions are plotted graphically via assigning the certain values to the parameters. Mathematica software 11.11 is used to handle all results as well as figures. Hence, searched results have rewarding recompenses in nonlinear science.

In this study, we explore the epidemic spread of the coronavirus using the Caputo fractional variable order derivative as variable order derivative provides a natural extension to classical as well as fractional order derivatives. Using the variable order derivatives in investigation of biological models of infectious diseases is an important area of research in the current time. Using the fixed point technique, we discuss the existence and uniqueness of solution to the corona virus infectious disease 2019 environmental transformation model. In order to demonstrate the existence and novelty of our findings, we examine the results numerically and graphically with the help of Euler’s method. There are several graphs provided that are related to different variable orders.

The swimming of motile gyrotactic microorganism’s phenomenon has recently become one of the most important topics in research due to its applicability in biotechnology, many biological systems, and numerous engineering fields. The gyrotactic microorganisms improve the stability of the nanofluids and enhance the mass/heat transmission. This research investigates the MHD fluid flow of a dissipative Sisko nanofluid containing microorganisms moving along an exponentially stretched sheet in the current framework. The mathematical model comprises equations that encompass the preservation of mass, momentum, energy, nanoparticle concentration, and microorganisms. The equations that govern are more complicated because of nonlinearity, and therefore to obtain the combination of ordinary differential equations, similarity transformations are utilized. The numerical results for the converted mathematical model are carried out with the help of the bvp4c solver. The resulting findings are compared to other studies that have already been published, and a high level of precision is found. The graphical explanations for velocity, temperature, and nanoparticles volume fraction distribution are shown with physical importance. Physical characteristics like Peclet number, Sisko fluid parameter, thermophoresis and Brownian motion parameter, and Hartmann number are taken into consideration for their effects. Based on the numerical outcomes, the bioconvection Peclet number enhances the density of mobile microorganisms, whereas thermal radiation contributes to an elevation in temperature. The velocity field decreases with the enhancement of magnetic parameter; however, the temperature field increases with increased magnetic parameter and thermophoresis parameter augmentation. Our numerical findings are ground breaking and distinctive, and they are used in microfluidic devices including micro instruments, sleeve electrodes, and nerve development electrodes. This study has various applications in nanoengineering, including nanomaterial synthesis, drug delivery systems, bioengineering, nanoscale heat transfer, environmental engineering.

In the context of the SU(2) quark flavor version of the Nambu–Jona-Lasinio model extended by the Polyakov loop, the effect of the regularization scheme on the quantum chromodynamics phase structure at finite volume was studied. The way in which the phase diagram changes with the type of Polyakov loop potential considered in this study was also investigated. In this study, a polynomial and a logarithmic potential were used. On the other hand, a regularization scheme that satisfies the thermodynamics properties such as the Stefan–Boltzmann limit was chosen.

The human immunodeficiency virus, which attacks the immune system and especially targets CD4 cells that are crucial for immunological defense against infections, is the cause of the severe illness known as acquired immunodeficiency syndrome (AIDS). This condition has the potential to take a patient’s life. Understanding the dynamics of AIDS and evaluating potential methods of prevention and treatment have both significantly benefited from the use of mathematical modeling. This research article proposes a unique technique that solves a model system of differential equations representing diverse populations, such as susceptible populations, acute populations, asymptomatic populations, and symptomatic populations or populations with AIDS. The method uses an artificial neural network (ANN) to do this. A specific Caputo–Fabrizio derivative is included in the suggested method to validate the system’s stability via the use of Krassnoselskii’s and Banach’s fixed-point approach in combination with the exponential kernel. In order to solve the differential equations and get the required data, the Laplace Adomian Decomposition (LAD) technique is used. Training the ANN involves obtaining simulated data from LAD and doing it within the context of a supervised learning framework. The performance of the ANN is assessed by comparing its predicted solutions to the LAD solutions. This allows for the calculation of the average error for each of the system’s functions. This study presents a potentially useful computational tool for understanding the dynamics of AIDS and delivering important insights into the design of new prevention and treatment methods.

The development of overhead lines has met the electricity demand of the rapidly developing society. However, the large-scale installation of overhead lines and the natural environmental differences in different regions increase the complexity of the real-time management of the lines. To improve the efficiency of line management, this article constructs a theoretical and simplified electromagnetic field model of 500 kV three-phase overhead lines and studies the method of monitoring the current-sag state of the lines based on analyzing the distribution of magnetic field intensity under the three-phase overhead lines. Moreover, the placement of the tunneling magnetoresistance (TMR) sensor array was analyzed, and the current and sag reconstruction algorithm of the line was further proposed. The calculation results show that the simplified magnetic field model is accurate in most areas under the overhead line. The comparison of condition number and sensor position sensitivity value on sensor placement evaluation shows that the sensor position sensitivity value is more comprehensive, and it is recommended to use dual-axis TMR magnetic sensors. The relative error of the line sag calculated by the proposed TMR sensor array and algorithm is less than 3% and 4% for balanced and unbalanced three-phase line currents, respectively.

