Band 19, Heft 1

In the literature, there were studies of Rydberg states of hydrogenic atoms/ions in a high-frequency laser field. It was shown that the motion of the Rydberg electron is analogous to the motion of a satellite around an oblate planet (for a linearly polarized laser field) or around a (fictitious) prolate planet (for a circularly polarized laser field): it exhibits two kinds of precession – one of them is the precession within the orbital plane and another one is the precession of the orbital plane. In this study, we study a helium atom or a helium-like ion with one of the two electrons in a Rydberg state, the system being under a high-frequency laser field. For obtaining analytical results, we use the generalized method of the effective potentials. We find two primary effects of the high-frequency laser field on circular Rydberg states. The first effect is the precession of the orbital plane of the Rydberg electron. We calculate analytically the precession frequency and show that it differs from the case of a hydrogenic atom/ion. In the radiation spectrum, this precession would manifest as satellites separated from the spectral line at the Kepler frequency by multiples of the precession frequency. The second effect is a shift of the energy of the Rydberg electron, also calculated analytically. We find that the absolute value of the shift increases monotonically as the unperturbed binding energy of the Rydberg electron increases. We also find that the shift has a nonmonotonic dependence on the nuclear charge Z : as Z increases, the absolute value of the shift first increases, then reaches a maximum, and then decreases. The nonmonotonic dependence of the laser field-caused energy shift on the nuclear charge is a counterintuitive result.

In this article, a generalized Hirota–Satsuma coupled Korteweg–de Vries (KdV) system is investigated from the group standpoint. This system represents an interplay of long waves with distinct dispersion correlations. Using Lie’s theory several symmetry reductions are performed and the system is reduced to systems of non-linear ordinary differential equations (NLODEs). Subsequently, the simplest equation method is invoked to find exact solutions of the NLODE systems, which then provides the solitary wave solutions for the system under discussion. Finally, we construct conservation laws of generalized Hirota–Satsuma coupled KdV system with the aid of general multiplier approach.

This work was devoted to unearth W-chirped to the famous Chen–Lee–Liu equation (CLLE) in optical monomode fibres. The results obtained will be useful to explain wave propagating with the chirp component. To attempt the main goal, we have used the new sub-ordinary differential equation (ODE) technique which was upgraded recently by Zayed EME, Mohamed EMA. Application of newly proposed sub-ODE method to locate chirped optical solutions to the Triki–Biswas equation equation. Optik. 2020;207:164360. On the other hand, we have used the modulation analysis to study the steady state of the obtained chirped soliton solutions in optical monomode fibres.

A solution to the problem of a hydrogenic atom in a homogeneous dielectric medium with a concentric spherical cavity using the oscillator representation method (ORM) is presented. The results obtained by the ORM are compared with a known exact analytic solution. The energy levels of the hydrogenic atom in a spherical cavity exhibit a shallow-deep instability as a function of the cavity radius. The sharpness of the transition depends on the value of the dielectric constant of the medium. The results of the ORM agree well with the results obtained by the analytic solution when the shallow-deep transition is not too sharp (i.e., when the dielectric constant is not too large) for all values of the cavity radius. The ORM results in the zeroth order approximation diverge significantly in the region of the shallow-deep transition (i.e., for the values of the radius where the shallow-deep transition occurs) when the dielectric constant is high and as a result the transition is sharp. Even for the sharp transition, the ORM results again agree very well with the analytic results at least for the ground state when a commonly used approximation in the ORM is removed. The ORM methodology for the cavity model presented in this article can potentially be used for two-electron systems in a quantum dot.

The Maxwell radiation field is an essential physical characteristic of a galaxy. Here, an analytical model is built to simulate that field in an axisymmetric galaxy. This analytical model is based on an explicit representation for axisymmetric source-free Maxwell fields. In a previous work, the general applicability of this representation has been proved. The model is adjusted by fitting to it the sum of spherical radiations emitted by the composing “stars.” The huge ratio distance/wavelength needs to implement a numerical precision better than the quadruple precision. The model passes a validation test based on a spherically symmetric solution. The results for a set of “stars” representative of a disk galaxy indicate that the field is highest near the disk axis, and there the axial component of E {\bf{E}} dominates over the radial one. This work will allow us in the future to check if the interaction energy predicted by an alternative theory of gravitation might be a component of dark matter.

This study reports the thermal analysis and species transport to manifest non-Newtonian materials flowing over linear stretch sheets. The heat transfer phenomenon is presented by the Cattaneo–Christov definition of heat flux. Mass transportation is modeled using traditional Fick’s second law. In addition, the contribution of Joule heating and radiation to thermal transmission is also considered. Thermo-diffusion and diffusion-thermo are significant contributions involved in thermal transmission and species. The physical depiction of the scenario under consideration is modeled through the boundary layer approach. Similar analysis has been made to convert the PDE model system into the respective ODE. Then, the transformed physical expressions are calculated for momentum, thermal, and species transport within the boundary layer. The reported study is a novel contribution due to the combined comportment of thermal relaxation time, radiation, Joule heating, and thermo-diffusion, which are not yet explored. Several engineering systems are based on their applications and utilization.

Vergence and accommodation responses of human vision are very important factors when a 3D image is observed, and a vergence-accommodation conflict (VAC) causes perceptual distortion, visual discomfort, and fatigue for an observer. Theoretically, a hologram is expected to provide a 3D image without such a conflict. In this article, natural focusing was verified by human accommodation response (A-R) measurement during on-axis analog reflection Denisyuk hologram observation. The A-R of a group of participants were measured for a real marker and its Denisyuk hologram at various visualization distances using an Nvision K5001 autorefractor. The experimental results statistically confirmed the equivalence of the responses to the Denisyuk hologram and its real counterpart, as well as the absence of a VAC.

In Newtonian mechanics, time and space are perceived as absolute entities. In Einstein’s relativity theory, time is frame dependent. Time is also affected by gravitational field and as the field varies in space, time also varies throughout space. In the present article, the thermodynamic-based time is investigated. In macroscopic view of thermodynamics, energy is conserved in every system or process. On the other hand, exergy (availability) is not conserved and can be destroyed, and “irreversibility” is generated. Since each thermodynamic system may generate different amounts of irreversibility, this quantity is system dependent. The present article investigates the characteristics of entity irreversibility. (1) It is found that the entity behaves in the similar manner as the clock time in the standard configuration of inertial frames under Lorentz transformation. (2) It is also found that the entity is affected by gravity fields in the similar manner as the clock time. We have demonstrated that, like clock time, irreversibility is frame dependent, and affected by gravity in the similar manner as the clock time. For these reasons, we propose to call the irreversibility of the system as the thermodynamic time. The time’s arrow is automatically satisfied, since irreversibility generation always proceeds in one direction (toward future). Based on the strength of the findings (1) and (2), a possible application of the irreversibility is an interpretation and management of the aging of biological systems. It is shown by other authors that entropy generation (equivalent to irreversibility) is a parameter for the human life span. Our sensation of time flow may be attributed to the flow of availability and destruction of it through the living system.

Purpose The aim of this study is to investigate an implementation method and the results of a voxel-based self-adaptive prescription dose optimization algorithm for intensity-modulated radiotherapy. Materials and methods The self-adaptive prescription dose optimization algorithm used a quadratic objective function, and the optimization engine was implemented using the molecular dynamics. In the iterative optimization process, the optimization prescription dose changed with the relationship between the initial prescription dose and the calculated dose. If the calculated dose satisfied the initial prescription dose, the optimization prescription dose was equal to the calculated dose; otherwise, the optimization prescription dose was equal to the initial prescription dose. We assessed the performance of the self-adaptive prescription dose optimization algorithm with two cases: a mock head and neck case and a breast case. Isodose lines, dose–volume histogram, and dosimetric parameters were compared between the conventional molecular dynamics optimization algorithm and the self-adaptive prescription dose optimization algorithm. Results The self-adaptive prescription dose optimization algorithm produces the different optimization results compared with the conventional molecular dynamics optimization algorithm. For the mock head and neck case, the planning target volume (PTV) dose uniformity improves, and the dose to organs at risk is reduced, ranging from 1 to 4%. For the breast case, the use of self-adaptive prescription dose optimization algorithm also leads to improvements in the dose distribution, with the dose to organs at risk almost unchanged. Conclusion The self-adaptive prescription dose optimization algorithm can generate an ideal clinical plan more effectively, and it could be integrated into a treatment planning system after more cases are studied.

This research paper uses a direct algebraic computational scheme to construct the Jacobi elliptic solutions based on the conformal fractional derivatives for nonlinear partial fractional differential equations (NPFDEs). Three vital models in mathematical physics [the space-time fractional coupled Hirota Satsuma KdV equations, the space-time fractional symmetric regularized long wave (SRLW equation), and the space-time fractional coupled Sakharov–Kuznetsov (S–K) equations] are investigated through the direct algebraic method for more explanation of their novel characterizes. This approach is an easy and powerful way to find elliptical Jacobi solutions to NPFDEs. The hyperbolic function solutions and trigonometric functions where the modulus and, respectively, are degenerated by Jacobi elliptic solutions. In this style, we get many different kinds of traveling wave solutions such as rational wave traveling solutions, periodic, soliton solutions, and Jacobi elliptic solutions to nonlinear evolution equations in mathematical physics. With the suggested method, we were fit to find much explicit wave solutions of nonlinear integral differential equations next converting them into a differential equation. We do the 3D and 2D figures to define the kinds of outcome solutions. This style is moving, reliable, powerful, and easy for solving more difficult nonlinear physics mathematically.

