Статті в журналах: "Coefficients of engineering solutions efficiency"

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Dong, Guirong, Chengyang Liu, Yijie Liu, Ling Wu, Xiaoan Mao, and Dianzi Liu. "Computationally Efficient Approximations Using Adaptive Weighting Coefficients for Solving Structural Optimization Problems." Mathematical Problems in Engineering 2021 (March 10, 2021): 1–12. http://dx.doi.org/10.1155/2021/1743673.

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With rapid development of advanced manufacturing technologies and high demands for innovative lightweight constructions to mitigate the environmental and economic impacts, design optimization has attracted increasing attention in many engineering subjects, such as civil, structural, aerospace, automotive, and energy engineering. For nonconvex nonlinear constrained optimization problems with continuous variables, evaluations of the fitness and constraint functions by means of finite element simulations can be extremely expensive. To address this problem by algorithms with sufficient accuracy as well as less computational cost, an extended multipoint approximation method (EMAM) and an adaptive weighting-coefficient strategy are proposed to efficiently seek the optimum by the integration of metamodels with sequential quadratic programming (SQP). The developed EMAM stems from the principle of the polynomial approximation and assimilates the advantages of Taylor’s expansion for improving the suboptimal continuous solution. Results demonstrate the superiority of the proposed EMAM over other evolutionary algorithms (e.g., particle swarm optimization technique, firefly algorithm, genetic algorithm, metaheuristic methods, and other metamodeling techniques) in terms of the computational efficiency and accuracy by four well-established engineering problems. The developed EMAM reduces the number of simulations during the design phase and provides wealth of information for designers to effectively tailor the parameters for optimal solutions with computational efficiency in the simulation-based engineering optimization problems.

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Navickas, Zenonas, Tadas Telksnys, Romas Marcinkevicius, Maosen Cao, and Minvydas Ragulskis. "F-Operators for the Construction of Closed Form Solutions to Linear Homogenous PDEs with Variable Coefficients." Mathematics 9, no. 9 (April 21, 2021): 918. http://dx.doi.org/10.3390/math9090918.

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A computational framework for the construction of solutions to linear homogenous partial differential equations (PDEs) with variable coefficients is developed in this paper. The considered class of PDEs reads: ∂p∂t−∑j=0m∑r=0njajrtxr∂jp∂xj=0 F-operators are introduced and used to transform the original PDE into the image PDE. Factorization of the solution into rational and exponential parts enables us to construct analytic solutions without direct integrations. A number of computational examples are used to demonstrate the efficiency of the proposed scheme.

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Mardani, A., M. R. Hooshmandasl, M. M. Hosseini, and M. H. Heydari. "Moving Least Squares (MLS) Method for the Nonlinear Hyperbolic Telegraph Equation with Variable Coefficients." International Journal of Computational Methods 14, no. 03 (April 13, 2017): 1750026. http://dx.doi.org/10.1142/s0219876217500268.

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Telegraph equation which widely used for modeling many engineering and physical phenomena has considered by some researchers in recent years. In this paper, a numerical scheme based on the moving least squares (MLS) approximation and finite difference method (FDM) is proposed for solving a class of the nonlinear hyperbolic telegraph equation with variable coefficients. In the new developed scheme, we use collocation points and approximate solution of the problem under study by using MLS approximation. The MLS method is a meshless approach and does not need any background mesh structure. A time stepping approach is employed for the first- and second-order time derivatives. The proposed method provides a semi-discrete solutions for the problems under study. In space domain, the MLS approximation and in time domain, the finite difference technique are employed. This method after discretization leads to a linear system of algebraic equations. Some numerical results are given and compared with analytical solutions to demonstrate the validity and efficiency of the proposed technique.

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Batko, Kornelia M., Izabella Ślęzak-Prochazka, Andrzej Ślęzak, Wioletta M. Bajdur, and Maria Włodarczyk-Makuła. "Management of Energy Conversion Processes in Membrane Systems." Energies 15, no. 5 (February 23, 2022): 1661. http://dx.doi.org/10.3390/en15051661.

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The internal energy (U-energy) conversion to free energy (F-energy) and energy dissipation (S-energy) is a basic process that enables the continuity of life on Earth. Here, we present a novel method of evaluating F-energy in a membrane system containing ternary solutions of non-electrolytes based on the Kr version of the Kedem–Katchalsky–Peusner (K–K–P) formalism for concentration polarization conditions. The use of this formalism allows the determination of F-energy based on the production of S-energy and coefficient of the energy conversion efficiency. The K–K–P formalism requires the calculation of the Peusner coefficients Kijr and Kdetr (i, j ∈ {1, 2, 3}, r = A, B), which are necessary to calculate S-energy, the degree of coupling and coefficients of energy conversion efficiency. In turn, the equations for S-energy and coefficients of energy conversion efficiency are used in the F-energy calculations. The Kr form of the Kedem–Katchalsky–Peusner model equations, containing the Peusner coefficients Kijr and Kdetr, enables the analysis of energy conversion in membrane systems and is a useful tool for studying the transport properties of membranes. We showed that osmotic pressure dependences of indicated Peusner coefficients, energy conversion efficiency coefficient, entropy and energy production are nonlinear. These nonlinearities were caused by pseudophase transitions from non-convective to convective states or vice versa. The method presented in the paper can be used to assess F-energy resources. The results can be adapted to various membrane systems used in chemical engineering, environmental engineering or medical applications. It can be used in designing new technologies as a part of process management.