This study systematically examines the behavior of multi-stacked long Josephson junctions (multi-sLJJs) under various magnetic inductances and a variety of drives. To investigate the localized modes in the multi-sLJJs, the tripled sine-Gordon equation (sGE) with a phase shift formation recognized as 0- π \pi -0 junction is analyzed. The amplitude equations are derived through asymptotic analysis. It is revealed that synchronized oscillations occur in the multi-sLJJs under both strong and weak couplings; however, the system experiences exponential decay in the absence of external drives. The stack naturally exhibits damping due to the energy produced by the oscillating mode through radiation, which arises from the higher harmonic excitation introduced into the system. It is observed that when an AC drive is present, the system exhibits synchronous oscillations for both strong and weak inductances but eventually becomes stable. However, for parametric drives under both coupling conditions, the system experiences exponential decay. Our findings suggest that weak coupling renders parametric drives ineffective. Nevertheless, numerical simulations demonstrate that a large driving amplitude induces oscillations in the system and causes it to approach a steady position under strong coupling.

This article proposes an on-chip optical temperature sensor based on a cascaded microring resonator, which is composed of a reference ring and a sensing ring cascaded with different temperature sensitivities and free spectral ranges. By changing the temperature of the sensing window environment, the thermal optical effect of the waveguide causes a change in the refractive index of the waveguide, which affects the temperature sensitivity and free spectrum changes of the sensor. The output spectral response of the sensor shifts, achieving temperature sensing detection. The experimental results show that the temperature sensitivity of this microring cascaded temperature sensor is 303.6 pm/°C, which is 3.65 times the limit of a single microring temperature sensitivity of 83 pm/°C. The temperature-sensing range of the sensor is 100°C, which can well meet the temperature-monitoring requirements of ultra-large-scale integrated circuits.

A pathological study in the definition of uncertain numbers is carried out, and some solutions are proposed. Fundamental theorems for uncertain discrete fractional and integer order calculus are established. The concept of maximal solution for obtaining a unique uncertain solution is introduced. The solutions of uncertain discrete relaxation equations for the integer and the fractional order are obtained. Various numerical examples are accompanied to clarify the theoretical results and study of uncertain system behavior.

The main aim of this article is to focus on the dynamics and traveling wave solution of stochastic coupled Konno–Oono equation with multiplicative noise in the Stratonovich sense. First, the considered model is converted to the nonlinear ordinary differential equations by using traveling wave transformation. Secondly, two-dimensional phase portrait of the nonlinear ordinary differential equation and its periodic perturbation system are drawn by using Maple software. Finally, the traveling wave solutions of the investigated equation are obtained via the planar dynamic system method. Moreover, three-dimensional graphs of some obtained solutions are drawn.

The impact of variable thermal conductivity plays a key role in the analysis of fluid mechanics. The applications of liquid are significant in nuclear reactors, automobiles, technical and manufacturing industry, electronic appliances, and so on. The novelty of this analysis is to exhibited the variable thermal conductivity in motion of Casson liquid via porous stretching sheet. In energy equation is consider thermal radiation and heat generation. Rosseland approximation plays a key role in the current work. Under the liquid motion assumptions, BL approximation is applied on numerical model and developed partial differential equations (PDE). The similarity transportation variable is taken by transporting PDE’s to ordinary differential equations. Numerical model is explored with the help of fourth-order boundary value problem with R–K–F procedure via shooting technique. The main key points noticed are: the heat transfer rate is more effective in the presence of heat generation than that in the absence of heat generation parameter. The temperature is enhanced in presence of variable thermal radiation while comparing absence of variable thermal radiation for large numerical values of Biot Number.

In this article, we propose a novel new iteration method and homotopy perturbation method (HPM) along with the Elzaki transform to compute the analytical and semi-analytical approximations of fractional Airy’s-type partial differential equations (FAPDEs) subjected to specific initial conditions. A convergent series solution form with easily commutable coefficients is used to examine and compare the performance of the suggested methods. Using Maple graphical method analysis, the behavior of the estimated series results at various fractional orders ς \varsigma and its modeling in two-dimensional (2D) and three-dimensional (3D) spaces are compared with actual results. Also, detailed descriptions of the physical and geometric implications of the calculated graphs in 2D and 3D spaces are provided. As a result, the obtained solutions of FAPDEs that are subject to particular initial values quite closely match the exact solutions. In this way, to solve FAPDEs quickly, the proposed approaches are considered to be more accurate and efficient.

In this research, we use the homotopy perturbation method (HPM) combined with the Elzaki transform to investigate the fractional Biswas–Milovic equation (BME) within the framework of the Caputo operator. The fractional BME is a significant mathematical model with applications in various scientific and engineering fields, including physics, biology, and chemistry. However, its fractional nature introduces analytical complexities. By integrating the HPM with the Elzaki transform, we aim to provide an effective approach for obtaining accurate solutions to this equation. The combination of these mathematical techniques allows us to explore the behavior of the fractional BME in a comprehensive manner. The research outcomes are supported by numerical results and comparisons, demonstrating the reliability and efficiency of the proposed methodology. This study contributes to advancing the tools for solving fractional equations and enhances our understanding of the intricate dynamics described by the fractional BME.

