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Objective: Centrifugal pendulum vibration absorbers (CPVAs) are efficient devices for reducing torsional vibrations in rotating machinery. This study focuses on a circular-path unifilar CPVA and investigates its nonlinear behavior. Methods: A multibody dynamics (MBD) model of a CPVA-rotor system with two rotors was developed. The system's nonlinear behavior was analyzed using the shooting method to ensure model accuracy. Time integration results were used to validate the shooting method's outcomes. Frequency response analysis was conducted across a range of rotational speeds, including critical speeds, to evaluate the CPVA's vibration suppression performance. Results: The combination of MBD and shooting methods proved effective in analyzing the CPVA-rotor system with high accuracy. The study investigated the effects of varying the CPVA's radius of gyration while keeping mass constant. It was observed that small CPVA inertia or large excitation amplitudes could lead to saddle-node bifurcation, resulting in jump phenomena and large amplitude vibrations. Ranges of radius length and excitation amplitudes that prevent bifurcation were identified. Experimental results corroborated the numerical findings, including the observed frequency responses and bifurcation points. Conclusions: The combination of MBD and shooting methods offers an innovative approach for accurate CPVA system analysis. The study demonstrates the significant effect of CPVA inertia on vibration suppression performance. Experimental validation confirms the numerical analysis results, ensuring their reliability. [ABSTRACT FROM AUTHOR]

The purpose of this work is to propose a new efficient initial guess algorithm rather than the conventional Newton method to meet the adjoint terminal conditions, rapidly. Thus, the focus of this paper is to use better algorithms for obtaining refined initial guesses with shooting method to solve the coupled boundary value problems. The boundary value problem is formulated as a system of equations i.e. initial value problems with one unknown initial condition. The efficiency and accuracy of the Shooting method is enhanced by improving the initial guess and then solving the problem iteratively. [ABSTRACT FROM AUTHOR]

This paper presents a novel framework combining proper generalized decomposition (PGD) with the shooting method to determine the steady-state response of nonlinear dynamical systems upon a general periodic input. The proposed PGD approximates the response as a low-rank separated representation of the spatial and temporal dimensions. The Galerkin projection is employed to formulate the subproblem for each dimension, then the fixed-point iteration is applied. The subproblem for the spatial vector can be regarded as computing a set of reduced-order basis vectors, and the shooting problem projected onto the subspace spanned by these basis vectors is defined to obtain the temporal coefficients. From this procedure, the proposed framework replaces the complex nonlinear time integration of the full-order model with the series of solving simple iterative subproblems. The proposed framework is validated through two descriptive numerical examples considering the conventional linear normal mode method for comparison. The results show that the proposed shooting method based on PGD can accurately capture nonlinear characteristics within 10 modes, whereas linear modes cannot easily approximate these behaviors. In terms of computational efficiency, the proposed method enables CPU time savings of about one order of magnitude compared with the conventional shooting methods. [ABSTRACT FROM AUTHOR]

【Objective】The emergence of new technologies is driving the continuous improvement of fiber optic communication capacity, which poses new requirements for the working wavelength range of fiber amplifiers. Therefore, there is an urgent need for fiber amplifiers that can achieve ultra wideband amplification.【Methods】In order to achieve ultra wideband Raman Fiber Amplifier (RFA) with gain ranges covering Super-C and Super-L bands, a transmission model of RFA was theoretically established, and numerical solutions for the transmission model of backward RFA were introduced. The pump power and wavelength range were selected considering the actual situation. Six pump wavelengths and seven pump lasers were used to simulate an optimized set of pump wavelength configurations in G.652 fiber. Based on the configuration of these pump wavelengths, experimental tests were conducted on three types of fibers: G.652, G.654, and Large Effective Area Fiber (LEAF). The simulation and experimental results were compared and analyzed.【Results】The results show that a net gain of 18.07 dB and a gain flatness of 1.54 dB were obtained through testing in G.652 fiber. A net gain of 13.9 dB and a gain flatness of 1.21 dB were obtained through testing in G.654 fiber. A net gain of 21.99 dB and a gain flatness of 1.80 dB were tested in LEAF. The difference between the simulation results and the test results is less than 0.2 dB, and the difference in gain flatness is less than 0.4 dB.【Conclusion】The comparison between simulation results and test results indicates that the numerical solution method used in this paper can accurately predict the gain spectrum of RFA. The pump wavelength configuration used in this article has been experimentally verified to have significant gain and good gain flatness among the three types of fibers, which has reference value for wavelength selection in commercial ultra wideband RFA.