Based on the characteristics of intelligent manufacturing and the theory of technology diffusion, this paper constructs a cellular automata model with government support policy, information exchange, technology maturity, diffusion intermediary, and market competition as the influencing factors and analyzes the influence mechanism of the first three main factors on the diffusion of intelligent manufacturing technology in industrial clusters using MATLAB. This paper also makes an empirical analysis of the diffusion of intelligent manufacturing technology in the bearing industry cluster in Xinchang County and finds that the results are basically consistent by comparing the simulation data with the fit degree of the real data. In this paper, the diffusion intermediary and government support policy have the greatest influence on the application of intelligent manufacturing in small- and medium-sized enterprises, and the model proposed in this paper is effective.

The problem of the numerical analysis of natural convection from a spinning cone with variable wall temperature, viscous dissipation and pressure work effect is studied. The numerical method used is based on the spectral analysis. The method used to solve the system of partial differential equations is the multi-domain bivariate spectral quasi-linearization method (MD-BSQLM). The numerical method is compared with other methods in the literature, and the results show that the MD-BSQLM is robust and accurate. The method is also stable for large parameters. The numerical errors do not deteriorate with increasing iterations for different values of all parameters. The numerical error size is of the order of 1 0 − 10 1{0}^{-10} . With the increase in the suction parameter ξ \xi , fluid velocity, spin velocity and temperature profiles decrease.

In offshore oil and gas exploration and transportation, it is often encountered that the multi-floating structures work side by side. In some sea conditions, there is a strong coupling between the multi-floating structures that seriously affects the safety of offshore operations. Therefore, the prediction of the relative motion and force between the multi-floating structures and the wave elevation around the multi-floating-system has become a hot issue. At present, the problem of double-floating-system is mostly based on linear potential flow theory. However, when the gap width between two floating bodies is small, the viscous and nonlinear effects are not negligible, so the potential flow theory has great limitations. Based on the viscous flow theory, using the finite difference solution program of FLOW3D and using volume of fluid technology to capture the free surface, a three-dimensional numerical wave basin is established, and the numerical results of the wave are compared with the theoretical solution. On this basis, the hydrodynamic model of side-by-side double-floating-system with a narrow gap is established, and the flow field in the narrow gap of the fixed double-floating-system under the regular wave is analyzed in detail. The law of the gap-resonance is studied, which provides valuable reference for the future research on the multi-floating-system.

To obtain closed-form solutions for the radial Schrödinger wave equation with non-solvable potential models, we use a simple, easy, and fast perturbation technique within the framework of the asymptotic iteration method (PAIM). We will show how the PAIM can be applied directly to find the analytical coefficients in the perturbation series, without using the base eigenfunctions of the unperturbed problem. As an example, the vector Coulomb ( ∼ 1 / r ) \left( \sim 1\hspace{0.1em}\text{/}\hspace{0.1em}r) and the harmonic oscillator ( ∼ r 2 ) \left( \sim {r}^{2}) plus linear ( ∼ r ) \left( \sim r) scalar potential parts implemented with their counterpart spin-dependent terms are chosen to investigate the meson sectors including charm and beauty quarks. This approach is applicable in the same form to both the ground state and the excited bound states and can be easily applied to other strongly non-solvable potential problems. The procedure of this method and its results will provide a valuable hint for investigating tetraquark configuration.

The packer is one of the most important tools in deep-water perforation combined well testing, and its safety directly determines the success of perforation test operations. The study of dynamic perforating pressure on the packer is one of the key technical problems in the production of deep-water wells. However, there are few studies on the safety of packers with shock loads. In this article, the three-dimensional finite element models of downhole perforation have been established, and a series of numerical simulations are carried out by using orthogonal design. The relationship between the perforating peak pressure on the packer with the factors such as perforating charge quantity, wellbore pressure, perforating explosion volume, formation pressure, and elastic modulus is established. Meanwhile, the database is established based on the results of numerical simulation, and the calculation model of peak pressure on the packer during perforating is obtained by considering the reflection and transmission of shock waves on the packer. The results of this study have been applied in the field case of deep-water well, and the safety optimization program for deep-water downhole perforation safety has been put forward. This study provides important theoretical guidance for the safety of the packer during deep-water perforating.

Hydrogen-bonded mixtures with varying concentration are a complicated networked system that demands a detection technique with both time and frequency resolutions. Hydrogen-bonded pyridine–water mixtures are studied by a time-frequency resolved coherent Raman spectroscopic technique. Femtosecond broadband dual-pulse excitation and delayed picosecond probing provide sub-picosecond time resolution in the mixtures temporal evolution. For different pyridine concentrations in water, asymmetric blue versus red shifts (relative to pure pyridine spectral peaks) were observed by simultaneously recording both the coherent anti-Stokes and Stokes Raman spectra. Macroscopic coherence dephasing times for the perturbed pyridine ring modes were observed in ranges of 0.9–2.6 ps for both 18 and 10 cm − 1 10\hspace{0.33em}{{\rm{cm}}}^{-1} broad probe pulses. For high pyridine concentrations in water, an additional spectral broadening (or escalated dephasing) for a triangular ring vibrational mode was observed. This can be understood as a result of ultrafast collective emissions from coherently excited ensemble of pairs of pyridine molecules bound to water molecules.

When a tunnel is constructed in a karst area, crystallization of the drainage pipe caused by karst water often threatens the normal operation of the tunnel. This work contributes to this field of research by proposing a functional model based on the diffusion boundary layer (DBL) theory proposed by Dreybrodt in the 1990s. The model is formed by determining the flow rate distribution of the drainage pipe in a laminar flow state and turbulent state, and then by applying Fick’s diffusion law and Skelland’s approximate formula. Then, to further verify the applicability of the functional model, a model test was carried out in the laboratory and the test results are compared to the theoretical results. The results show that the crystallization rate of karst water is mainly affected by the roughness of the pipe wall, followed by the slope of pipes. The slope can affect flow state by controlling the flow rate, which in turn affects the crystallization rate of karst water. When the slope of the drainage pipe is 3, 4, and 5%, the error between the experimental results and the theoretical calculation results is 24.7, 8.07, and 27.9%, respectively, and when the liquid level in the pipe is 7.2, 10.2, and 13.3 mm, the error is 27.9, 9.82, and 2.07%, respectively. Considering that the flow will take away the crystalline deposits on the pipe wall in the experiment, although some results have certain errors, they do not affect the overall regularity.

We formulated the oscillators with position-dependent finite symmetric decreasing and increasing mass. The classical phase portraits of the systems were studied by analytical approach (He’s frequency formalism). We also study the quantum mechanical behaviour of the system and plot the quantum mechanical phase space for necessary comparison with the same obtained classically. The phase portrait in all the cases exhibited closed loop reflecting the stable system but the quantum phase portrait exhibited the inherent signature (cusp or kink) near origin associated with the mass. Although the systems possess periodic motion, the discrete eigenvalues do not possess any similarity with that of the simple harmonic oscillator having m = 1.

The fast marching method (FMM) is an efficient, stable and adaptable travel time calculation method. In the realization of this method, it is necessary to select the minimum travel time node from the narrow band many times. The selection method has an important influence on the calculation efficiency of FMM. Traditional FMM adopts the binary tree heap sorting method to achieve this step. Fibonacci heap sort method to FMM will be applied in this study. Compared with the binary tree heap sorting method, the Fibonacci heap sort method can realize the minimum travel time node selection in the narrow band in a more efficient way when the number of the narrow-band nodes is huge. The new method will be verified through error analysis and two numerical model calculations.

The hydrodynamic flow of an incompressible and isotropic Casson fluid through a yawed cylinder is investigated by employing continuity, momentum, and energy equations satisfying suitable boundary conditions. The density variation is governed by Boussinesq approximation. The model equations consisting of coupled partial differential equations (PDEs) are transformed by applying non-similar transformation relations. The set of transformed PDEs is solved using the analytical technique of homotopy analysis method (HAM). The impacts of varying yaw angle, and mixed convection and Casson parameters over fluid velocity (chordwise and spanwise components), its temperature, Nusselt number, and skin friction coefficients are investigated and explained through various graphs. It is found that the enhancing yaw angle, Casson parameter, and convection parameter augment the fluid velocity, heat transfer rate, and skin friction and reduce the fluid temperature. The agreement of present and published results justifies the application of HAM in modeling the mixed convective Casson fluid flow past a yawed cylinder.

Photon-enhanced thermionic emission (PETE) is a new type of solar cell. The existing papers on PETE research do not consider the structure of actual PETE devices; in practical PETE structure, the original incident light intensity is attenuated by the window layer and the buffer layer (include anode in reflection PETE devices). In this paper, according to two kinds of the common structure of PETE device, the influence of transmission and reflection of sunlight on the conversion efficiency of PETE device is analyzed. Using a light-trapping structure on the cathode of the PETE device is a valid method to reduce the reflection of the incident light. The calculation results show that the optical attenuation has a great influence on the actual photon flux received by the cathode effective layer. Under the condition of reasonable operation of the device, the efficiency of PETE can be improved by reducing the size of the material, improving the light transmittance of the buffer layer and window layer, and using the light-trapping structure.

In the forming process of galvanized sheet, the friction between the die and the blank often causes the zinc coating of galvanized sheet to peel off, scratch, and crack. The aim of this study is to evaluate and calculate the fractal characteristics of the surface morphology of galvanized sheet and the effect of pressure on the interfacial friction behavior. Two steel plates, GA and GI, produced by Shanghai Baosteel Company, were used as materials to conduct tribological experiments, measure the surface profile and three-dimensional shape of the galvanized sheet, and calculate the fractal dimension and fractal roughness parameters. According to the analysis results of friction surface damage of galvanized sheet, the damage failure parameters of galvanized sheet are calculated. On this basis, according to the adhesive friction theory, the total surface friction value of galvanized sheet is obtained, and the fractal calculation model of galvanized sheet friction is established. The simulation results show that the galvanized sheet has fractal characteristics. The average values of fractal dimension and scale factor of SP781BQ alloy hot-dip galvanized sheet are 1.52 and 0.23 µm, respectively. The average fractal dimension and scale coefficient of HC420/780DPD + Z hot-dip galvanized sheet are 1.60 and 0.11 µm, respectively. The friction coefficient calculated by the proposed method is consistent with the theoretical value, and the error is less than 10%, which proves the accuracy and feasibility of the friction fractal calculation method.