This study examines the heat transfer properties of a recently created hybrid nanofluid in contrast to a traditional nanofluid. The aim is to improve the transfer of heat in the flow of the boundary layer by employing this novel hybrid nanofluid. Our study investigates the impact of the Lorentz force on a three-dimensional stretched surface. We utilize a new model that incorporates thermo-physical factors. A quantitative parametric study is performed to investigate the influence of different physical parameters, enabling meaningful comparisons. The results demonstrate that the hybrid nanofluid exhibits a higher heat transfer rate compared to the conventional fluid, even in the presence of a magnetic field. Moreover, the efficiency of heat transfer can be enhanced by modifying the concentration of nanoparticles in the hybrid nanofluid.

There is growing evidence that the net acceleration of the Universe over its entire history is essentially zero. This finding is critical in light of a recent examination of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric using the local flatness theorem (LFT) in general relativity, which argues that FLRW is consistent with the principle of equivalence only if the total energy density ρ \rho and pressure p p satisfy the zero active mass condition, ρ + 3 p = 0 \rho +3p=0 . This equation-of-state produces zero acceleration, and significantly mitigates the growing tension between lambda cold dark matter ( Λ \Lambda CDM) and the ever-improving observations. This article takes an alternative approach to this critical issue and directly tests the expansion rate predicted by the standard model against the requirements of the LFT. It demonstrates that Λ \Lambda CDM simply does not satisfy the principle of equivalence. Some of the many important consequences of this outcome are discussed in the conclusions.

The heat transfer phenomenon associated with the lubricated surfaces offers applications in the manufacturing processes, thermal systems, industrial systems, and engineering phenomenon. It is a well-established fact that improvement in heat transfer is recently successfully claimed with the interaction of nanoparticles. Following such motivation in mind, the prime objective of current continuation is to perform the prediction of heat transfer in second-grade material subject to the lubricated surface. The lubricants are filled with non-Newtonian power law material. The varying thickness of the thin lubricating layer permits an imperfect slip surface. The second-grade fluid interfaces with the boundary condition. The modified semi-analytical tool termed as hybrid homotopy scheme is used to perform the simulations. Shooting and homotopy methods are combined in this new approach. Relevant effects of parameters on physical phenomenon are explained. The importance of influencing parameters in relation to the velocity field, temperature, and concentration profiles is investigated graphically. It is claimed that analytical computations existed for shear thinning case. It is observed that there is a noticeable drop in concentration and thermal profiles due to the variation of viscoelastic parameter. The control of free stream velocity is claimed due to the interaction of slip parameters.

In recent years, many numerical and analytical attempts have been reported by the researchers to explore the technological and industrial processes. Thermal management, hybrid-powered engine, microelectronics, heat exchanger, solar systems, energy generators are some recent applications of the heat and mass transfer flow. In this article, we have theoretically analyzed the convection flow of Walters-B fluid past a vertical extending surface. The Walters-B nanofluid contains the gyrotactic microorganisms and nanoparticles. The slip and convective conditions are imposed on the velocity and temperature equations. The modeled equations are reformed into the system of ordinary differential equations. Further, the transformed ordinary differential equations are solved analytically. The analytical results are compared with numerical solution and have found great resemblance to each other. The convergence analysis of analytical solution is also presented in this study. The impacts of the embedded factors on Walters-B nanofluid have been presented and deliberated in detail. The results show that the improvement in viscoelastic and magnetic parameter declined the nanofluid motion for both slip and no-slip conditions. The escalated mixed convection parameter has augmented the nanofluid motion. Additionally, at the surface of sheet, the slip condition reduces the fluid motion, however, away from the stretching surface, an increasing conduct up-to some points and then free stream velocity is found. The increased bioconvection Lewis number has increased the microorganisms’ profile while the greater bioconvection Peclet number has increased the microorganisms’ profiles reduced. The streamline patterns for Newtonian, non-Newtonian, magnetized, and non-magnetized cases have different behaviors. The flow factors have dominant impact on velocity profiles for the case of slip condition.

The lubrication phenomenon plays a novel role in the chemical industries, manufacturing processes, extrusion systems, thermal engineering, petroleum industries, soil sciences, etc . Owing to such motivated applications, the aim of the current work is to predict the assessment of heat and mass transfer analysis for non-Newtonian nanomaterial impinging over a lubricated surface. The flow is subject to the oblique stagnation point framework. The lubricated phenomenon is observed due to viscoelastic nanofluid. The impacts of chemical reaction are also endorsed. The fundamental conservation laws are utilized to model the flow problem and similarity transformation are used to transform the governing system of partial differential equations into ordinary differential equations. A thin layer of power law lubricant is used to enhance the lubrication features. The numerical object assessment regarding the simulation process is captured by implementing the Keller Box scheme. The physical characterization endorsing the thermal fluctuation with flow parameters is inspected.

This article puts forth a novel category of probability distributions obtained from the Topp–Leone distribution, the inverse- K K exponential distribution, and the power functions. To obtain this new family, we used the original cumulative distribution functions. After introducing this new family, we gave the motivations that led us to this end and the basis of the new family obtained, followed by the mathematical properties related to the family. Then, we presented the statistic order, the quantile function, the series expansion, the moments, and the entropy (Shannon, Reiny, and Tsallis), and we estimated the parameters by the maximum likelihood method. Finally, using real data, we presented numerical results through data analysis with a comparison of rival models.