The modern research aims to explore the influence of free stream flow on the motion of MHD Non-Newtonian nanofluid through a permeable extending surface in a three-dimensional domain. The primary goal of this research is to examine the significance of distinct fluid parameters, including Casson fluid parameter ß, free stream velocity parameter λ, Brownian motion parameter Nb, magnetic parameter M, Prandtl number Pr, thermophoresis parameter Nt, Lewis number Le on distribution of velocity, concentration of nanoparticle and temperature. When similarity variables are incorporated into the set of governing partial differential equations, the equations are modified into a set of ordinary differential equations. Runge-Kutta fourth order is employed with the help of shooting approach in order to achieve the computational approach of the model that has been reduced. Numerical values of physical characteristics, like that the Nusselt number, the Sherwood number, and skin friction, have been assessed contrary to numerous parameters and disclosed in tables for the subject of engineering. Results for distribution of temperature, velocity and concentration of nanoparticles are explored in detail, including their rate of convergence. The principal results of the research revealed that the influence of both Casson fluid and magnetic parameter on the distribution of velocity exhibits a pattern of decline. Additionally, the effects of Brownian motion parameter on temperature demonstrate a rising pattern, while its impact on concentration distribution shows a diminishing trend. The use of permeable materials has shown that the heat transport process along an expanding surface prevents thermal loss and promotes the cooling process, which is a significant outcome of the study. The findings of this research have numerous applications in biomedical engineering and are useful for the analysis of fluids that are not Newtonian under various conditions. The recent study in the three-dimensional extending region is important for the development of novel industrial processes involving nanoparticles and the idea of magnetohydrodynamics flow of non-Newtonian fluids in existence of free stream flow. [ABSTRACT FROM AUTHOR]

The current manuscript aims to present an efficient numerical technique for solving third-order reaction-diffusion singularly perturbed boundary-value problems. The method is based on coupling the restarted Adomian decomposition method and the shooting method. The study further provided a complete outline of the coupled numerical method and used it in tackling the governing class of third-order differential equations. The efficacy of the proposed method is demonstrated on test problems. Lastly, a high level of exactitude between the obtained approximate solution and the exact solution is achieved through comparison tables and figures. [ABSTRACT FROM AUTHOR]

The designation of this research is to scrutinize the influence of convective nanofluids over a three-dimensional exponential surface with chemical reactive species in a free stream fluid flow by following Buongiorno's model. The continuity, momentum, energy, concentration and motile microorganism density partial differential equations that make up the physical governing equation problems are simultaneously transformed into ordinary differential equations system. By using MATLAB programming, the RKF approach has been followed in order to implement the shooting technique to solve this system that explores how changing fluid parameters affect the profile of physical quantities of interest. A parametric analysis has been done in the current study. The effects of fluid parameters such as chemical reaction, Brownian motion, free stream velocity, Lewis number, thermophoresis, and Prandtl number on concentration, temperature, and velocity profiles are graphically represented. Moreover, Contour plots are also drawn against computational fluid parameters to get desired results. Furthermore, calculated results are correlated with already existing outcomes along with residual error. It is inferred that; thermal and concentration fields increase for higher thermal and concentration Biot numbers serially. Additionally, it is found that skin friction coefficient declines with inclination in thermophoresis Nt (1.0 ≤ Nt ≤ 3.0) and Prandtl number Pr (1.0 ≤ Pr ≤ 4.0). The present investigation aims to support production businesses in achieving the desired level of quality of their products by effectively managing the transport phenomena. [ABSTRACT FROM AUTHOR]

In space, surface tension plays an important role and liquid behaviour is much different from that on the ground. The static capillary surfaces in the annular space between two coaxial cones under microgravity are studied in this paper. Theoretical expressions of the capillary surfaces are derived and a procedure is developed to predict the capillary surfaces based on the expressions. By considering various liquid contact angles, liquid volumes, and container geometries, numerical simulation with the volume of fluid method is carried out and microgravity experiments in Beijing Drop Tower are performed. The numerical and experimental results are in good agreement with theoretical predictions. Furthermore, capillary surfaces in an annulus with constant cross-section and in a spherical tank with a central column are also discussed. z ¯ 3 will decrease obviously with the increase of the liquid contact angle. The theoretical models and findings will be great helpful for liquid management in space and the evaluation of propellant residue. [ABSTRACT FROM AUTHOR]

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Ground state of the energy-critical Gross–Pitaevskii equation with a harmonic potential can be constructed variationally. It exists in a finite interval of the eigenvalue parameter. The supremum norm of the ground state vanishes at one end of this interval and diverges to infinity at the other end. We explore the shooting method in the limit of large norm to prove that the ground state is pointwise close to the Aubin–Talenti solution of the energy-critical wave equation in near field and to the confluent hypergeometric function in far field. The shooting method gives the precise dependence of the eigenvalue parameter versus the supremum norm. [ABSTRACT FROM AUTHOR]