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Karakoç, Seydi Battal Gazi, Aytekin Eryılmaz, and Musa Başbük. "The Approximate Solutions of Fredholm Integrodifferential-Difference Equations with Variable Coefficients via Homotopy Analysis Method." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/261645.

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Numerical solutions of linear and nonlinear integrodifferential-difference equations are presented using homotopy analysis method. The aim of the paper is to present an efficient numerical procedure for solving linear and nonlinear integrodifferential-difference equations. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system.

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Abbasov, T., and A. R. Bahadir. "The investigation of the transient regimes in the nonlinear systems by the generalized classical method." Mathematical Problems in Engineering 2005, no. 5 (2005): 503–19. http://dx.doi.org/10.1155/mpe.2005.503.

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This paper presents the use of the generalized classical method (GCM) for solving linear and nonlinear differential equations. This method is based on the differential transformation (DT) technique. In the GCM, the solution of the nonlinear transient regimes in the physical processes can be written as a functional series with unknown coefficients. The series can be chosen to satisfy the initial and boundary conditions which represent the properties of the physical process. The unknown coefficients of the series are determined from the differential transformation of the nonlinear differential equation of the system. Therefore, the approximate solution of the nonlinear differential equation can be obtained as a closed-form series.The validity and efficiency of the GCM is shown using some transient regime problems in the electromechanics processes. The numerical results obtained by the present method are compared with the analytical solutions of the equations. It is shown that the results are found to be in good agreement with each other.

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YÜZBAŞI, ŞUAYİP YÜZBAŞI, and MEHMET SEZER. "ON SOLUTIONS OF LINEAR FUNCTIONAL INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS VIA LAGRANGE POLYNOMIALS." Journal of Science and Arts 21, no. 3 (September 30, 2021): 707–20. http://dx.doi.org/10.46939/j.sci.arts-21.3-a11.

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In this study, a matrix-collocation method is developed numerically to solve the linear Fredholm-Volterra-type functional integral and integro-differential equations. The linear functional integro-differential equations are considered under initial conditions. The mentioned type problems often appear in various branches of science and engineering such as physics, biology, mechanics, electronics. The method essentially is a collocation method based on the Lagrange polynomials and matrix operations. By using presented method, the problem is reduced to a system of linear algebraic equations. The solution of this system gives the coefficients of assumed solution. An error analysis based on the residual function is studied. Some examples are solved to demonstrate the accuracy and efficiency of the method.

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Konuralp, Ali, and Sercan Öner. "Numerical Solutions Based on a Collocation Method Combined with Euler Polynomials for Linear Fractional Differential Equations with Delay." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 6 (October 25, 2020): 539–47. http://dx.doi.org/10.1515/ijnsns-2019-0018.

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AbstractIn this study, a method combined with both Euler polynomials and the collocation method is proposed for solving linear fractional differential equations with delay. The proposed method yields an approximate series solution expressed in the truncated series form in which terms are constituted of unknown coefficients that are to be determined according to Euler polynomials. The matrix method developed for the linear fractional differential equations is improved to the case of having delay terms. Furthermore, while putting the effect of conditions into the algebraic system written in the augmented form in which the coefficients of Euler polynomials are unknowns, the condition matrix scans the rows one by one. Thus, by using our program written in Mathematica there can be obtained more than one semi-analytic solutions that approach to exact solutions. Some numerical examples are given to demonstrate the efficiency of the proposed method.

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Gusu, Daba Meshesha, Dechasa Wegi, Girma Gemechu, and Diriba Gemechu. "Fractional Order Airy’s Type Differential Equations of Its Models Using RDTM." Mathematical Problems in Engineering 2021 (September 10, 2021): 1–21. http://dx.doi.org/10.1155/2021/3719206.

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In this paper, we propose a novel reduced differential transform method (RDTM) to compute analytical and semianalytical approximate solutions of fractional order Airy’s ordinary differential equations and fractional order Airy’s and Airy’s type partial differential equations subjected to certain initial conditions. The performance of the proposed method was analyzed and compared with a convergent series solution form with easily computable coefficients. The behavior of approximated series solutions at different values of fractional order α and its modeling in 2-dimensional and 3-dimensional spaces are compared with exact solutions using MATLAB graphical method analysis. