Analytical Solution Approach Research Articles

Analytical investigation of space–time shifted nonlocal stochastic Sasa–Satsuma equation using the enhanced modified extended tanh-expansion method for stochastic solitary waves Solutions

In this paper, discover exact solutions of the space–time shifted nonlocal stochastic Sasa–Satsuma equations using the enhanced modified extended tanh-expansion method. This method is a sophisticated mathematical approach for analytical and approximate solution of a nonlinear partial differential equations. The space–time shifted nonlocal stochastic Sasa–Satsuma equations define the behavior of two complex-valued functions, u and v, in a nonlinear system. These equations are complicated to solve analytically because they contain a number of components that describe space–time shifting, nonlocal interactions, and stochastic problems. To increase reliability and effectiveness of the solutions, this method couples the extended tanh-function method with an enhanced method. In order to demonstrate how white noise affects the solutions to the space–time shifted nonlocal stochastic Sasa–Satsuma equations, we also use Matlab to create 3D surfaces and contour graphs of exact solutions.

Predictive cruise control for hybrid electric vehicles based on hierarchical convex optimization

Predictive Cruise Control (PCC) achieves automated driving with improved vehicle economy by incorporating road gradient information from high-precision maps. However, existing research on PCC has primarily centered around conventional gasoline vehicles. Hybrid Electric Vehicle (HEV) offer superior fuel efficiency compared to their traditional counterparts. To further enhance vehicle economy by integrating the PCC system with HEVs, this paper proposes a hierarchical control architecture for HEV-PCC based on convex optimization. Firstly, considering spatial slope information from the road ahead, this paper introduces a Time-Space Integration Model Predictive Control (TSI-MPC) based on the principles of kinetic energy. Secondly, the paper combines a current regression model with the Pontryagin Minimum Principle (PMP) to present a Regression Analysis - Pontryagin Minimum Principle (RA-PMP) approach for the direct analytical solution of the energy management problem. Finally, the strategy is validated through simulation analysis and Hardware-in-Loop (HIL) testing on various real road scenarios. The result indicate that, in comparison to the Equivalent Consumption Minimization Strategy (ECMS) with constant speed cruising (CC), this method achieves an average fuel economy improvement of 9.45%.

An analytical framework for the best–worst method

Since the development of the best–worst method (BWM) in 2015, it has become a popular research focus in multi-criteria decision-making. The original optimization problem of the BWM is a nonlinear min–max model that can lead to multiple optimal solutions, while the linear model of the BWM produces a unique solution. The two models need to be solved by optimization software packages. In addition, although the linear model of the BWM can obtain a unique solution, it produces different feasible regions than the nonlinear model of the BWM, and it changes the objective function. This study aims to solve the nonlinear model of the BWM mathematically to obtain the analytical forms of the optimal solutions. First, we transform the original nonlinear model of BWM into an equivalent optimization model driven by the optimally modified comparison vectors. The equivalent BWM provides a solid basis for computing the analytical solutions. Second, for not-fully consistent pairwise comparison systems, we strictly prove that there is only one unique optimal solution with three criteria, and there might be multiple optimal solutions with more than three criteria. We further develop the analytical forms of these unique and multiple optimal solutions and the optimal interval weights. Third, we develop a secondary objective function to select a unique solution for the BWM. The secondary objective function retains all the characteristics of the original nonlinear model of the BWM, and we find the unique solution analytically. Finally, some numerical examples are examined, and a comparative analysis is performed to demonstrate the effectiveness of our analytical solution approach.

Analytical Approach for Solution of Linear and Non-linear Time-Fractional Schrödinger’s Equations by Employing Sumudu Transform Iterative Method

Analytical Approach for Solution of Linear and Non-linear Time-Fractional Schrödinger’s Equations by Employing Sumudu Transform Iterative Method

A proposed method to rotordynamic analysis of a high-speed permanent magnet synchronous machine by retention sleeve

In this paper, the authors present a novel analytical model for rotordynamic analysis of a high-speed permanent magnet synchronous machine (HS-PMSM) with a retention sleeve. The proposed analytical model has a fast response, accurate results, and sample formulation, and is validated with the finite-element method (FEM). The obtained results show the proper accuracy of the proposed analytical solution approach. The significant results are: The analytical formulation model proposed for the rotordynamic analysis of the HS-PMSMs can accurately calculate the displacement and the stress of the solid cylinder of the rotor at any high speeds and temperature rises. Furthermore, the proposed analytical model is concerning the temperature changes in the rotor and ensures requirements in any temperature rising and high rotational speeds.

The symplectic approach for analytical solution of micropolar plane stress problem

The symplectic method is adopted to derive analytical solution of the plane stress problem in the framework of the micropolar elasticity. The general micropolar plane stress problem is transformed into three types of problems with homogeneous boundary conditions at two opposite edges. The fundamental equations are converted into canonical Hamiltonian equations using the Legendre transformation. The eigensolutions of the Hamiltonian operator matrix are obtained for three types of homogeneous boundary conditions. The analytical solution for the micropolar plane stress problem is expressed as an eigensolution expansion. The size effect is analyzed based on the relationship between the eigenvalues and micropolar material constants. The numerical results obtained by the finite element method (FEM) and ABAQUS demonstrate the validity of the proposed method for different boundary conditions and confirm its ability to accurately capture the size effect.

Analytical Approach for the Approximate Solution of Harry Dym Equation with Caputo Fractional Derivative

This paper presents the concept of a new strategy that examines the analytical solution of the Harry Dym equation (HDEq) with fractional derivative in the Caputo sense. This new approach is called the Mohand homotopy perturbation transform scheme (MHPTS) which is constructed on the basis of the Mohand transform (MT) and the homotopy perturbation method (HPM). The implementation of MT produces the recurrence relation without any assumption and hypothesis theory whereas HPM is additionally used to overcome the nonlinearity in differential problems. Our primary focus is to handle the error analysis in the recurrence relation and generates the solution in the order of series. These obtained results yield the exact solution very rapidly due to its fast convergence. Some graphical representations are demonstrated to show the high efficiency and performance of this approach.

Developing a Lagrangian sediment transport model for open channel flows

A three-dimensional stochastic Lagrangian particle tracking sediment transport model is developed to solve the discrete advection–dispersion equation using a combination of empirical dispersion equations. The performance of three widely-used longitudinal dispersion coefficient equations was examined to select one of them as the primary dispersion equation term in the developed model. Also, a conditional empirical equation was used to consider the effect of vertical dispersion term in top layers near the water surface. The performance of particle tracking model (PTM) to calculate the sediment concentration was evaluated for various sediment classes (very fine sand, fine sand, and medium sand) using available laboratory dataset. Multiple statistical measures were calculated using the Taylor diagram for each dispersion equation. Based on the result, the developed particle tracking model estimated the suspended sediment concentration in a rectangular open channel with a correlation coefficient (R) of 0.96, standard deviation (STD) of 0.262, and root mean square deviation (RMSD) of 0.06 for three different sediment classes proving the acceptable accuracy of the developed model for different range of sediment gradations. In addition, the accuracy of PTM was compared to recently developed models. Comparison between the particle tracking model and the analytical solution of the advection–dispersion equation showed that the developed model predicted the maximum concentration of suspended sediment 6% and 9.4% lower than the analytical solution result for 30 and 50 s simulation time in the straight channel, respectively. However, there was a good agreement between the longitudinal and transverse sediment concentration distribution from the model and the analytical solution approach. The result of the sensitivity analysis and validation process showed that the model could be used to simulate sediment transport in open channel flows.

Size-Dependent Buckling Analysis of Microbeams by an Analytical Solution and Isogeometric Analysis

This paper proposes an analytical solution and isogeometric analysis numerical approach for buckling analysis of size-dependent beams based on a reformulated strain gradient elasticity theory (RSGET). The superiority of this method is that it has only one material parameter for couple stress and another material parameter for strain gradient effects. Using the RSGET and the principle of minimum potential energy, both non-classical Euler–Bernoulli and Timoshenko beam buckling models are developed. Moreover, the obtained governing equations are solved by an exact solution and isogeometric analysis approach, which conforms to the requirements of higher continuity in gradient elasticity theory. Numerical results are compared with exact solutions to reveal the accuracy of the current isogeometric analysis approach. The influences of length–scale parameter, length-to-thickness ratio, beam thickness and boundary conditions are investigated. Moreover, the difference between the buckling responses obtained by the Timoshenko and Euler–Bernoulli theories shows that the Euler–Bernoulli theory is suitable for slender beams.

Influence of thermal jump and inclined magnetic field on peristaltic transport of Jeffrey fluid with silver nanoparticle in the eccentric annulus

This study investigates the impacts of thermal jump and inclined magnetic field on the peristaltic transport of Jeffrey fluid containing silver nanoparticles in the eccentric annuls under the long wavelength and low Reynolds number assumption. In medical studies, the impact of thermal jumps and slanted magnetic fields on public health is of interest. Peristaltic motion's ability to transmit heat and create a magnetic field has several uses in biomedical and bioengineering. The non-Newtonian Jeffrey fluid with silver nanoparticles is considered in the space between two cylindrical tubes that are eccentrically aligned. The homotopic perturbation method is semi-analytical for modeling and nonlinear partial differential equations (HPM). Analytical solutions for velocity, pressure gradient, and pressure rise were found. To show how physical parameters affect temperature, velocity, concentration, frictional force, and pressure rise of inner and outer tubes were plotted. A comparison of the present method with the exact solution for temperature and nanoparticle concentration profile is shown graphically. The present analysis of analytical solution approaches to the exact solution. The most significant thing in the current investigation is that the Hartmann number and thermophoresis number make the velocity profile decline. Jeffrey fluid parameter and magnetic field angle make the velocity rise. The nanofluid's temperature rises as a result of the thermal jump. In addition, the Jeffrey nanofluid has a higher momentum and temperature than the Jeffrey fluid. This analysis can better evaluate the syringe's injection speed and fluid flow features during cancer treatment, artery blockage removal, and reduced bleeding throughout the surgery.

Free radial oscillations of an actuated cylindrical tube

This work investigates the free radial oscillations of an electrically actuated cylindrical tube. Classical Knowles’ tube problem is explored here with the application of an external electric field. One of the prime objectives is to study the effect of sudden pressure removal from the cylindrical actuator. We attempt to correlate our problem physiologically with an arterial tissue actuation. The tube is introduced to an electrical actuation with an externally applied electric field and is subjected to a sudden pressure which is removed instantly to explore the purely free radial oscillations. Generally, such kind dynamic effects are neglected in designing cylindrical actuators. The dielectric cylindrical tube is assumed to be incompressible, isotropic, and infinite. The obtained results assert that the application of an external electric field reduces the amplitude of the radial oscillations and thus makes the tube contract. Essentially, the actuation is elevating the stiffness of the tube. A similar effect is also observed in the blood vessels, wherein the electric signaling helps the vessels to contract. We propose a complete analytical solution approach that is highly significant in designing cylindrical muscle actuators for various futuristic applications in the biomimetic and medical field.

Theory of Microwave Remote Sensing of Vegetation Effects, SoOp and Rough Soil Surface Backscattering

In this paper, we provide updates on our recent work on the theory of microwave remote sensing for applications in remote sensing of soil moisture and snow water equivalent (SWE). The three topics are the following. (i) For the effects of forests and vegetation, we developed the hybrid method of NMM3D full-wave simulations over the vegetation field and forest canopies. In the hybrid method, we combined the use of commercial off-the-shelf software and wave multiple scattering theory (W-MST). The results showed much larger transmission than classical radiative transfer theory. (ii) In signals of opportunity at L-band and P-band, which are radar bistatic scattering in the vicinity of the specular direction, we developed the Analytical Kirchhoff solution (AKS) and Numerical Kirchhoff approach (NKA) in the calculations of coherent waves and incoherent waves. We also took into account of the effects of topographical elevations and slopes which have strong influences. (iii) In rough surface radar backscattering, we used the volume integral equation approach for NMM3D full-wave simulations for soil surfaces with kh up to 15. The simulations were calculated for the X-band and Ku-band and the results showed saturation effects. The simulation results can be applied to microwave remote sensing of SWE at these two frequencies.

Regression-based neural network for improving image reconstruction in diffuse optical tomography.

Diffuse optical tomography (DOT) is a non-invasive imaging technique utilizing multi-scattered light at visible and infrared wavelengths to detect anomalies in tissues. However, the DOT image reconstruction is based on solving the inverse problem, which requires massive calculations and time. In this article, for the first time, to the best of our knowledge, a simple, regression-based cascaded feed-forward deep learning neural network is derived to solve the inverse problem of DOT in compressed breast geometry. The predicted data is subsequently utilized to visualize the breast tissues and their anomalies. The dataset in this study is created using a Monte-Carlo algorithm, which simulates the light propagation in the compressed breast placed inside a parallel plate source-detector geometry (forward process). The simulated DL-DOT system's performance is evaluated using the Pearson correlation coefficient (R) and the Mean squared error (MSE) metrics. Although a comparatively smaller dataset (50 nos.) is used, our simulation results show that the developed feed-forward network algorithm to solve the inverse problem delivers an increment of ∼30% over the analytical solution approach, in terms of R. Furthermore, the proposed network's MSE outperforms that of the analytical solution's MSE by a large margin revealing the robustness of the network and the adaptability of the system for potential applications in medical settings.

A closed-form solution for thermoelastic stress analysis of perforated asymmetric functionally graded nanocomposite plates

Issues related to stress concentration in cracks, perforated plates, and the use of new generation materials to strengthen this type of plates are of great importance. When a functionally graded carbon nanotube-reinforced composite plate (FG-CNTRC) has a hole in its center of the plate that is exposed to a combination of mechanical and thermal loads, due to various couplings such as bending-extension, shear-extension, and bend-twist couplings that occur in the stress–strain relationships and due to the presence of nonhomogeneous equations, the analytical solution approach will be accompanied by new challenges. Hence, a general solution for the FG-CNTRC plates weakened by a central hole is presented. To achieve this goal, the Lekhnitskii complex potential approach is developed using the appropriate conformal mapping function. The present solution provides the ability to calculate the stress distribution of perforated plates made of asymmetric composite laminates and functionally graded materials by introducing holomorphic potential functions in the form of Laurent series. In this research, an attempt has been made to depict the effect of important parameters on the stress resultants and moments around the hole. The results clearly show that the studied parameters significantly change the stress resultants and moments due to thermal and mechanical loads applied to perforated FG-CNTRC plates. As a result, it is possible to significantly reduce stress resultants and moments by properly selecting the values of effective parameters in the design of such perforated plates.

Economic order quantity for growing items in the presence of mortality

Growth depicts the behavior of a class of inventories whose weight and size increase during their storage. Although the phenomenon is fundamental in the food industry, it still faces a lack of academic heed. Our research sheds new light on this area by illustrating the inventory system of a rearing farm that breeds fast-growing newborn animals (like broiler chickens) and finally slaughters them. The items are prone to different diseases during their growth which can lead to their death. This is modeled by applying a mortality rate that can be controlled by investing in preventive practices. The slaughtered items (such as chicken meat) that fall into the category of deteriorating inventory are quality controlled and exploited to satisfy demand. An analytic solution approach is developed to derive the optimal order quantity of newborn animals, their growth period, and action level for preventive practices. Experimental results show that choosing a hatchery with the best purchasing cost should be the first priority of the system to manage its costs. It is also depicted that the breeding period is not influenced by all input parameters of the model, and the nature of the items plays a key role in this regard.

Logarithmic Moments for Mixture of Symmetric Alpha Stable Modelling

Mixture of symmetric <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> -stable (s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> s) models can be used to model impulsive data with heavy-tailed distribution. Lack of closed-form expression for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> -stable distributions is a challenge for efficient mixture modeling in current methods. In this letter, we present an analytical approach for novel solution of parameter estimation in s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> s mixture models which improves the computational efficiency of the existing methods. In addition, by introducing a centro-symmetrization (CS) transform, we generalize the application of proposed method to non-centered skewed data as well. The proposed method employs the logarithmic moments of data in maximization of conditional expectation of log-likelihood and is called EMLM algorithm. The experimental results on the synthetic and real datasets show that EMLM outperforms current baseline models not only in terms of goodness of fit of model, but also by increasing the performance of down-stream applications such as classification.