Finding analytical solutions for nonlinear partial differential equations is physically meaningful. The Kaup-Kupershmidt (KK) equation is studied in this article. The KK equation is of fifth order, such that several solitary solutions are obtained. In this article, however, the modified auxiliary function approach is applied to this model to find solitary solutions. These solutions are written in terms of Jacobi functions. Therefore, the obtained solutions can be implemented graphically to show different patterns for appropriate parameters.

Ibn Tofail University of Kenitra, Morocco, is committed to a national policy of control and mobilization of water resources and the adoption of a planning approach and integrated water management. Within this framework, the university, which contains 40,000 students, produces a quantity of wastewater of 200 m 3 per day. After treatment, the water is used for watering the university’s green space. The treatment process chosen is a membrane bioreactor (MBR), which is considered to be energy intensive. Therefore, the production of energy for the station will be made by renewable energy wind and photovoltaic (PV). The dimensioning of the MBR was made by a research department, which estimated that the energy necessary for the station is 1061.76 kW h/day. The aim of this work is to dimension and optimize the platform for the production of energy, using the Matlab program for the wind turbine and the PVsyst program for PV. The results of coupling our plant with an on-grid PV system and wind turbine show that it was able to reach an electrical coverage of about 72% of the wastewater treatment (WWT) plant’s energy needs. Thus, an estimated reduction of electricity of 0.53 euro on each m 3 of water produced by the WWT plant and thus 106.76 euro on the 200 m 3 produced daily by the station.

Every day of the week, wireless communication is almost all around us. The Internet of Things (IoT) is a standard protocol used to describe the rapidly advancing technology in which almost every electronic device is or may be connected to the Internet. These electronic gadgets constantly provide data signals to the gateways, which satellites such as those in Low Earth Orbit may transmit. Because of these networks’ limited resources and the IoT, these transactions must be completed with the least amount of latency and data loss possible. We also analyze the performance implications of implementing RF-based powering for such a network. The techniques presented in this paper may benefit the scientific community and industry in general when it comes to the dynamic distributed parameter allocation methodology for IoT network devices. We will also discuss how research on animals and the natural environment has been impacted by IoT breakthroughs, in particular, animal sensors’ limits and incapacity to broadcast from everywhere. Our analysis illustrates the most effective data transmission technique and establishes the bounds of these restrictions. Furthermore, the physics of the RF channel plays a critical role in the uncertainty of the channel as well as the amount of energy harvested. By employing simulation based on the physics of the RF channel, the article shows the performance of the system considering both the uncertainty of data arrival as well as the variability of the channel. The findings of the simulation show that the devices consume less energy overall as the signal-to-noise ratio rises. Furthermore, a timing factor of 10–15% is shown to be effective in maintaining a constant mean rate and increasing the energy efficiency of the system.

In today’s era of rapid technological development, there is an increasing requirement for high-functioning investiture solutions, working liquids and materials that can satisfy the benchmarks of energy efficacy. Specifically, within the domain of heat transference-based industries, an essential challenge is to fabricate a cooling medium that can effectually cope with dissipation of substantial heat flux engendered by high-energy utilizations. At present, nanoliquids are extensively deliberated as some of the most promising aspirants for such effectual cooling mediums. The current investigation features hybrid nanoliquid flow adjacent to magnetized non-isothermal incompressible sphere. Rheological expressions representing micropolar liquid are accounted for flow formulation. The rheological analysis is developed using the boundary-layer concept. Buoyancy impact is accounted for heat transference analysis. Nanoparticles with distinct shapes are considered. The developed nonlinear systems are computed numerically and non-similar simulations are performed.

Warranty can improve customer satisfaction and increase product sales, but it will bring additional economic burden to manufacturers, so making reasonable warranty decisions is particularly important. The current research focuses more on the interests of manufacturers, while there is less attention paid to indicators that consumers are concerned about, such as system availability. To solve this problem, a joint optimization model of the two-dimensional warranty period and preventive maintenance (PM) strategy considering availability and cost constraints was established. Based on the failure dependence analysis of multi-component systems, the actual failure rate function is constructed by using the failure dependence coefficient matrix. Based on the comprehensive consideration of imperfect PM and minimum maintenance, the two-dimensional warranty cost model and system availability model are established, respectively. Aiming at maximum availability and considering the warranty cost budget constraint, a joint optimization model of the two-dimensional warranty period and PM strategy was built, and a model-solving algorithm combining grid search and binary search was introduced. The effectiveness of the model is verified by the case analysis, and the necessity of the PM strategy and considering failure dependence are reflected in the model comparative analysis and parameter sensitivity analysis. Finally, reasonable suggestions are put forward for manufacturers’ warranty decisions through the result analysis.