In this work, we study the energy levels of electrons and holes of InAs quantum dots inside InP/InAs 0.25 P 0.75 /InP semiconductor nanowires. Taking into account the nonparabolicity of the dispersion law, the energy levels are calculated in two different ways. The change in the energy levels of a quantum dot at different positions inside a quantum nanowire is considered. The energy levels of semiconductor nanowire of various sizes are studied at a constant size. Changes in the energy levels of a quantum nanodot of a cubic shape are found when its size changes from 5 to 25 nm, located inside a quantum nanowire with a square section of 25 × 25 nm. [ABSTRACT FROM AUTHOR]

The current theoretical investigation focuses on the thermal behavior of a power-law nanofluid flow on a rotating circular disc. In which nanofluid is made by taking colloidal suspension of copper (Cu) and copper oxide (CuO) nanoparticles in a base fluid like water. A theoretical investigation is conducted by formulating a mathematical model of a power-law fluid (which exhibits shear thickening and thinning effects) along with the Tiwari and Das model. A similarity transformation is employed to transform the nonlinear partial differential equations (PDEs) into ordinary differential equations (ODEs) and these ODEs are then numerically solved using the shooting technique. The study's findings are analyzed graphically by plotting radial, tangential, and axial velocity profiles, temperature profiles, Nusselt number, and skin friction coefficients to show how various factors affect the fluid's flow and heat transfer. It is revealed that drag force reduces in Cu-water nanofluid as compared to CuO-water nanofluid for all types of fluids (Newtonian, pseudoplastic, and dilatant fluids) and Nusselt number becomes high in Cu-water nanofluid for both Newtonian and dilatant fluids as compared to CuO-water nanofluid but in case of pseudoplastic reverse behavior is observed. Heat transfer rate in Cu-water dilatant and pseudoplastic nanofluids increases up to 20.4 % and 12.5 % with respect to base fluid and in CuO-water dilatant and pseudoplastic water nanofluids, it increases up to 18.6 % and 15.2 %.

In this paper, we study the uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball in ℝ3$$ {\mathrm{\mathbb{R}}}^3 $$. Under suitable conditions, we prove that, for any given positive integer k$$ k $$, the problem we considered has at most one solution possessing exactly k−1$$ k-1 $$ nodes. Together with the results presented by Nagasaki [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (2): 211–232, 1989] and Tanaka [Proc. Roy. Soc. Edinburgh Sect. A. 138 (6): 1331–1343, 2008], we can prove that more types of nonlinear elliptic equations have the uniqueness of nodal radial solutions. [ABSTRACT FROM AUTHOR]

Most space shuttle fuel tanks use a center column to hold the Propellant Management Device (PMD). This paper analyzes the gas–liquid interface state in the tanks with a central column during microgravity experiments conducted in the Chinese Space Station. It launches an extended study to investigate the gas–liquid interface state under different gravity conditions. Using the perturbation method and boundary layer theory, we numerically calculated the morphology of the gas–liquid interface under varying gravity conditions based on the Young–Laplace equation. The results were then compared to those obtained from existing commercial software and were found to be consistent. Based on this, the study develops two types of calculation procedures. The first procedure generates the corresponding shape of the liquid surface by inputting the height of the liquid surface endpoints and the gravity level. The second procedure is based on the targeting method and generates the corresponding liquid surface by inputting the volume of the liquid in the storage tank and the gravity level. The procedures were used to analyze the variation of gas–liquid interface properties under different gravity conditions. This study offers theoretical support for liquid management in aerospace engineering fuel tanks. [ABSTRACT FROM AUTHOR]

In this research, we present an approach to identify variable characteristics of an inhomogeneous thermoelectroelastic radially polarized elongated hollow cylinder. The cylinder's thermomechanical characteristics depend on the radial coordinate. We consider two loading types for the cylinder—the mechanical and the thermal ones. The radial displacement is considered as the additional data collected on the outer cylinder's surface under the first type load, while the temperature measured over a certain time interval is considered for the second type load. The direct problem after non-dimensioning and applying the Laplace transform is solved by jointly applying the shooting method and the transform inversion based on expanding the actual space in terms of the shifted Legendre polynomials. The effect of the laws of change in variable characteristics on the input data values taken in the experiment is analyzed. A nonlinear inverse problem on the reconstruction of the cylinder's variable properties is formulated and solved on the basis of an iterative technique. The initial approximation is set in the class of positive bounded linear functions whose coefficients are determined from the condition of minimizing the residual functional. To find the corrections at each stage of the iterative process, the Fredholm integral equations of the first kind are solved by means of the Tikhonov method. A series of computational experiments on recovering one and two variable characteristics is conducted. The effect of coupling parameters and input noise on the reconstruction results is revealed. [ABSTRACT FROM AUTHOR]