The FOOT (FragmentatiOn Of Target) experiment is an international project designed to carry out the fragmentation cross-sectional measurements relevant for charged particle therapy (CPT), a technique based on the use of charged particle beams for the treatment of deep-seated tumors. The FOOT detector consists of an electronic setup for the identification of Z ≥ 3 Z\ge 3 fragments and an emulsion spectrometer for Z ≤ 3 Z\le 3 fragments. The first data taking was performed in 2019 at the GSI facility (Darmstadt, Germany). In this study, the charge identification of fragments induced by exposing an emulsion detector, embedding a C 2 H 4 {{\rm{C}}}_{2}{{\rm{H}}}_{4} target, to an oxygen ion beam of 200 MeV/n is discussed. The charge identification is based on the controlled fading of nuclear emulsions in order to extend their dynamic range in the ionization response.

In this article, the Hamiltonian for the conformable harmonic oscillator used in the previous study [Chung WS, Zare S, Hassanabadi H, Maghsoodi E. The effect of fractional calculus on the formation of quantum-mechanical operators. Math Method Appl Sci. 2020;43(11):6950–67.] is written in terms of fractional operators that we called α \alpha -creation and α \alpha -annihilation operators. It is found that these operators have the following influence on the energy states. For a given order α \alpha , the α \alpha -creation operator promotes the state while the α \alpha -annihilation operator demotes the state. The system is then quantized using these creation and annihilation operators and the energy eigenvalues and eigenfunctions are obtained. The eigenfunctions are expressed in terms of the conformable Hermite functions. The results for the traditional quantum harmonic oscillator are found to be recovered by setting α = 1 \alpha =1 .

The arranged paths of dominoes have many shapes. The scaling law for the propagation speed of domino toppling has been extensively investigated. However, in all previous investigations the scaling law for the velocity of domino toppling motion in curved lines was not taken into account. In this study, the finite-element analysis (FEA) program ABAQUS was used to discuss the scaling law for the propagation speed of domino toppling motion in curved lines. It is shown that the domino propagation speed has a rising trend with increasing domino spacing in a straight line. It is also found that domino propagation speed is linearly proportional to the square root of domino separation. This research proved that the scaling law for the speed of domino toppling motion given by Sun [Scaling law for the propagation speed of domino toppling. AIP Adv. 2020;10(9):095124] is true. Moreover, the shape of domino arrangement paths has no influence on the scaling law for the propagation speed of dominoes, but can affect the coefficient of the scaling law for the velocity. Therefore, the amendatory function for the propagation speed of dominoes in curved lines was formulated by the FEA data. On one hand, the fitted amendatory function, φ revise {\varphi }_{{\rm{revise}}} , provides the simple method for a domino player to quickly estimate the propagation speed of dominoes in curved lines; on the other hand, it is the rationale for the study of the domino effect.

In order to achieve wide-band high-resolution frequency measurement, a frequency synchronization detection method based on adaptive frequency standard tracking is proposed based on the quantized phase processing. First, the nominal value of the measured frequency signal was obtained from the rough frequency measurement module. Then, the field programmable gate array generated the nominal value of the measured frequency. After that, the direct comparison between the tracking frequency and the measured signal was carried out. Finally, the group quantized processing module gave the final result according to the phase full-period change time. Experimental results showed that the method has a wide frequency measurement range and high accuracy and can obtain frequency stability of the order of 10 −13 /s.

The fracture direction and its intensity are critical properties related to hydrocarbon characterization and identification. Both these properties have an essential role in identifying the direction of hydrocarbon migration, determining the sweet spot area, and optimizing the drilling design. The velocity variation with azimuth (VVAz) is a well-known method to estimate the fracture direction and its intensity. This method is of widespread interest because it predicts the properties based on seismic data without any practical constraints. Despite this interest, the technique requires rich azimuth 3D seismic data in our case, which is rare. This study aims to apply regularization and interpolation by including the wave front attributes based on the Common Reflection Surface (CRS) method before the VVAz inversion. The motivation of using the CRS method is to enrich the current azimuth of the 3D seismic data and improve the S/N ratio. The synthetic and the real 3D seismic data are evaluated to examine the interpolation scheme of the proposed CRS method’s performance. Based on the evaluation of the 3D seismic data after regularization, the amplitude versus offset (AVO) phenomena, and the VVAz inversion results are relatively consistent (or matched) with the model. A similar result is found for the case of real 3D seismic data. A significant positive correlation between the fracture intensity of FMI and the real seismic data of about 0.9 is obtained. Therefore, CRS can be used as a regularization and interpolation method before the VVAz inversion of the relatively narrow azimuth 3D seismic data.

To explore the synergistic mechanism of polymer and surfactant in the binary combination flooding of low-permeability reservoirs, the adaptability experiment of polymer salt-resistant partially hydrolyzed polyacrylamide and nonionic surfactant was carried out in the indoor system. Experiments at different ratios are also performed. The results show that the selected poly/surface binary flooding system increases with the concentration of polymer or surfactant, the viscosity of the poly/surface binary system also increases and, at the same time, has better temperature and salt resistance. The viscosity of the binary system will decrease when the salinity increases. When the surfactant concentration CS = 0.2% and the polymer concentration CP = 0.2%, the viscosity of the system is the highest. The viscosity of the poly/table binary system at different concentrations decreases when the temperature rises: pure polymer (CP = 0.2%), poly/table binary system displacement fluid CP = 0.1% + CS = 0.2% and CP = 0.2% + CS = 0.2%; and the injection pressure first rises and then drops. The final recovery rate is 51.8%, which meets the development of most oil reservoirs.

Simulations and numerical analysis of physical problems are important steps toward understanding underlying mechanisms of the processes. Important examples would be medical physics and medical imaging. Compartmental modeling has been found useful for estimating the transport and temporal variations of drugs/contaminants (commonly used in medical physics and medical imaging) in different organs, given that different organs would be modeled as compartments. Recycling among these modeled compartments (i.e., organs) was allowed through defining sets of constant transfer rates. In order to mathematically define these systems, one needs to use sets of differential equations (depending on the number of compartments) which would in fact be time-consuming and prone to mathematical error. Considering these issues, there is a need for a versatile computer program that is accurate, robust, and user-friendly to perform the required computations automatically. In the present work, we developed and benchmarked an open-source computer program entitled CompVision that was able to simulate five-compartmental systems. The present software had an easy-to-use graphical user interface (GUI) for the users. The executable program and the source codes were made available publicly under GPLv3 license, which would allow everyone to use, modify, and distribute without any restriction. The present program would be useful in a variety of research fields and applications.

Graphene has the capability of dynamically tuning its conductivity through gate voltage. Based on this fact, an electrically switchable wideband metamaterial absorber at low frequencies is presented and investigated in this paper. Our calculated results show that its absorption is over 90% from 400 to 1,000 MHz with the Fermi level of graphene being at 0 eV and the absorption band can be switched by adjusting the Fermi level of graphene without changing its physical structure. Moreover, the surface current distribution enables us to reveal the switchable wideband absorption characteristics of our designed metamaterial absorber. At last, we prove that its absorption property is polarization-insensitive due to the rotational symmetry of the structural unit. This work may provide a further step in the development of switchable sensors and absorbers at low frequencies.

The effect of post-growth annealing treatment of zinc oxide (ZnO) nanorods on the electrical properties of their heterojunction diodes (HJDs) is investigated. ZnO nanorods are synthesized by the low-temperature aqueous solution growth technique and annealed at temperatures of 400 and 600°C. The as-grown and annealed nanorods are studied by scanning electron microscopy (SEM) and photoluminescence (PL) spectroscopy. Electrical characterization of the ZnO/Si heterojunction diode is done by current–voltage ( I – V ) and capacitance–voltage ( C – V ) measurements at room temperature. The barrier height ( ϕ B ), ideality factor ( n ), doping concentration and density of interface states ( N SS ) are extracted. All HJDs exhibited a nonlinear behavior with rectification factors of 23, 1,596 and 309 at ±5 V for the as-grown, 400 and 600°C-annealed nanorod HJDs, respectively. Barrier heights of 0.81 and 0.63 V are obtained for HJDs of 400 and 600°C-annealed nanorods, respectively. The energy distribution of the interface state density has been investigated and found to be in the range 0.70 × 10 10 to 1.05 × 10 12  eV/cm 2 below the conduction band from E C = 0.03 to E C = 0.58 eV. The highest density of interface states is observed in HJDs of 600°C-annealed nanorods. Overall improved behavior is observed for the heterojunctions diodes of 400°C-annealed ZnO nanorods.

A facile method for fabricating superhydrophobic and superoleophilic powder with 5A zeolite and stearic acid (SA) is reported in this study. The effect of different contents of SA on contact angle (CA) was investigated. The maximum water CA was 156.2°, corresponding to the optimum SA content of 1.5 wt%. The effects of SA and the mechanism of modified 5A zeolite powder by SA were analyzed by sedimentation analysis experiment, FTIR analysis, particle size analysis, and SEM characterization. The SA-modified 5A zeolite was used as an oil sorbent to separate oil–water mixture with potential use in floating oil. The separation efficiency was above 98%.

We solved a one-dimensional time-dependent Feinberg–Horodecki equation for an improved Wei molecular energy potential function using the parametric Nikiforov–Uvarov method. The quantized momentum and the corresponding wave functions were obtained. With the help of the wave functions obtained, we calculated Shannon entropy for both the position space and momentum space. The results were used to study four molecules. The results of Shannon entropy were found to be in excellent agreement with those found in the literature. For more usefulness of these studies, the quantized momentum obtained was transformed into an energy equation with certain transformations. The energy equation was then used to calculate some thermodynamic properties such as vibrational mean energy, vibrational specific heat, vibrational mean free energy, and vibrational entropy via computation of the partition function. The thermodynamic properties studied for CO, NO, CH, and ScH showed that for a certain range of the temperature studied, the molecules exhibited similar features except for the vibrational entropy.

In this article, a fuel tank is coupled with gyrostat in a moving spacecraft to discuss its dynamical behaviour and bringing stability in velocity vectors. Parametric study is performed using Hopf bifurcation to find the bifurcation parameter for a considered mechanical model. Furthermore, a region is constructed in which negligible limit cycles appear around unstable spirals for angular momentum greater than bifurcation point. Based on local dynamical analysis, trajectories of angular velocities are observed with respect to damping constant, which is formulated in the form of bifurcation parameter. Moreover, a controller is designed in this article for considered dynamical system by achieving global stability, with the help of Lyapunov theory, into the spacecraft coupled with filled fuel tank, and their results are compared with effective spacecraft control strategies to observe the effectiveness of our proposed control technique. Finally, in presented research, numerical simulations are performed using MATLAB for validation of analytical results, which the authors have achieved for Hopf bifurcation and designed controller.

The Hamiltonian and wavefunctions of two-dimensional two-electron quantum dots (2D2eQD) in parabolic confinement are determined. The ground and excited state energies are calculated solving the Schrödinger equation analytically and numerically. To determine the energy eigen-value of the system variational method is employed due to the large coupling constant λ ≈ 1.1 \lambda \approx 1.1 . The trial wavefunctions are developed for both ground and excited states. The ground state wave function is a para state and the excited state wavefunctions belong to both para and ortho states based on the symmetry and antisymmetry of spatial wavefunctions. Using the obtained energy eigen-values at the two states, the first- and third-order nonlinear absorption coefficient and refractive index are analytically obtained with the help of density matrix formalism and iterative procedure.

In this article, the collective variable method to study two types of the Chen–Lee–Liu (CLL) equations, is employed. The CLL equation, which is also the second member of the derivative nonlinear Schrödinger equations, is known to have vast applications in optical fibers, in particular. More specifically, a consideration to the classical Chen–Lee–Liu (CCLL) and the perturbed Chen–Lee–Liu (PCLL) equations, is made. Certain graphical illustrations of the simulated numerical results that depict the pulse interactions in terms of the soliton parameters are provided. Also, the influential parameters in each model that characterize the evolution of pulse propagation in the media, are identified.

The purpose of the present investigation is to examine the heat, mass and microorganism concentration transfer rates in the magnetohydrodynamics (MHD) stratified boundary layer flow of tangent hyperbolic nanofluid past a linearly, uniform stretching surface comprising gyrotactic microorganisms as well as nanoparticles. The governing PDEs with relevant end point conditions are molded into a non-dimensional ordinary differential equation (ODE) form by means of the similarity transformation. The numerical solution of dimensionless problem is acquired within the frame of robust Keller-Box technique. The velocity, temperature, mass and motile microorganism density are investigated graphically within the context of different significant parameters. Numerical results have been inspected via plots and table (namely as the local Nusselt number, the local wall mass flux and the local microorganisms wall flux). This article proves that the energy, concentration and motile microorganism density reduce with increase in thermal, solutal and motile density stratification parameters. The asserted outcomes are beneficial to enhance the cooling and heating processes, energy generation, thermal machines, solar energy systems, industrial processes etc.

With the development of light-screen targets for ballistic projectiles, not only must accuracy in the measurement of projectiles be assured but also the installation of the system and error compensation in the initial calibrations must be considered. We have designed a triangular composition light-screen target that is easy to install, derived expressions for the speed and direction of ballistic trajectories based on intersecting-CCD vertical targets, and conducted analyses of the points of impact and projectile speed. Results show that errors in the point of impact are affected by the coordinates of the target plane. Positional errors gradually increase with the distance from the origin. The horizontal angle error with the trajectory line does not exceed 0.3°, whereas the vertical angle error does not exceed 0.2°. Errors in the speed of the projectile remain relatively stable when the vertical coordinates are greater. Errors in speed and direction, as well as error fluctuations, are smaller on the x = 0 plane, making it the ideal region for error compensation in initial calibrations.

In this article, we first consider approach of optical spherical magnetic antiferromagnetic model for spherical magnetic flows of ϒ \Upsilon -magnetic particle with spherical de-Sitter frame in the de-Sitter space S 1 2 {{\mathbb{S}}}_{1}^{2} . Hence, we establish new relationship between magnetic total phases and spherical timelike flows in de-Sitter space S 1 2 {{\mathbb{S}}}_{1}^{2} . In other words, the applied geometric characterization for the optical magnetic spherical antiferromagnetic spin is performed. Moreover, this approach is very useful to analyze some geometrical and physical classifications belonging to ϒ \Upsilon -particle. Besides, solutions of fractional optical systems are recognized for submitted geometrical designs. Geometrical presentations for fractional solutions are obtained to interpret the model. These obtained results represent that operation is a compatible and significant application to restore optical solutions of some fractional systems. Components of models are described by physical assertions with solutions. Additionally, we get solutions of optical fractional flow equations with designs of our results in de-Sitter space S 1 2 {{\mathbb{S}}}_{1}^{2} .

The influence of acoustic radiation is considered in the prediction of noise attenuation effect of sound barrier, which provides a theoretical reference for further improving the insertion loss of sound barrier. Based on the theory of thin plate vibration, the vibration mode and natural frequencies of sound barrier under arbitrary boundary conditions are established by using two-dimensional beam function method, and the forced vibration response of the sound barrier is calculated based on the modal superposition method. MATLAB software (MathWorks Company, Natick, Massachusetts, USA) is used to calculate the natural frequencies and the radiated sound power level of the sound barrier, which indicated that the sound radiation caused by external excitation would significantly increase the sound pressure level at the received point, which should be considered as one of the influencing factors in the prediction of noise attenuation effect. The influence of diverse structural parameters on the radiated acoustic power is compared, providing an excellent reference for the design of sound barrier with low noise.

In this study, the tribological properties of hybrid polytetrafluoroethylene (PTFE)/Nomex fabric/phenolic resin composites were investigated under three operating conditions: dry sliding, dry sliding after soaking in water for 12 h, and water dripping lubrication. The friction coefficient (COF) was measured with a pin-on-disk tribometer. The wear surface was analyzed with a scanning electron microscope. The results show that water weakens the tribological properties of single-layer hybrid PTFE/Nomex fabric/phenolic resin composites. The fabric composites show slight abrasive wear with stable COF under dry sliding conditions, significant abrasive wear with oscillating COF after soaking, and destruction with severely oscillating COF under water dripping lubrication. Generally, water weakens the effect in two ways. The first is weakening the binding force between phenolic resin and Nomex fiber. The second is that Nomex fiber absorbs water and expands, which reduces its strength. Finally, the ideas to improve the tribological properties under water dripping lubrication are presented.

The aim of this study was to improve the low accuracy of equipment spare parts requirement predicting, which affects the quality and efficiency of maintenance support, based on the summary and analysis of the existing spare parts requirement predicting research. This article introduces the current latest popular long short-term memory (LSTM) algorithm which has the best effect on time series data processing to equipment spare parts requirement predicting, according to the time series characteristics of spare parts consumption data. A method for predicting the requirement for maintenance spare parts based on the LSTM recurrent neural network is proposed, and the network structure is designed in detail, the realization of network training and network prediction is given. The advantages of particle swarm algorithm are introduced to optimize the network parameters, and actual data of three types of equipment spare parts consumption are used for experiments. The performance comparison of predictive models such as BP neural network, generalized regression neural network, wavelet neural network, and squeeze-and-excitation network prove that the new method is effective and provides an effective method for scientifically predicting the requirement for maintenance spare parts and improving the quality of equipment maintenance.

In this article, the hydrogen molecular ground-state energies using our algorithm based on quantum variational principle are calculated. They are calculated through a simulator since the system of the present study ( i.e. , the hydrogen molecule) is relatively small and hence the ground-state energies for this molecule are efficiently classically simulable using a simulator. Complete details of this algorithm are elucidated. For this, a full description on the fermions–qubits and the molecular Hamiltonian–qubit Hamiltonian transformations, is given. The authors search for qubit system parameters ( θ 0 {\theta }_{0} and θ 1 {\theta }_{1} ) that yield the minimum energies for the system and also study the ground state energies as a function of the molecular bond length. Proposed circuit is humble and does not include many parameters compared with that of Kandala et al. , the authors control only two parameters ( θ 0 {\theta }_{0} and θ 1 {\theta }_{1} ).

Synthetic ester can replace the mineral oil traditionally used in transformers to avoid the environmental problems caused by oil leakage. However, the fast discharge phenomenon in a high electric field in transformers using synthetic ester seems to indicate its insulation property is inferior to that of mineral oil. In this paper, typical molecular models of synthetic ester, including F2, F4, F6, F8, and F10, are constructed. We studied the effect of electric fields on the molecular properties of the five molecules by density functional theory and time-dependent density functional theory. According to the electric field intensity required for discharge initiation and propagation in insulating oil, the electric field intensity applied in this study varied from 10 8 to 10 9  V/m. The results showed that the molecular bond lengths are obviously dependent on the electric field. The ionization potential (IP) of the F8 and F10 molecules decreases sharply under electric field intensities of 3.1 × 10 9 and 4.0 × 10 9  V/m. It can be inferred that the IP reduction of the long carbon chain molecules, such as F8 and F10, is the reason for the formation of fast discharge in the case of synthesis ester. Calculations for excited states show that the introduction of an electric field makes the electron transition more active. The results obtained by this work improve our understanding of the discharge mechanism in synthetic ester dielectrics and provide theoretical support for improvement in the performance of synthetic ester insulating oil.