The aim of the present research is to discuss the numerical aspects of heat-mass transfer in power-law nanofluids on an stretched surface. In addition, the novelty in this research lies in its thorough exploration and incorporation of parameters such as viscous dissipation, slip velocity, and convective boundary conditions into the analysis. This distinguishes the study from previous work and underscores its originality. For non-Newtonian fluids, a power-law model is employed, while the nanofluid system associate the influences of thermophoresis and the Brownian motion. The fluid’s thermal conductivity is considered to change based on temperature, while the concentration of nanoparticles at the surface is maintained at a constant level. A heated fluid situated beneath the lower surface can act as a heat convection mechanism source. A process of similarity transformation is employed to simplify the equations related to the mass, momentum, thermal energy, and nanoparticle concentration into nonlinear ordinary differential equations. These equations are then treated numerically with the help of the shifted Chebyshev polynomials of the sixth order and the spectral collocation method. The proposed technique reduces the existing problem into a system of algebraic equations formulated as a constrained optimization challenge. Subsequently, the optimization technique is applied to determine the unknown coefficients of the series solution. Graphical representations depict the impacts of nanofluid parameters. A quantitative assessment is presented in a tabular format to illustrate a comparison with previously published results for specific scenarios, revealing a notable level of agreement.

Spectral uncertainty is one of the most prominent spectral characteristics of hyperspectral images. Compared to the process of remote sensing hyperspectral imaging, hyperspectral imaging under land-based imaging conditions has the characteristics of variable detection directions, random imaging times, and complex environmental conditions, resulting in increased spectral uncertainty of targets in land-based hyperspectral images. The spectral uncertainty of the target mainly refers to the phenomenon of “Same spectral reflectance but different objects” and “Same object but different spectral reflectance” which poses significant difficulties for subsequent hyperspectral image target detection and recognition. In order to analyze the spectral uncertainty of hyperspectral images in land-based applications and address the issue of spectral uncertainty in similar targets, a spectral uncertainty evaluation index based on standard deviation vector was proposed. For the overall spectral separability between different types of targets, a quantitative index based on Jaccard Distance (JD-SSI) is proposed to measure the spectral separability of different kinds of targets. The experiment focused on grassland and its four typical camouflage materials, analyzing the spectral intra class differences and inter class separability of each target with grassland. It is a fundamental work for studying the spectral characteristics of land-based hyperspectral images, providing a new approach for subsequent spectral band extraction, hyperspectral image classification, and target detection tasks.

The rapid development of the aviation industry has attracted great attention to aviation safety, and the identification and early warning of low-level wind shear have become crucial. Therefore, it is also necessary to improve the performance of laser wind radar technology and achieve accurate recognition of low-level wind shear. In this regard, this study is based on laser wind radar technology and uses the K-neighborhood frequency method to denoise radar data. And based on the least squares fitting method, two-dimensional synthetic wind shear is obtained, and a low altitude wind shear recognition model based on laser wind radar is constructed. These test results confirm that the correlation coefficient values of the wind speed fitting curve measured by the laser detection radar on sunny, cloudy, and fog days are 0.978, 0.954, and 0.961, respectively. And the correlation coefficient values of wind direction fitting curve are 0.984, 0.982, and 0.952, respectively. On sunny, cloudy, and fog days, the recognition accuracy values of the low-level wind shear recognition model are 85.92, 82.17, and 72.43%, respectively. And the recognition accuracy values of wind analyzer radar are 70.18, 62.57, and 55.89%, respectively. In practical applications, the low-level wind shear recognition model accurately recognizes the occurrence of low-level wind shear. This study has achieved accurate recognition of low-level wind shear and has better performance compared to other existing radars. It has played an important reference role in aviation safety.

Direct ink writing provides a new method for ceramic material forming. The single-screw extruder is used here to extrude viscous SiC slurry. Because the flow mechanism of ceramic slurry in the slurry direct writing extrusion device is unclear, lattice Boltzmann method (LBM) is used to analyze the flow process of ceramic slurry in the extrusion device. In this study, three different types of special-shaped, single-screw extruders (constant depth variable pitch screw, variable depth constant pitch screw, and variable depth variable pitch screw) are investigated to explore the effects of the shapes on the flow process. Compared with the traditional single-screw extruder, more attention should be paid to the difference in the flow channel. The non-Newtonian rheological model of SiC slurry is built, then the LBM for the non-Newtonian slurry is introduced and used to conduct the simulations based on the aforementioned three different cases. The results show that the effect of constant depth and variable pitch screw on the flow of ceramic slurry is the least and the flow of ceramic slurry in variable depth and variable pitch screw is the most complex.

In the operation of power grid, the low frequency subharmonics in power lines are easy to cause harmonic current problems. A harmonic current suppression method is constructed based on fuzzy sliding mode and virtual DC motor (VDC). First, the adaptive linear network is introduced to compare and analyze the output value and the actual value in the power line, and the possible harmonic current is obtained, which is detected and discretized. After that, this study adopts Fuzzy sliding mode control (FSMC) strategy for VDC, uses FSMC to participate in on-off control of VDC, and then realizes the suppression of harmonic current in VDC ports. In addition, the model also uses the circuit superposition theorem and the amount of harmonic data to be compensated by FSMC. The whole method uses VDC control technology to ensure the voltage stability of DC bus and load side when the load changes. In this physical experiment, harmonic current generated by load disturbance is eliminated by reducing DC harmonic voltage, so as to achieve the suppression of DC port harmonic current. Experimental results show that the third and fifth harmonics in power lines can be eliminated by this method to a large extent. Therefore, the proposed method can accurately detect and eliminate the harmonic current caused by sudden load change, and then realize the suppression of VDC harmonic current.