The present analysis illustrates the ratification of chemically reactive tangent hyperbolic fluid owing to bidirectional stretchable sheet in the manifestation of heat and mass occurrence with nanoparticles. The phenomena of chemical diffusion, solar radiation with swimming microorganism, have been deliberated. For incentive of problem, the impact of joule heating with convective boundary conditions is investigated. The modeled set of PDEs of chemical reactive tangent hyperbolic nanofluid is mended into set of ODEs with the help of misappropriate similarity functions. Likewise, the resulting system of ODEs is numerically tackled with the help of computational MATLAB using bvp4c command via shooting approach. Further, the impressions of protuberant parameters such as Hartmann number M, Prandtl number Pr, Schmidt number Sc, power-law index n on fluid velocity, temperature, concentration, and density of microorganism distribution are scrutinized through graphs and tables. The inspiration of emerging parameters on physical quantities of interest involved in this study is discussed in form of tables. We renowned that the velocity curve power diminished for growing value of power law index n and Hartmann number M. The enhancement in the values of the thermal radiation Nr and Hartmann number M improved in temperature curve. Investigating the chemical reactive tangent hyperbolic nanofluid exhibited a notable 15% surge in thermal conductivity facilitated by Joule heating. Furthermore, motile micrograms on stretchable surfaces amplified heat transfer by 20%, showcasing promising advancements in enhancing heat transfer efficiency for various applications. [ABSTRACT FROM AUTHOR]

The vibrations of plate structures placed in a supersonic flow was considered. The undisturbed fluid flow was parallel to the plate. This type of problem is especially important in the aerospace industry, where it is named panel flutter. It has been noticed for a long time that panel flutter may be problematic at high speeds. In this article, two specific problems were treated: in the first one, the plate was in the form of an infinite strip and the flow was in the direction of its finite length. Rigid walls indefinitely extended from the sides of the plate. In the second problem, the plate was a finite rectangle and the flow was parallel to one of its sides. The rest of the plane of the rectangle was again rigid. The first problem was a limiting case of the second problem. The flow was modeled by piston theory, which assumes that the fluid pressure on the plate is proportional to its local slope. This approximation is widely used at high speeds (supersonic speeds in the range of M > 1), and reduces the interaction between the fluid flow and the vibrations of the plate to an additional term in the vibration equation. The resulting problem can be solved by assumed mode methods. In this study, the solution was also found by using the collocation method. The contribution of this study is the correlation between the flutter velocity and the other parameters of the plate. The main result is the flutter velocity of the free fluid flow under which the plate vibrations become unstable. Finally, simple expressions are proposed between the various non-dimensional parameters that allows for the quick estimation of the flutter velocity. These simple expressions were deduced by least squares fits to the computed flutter velocities. [ABSTRACT FROM AUTHOR]

For surfaces of revolution we prove the existence of infinitely many sign-changing rotationally symmetric solutions to a wide class of $ p $-Laplace-Beltrami equations with polynomial like nonlinearities. We combine the methods in [10] where the semilinear case $ (p = 2) $ with positive weight was studied with those in [5] and [6] where radial solutions to a $ p $-Laplacian Dirichlet problem in a ball was considered. Our equations lead to ordinary differential equations with two singularities and a sign changing weight function which leads to an initial value problem that may blow up in the region of definition of the equation. [ABSTRACT FROM AUTHOR]

This paper presents an accurate and efficient initialization strategy for modular multilevel converters (MMCs) based on the shooting method, a numerical technique aimed at deriving the periodic steady-state operating condition of any circuit. This technique is compatible with MMC models of different levels of detail and whose control scheme may include modulation strategies and capacitor voltage balancing algorithms. Electromagnetic transient simulations of the NORDIC32 power system modified by adding a high-voltage direct current link with 128-level MMCs prove that the proposed initialization strategy allows starting simulations close to steady-state, thereby significantly limiting initialization transients and their corresponding extra CPU time.

The present manuscript proposes a computational approach to efficiently tackle a class of two-point boundary value problems that features third-order nonlinear ordinary differential equations. Specifically, this approach is based upon a combination of the shooting method with a modification of the renowned Adomian decomposition method. The approach starts by transforming the governing BVP into two appropriate initial-value problems, and thereafter, solves the resulting IVPs recurrently. In addition, the application of this method to varied test models remains feasible—of course, this is supported by the competing Runge–Kutta method, among others, and reported through comparison plots and tables. [ABSTRACT FROM AUTHOR]

Different approaches are used to define the optimal path in terms of construction costs. Such problems in practice are usually solved by various heuristic procedures. To obtain a theoretically justified result, one can derive an integral cost functional under certain assumptions and use variational principles. Thus, the classical problem of the calculus of variations is obtained. The necessary condition for the minimum of such a functional has the form of an integrodifferential equation. This paper describes a numerical algorithm for solving this equation, which is based on the prominent shooting method, which has been studied in detail in the literature. Under additional assumptions, the existence of a solution is proved using Schauder's fixed point principle. The problem of the uniqueness of the solution is studied. A numerical example is provided. [ABSTRACT FROM AUTHOR]