The space–time fractional generalized equal width (GEW) equation is an imperative model which is utilized to represent the nonlinear dispersive waves, namely, waves flowing in the shallow water strait, one-dimensional wave origination escalating in the nonlinear dispersive medium approximation, gelid plasma, hydro magnetic waves, electro magnetic interaction, etc . In this manuscript, we probe advanced and broad-spectrum wave solutions of the formerly betokened model with the Riemann–Liouville fractional derivative via the prosperously implementation of two mathematical methods: modified elongated auxiliary equation mapping and amended simple equation methods. The nonlinear fractional differential equation (NLFDE) is renovated into ordinary differential equation by the composite function derivative and the chain rule putting together along with the wave transformations. We acquire several types of exact soliton solutions by setting specific values of the personified parameters. The proposed schemes are expedient, influential, and computationally viable to scrutinize notches of NLFDEs.

The Pareto distribution satisfies the power law, which is widely used in physics, biology, earth and planetary sciences, economics, finance, computer science, and many other fields. In this article, the logarithmic Pareto distribution, a logarithmic transformation of the Pareto distribution, is presented and studied. The moments, percentiles, skewness, kurtosis, and some dynamic measures such as hazard rate, mean residual life, and quantile residual life are discussed. The parameters were estimated by quantile and maximum likelihood methods. A simulation study was conducted to investigate the efficiency, consistency, and behavior of the maximum likelihood estimator. Finally, the proposed distribution was fitted to some datasets to show its usefulness.

In the present work, we investigate soliton structures in optical fiber communications. The medium is described by the Kundu–Mukherjee–Naskar model. With the aid of the ansatz approach, the exact solutions are constructed. Consequently, distinct wave structures including W-shaped, bright and dark solitons are derived. These new soliton solutions are retrieved under certain parametric conditions. Besides, it is found that the bright soliton has two different types in a particular limit. Optical solitons are displayed graphically to shed light on their behaviors.

Coronavirus disease 2019 (COVID-19) is a disease caused by severe acute respiratory syndrome coronavirus 2 (SARS CoV-2). It was declared on March 11, 2020, by the World Health Organization as a pandemic disease. Regrettably, the spread of the virus and mortality due to COVID-19 have continued to increase daily. The study is performed using the Atangana–Baleanu–Caputo operator with a harmonic mean type incidence rate. The existence and uniqueness of the solutions of the fractional COVID-19 epidemic model have been developed using the fixed point theory approach. Along with stability analysis, all the basic properties of the given model are studied. To highlight the most sensitive parameter corresponding to the basic reproductive number, sensitivity analysis is taken into account. Simulations are conducted using the first-order convergent numerical approach to determine how parameter changes influence the system’s dynamic behavior.

This article proposes a metamaterial-based temperature sensor with high sensitivity using the thermally tunable liquid metal of mercury. The response of the metamaterial at different temperatures is theoretically investigated. In the merit of the temperature-sensitive thermal expanding of the embedded mercury resonant structure, different absorption peak frequencies can be observed at different temperatures, which enables the proposed metamaterial capability of temperature sensing. The numerical simulations show that the temperature sensitivity of the proposed sensor can reach up to 27.64 MHz/°C within the range of 0–21.8°C. The calculated electric field and surface current distributions illustrate that the high sensitivity is originated from the dual-dipole mode of the resonant structure. Meanwhile, the dependence of the structural dimensions on temperature sensitivity is discussed to optimize the sensor design. The proposed strategy paves a new way for developing temperature sensors with high sensitivity.

The aim of this investigation was to synthesize propolis-mediated silver nanoparticles (Pro-AgNPs) and to test their biological activities in comparison with the raw materials (Saudi propolis). The chemical–physical characterization of the product showed that Pro-AgNPs were well synthesized. For the study of biological properties, aqueous and methanolic extracts were prepared from both propolis and Pro-AgNPs. Total polyphenol contents (TPCs) and antiradical activities showed their highest values in methanolic extracts, in particular in propolis extract. But, a higher TPC was found in Pro-AgNP aqueous extract as compared to propolis aqueous extract. It seems that Pro-AgNP synthesis helped extract more phenolic compounds with water. These compounds did not enhance antiradical activity in Pro-AgNP aqueous extract but increased its antibacterial activity.

The objective of this work is to propose a collocation technique based on new cubic trigonometric B-spline (NCTB-spline) functions to approximate the regularized long-wave (RLW) equation. This equation is used for modelling numerous problems occurring in applied sciences. The NCTB-spline collocation method is used to integrate the spatial derivatives. We use the Rubin–Graves linearization technique to linearize the non-linear term. The accuracy and efficiency of the technique are examined by employing it on three important numerical examples which have three invariants of motion viz . mass, momentum, and energy. It is observed that the error norms of the present method are less than the error norms of the methods available in the literature. The numerical values of these invariants have also been approximated, which remain conserved during the program run which shows that the propagation of the solitary wave is represented perfectly. The propagation of one and two solitary waves and undulations of waves are depicted graphically. The stability analysis shows that the method is unconditionally stable.

The flexspline features several modal characteristics that are related to its structural parameters, which could impose an impact on the stability and reliability of the system of harmonic gear transmission. In this article, we have integrated the method of orthogonal design with the approach of finite element, so as to study the modal characteristics of flexspline under varying structural parameters. Furthermore, we have analyzed the ways of how varying structural parameters could impose an impact on the first eight-order natural frequencies of flexspline. In addition, by adopting the method of range and variance analysis for the obtained data, we have examined the influence imposed by varying structural parameters on the modal characteristics of flexspline, which could lay a foundation for the optimal design of the structural parameters of flexspline.

This study revisits the Reynolds-averaged Navier–Stokes (RANS) equations and finds that the existing literature is erroneous regarding the primary unknowns and the number of independent unknowns in the RANS. The literature claims that the Reynolds stress tensor has six independent unknowns, but in fact the six unknowns can be reduced to three that are functions of the three velocity fluctuation components, because the Reynolds stress tensor is simply an integration of a second-order dyadic tensor of flow velocity fluctuations rather than a general symmetric tensor. This difficult situation is resolved by returning to the time of Reynolds in 1895 and revisiting Reynolds’ averaging formulation of turbulence. The study of turbulence modeling could focus on the velocity fluctuations instead of the Reynolds stress. An advantage of modeling the velocity fluctuations is, from both physical and experimental perspectives, that the velocity fluctuation components are observable whereas the Reynolds stress tensor is not.

In this article, we investigate the time-periodic pulse electroosmotic flow (EOF) of Jeffreys fluids through a microannulus. By using the Laplace transform method, the velocity expression of the pulse EOF is derived. The effect of some variables on the time it takes for the fluid to go from a static state to a flowing state is analyzed. We find that increasing the relaxation time λ ¯ 1 {\bar{\lambda }}_{\text{1}} and decreasing the inner and outer radius ratio α \alpha will result in longer time for the fluid to reach the flowing state, but the retardation time λ ¯ 2 {\bar{\lambda }}_{\text{2}} and the inner and outer zeta potential ratio β \beta have little effect on it. The impact of some related parameters on the pulse EOF velocity for different inner and outer radius ratios ( α \alpha ) is discussed in detail. The results show that for a smaller inner and outer radius ratio α \alpha , the velocity amplitude increases with the relaxation time λ ¯ 1 {\bar{\lambda }}_{\text{1}} and decreases with the retardation time λ ¯ 2 {\bar{\lambda }}_{\text{2}} . As the inner and outer radius ratio α \alpha increases, the effect of relaxation time λ ¯ 1 {\bar{\lambda }}_{\text{1}} on velocity amplitude gradually weakens or even becomes insignificant, and the effect of the retardation time λ ¯ 2 {\bar{\lambda }}_{\text{2}} on the velocity amplitude remains unchanged. Moreover, the velocity amplitude will decrease with the increase in the inner and outer radius ratio α \alpha and its change range will expand from the electric double layer near the annular wall to the entire flow region.

The purpose of the current study is to find exact travelling wave solutions of the Rosenau equation. By the use of the extended auxiliary equation method, various exact solutions are obtained in terms of Jacobi elliptic functions and exponential functions. Moreover, several solitary and periodic wave solutions are given as special cases. When the parameters take some values, some graphical illustrations are shown in order to understand the behaviour of these new solutions. Furthermore, we compare our solutions with some familiar solutions, which can be considered as special cases.

In this research, we analyze the magnetohydrodynamics heat act of a viscous incompressible Jeffrey nanoliquid, which passed in the neighborhood of a linearly extending foil. As a process, we employ alumina ( Al 2 O 3 ) \left({{\rm{Al}}}_{2}{{\rm{O}}}_{3}) as nanoparticles, assuming that the base fluid is ethylene glycol. In this involvement, we consider the heating by Joule effect and viscous dissipation. We select the passable transformations, motion, and temperature formulas converting into non-linear differential equation arrangement. We solved the system by using a Keller-box method. Then, we provide a graphical description of outcomes according to the selected control parameters. Higher values of dissipation parameter cause a surge in temperature field as well as strengthen width of the heat boundary layer. The velocity, drag coefficient, and heat transfer (HT) rate for the base fluid are comparatively greater than that of the Al 2 O 3 {{\rm{Al}}}_{2}{{\rm{O}}}_{3} –ethylene glycol nanofluid, although the temperature is embellished by the inclusion of nanoparticles. Moreover, we report depreciation in surface drag as well as HT by the virtue of amplification in the Deborah number. The proclaimed outcomes are advantageous to boost the incandescent light bulb’s, cooling and heating processes, filament emitting light, energy generation, multiple heating devices, etc .

A numerical analysis of a compact microring resonator that was defined on a yttrium-aluminum-garnet (YAG) thin film bonded on top of a SiO 2 cladding layer and operated at the wavelengths of approximately 1.064 and 1.6 μm was performed. The single-mode conditions of YAG waveguides at different waveguide geometries and their propagation losses at different SiO 2 cladding layer thicknesses were systematically analyzed. The key design parameters of the microring resonator, such as gap size and ring radius, were simulated based on the 2.5-dimensional variational finite-difference time-domain method. This study could be helpful in understanding the mechanism of microring resonators defined on YAG thin films and fabricating integrated microlaser sources on YAG-on-insulators.