Food supply chain coordination for growing items: A trade-off between market coverage and cost-efficiency

The accurate operation of a Food Supply Chain (FSC) is a critical issue as it directly interfaces with health and safety matters. This study addresses coordination and conflict management in a three-level FSC that embraces a new inventory type known as growing items like poultry and livestock. The chain involves a rearing farm as the supplier, a processed food producer as the manufacturer, and multiple processed food retailers. Vendor Managed Inventory (VMI) is applied by the manufacturer to handle the retailers' systems and prevent replenishment mismatches and thereby food waste. To increase its market coverage, the manufacturer needs to provide the retailers with enough incentives to enter this setting. So, a cost-sharing contract is designed under which the manufacturer undertakes a fraction of the retailers’ holding costs. Accordingly, the manufacturer faces two contradictory targets, increasing its market coverage by convincing the retailers to enter the system on the one hand and managing its costs efficiently on the other hand. An analytic solution approach with a game-theoretic perspective is developed to solve the model. Extensive numerical experiments and a case study are provided, presenting fruitful managerial insights that can be utilized by the policymakers and chain members under different settings. The results highlight the efficiency of our VMI and cost-sharing collaboration scheme in enhancing the performance of the chain.

Fluid dynamics investigation of a large array

The influence of surrounding fluid on a large array of oscillators is important to study for applications in fields such as medicine, biology, and atomic force microscopy. In the present study, we investigate a large array of cantilever beams oscillating in an unbounded fluid to better understand the fluid dynamic behavior. The two-dimensional boundary integral method is applied to analyze a large array of cantilever oscillators using an analytical solution approach for the unsteady Stokes and continuity equations. We analyze array sizes from 5 to 50 beams by comparing hydrodynamic transverse force and velocity profiles for two different velocity configurations. Including the interactions of neighbor and non-neighbor members leads to distinct array effects. With an increase in the number of oscillators in an array, the array effect influences the overall dynamics. Furthermore, to justify the influence of an array effect, the hydrodynamic loading is compared to the same and varying array surface area of different array sizes. Our analysis and new findings strengthen our hypothesis that the predictions of existing knowledge obtained from small-size arrays and coupled oscillators cannot readily inform dynamic predictions of large-size arrays. The underlying reason being the additional array effect(s) which are not present in a small-size array. The novelty of this paper is the ability to model such large arrays and investigate the array effect in an unbounded fluid.

A fast reduced model for a shell-and-tube based latent heat thermal energy storage heat exchanger and its application for cost optimal design by nonlinear programming

Numerical simulation of latent heat thermal energy storage (LHTES) systems plays a fundamental role in studying the physical process and guiding the engineering design. Discretization of the PDEs describing the nonlinear solidification/melting process of phase change materials (PCMs) leads to a large-scale complex dynamics system, where the system behavior depends on a set of parameters. In a design setting, repeated model evaluations are required over the set of parameters results in significant computational burden. In this paper, an explicit analytic solution was built for the propagation of the solidification front in a cylindrical coordinate. The analytic solution approach is further employed to develop a low computational reduced model (RM) as a module for a shell-and-tube based LHTES heat exchanger. The levelized Cost of Energy (LCOE) is used as a design metric and the RM model is used to apply system-level constraints in the nonlinear programming formulation that facilitates efficient global optimal design of the PCM properties, flow conditions and tube geometries. The use of LCOE as the design metric prevents over design of the heat transfer rate and also establishes a fair ground for evaluation of different thermal storage technologies and their integrated applications with other systems. Optimal results showed that a higher effectiveness results in a higher LCOE; the velocity of the HTF and the length of the channel are highly correlated with each other; both larger PCM latent energy and conductivity result in lower LCOE.

Crack growth modeling and simulation of a peridynamic fatigue model based on numerical and analytical solution approaches

Fatigue crack growth assessment of 2024-T3 aluminum alloy is carried out on the basis of a recently developed peridynamic fatigue model. The governing remaining-life equation of the peridynamic fatigue model has been solved by two different approaches i.e. numerical and analytical approaches to perform fatigue-crack growth simulations for 2024-T3 aluminum specimen with a pre-existing crack. Remaining-life parameters of the numerical and analytical solution approaches are determined by calibrating with the experimental crack growth data. Fatigue crack growth predictions, and associated material deformation of the specimen under various loading conditions are simulated by the two approaches. Predicted results show that the numerical approach has shortcomings in accurate predictions of crack growth rates for the application of different loading conditions, while the analytical approach can be applied for a wide range of loading conditions with good prediction accuracy and stable simulations of the material deformation with a growing crack. Furthermore, it is found that the computational time of the analytical approach is considerably shorter in comparison with the numerical approach.