We establish a priori bounds, existence and qualitative behaviour of positive radial solutions in annuli for a class of nonlinear systems driven by Pucci extremal operators and Lane-Emden coupling in the superlinear regime. Our approach is purely nonvariational. It is based on the shooting method, energy functionals, spectral properties, and on a suitable criteria for locating critical points in annular domains through the moving planes method that we also prove. [ABSTRACT FROM AUTHOR]

To investigate the consequence of thermophoresis and Brownian diffusion on convective boundary layer micropolar fluid flow over a stretching wedge-shaped surface. The effects of non-dimensional parameters namely coupling constant parameter (0.01 ≤ B1 ≤ 0.05), magnetic parameter (1.0 ≤ M ≤ 15.0), Grashof number (0.3 ≤ Gr ≤ 0.9), modified Grashof number (0.3 ≤ Gm ≤ 0.8), micropolar parameter (2.0 ≤ G2 ≤ 7.5), vortex viscosity constraint (0.02 ≤ G1 ≤ 0.2), Prandtl number (7.0 ≤ Pr ≤ 15.0), thermal radiation parameter (0.25 ≤ R ≤ 0.50), Brownian motion parameter (0.2 ≤ Nb ≤ 0.62), thermophoresis parameter (0.04 ≤ Nt ≤ 0.10), heat generation parameter (0.1 ≤ Q ≤ 0.5), Biot number (0.65 ≤ Bi ≤ 1.0), stretching parameter (0.2 ≤ A ≤ 0.5), Lewis number (3.0 ≤ Le ≤ 7.0), and chemical reaction parameter (0.2 ≤ K ≤ 0.7) on the steady MHD heat and mass transfer is investigated in the present study. The coupled non-linear partial differential equations are reduced into a set of non-linear ordinary differential equations employing similarity transformation. Furthermore, by using the Runge-Kutta method followed by the shooting technique, the transformed equations are solved. The main goal of this study is to investigate the numerical analysis of nanofluid flow within the boundary layer region with the effects of the microrotation parameter and velocity ratio parameter. The novelty of this paper is to propose a numerical method for solving third-order ordinary differential equations that include both linear and nonlinear terms. To understand the physical significance of this work, numerical analyses and tabular displays of the skin friction coefficient, Nusselt number, and Sherwood number are shown. The new approach of the present study contributes significantly to the understanding of numerical solutions to nonlinear differential equations in fluid mechanics and micropolar fluid flow. Micropolar fluids are becoming even more of a focus due to the desire for engineering applications in various fields of medical, mechanical engineering, and chemical processing. [ABSTRACT FROM AUTHOR]

Satellite constellation deployment is a cohesive mission where the trajectories of satellites must be planned concurrently. This paper presents an Integrated Program for Optimal Deployment of a Satellite Constellation (PODSC) consisting of m non-identical satellites in any desired arrangement in n orbital planes. The PODSC can optimize the scheduling of mission timelines, ensuring effective coordination with the trajectory of each satellite. This involves meticulous planning that considers temporal constraints and regards collision avoidance constraint. Additionally, the PODSC can select the most favorable deployment strategy, considering the trade-offs between time and fuel consumption across all possible deployment methods. The PODSC also utilizes an innovative Perturbed Multi-impulsive Inclined transfer trajectory Amalgamated with a modified Lambert targeting problem (PMIAL). The main idea of designing the mentioned maneuver is to eliminate the defects of the Lambert Targeting Problem (LTP). The LTP cannot account for space perturbations. Moreover, the LTP faces challenges when attempting to align the transfer trajectory tangentially with the final orbit in situations where there exists a substantial disparity in inclination and right ascension between the initial and final orbits. The PMIAL establishes three consecutive steps to fix the mentioned defects. Balancing the trade-off between time and achieving optimal fuel consumption will be possible by applying a hybrid IWO/PSO (The hybrid Invasive Weed Optimization/Particle Swarm Optimization) optimization algorithm in both PMIAL and PODSC. The case study will involve simulating two constellation deployment missions, with a particular focus on considering the Earth's oblateness as a notable perturbation; however, the proposed algorithms can consider any space perturbations. [ABSTRACT FROM AUTHOR]

In this study, we numerically solve a class of two-point boundary-value-problems with a Riemann-Liouville-Caputo fractional derivative, where the solution might contain a weak singularity. Using the shooting technique based on the secant iterative approach, the boundary value problem is first transformed into an initial value problem, and the initial value problem is then converted into an analogous integral equation. The functions contained in the fractional integral are finally approximated using linear interpolation. An adaptive mesh is produced by equidistributing a monitor function in order to capture the singularity of the solution. A modified Gronwall inequality is used to establish the stability of the numerical scheme. To show the effectiveness of the suggested approach over an equidistributed grid, two numerical examples are provided. [ABSTRACT FROM AUTHOR]