Multiple coating assessments of fiber optics utilizing micropolar convection non-Newtonian third-order liquid in the existence of Hall effect are examined and executed throughout this academic article. The wet-on-wet (WOW) coating process is used in the research. The fourth Runge–Kutta–Fehlberg algorithm is used to computationally solve the governing equations which dictate the movement of fluid inside the container. In this research, the RK4-Fehlberg algorithm is applied to get numerical results for a list of nonlinear ordinary differential equations (ODEs) describing liquid motion. Pictorially, the contribution of regulating variables on velocity and temperature profiles is examined. It is observed that the velocity profile enhances as the viscoelastic parameter increases and the velocity profile increases for both the non-Newtonian and Hall current increasing parameters in the presence and absence of magnetic parameter M . It is observed that the velocity of the fluid decreases with the increasing values of the Hartmann number m , Brinkman number Br , and magnetic parameter M . Furthermore, the temperature profile increase for B r Br , K , M , and opposite effect is observed for β \beta increases. The suggested approach is compared to homotopy analysis method (HAM) for verification purpose, and excellent agreement is obtained. In addition, as a restricted scenario, a connection is made with the existing literature.

This article analyzes some aeromagnetic filtering techniques for mitigating deceptive geophysical conceptions that may result in a distorted range of geological information from aeromagnetic data. The implication of using the aeromagnetic method, data processing, and enhancement to distinguish sediment-produced anomalies was considered. Two methods to locate buried faults in aeromagnetic data were compared: Edge and fault detection were considered using the magnetic contrast and horizontal gradient methods, whereas rapid depth estimation was considered using the Euler deconvolution method and Signum method. The general challenge to find the magnetic anomaly depth and delineate edges relies on geophysical filtering techniques discussed in order to maintain its geological relevance. The magnetic-contrast layer model signatures help clarify the existence of intra-sedimentary faults. The horizontal gradient approach relative to other derivative methods has better noise stability and fast adaptation to grids without modifying parameters. However, the Signum transform (ST) approach offers a more special solution in depth estimation than the Euler’s deconvolution approach whose solution relies on the required choice of default shape parameters and windows. The Euler deconvolution procedure may not be able to detect structures found by the ST approach and vice versa . As a result, these techniques may be used in conjunction with one another during analysis, as complementary interpretation tools. This review will however aid in the analysis of information used as a criterion for determining faults using various analytical techniques like ST or Euler deconvolution.

Compartmental modelling refers to modelling the transport of substances in a system consisting of multiple compartments, which is characterized by the transfer rates among the relevant compartments. In a generalized compartmental system, recycling of substances among the compartments is allowed. Compartmental modelling is a generic technique which is needed in many branches of applied physics. The most challenging task is to determine the transfer rates. The present work described the use of the Hooke and Jeeves (HJ) derivative free direct search method in determining the transfer rates to construct a multi-compartmental model with recycling among the compartments. The use of a direct search method ensures the applicability of the model to functions which are not continuous or differentiable. The present model was successfully validated using previously reported experimental data for distribution of trace elements in four compartments in an animal.

Many researchers numerically investigated U-tube underground heat exchanger using a two-dimensional simplified pipe. However, a simplified model results in large errors compared to the data from construction sites. This research is carried out using a three-dimensional full-size model. A model validation is conducted by comparing with experimental data in summer. This article investigates the effects of fluid velocity and buried depth on the heat exchange rate in a vertical U-tube underground heat exchanger based on fluid–structure coupled simulations. Compared with the results at a flow rate of 0.4 m/s, the results of this research show that the heat transfer per buried depth at 1.0 m/s increases by 123.34%. With the increase of the buried depth from 80 to 140 m, the heat transfer per unit depth decreases by 9.72%.

Knocking becomes an increasingly important issue in direct injection natural gas engines with the application of new combustion modes. In this article, the knocking characteristics of natural gas engine operating in stratified combustion mode were studied with the aid of cylinder pressure oscillations and combustion parameters. The results indicated that knocking tendency will be stronger when operating in stratified combustion mode. The first to the fourth circumferential modes and the first radial mode are the featured modes for knocking behavior, while knocking is more serious when the duration of 10–50% of total energy released is shorter.

ZnO–water nanofluid in an inner pipe was experimentally investigated to improve the thermal efficiency of double-pipe heat exchangers. In this work, a 57.6% increase in the Nusselt number was obtained at Re = 14,340 when the ZnO–water nanofluid flowed through a helically corrugated tube. It was found that helical corrugation played a more important role in heat transfer enhancement than thermophysical properties of the nanofluid at the Reynolds number below 10,221. In addition, with the increase of the Reynolds number, the advantages of nanofluids in thermal performance become obvious, and Nusselt numbers increase by 28.5 and 30.6% with the effects of helical corrugation and ZnO–nanofluid, respectively, at Re = 14,349.

The aim of this article was to address the lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation with the aid of Hirota bilinear technique. This model concerns in a massive nematic liquid crystal director field. By choosing the function f in Hirota bilinear form, as the general quadratic function, trigonometric function and exponential function along with appropriate set of parameters, we find the lump, lump-one stripe, multiwave and breather solutions successfully. We also interpreted some three-dimensional and contour profiles to anticipate the wave dynamics. These newly obtained solutions have some arbitrary constants and so can be applicable to explain diversity in qualitative features of wave phenomena.

In the present study, two new classes of convex functions are established with the aid of Raina’s function, which is known as the ψ - s -convex and ψ -quasi-convex functions. As a result, some refinements of the Hermite–Hadamard ( ℋℋ {\mathcal{ {\mathcal H} {\mathcal H} }} )-type inequalities regarding our proposed technique are derived via generalized ψ -quasi-convex and generalized ψ - s -convex functions. Considering an identity, several new inequalities connected to the ℋℋ {\mathcal{ {\mathcal H} {\mathcal H} }} type for twice differentiable functions for the aforesaid classes are derived. The consequences elaborated here, being very broad, are figured out to be dedicated to recapturing some known results. Appropriate links of the numerous outcomes apprehended here with those connecting comparatively with classical quasi-convex functions are also specified. Finally, the proposed study also allows the description of a process analogous to the initial and final condition description used by quantum mechanics and special relativity theory.

In this analysis, the baffling method is used to increase the efficiency of channel heat exchangers (CHEs). The present CFD (computational fluid dynamics)-based work aims to analyze the constant property, steady, turbulent, Newtonian, and incompressible fluid flow (air), in the presence of transverse-section, arc-shaped vortex generators (VGs) with two various geometrical models, i.e., arc towards the inlet section (called arc-upstream) and arc towards the outlet section (called arc-downstream), attached to the hot lower wall, in an in-line situation, through a horizontal duct. For the investigated range of Reynolds number (from 12,000 to 32,000), the order of the thermal exchange and pressure loss went from 1.599–3.309 to 3.667–21.103 times, respectively, over the values obtained with the unbaffled exchanger. The arc-downstream configuration proved its superiority in terms of thermal exchange rate by about 14% than the other shape of baffle. Due to ability to produce strong flows, the arc-downstream baffle has given the highest outlet bulk temperature.

In this study, we propose a simple direct meshless scheme based on the Gaussian radial basis function for the one-dimensional linear and nonlinear convection–diffusion problems, which frequently occur in physical phenomena. This is fulfilled by constructing a simple ‘anisotropic’ space–time Gaussian radial basis function. According to the proposed scheme, there is no need to remove time-dependent variables during the whole solution process, which leads it to a really meshless method. The suggested meshless method is implemented to the challenging convection–diffusion problems in a direct way with ease. Numerical results show that the proposed meshless method is simple, accurate, stable, easy-to-program and efficient for both linear and nonlinear convection–diffusion equation with different values of Péclet number. To assess the accuracy absolute error, average absolute error and root-mean-square error are used.

The symbolic computation with the ansatz function and the logarithmic transformation method are used to obtain a formula for certain exact solutions of the ( 3 + 1 ) \left(3+1) Zakharov–Kuznetsov (Z–K) equation. We use homoclinic breather, three waves method, and double exponential. There is a conflict of results with considerably known results, which indicates the solutions found in this study are new. By selecting appropriate parameter values, 3d representations are plotted to establish W-shaped, multi-peak, and kinky breathers solutions.

In this article, the sine-Gordon expansion method is employed to find some new traveling wave solutions to the nonlinear Schrödinger equation with the coefficients of both group velocity dispersion and second-order spatiotemporal dispersion. The nonlinear model is reduced to an ordinary differential equation by introducing an intelligible wave transformation. A set of new exact solutions are observed corresponding to various parameters. These novel soliton solutions are depicted in figures, revealing the new physical behavior of the acquired solutions. The method proves its ability to provide good new approximate solutions with some applications in science. Moreover, the associated solution of the presented method can be extended to solve more complex models.

In this article, the generalized plane Couette flow of Vogel’s model of incompressible, non-isothermal, couple stress fluid flowing steadily between two parallel walls is investigated. The governing equations are reduced to ordinary differential equations. To investigate the non-linear coupled system of differential equations, the optimal homotopy asymptotic method with DJ polynomial and asymptotic homotopy perturbation method have been used. Important flow properties are presented and discussed. We have obtained expressions for velocity, average velocity, shear stress, volume flux and temperature. The results gained employing these techniques are in the form of infinite series; thus, the results can be easily calculated. Comparison of various results, obtained through the suggested approaches, is carried out and an excellent agreement is achieved.