This research investigates the flow of micropolar fluid and heat transfer through a permeable channel using the successive linearization method (SLM). The study considers parameters such as coupling, spin-gradient viscosity, and micro-inertia density. The partial differential equations involved are transformed into a system of ordinary differential equations using similarity variables. The resulting nonlinear equations are solved using the SLM technique, and their accuracy and computational efficiency are validated through comparative analysis with previous results. The study shows that increasing the parameters of coupling and spin-gradient viscosity has a positive impact on fluid flow, microrotation, heat transfer, and mass transport, as demonstrated by the increased dimensionless profiles. Conversely, an increase in the micro-inertia density parameter leads to a reduction in these profiles. This decrease can be attributed to the increase in the micro-inertia effect of fluid flow and heat transfer, resulting in a decrease in convection and a change in the flow pattern in the channel. Additionally, higher Reynolds numbers are associated with decreases in velocity, microrotation, temperature, and concentration distribution. This implies a reduction in fluid flow intensity, weaker heat transfer, and decreased mass transport. However, an increased Peclet number results in increased fluid temperature and concentration profiles, indicating enhanced thermal convection and mass transport. These findings have significant implications for applications involving micropolar fluids, such as lubrication systems, blood flow, microchannels, and filtration systems.

In this article, the (2+1)-dimensional KdV equation by Hirota’s bilinear scheme is studied. Besides, the binary bell polynomials and then the bilinear form is created. In addition, an interaction lump with k k -soliton solutions of the addressed system with known coefficients is presented. With the assistance of the stated methodology, a cloaked form of an analytical solution is discovered in expressions of lump-soliton rational functions with a few lovable parameters. Solutions to this study’s problems are identified specifically as belonging to the lump-one, two, three, and four soliton solutions. By defining the specific advantages of the epitomized parameters by the depiction of figures and by interpreting the physical occurrences are established acceptable soliton arrangements and dealt with the physical importance of the obtained arrangements. Finally, under certain conditions, the physical behavior of solutions is analyzed by using the mentioned method. Moreover, the graphs with high resolutions including three-dimensional plots, density plots, and two-dimensional plots to determine a deep understanding of plotted solutions that will arise in the applied mathematics and nonlinear physics are employed.

This article features the buoyancy-driven electro-magnetohydrodynamic micropolar nanomaterial flow subjected to motile microorganisms. The flow is engendered via an elongating surface, and the energy relation includes heat source generation, magnetohydrodynamics, and radiation. A Buongiorno nanomaterial model (which includes thermophoretic and Brownian diffusions) together with chemical reaction and bioconvection aspects is pondered. The nonlinear governing expressions are transfigured into a dimensionless system, and the dimensionless expressions are computed using the numerical differential-solve scheme. Graphical analyses are conducted to examine the liquid flow, microrotation velocity, microorganism concentration, and temperature in relation to secondary variables. It is observed that a higher Hartman number has an opposite influence on temperature and velocity profiles. A rise in material variables engenders a decline in microrotation velocity. The temperature is enhanced through radiation. The concentration shows conflicting trends for both thermophoretic and random factors. The presence of motile microorganisms reduces the bioconvection Lewis and Peclet numbers.

In the window function spectrum of the low signal-to-noise ratio photon Doppler signal after the short-time Fourier transform, the weak beat frequency cannot be obtained by extracting the maximum amplitude spectrum frequency of each window because the amplitude of the noise spectrum exceeds the weak beat frequency. In this article, the value of the beat frequency is first estimated by the Kalman filter. Then, a multiple analytical bandpass filter is constructed to refine the spectrum of the high noise signal with the value of the beat frequency estimate as the spectrum band center. This technique extracts only the beat frequencies from the narrowband refinement spectrum by removing the interference spectrum band range. We use this technique to process the photon Doppler signals from the tiny high-speed flying fragments explosion experiment. After data processing, the beat frequency value heavily affected by high-frequency noise can reduce the error by up to 64.9%. The beat frequency value of the low noise signal can be accurate to 10 6 Hz, equivalent to 0.775 m/s after velocity demodulation. This method fully considers the positioning and protection of the beat frequency characteristics. It makes weak beat frequencies more obvious in the refined narrowband spectrum without changing the signal amplitude. This article describes a method for extracting the weak beat frequency of the photon Doppler signal or a signal optimization algorithm for needing high-precision beat frequencies in a test environment.

Micro-devices fabrication has led to extensive scientific research on microfluidics and microelectromechanical systems. These devices are used for a wide range of technological applications, but research on microfluidic devices for nanofluids is relatively scarce. In response to this problem, the electrokinetic energy conversion (EKEC) efficiency of nanofluids is provided under the coupling effect of pressure gradient and magnetic field through porous microtubes using the Debye–Hückel linearization and the Green’s function method. The results show that the periodic excitation of the square waveform is more effective in increasing the EKEC efficiency. In addition, compared with previous studies, the average velocity is in good agreement with the cosine waveform at R = 0.2. It is worth noting that compared to cosine waves, the average velocity reaches 47% in triangular waves and 85% in square waves.