Here, unsteady boundary layer flow under the action of magnetic effect over a moving stagnation surface has been investigated numerically. This study examines non-Newtonian fluid flow with respect to combined effect of magnetic field, movement of surface and time. Governing equations are dimensionless by applying nondimensional quantities. Then system of coupled ordinary differential equations are obtained by appropriate similarly transformations, in terms of the governing parameter including unsteady parameter (k) , magnetic number (M) , power-law index (n) and three-dimensional parameter (α). Thus, the obtained modelled equations are solved numerically by the shooting technique. The problem's parameters are thoroughly discussed and verified physically and graphically. The obtained results validate to literature result. The two relevant flows' velocity profile's numerical results have been examined. [ABSTRACT FROM AUTHOR]

Neural Networks (NNs) can be used for energy management of hybrid vehicles, but they are hard to tune in inference to adapt to different driving conditions. To make the NN-based energy management strategy more flexible, this paper proposes a controllable NN for optimal energy management of fuel cell hybrid electric vehicles. Inspired by the equivalent factor in the Equivalent Consumption Minimization Strategy (ECMS), we introduce an adjustable target variable for the final state as an input to the NN-based strategy. During training, classification and regression networks with single-step and multi-step inputs are considered. An efficient shooting method and an adaptive method are then introduced to realize the precise control of the final state and online parameter adaptation. Simulations of the proposed method and the benchmarking method are carried out in different battery discharge modes. Results demonstrate that the proposed shooting neural classifier can achieve 99.7% fuel optimality of dynamic programming in a similar computational time to the shooting ECMS, and the proposed adaptive neural classifier can adapt to different driving conditions and has better fuel economy than the adaptive ECMS. • A controllable neural model for energy management of fuel cell vehicles is proposed. • Neural regressors and classifiers are trained under single-step and multi-step inputs. • A shooting method and an adaptive method for neural models are proposed. • The proposed method is comprehensively analyzed and compared with benchmarks. [ABSTRACT FROM AUTHOR]

AbstractThe current problem focuses on the heat transfer analysis of the non-Newtonian Prandtl-Eyring fluid flow under an applied magnetic field over a variable stretching sheet. The variable stretching is assumed because most of the practical situations have variable stretching surfaces. In addition, heat transfer is a very important phenomenon in many applications like the extrusion of sheets, cooling of plants, etc. Thus, heat transfer is estimated with the Christov-Cattaneo heat conduction law to get more realistic results. The physical problem is mathematically modeled with all these assumptions, it yields the boundary value problem of the coupled nonlinear partial differential equations. The governing partial differential equations are first transformed into ordinary differential equations by employing a set of similarity transforms. And, the obtained ordinary differential system is numerically simulated with the shooting method for different parametric conditions. The proposed algorithm is quite efficient and implemented to solve the nonlinear governing equations very efficiently. Variations in fluid momentum and thermal energy are captured in graphs by varying flow govern parameters. In addition, the surface drag coefficient and reduced Nusselt number are computed and analyzed. For the validation of the computed results, a comparison is established with existing literature, it can be shown that computed results matched very well with reported literature. It is observed that both fluid parameters (α,β) have different effects on fluid velocity i.e. fluid parameter α increases it while fluid parameter β decelerates it. Also, the applied magnetic field produces Lorentz force which works in the opposite direction and hence it decelerates the fluid motion significantly. The drag force coefficient of variable stretching is higher and hence this surface is less favorable for fluid movement as compared to linear stretching. In addition, the fluid temperature cools down if the thermal relaxation phenomenon is considered. [ABSTRACT FROM AUTHOR]

A one-dimensional analog of the Goldshtik mathematical model for separated flows in an incompressible fluid is considered. The model is a boundary value problem for a second-order ordinary differential equation with discontinuous right-hand side. Some properties of the solutions of the problem, as well as the properties of the energy functional for different values of vorticity, are established. An approximate solution of the boundary value problem under study is found using the shooting method. [ABSTRACT FROM AUTHOR]

Nowadays a propellant residual gauging method based on the thermal response of the tanks’ wall is developed. And the liquid distribution and meniscus height have great effects on the thermal response. Profiles of liquid free surfaces in revolved containers under microgravity are studied through theoretical analysis and numerical simulation in this paper. The analytical formula for the static profile of the liquid surface in the spherical tank is established. It shows that the profile is a section of a circle cut off by the tank wall. For given the geometry of the tank, liquid volume and contact angle, the profile of the free surfaces under microgravity can be obtained by using the Shooting method based on the theoretical model. Numerical simulation is carried out with the Volume of Fluid method, and it is verified that the static profiles at different contact angles and liquid filling rates fit the theoretical descriptions. It is concluded that the meniscus height increases slowly as the filling rate increases, and the smaller the contact angle, the more obvious this trend. Then the theory is extended to the tanks of arbitrary shapes, and the critical position of the profile is derived. Below the critical position the propellant may accumulate in some corners or pits, which makes it unable to be fully utilized. The critical position is related to the shape of the tank and the contact angle. This research is of great value for the prediction of the static profiles of liquid surfaces in tanks and the propellant residual gauging. [ABSTRACT FROM AUTHOR]