This article proposes a new approach based on quantum calculus framework employing novel classes of higher order strongly generalized Ψ \Psi -convex and quasi-convex functions. Certain pivotal inequalities of Simpson-type to estimate innovative variants under the q ˇ 1 , q ˇ 2 {\check{q}}_{1},{\check{q}}_{2} -integral and derivative scheme that provides a series of variants correlate with the special Raina’s functions. Meanwhile, a q ˇ 1 , q ˇ 2 {\check{q}}_{1},{\check{q}}_{2} -integral identity is presented, and new theorems with novel strategies are provided. As an application viewpoint, we tend to illustrate two-variable q ˇ 1 q ˇ 2 {\check{q}}_{1}{\check{q}}_{2} -integral identities and variants of Simpson-type in the sense of hypergeometric and Mittag–Leffler functions and prove the feasibility and relevance of the proposed approach. This approach is supposed to be reliable and versatile, opening up new avenues for the application of classical and quantum physics to real-world anomalies.

In this article, contact problem with fractional derivatives is studied. We use fractional derivative in the sense of Caputo. We deploy penalty function method to degenerate the obstacle problem into a system of fractional boundary value problems (FBVPs). The series solution of this system of FBVPs is acquired by using the variational iteration method (VIM). The performance as well as precision of the applied method is gauged by means of significant numerical tests. We further study the convergence and residual errors of the solutions by giving variation to the fractional parameter, and graphically present the solutions and residual errors accordingly. The outcomes thus obtained witness the high effectiveness of VIM for solving FBVPs.

In this article, a new generalized exponential rational function method (GERFM) is employed to extract new solitary wave solutions for the ionic currents along microtubules dynamical equations, which is very interested in nanobiosciences. In this article, the stability of the solutions is also studied. As a result, a variety of solitary waves are obtained with free parameters such as periodic wave solution and dark and bright solitary wave solutions. The solutions are plotted and used to describe physical phenomena of the problem. The work shows the power of GERFM. We found that the proposed method is reliable and effective and gives analytical and exact solutions.

In the past few decades, many models have been proposed to address the shortcomings found in the classical theories of thermoelasticity and to allow limited speeds of heat waves. In this context, in the current paper a new generalized model of thermoelasticity based on the Moore–Gibson–Thompson (MGT) equation has been introduced. This new model can be derived by introducing the relaxation time factor into the third type of Green–Naghdi model (GN-III). In contrast to the previous works, it was taken into account that the physical properties of the material are dependent on temperature and on the viscous type. The viscoelastic medium has been assumed to obey the Kelvin–Voigt model. On the basis of the present model, thermo-viscoelastic interactions have been investigated in an unbounded orthotropic body with a cylindrical cavity. The surface of the cavity is restricted and exposed to a pulse-formed heat flow that dissolves exponentially. The characteristic thermal modulus of the material is assumed to be a linear function of temperature. The Laplace transform can be used to eliminate time dependency from control equations. Using a suitable approximate method, the transformed equations have been finally inverted by numerical inversion of the Laplace transform. Certain comparisons have been introduced to estimate the effects of the viscosity, pulsed heat, and thermal temperature-independent properties on all studied fields. A comparison with previous models of thermoelasticity is also performed in tables to verify the accuracy of the proposed model. We found from the results that the physical fields strongly depend on the viscoelastic parameter, the change of the thermal conductivity, and pulsed heat, so it is not possible to neglect their effect on the manufacturing process of machines and devices.

In a microscopic model of the photoelectric effect, it becomes clear that the conservation of energy is exclusively determined by Doppler shift processes, i.e. , the whole energy of the photon vanishes by means of Doppler redshifts. Accordingly, if a photon is generated, the energy is won by Doppler blueshifts. This is supposed to be valid for all processes with energy conservation. An experiment is carried out to make this Doppler energy flow visible by means of interactions with probes. The result of this experiment is that a weak force is measurable in the vicinity of processes with energy conservation. With the aid of a twisted rubber-driven low-power device ( P ˜ = 10 W \tilde{P}=10\hspace{.5em}\text{W} ), periodic accelerations and decelerations of about 10 −6  m/s 2 are measurable. In the close vicinity of the device, accelerations with values up to 10 −3  m/s 2 can be concluded. The consequences that result from this force are discussed.

This article studies the fifth-order KdV (5KdV) hierarchy integrable equation, which arises naturally in the modeling of numerous wave phenomena such as the propagation of shallow water waves over a flat surface, gravity–capillary waves, and magneto-sound propagation in plasma. Two innovative integration norms, namely, the G ′ G 2 \left(\frac{{G}^{^{\prime} }}{{G}^{2}}\right) -expansion and ansatz approaches, are used to secure the exact soliton solutions of the 5KdV type equations in the shapes of hyperbolic, singular, singular periodic, shock, shock-singular, solitary wave, and rational solutions. The constraint conditions of the achieved solutions are also presented. Besides, by selecting appropriate criteria, the actual portrayal of certain obtained results is sorted out graphically in three-dimensional, two-dimensional, and contour graphs. The results suggest that the procedures used are concise, direct, and efficient, and that they can be applied to more complex nonlinear phenomena.

This study aims to investigate heat transfer and flow characteristics of ethylene glycol/water (EGW) and CuO–EGW nanofluids in circular tubes with and without trapezoid ribs. Nusselt number and friction factor in tubes with trapezoid ribs are analysed under a constant heat flux by changing rib bottom angles. This study compares the convective heat transfer coefficients of 6 vol.% CuO–EGW nanofluid and base fluid. It is found that under a constant Reynolds number, the Nusselt number and friction factor for CuO–EGW nanofluid and base fluid increase with an increase in the inclination angle. The Nusselt number for the CuO–EGW nanofluid in the tube with 75° rib bottom angle averagely increases by 135.8% compared to that in the smooth tube, and the performance evaluation criterion is 1.64.

This work focuses on the heat transfer and flow characteristics with the different placement of the multi-deck display cabinet and tries to optimize the placement position of refrigerated display cabinet. First, the temperature distribution in a refrigerated display cabinet was experimentally investigated. The result showed that the food temperature in front is 3.6–4.8°C higher than back row of the same layer, and temperature fluctuation of 0.3–0.7°C less than the back row. Then, a three-dimensional numerical model of the display cabinet was established, and the k – ε model is employed to compare and analyze the heat transfer and air curtain characteristics. The results show that the placement methods have great influence on the performance of the display cabinet. The face-to-back placement method can acquire a better food refrigeration performance, and the food temperature of the face-to-back placement method is 0.3–0.5°C lower than that of the face-to-face placement method.

Thermal performance prediction with high precision and low cost is always the need for designers of heat exchangers. Three typical design of experiments (DOE) known as Taguchi design method (TDM), Uniform design method (UDM), and Response surface method (RSM) are commonly used to reduce experimental cost. The radial basis function artificial neural network (RBF) based on different DOE is used to predict the thermal performance of two new parallel-flow shell and tube heat exchangers. The applicability and expense of ten different prediction methods (RBF + TDML9, RBF + TDML18, RBF + UDM, RBF + TDML9 + UDM, RBF + TDML18 + UDM, RBF + RSM, RBF + RSM + TDML9, RBF + RSM + TDML18, RBF + RSM + UDM, RSM) are discussed. The results show that the RBF + RSM is a very efficient method for the precise prediction of thermal-hydraulic performance: the minimum error is 2.17% for Nu and 5.30% for f . For RBF, it is not true that the more of train data, the more precision of the prediction. The parameter “spread” of RBF should be adjusted to optimize the prediction results. The prediction using RSM only can also obtain a good balance between precision and time cost with a maximum prediction error of 14.52%.

To further improve the thermal efficiency of diesel engines, a waste heat recovery system model utilizing organic Rankine cycle (ORC) is constructed and verified through system bench test and heat exchanger bench test. To recover waste heat from diesel engine exhaust, ethanol, cyclopentane, cyclohexane, R1233zd (E), and R245fa were selected for comparison. The quality of heat source, the quality of evaporator, the system output, and the system complicity were taken as variables for comparison. Analysis shows that for ORC systems without recuperator, ethanol system has the best system output of the five in a wide operation temper range, with the highest exergy efficiency of 24.1%, yet the exergy efficiency increase after the application of recuperator, 9.0%, is limited. For low temperature exhaust, cyclopentane system has the best performance with or without recuperator, and the cyclopentane system with recuperator has the best performance in terms of exergy efficiency, 27.6%, though complex heat exchangers are also required for high power output. The system output of the R1233zd system is better than the R245fa system, yet the advantage of low evaporate temperature can be better utilized for low quality waste heat recovery.

The load of the showcase is a nonlinear and unstable time series data, and the traditional forecasting method is not applicable. Deep learning algorithms are introduced to predict the load of the showcase. Based on the CEEMD–IPSO–LSTM combination algorithm, this paper builds a refrigerated display cabinet load forecasting model. Compared with the forecast results of other models, it finally proves that the CEEMD–IPSO–LSTM model has the highest load forecasting accuracy, and the model’s determination coefficient is 0.9105, which is obviously excellent. Compared with other models, the model constructed in this paper can predict the load of showcases, which can provide a reference for energy saving and consumption reduction of display cabinet.

The increasing demand of cooling in internal combustion engine (ICE) may require the shift of heat removal method from traditional single phase liquid convection to subcooled flow boiling in order to fulfill the desired functional temperature. Thus, the characteristics of subcooled flow boiling heat transfer should be studied exclusively considering the practical conditions in ICEs. Accordingly, in this article, subcooled flow boiling experiments were conducted in a rectangular channel using 50/50 volume mixture of ethylene glycol and water coolant (EG/W) as working fluid. Aluminum and cast iron surfaces were selected as the heated surfaces to simulate the material of cylinder head in gasoline and diesel engines, respectively. Experimental results showed a trend that the aluminum surface had a better performance than the cast iron surface in terms of heat transfer coefficient in the boiling region. The difference between these two surfaces was concluded as results of different surface thermophysical properties. A modified wall heat flux model was proposed based on the power-type addition method. The proposed model modified the nucleation boiling contribution by introducing a new parameter which accounts for the influence of thermophysical properties of heated surface on the boiling process. Thus, one such modified model could be useful for practical engine cooling applications.