This work investigates the behavior of a nanofluid in a horizontal channel under advection boundary conditions within the domain of magnetohydrodynamic radiative Couette-Poiseuille flow. We utilize the Haar wavelet collocation method (HWCM) to investigate the effects of energy activation. This research relies on the mathematical model introduced by Buongiorno, which effectively captures the flow dynamics and incorporates the influence of chemical processes. To streamline the governing flow equations, we employ boundary layer approximations. The HWCM is employed to numerically solve the non-linear coupled partial differential equations that regulate momentum, heat transport, and mass transfer processes. We examine the impact of several dimensionless convergence parameters on the velocity, temperature, and concentration profiles and give visual representations of these results. It is crucial to highlight that the activation energy of the specific chemical reaction is directly linked to the concentration of nanoparticles. The effect of Brownian motion on nanoparticle concentration varies from that of the thermophoresis parameter.

Poly(vinylidene fluoride) (PVDF) and its copolymers are promising candidates for energy-harvesting devices because of their flexibility, environmental friendliness, lightweight, and high halogen and acid resistance. However, the relatively low piezoelectricity limits their applications. The piezoelectricity of PVDF and its copolymers highly depends on the polar β-phase, while the non-polar α-phase is the most common one. As a result, the β-phase formation and α- to β-phase transformation have attracted much attention in recent years. Stretching is a widely used method to induce the α- to β-phase transformation for the improvement of piezoelectricity. In this work, the influences of the parameters during stretching on phase evolution and piezoelectricity are discussed and summarized. Besides, nontraditional stretching methods are also introduced and discussed. This work will provide important information for preparing high-performance piezoelectric polymer films.

In this study, data fusion algorithm is used to classify the soil species and calibrate the soil humidity sensor, and by using edge computing and a wireless sensor network, farmland environment monitoring system with a two-stage calibration function of frequency domain reflectometer (FDR) is established. Edge computing is used in system nodes, including the saturation value of the soil humidity sensor, the calculated soil hardness, the calculation process of the neural network, and the model of soil classification. A bagged tree is adopted to avoid over-fitting to reduce the prediction variance of the decision tree. A decision tree model is established on each training set, and the C4.5 algorithm is adopted to construct each decision tree. After primary calibration, the root mean squared error (RMSE) between the measured and standard values is reduced to less than 0.0849%. The mean squared error (MSE) and mean absolute error (MAE) are reduced to less than 0.7208 and 0.6929%. The bagged tree model and backpropagation neural network are used to classify the soil and train the dynamic soil dataset. The output of the trained neural network is closer to the actual soil humidity than that of the FDR soil humidity sensor. The MAE, the MSE, and the RMSE decrease by 1.37%, 3.79, and 1.86%. With accurate measurements of soil humidity, this research shows an important guiding significance for improving the utilization efficiency of agricultural water, saving agricultural water, and formulating the crop irrigation process.

Two standard and two nonstandard finite difference schemes are constructed to solve a basic reaction–diffusion–chemotaxis model, for which no exact solution is known. The continuous model involves a system of nonlinear coupled partial differential equations subject to some specified initial and boundary conditions. It is not possible to obtain theoretically the stability region of the two standard finite difference schemes. Through running some numerical experiments, we deduce heuristically that these classical methods give reasonable solutions when the temporal step size k k is chosen such that k ≤ 0.25 k\le 0.25 with the spatial step size h h fixed at h = 1.0 h=1.0 (first novelty of this work). We observe that the standard finite difference schemes are not always positivity preserving, and this is why we consider nonstandard finite difference schemes. Two nonstandard methods abbreviated as NSFD1 and NSFD2 from Chapwanya et al . are considered. NSFD1 was not used by Chapwanya et al . to generate results for the basic reaction–diffusion–chemotaxis model. We find that NSFD1 preserves positivity of the continuous model if some criteria are satisfied, namely, ϕ ( k ) [ ψ ( h ) ] 2 = 1 2 γ ≤ 1 2 σ + β \frac{\phi \left(k)}{{\left[\psi \left(h)]}^{2}}=\frac{1}{2\gamma }\le \frac{1}{2\sigma +\beta } and β ≤ σ \beta \le \sigma , and this is the second novelty of this work. Chapwanya et al . modified NSFD1 to obtain NSFD2, which is positivity preserving if R = ϕ ( k ) [ ψ ( h ) ] 2 = 1 2 γ R=\frac{\phi \left(k)}{{\left[\psi \left(h)]}^{2}}=\frac{1}{2\gamma } and 2 σ R ≤ 1 2\sigma R\le 1 , that is σ ≤ γ \sigma \le \gamma , and they presented some results. For the third highlight of this work, we show that NSFD2 is not always consistent and prove that consistency can be achieved if β → 0 \beta \to 0 and k h 2 → 0 \frac{k}{{h}^{2}}\to 0 . Fourthly, we show numerically that the rate of convergence in time of the four methods for case 2 is approximately one.