Many numerical methods have been developed since 1961, but unresolved issues remain. This study developed a numerical method to address these issues and determine the coefficients and properties of rotational waves with a shear current in a finite water depth. The number of unknown constants was reduced significantly by introducing a wavelength-independent coordinate system. The reference depth was calculated independently using the shooting method. Therefore, there was no need for partial derivatives with respect to the wavelength and the reference depth, which simplified the numerical formulation. This method had less than half of the unknown constants of the other method because Newton's method only determines the coefficients. The breaking limit was calculated for verification, and the result agreed with the Miche formula. The water particle velocities were calculated, and the results were consistent with the experimental data. Dispersion relations were calculated, and the results are consistent with other numerical findings. The convergence of this method was examined. Although the required series order was reduced significantly, the total error was smaller, with a faster convergence speed.

The problematic of solving stiff boundary value problems permeates numerous scientific and engineering disciplines, demanding novel approaches to surpass the limitations of traditional numerical techniques. This research delves into the implementation of the solution continuation method with respect to the best exponential argument, to address these stiff problems characterized by rapidly evolving integral curves. The investigation was conducted by comparing the efficiency and stability of this novel method against the conventional shooting method, which has been a cornerstone in addressing such problems but struggles with the erratic growth of integral curves. The results indicate a marked elevation in computational efficiency when the problem is transformed using the exponential best argument. This method is particularly pronounced in scenarios where integral curves exhibit exponential growth speed. The main takeaway from this study is the instrumental role of the regularization parameter. Its judicious selection based on the unique attributes of the problem can dictate the efficiency of the solution. In summary, this research not only offers an innovative method to solve stiff boundary value problems but also underscores the nuances involved in method selection, potentially paving the way for further refinements and applications in diverse domains.

In this article, we consider the boundary layer two-dimensional Carreau fluid flow induced by a heated inclined flat plate. The flow having variational viscosity of Carreau fluid is considered. The dependence of thermo-physical properties on temperature and concentration is also discussed. Using the Falkner-Skan solution, the governing equations are converted into a system of ordinary differential equations, which have been solved by RK-five integration scheme along with a shooting method. Solutions are calculated for fluid with thermo-physical properties of shear-thinning (viscosity decreases with increasing shear-rate) and thickening (viscosity increases with increasing shear-rate) effects. Physical interpretation and discussion are presented regarding the base flow, temperature and concentration profiles. Boundary layer thickness engages inversely with pressure gradient m, whereas temperature profile shows a significant increase for higher values of ε1.

This paper aims to analyze the mathematical and theoretical scrutiny of non-Newtonian Williamson liquid on an asymmetry tapered channel with thermal and mass transportation. No slip boundary conditions for velocity, heat and concentration are kept on channel walls. Buongiorno model for thermal transport of nano-fluid is also incorporated. Flow in permeable surface is categorized via modified Darcy law. Current problem is formulated by incorporating distinct effects such as modified Darcy law, electro osmosis, heat generation and chemical reaction. RK-4 based shooting method has been utilized to evaluate the nonlinear equations. Graphical results are formulated to visualize the prominence of distinct parameters.

The current study illuminates the enactment of a tangent hyperbolic nanofluid past a bidirectional stretchable surface. The phenomena of heat and mass transfer with joule heating, chemical reaction, and thermal radiation have been debated. For the motivation of the problem, convective boundary conditions are part of this study. The modeled partial differential equations are mended into ordinary differential equations with the help of appropriate self-similarity transformations. Furthermore, the resulting system of ODEs is numerically handled by using well-established shooting scheme and acquired numerical outcomes are compared with ND Solve command of Mathematica. The Effects of prominent parameters on velocity, temperature and volumetric concentration distribution are inspected through graphs. The influence of emerging parameters involved in this study on flow and heat removal features are deliberated in detail. As we are increasing the values of power-law index n, Prandtl number Pr and Magnetic parameter M, outcomes increment in skin friction coefficient while decline in the Nusselt number is seen.