Based on the first principle, this paper studies the optical properties of Ni, Mo, CoO, and Cr 2 O 3 according to the Materials Studio software. It is found that the absorptivity of Ni is low, while Ni has low emissivity. Hence, it can be used to reduce emissivity. The absorption rate of CoO is very high. Therefore, Ni and CoO are very suitable to be composed to make a solar selective absorption coating with high absorptivity and low emissivity. The mass ratio of Ni and CoO has a greater impact on the optical properties of the composite material, so the absorption–emission ratios of the composite material Ni–CoO at different mass ratios are calculated. The absorption–emission ratio is the highest when the mass ratio is 1:1, and the performance is the best, which is in good agreement with the result of the experiment. And we hope that our method will provide some help for the study of solar selective absorption composite coatings.

The aim of this study was to reveal the internal mechanism of enhanced condensation heat transfer, by experimentally performing steam condensation with higher inlet velocity in the horizontal multi-start helical channels (HMSHCs), and investigating the influences of pressure of steam, mass flowrate of cooling water, and mass fraction of noncondensable (NC) gas on steam condensation performance. Taking steam condensation in horizontal circular condensation channel (HCCC) as a reference, the condensation heat transfer coefficients (CHTCs), the outlet condensate mass flowrates (CMFRs), and the total steam condensation pressure drops (SCPDs) were compared and discussed, respectively. The results indicated that NC gas had a strong inhibitory effect on steam condensation, and average condensation characteristics decreased with the increase in NC gas fraction for lower Re m . But for higher Re m , the gas–liquid interfacial shearing stress can likely weaken the negative effect of NC gas. In addition, increasing the cooling water flowrate can entirety promote steam condensation. The comparison results indicated that steam condensation performance of HMSHC is better than that of HCCC under same experimental conditions. For the specific experimental scope, the average CHTCs and the outlet CMFRs in HMSHC are approximately 2.35 and 1.25 times of that inside HCCC, respectively, while the overall SCPDs in HMSHC are about 1.16 times of that inside HCCC. After introducing the performance evaluation factor, the calculation results revealed that the performance evaluation factor h PEC {h}_{\text{PEC}} of the average CHTCs in HMSHC is approximately 2.02, and the performance evaluation factor m PEC {{m}}_{\text{PEC}} of the outlet CMFRs in HMSHC is approximately 1.08. The two evaluating values are reasonable.

In this article, thin film flow of non-Newtonian pseudo-plastic fluid is investigated on a vertical wall through homotopy-based scheme along with fractional calculus. Three cases were examined after considering (i) partial fractional differential equation (PFDE) by altering first-order derivative to fractional derivative in the interval (0, 1), (ii) PFDE by altering second-order derivative to fractional derivative in the interval (1, 2), and (iii) fully FDE by altering first-order derivative to fractional derivative in (0, 1) and second-order derivative to fractional derivative in (1, 2). Different physical quantities such as the velocity profile and volume flux were computed and analyzed. Validity of obtained results was checked by finding residuals. Moreover, consequence of different parameters on the velocity were also explored in fractional space.

In this article, a hybrid Haar wavelet collocation method (HWCM) is proposed for the ill-posed inverse problem with unknown source control parameters. Applying numerical techniques to such problems is a challenging task due to the presence of nonlinear terms, unknown control parameter sources along the solution inside the given region. To find the numerical solution, derivatives are discretized adopting implicit finite-difference scheme and Haar wavelets. The computational stability and theoretical rate of convergence of the proposed HWCM are discussed in detail. Two numerical experiments are incorporated to show the well-condition behavior of the matrix obtained from HWCM and hence not required to supplement some regularization procedures. Moreover, the numerical solutions of the considered experiments illustrate the reliability, suitability, and correctness of HWCM.

This article investigates the dynamical and physical behavior of the second positive member in a new, utterly integrable hierarchy. This investigation depends on constructing novel analytical and approximate solutions to the Qiao model. The model’s name is after the researcher who derived the mathematical formula of it in 2007. This model possesses a Lax representation and bi-Hamiltonian structure. This study employs the unified and variational iteration (VI) method to obtain analytical and numerical solutions to the considered model. The obtained analytical solutions are used to calculate the necessary conditions for applying the suggested numerical method that makes checking the obtained solutions’ accuracy a valuable option. The obtained solutions are sketched in different techniques to explain more physical and dynamics details of the Qiao model and show the matching between obtained solutions.

This work deals the construction of novel soliton solutions to the Atangana–Baleanu (AB) fractional system of equations for the ion sound and Langmuir waves by using Sardar-subequation method (SSM). The outcomes are in the form of bright, singular, dark and combo soliton solutions. These solutions have wide applications in the arena of optoelectronics and wave propagation. The bright solitons will be a vast advantage in controlling the soliton disorder, dark solitons are also beneficial for soliton communication when a background wave exists and singular solitons only elaborate the shape of solitons and show a total spectrum of soliton solutions created from the model. These results would be very helpful to study and understand the physical phenomena in nonlinear optics. The performance of the SSM shows that this is powerful, talented, suitable and direct technique to discover the exact solutions for a number of nonlinear fractional models.

The oscillation of nonlinear differential equations is used in many applications of mathematical physics, biological and medical physics, engineering, aviation, complex networks, sociophysics and econophysics. The goal of this study is to create some new oscillation criteria for fourth-order differential equations with delay and advanced terms ( a 1 ( x ) ( w ‴ ( x ) ) n ) ′ + ∑ j = 1 r β j ( x ) w k ( γ j ( x ) ) = 0 , {({a}_{1}(x){({w}^{\prime\prime\prime }(x))}^{n})}^{^{\prime} }+\mathop{\sum }\limits_{j=1}^{r}{\beta }_{j}(x){w}^{k}({\gamma }_{j}(x))=0, and ( a 1 ( x ) ( w ‴ ( x ) ) n ) ′ + a 2 ( x ) h ( w ‴ ( x ) ) + β ( x ) f ( w ( γ ( x ) ) ) = 0 . {({a}_{1}(x){({w}^{\prime\prime\prime }(x))}^{n})}^{^{\prime} }+{a}_{2}(x)h({w}^{\prime\prime\prime }(x))+\beta (x)f(w(\gamma (x)))=0. The method is based on the use of the comparison technique and Riccati method to obtain these criteria. These conditions complement and extend some of the results published on this topic. Two examples are provided to prove the efficiency of the main results.

This article proposes and analyzes a fractional-order susceptible, infectious, susceptible (SIS) epidemic model with saturated treatment and disease transmission by employing four recent analytical techniques along with a novel fractional operator. This model is computationally handled by extended simplest equation method, sech–tanh expansion method, modified Khater method, and modified Kudryashov method. The results’ stable characterization is investigated through the Hamiltonian system’s properties. The analytical solutions are demonstrated through several numerical simulations.

For the stochastic heat equation (SHE), a very accurate spectral method is considered. To solve the SHE, we suggest using a shifted Legendre Gauss–Lobatto collocation approach in combination with a shifted Legendre Gauss–Radau collocation technique. A comprehensive theoretical formulation is offered, together with numerical examples, to demonstrate the technique’s performance and competency. The scheme’s superiority in tackling the SHE is demonstrated.

Magnesium alloy will decrease strength with corrosion in use, thus affecting their service life. Service life as a structural material under stress and corrosion is one focus of the magnesium alloy used as structural material, and how to improve the residual service life of magnesium alloy is an important scientific issue. The X-ray diffraction, scanning electron microscopy, and slow strain rate tensile (SSRT) tests are used to study the residual service life of erbium (Er) effect in the AM50 magnesium alloy in air, distilled water, and NaCl solution. The results show that after rare earth Er addition to the AM50, the white granular Al 3 Er intermetallic compound was formed. With Er content increasing, the quantity of Al 3 Er phase was increased and the volume of β-Mg 17 Al 12 phase was decreased. The SSRT results show that residual service life ratio increased with the Er addition compare with no Er alloy in distilled water. However, in 3.5% NaCl solution, 0.5% Er alloy shows the best service life. Moreover, Er addition does not change the alloy fracture mode, which remains quasi-cleavage. The main cause of the decline in service life in magnesium alloys is the change in surface morphology owing to the pitting corrosion nucleation and growth, which affects the stress distribution of the sample. The mechanism of film cracking plays a major role in the fracture process with the Er increased to change the surface morphologies.

The shallow water wave model is one of the completely integrable models illustrating many physical problems. In this article, we investigate new exact wave structures to Kadomtsev–Petviashvili–Benjamin–Bona–Mahony and the Benney–Luke equations which explain the behavior of waves in shallow water. The exact structures are expressed in the shapes of hyperbolic, singular periodic, rational as well as solitary, singular, shock, shock-singular solutions. An efficient computational strategy namely modified direct algebraic method is employed to construct the different shapes of wave structures. Moreover, by fixing parameters, the graphical representations of some solutions are plotted in terms of three-dimensional, two-dimensional and contour plots, which explain the physical movement of the attained results. The accomplished results show that the applied computational technique is valid, proficient, concise and can be applied in more complicated phenomena.

This paper aims to examine the heat and mass characteristics for thermally stratified chemically heated, dissipative flow under the cross-diffusion and imposed Lorentz forces. A self-similar model is obtained employing suitable similarity transformations. Then, the RK technique is used for mathematical analysis. The stimulations of pertinent physical quantities in the flow regimes, shear stresses, and the Nusselt number were examined graphically. It is noted that more radiative flow favors the thermal behavior of the fluid and increases in the Prandtl number causes the decrease in thermal characteristics. Moreover, decreases in mass characteristics were examined by the fluctuating chemical reaction and Schmidt parameters. Lastly, key outcomes of the work are pinpointed.