As an important unconventional resource, shale gas can alleviate energy shortage, and its efficient development ensures the long-term growth of oil and gas. The prediction of production levels and estimated ultimate recovery with high accuracy is necessary for shale gas development. Conventional methods are widely applied in the oil and gas industry owing to their simplicity and effectiveness; however, none of them can accurately predict the results for frac hits affected wells. In this work, a probability method based on the numerical model of shale gas reservoir has been formed. In view of the impact of frac hits on the productivity of production wells during the development of shale gas reservoirs, an embedded discrete fractured numerical simulation method for gas reservoirs is proposed to simulate the geological engineering parameter range of wells before frac. And aiming at the established numerical model of shale gas reservoir, this method adopts the ensemble smoother with multiple data assimilation automatic history matching technology to carry out the history matching process of the model. Based on the probability theory and numerical simulation results, this study analyses the influence of different distribution functions of parameters on the calculation results of reserves, and obtains the expected curve of reserves through combination calculation. Besides, the effectiveness of this method was verified by comparing with other traditional predicted method.

Differential equations (DEs) performed a vital role in the implementation of almost all the mechanical, physical, or biological processes. Higher order DEs had always been challenging to solve for the researchers so numerous numerical techniques were developed to attain the vital numerical approximations of such types of problems. In this work, highly advanced numerical techniques are established for the approximation of the fourteenth (14th)-order boundary value problems using Adomian decomposition method. The mathematical outcomes of the equations are attained in the form of convergent series that have effortlessly assessable components having step size h = 10. Some numerical examples are also deliberated to demonstrate the capability and application of the established procedure.

In this article, first integral method (FIM) is used to acquire the analytical solutions of (3+1)-D Wazwaz–Benjamin–Bona–Mahony and (2+1)-D cubic Klein–Gordon equation. New soliton solutions are obtained, such as solitons, cuspon, and periodic solutions. FIM is a direct method to acquire soliton solutions of nonlinear partial differential equations (PDEs). The proposed technique can be used for solving higher dimensional PDEs. FIM can be implemented to solve integrable and ion-integrable equations.

We use a general transformation, to find exact solutions for the Manakov system with variable coefficients (depending on the time ε \varepsilon ) using an improved tanh–coth method. The solutions obtained in this work are more general compared to those in other works because they involve variable coefficients. The implemented computational method is applied in a direct way on the reduced system, avoid in this way the reduction to only one equation, as occurs in the works respect to exact solutions, made by other authors. Clearly, from the solutions obtained here, new solutions are derived for the standard model (constant coefficients), complementing in this way the results obtained by other authors mentioned here. Finally, we give some discussion on the results and give the respective conclusions.

In this article, we used a novel semi-analytical approach, named the optimal auxiliary function method (OAFM), to solve integro-differential equations (IDEs). The OAFM includes an auxiliary function and convergence control parameters, which expedite the convergence of the method. To apply the proposed method, some assumptions regarding small or large parameters in the problem are necessary. We present numerical outcomes acquired via the OAFM alongside those obtained from other numerical techniques in tables. Furthermore, we demonstrate the efficacy and ease of implementing the proposed method for various IDEs using 2D graphs.

This article presents the mathematical formulation for the monkeypox infection using the Mittag–Leffler kernel. A detailed mathematical formulation of the fractional-order Atangana-Baleanu derivative is given. The existence and uniqueness results of the fractional-order system is established. The local asymptotical stability for the disease-free case, when ℛ 0 < 1 {{\mathcal{ {\mathcal R} }}}_{0}\lt 1 , is given. The global asymptotical stability is given when ℛ 0 > 1 {{\mathcal{ {\mathcal R} }}}_{0}\gt 1 . The backward bifurcation analysis for fractional system is shown. The authors give a numerical scheme, solve the model, and present the results graphically. Some graphical results are shown for disease curtailing in the USA.

In this work, a numerical scheme based on shifted Jacobi polynomials (SJPs) is deduced for variable-order fractional differential equations (FDEs). We find numerical solution of consider problem of fractional order. The proposed numerical scheme is based on operational matrices of variable-order differentiation and integration. To create the mentioned operational matrices for variable-order integration and differentiation, SJPs are used. Using the aforementioned operational matrices, we change the problem under consideration into matrix equation. The resultant matrix equation is solved by using Matlab, which executes the Gauss elimination method to provide the necessary numerical solution. The technique is effective and produced reliable outcomes. To determine the effectiveness of the suggested method, the results are compared to the outcomes of some other numerical procedure. Additional examples are included in this article to further clarify the process. For various scale levels and fractional-order values, absolute errors are also recorded.

Additive manufacturing has been gaining popularity in many industries and has made significant growth over the last 5 years. Many industries use additive manufacturing three-dimensional (3D) printing to produce complex shape objects that is a challenge to be manufactured by casting or conventional methods. In this study, the impact of heat treatment and build orientation is examined for the mechanical characteristics of 3D-printed parts. The study used samples constructed of titanium alloy Ti-6Al-4V, which is frequently used in AM applications. The parts were printed at various build orientations such as 0°, 45°, and 90°. Following printing, the samples underwent four distinct heat-treatments at 0, 700, 800, and 900°C. The variation in mechanical properties (Young’s modulus, strain-stress, and tensile strength) has been monitored to determine the best heat treatment and tilt orientation to obtain the best mechanical properties. These findings provide a systematic analysis and support the 3D printing of the parts used with a desired mechanical strength.