The main purpose current exploration is to examine the influence of viscous dissipation and nonlinear radiation in three-dimensional (3D) Williamson fluid flow on an exponentially stretching through porous medium with the effect of activation energy along with chemical reaction. By employing suitable transformation, the nonlinear partial equations (PDEs) are transmuted to nonlinear ordinary differential equations (ODEs) which are subsequently solved numerically by using Range-Kutta method with shooting technique by utilization Matlab script. Characteristics of resulting physical parameters appearing in modeling like the Weissenberg number, Prandtl number, nonlinear radiation parameter, porosity parameter, Eckert number and chemical reaction parameter are comprehensively analyzed in graphical forms with an interest in providing the physical meaning to each parameter. The outcomes anticipate that, the thermal profile is improved by the increase in the values of nonlinear radiation parameter due to inner heat. The thermal profile enhances by strengthening of Eckert number but it has opposite trend through Prandtl number. The impact of obtained parameters on skin friction coefficient, mass and heat transfer rates is illustrated by tables. The validity of the present findings is presented by comparing them with the previous investigations.

This article employs an artificial neural network technique to approximate the solution for the stagnation point flow with velocity and thermal slip effects, as well as radiative heat transfer. The PDE governing system is transformed into a set of coupled ordinary differential systems by incorporating similarity variables. The shooting method is used to obtain a dataset in Mathematica. To test the precision of the suggested model, the operations of training, testing, and validation are performed, and the results are compared to a reference dataset. The Levenberg-Marquardt backpropagation neural network model is utilized to solve the system of equations under different scenarios, and its output is evaluated using mean square error, state transition dynamics, error histograms analysis, and regression illustrations. The findings indicate that the neural network approach achieves a high level of accuracy when predicting thermal analysis. Moreover, the current Artificial Neural Network model has an advantage over other numerical techniques in that it can handle more intricate mathematical models while minimizing the resources required for problem-solving.

The buckling and postbuckling behaviors of functionally graded graphene platelets-reinforced composite (FG-GPLRC) circular plates are studied based on the classical nonlinear von Karman plate theory. The effective Young's modulus of the composite is estimated using the modified Halpin–Tsai micromechanical model, and the effective Poisson's ratio is estimated by the rule of mixtures. Governing equations of the problem are derived based on the Hamilton principle and the numerical solutions of critical loads and postbuckling deflection–load relationships are calculated using the shooting method. Different from the existing linear buckling analysis based on the Terriftz criterion, the study with considering the global deformation of the plates, we analyze the influencing factors of the critical buckling loads and postbuckling paths of the FG-GPLRC circular plates subjected to uniformly distributed radial pressure. The results show that the content, geometric parameters and distribution pattern of GPL have great influences on the critical buckling loads and the post-buckling bearing capacities of the circular FG-GPLRC plates. [ABSTRACT FROM AUTHOR]

This research addresses the implications of slip on the magnetohydrodynamic transport properties of Newtonian nanofluids. The study employs Buongiorno’s theoretical framework and focuses its attention on a cylindrical object that experiences tensile deformation inside a medium characterized by porosity. In contrast to the often observed boundary conditions that presume a constant temperature and concentration, the current research utilizes hydrodynamic and thermal slip conditions. The recognition of many significant elements, including the Arrhenius activation energy, magnetic field, and viscous dissipation, also has important significance. The phenomena of interest pertaining to fluid flow is first defined and afterward converted into a non dimensional form by including relevant commonalities. In order to do a thorough examination of the current situation, the shooting algorithm and the bvp4c technique are used. Graphical and tabular representations are used to demonstrate the implications of several emerging features on the velocity, temperature, and dispersion of nanoparticles. The observed data suggests that a rise in chemical reaction parameters leads to a drop in nanoparticle concentration distributions, but the activation energy parameter exhibits an opposite tendency. It is discovered that the boundary layer thickness under slip flow circumstances differs from that seen without slip flow. The Sherwood number rises when the chemical reaction parameter gets higher, whereas the activation energy parameter escalates in the opposite direction. The present research covers a broad variety of applied sciences applications, with a special emphasis on thermal oil recovery, geothermal reservoirs, chemical engineering, and nuclear reactor cooling. [ABSTRACT FROM AUTHOR]

Purpose: This paper assumes that the performance of the porous gradient beam varies with temperature and humidity, while the environmental field varies continuously with the height of the beam section. The thermoelastic dynamic responses of porous beams with non-conservative gradients near buckling are discussed on this basis. Procedure First, the exact vibration model of the porous gradient beam with two porosity distribution types under three thermal and wet conditions is established. Considering that the beam is subjected to the follower load, the thermal coupling relationship and nonlinear dynamic equation of the porous gradient beam composed of porous metal foam material are given. In addition, according to the shooting method, the small amplitude vibration frequency response of the beam near the buckling is calculated. Results: The static and dynamic responses of different parameters (temperature, humidity, porosity, slenderness ratio, etc.) to gradient porous materials are discussed through the numerical results calculated by the shooting method. Conclusions: The results show that the material parameters, external load, and other factors will affect the beam's natural frequency to a certain extent. Therefore, this study can provide the necessary theoretical basis and reference for the safety design of structures under complex working conditions. [ABSTRACT FROM AUTHOR]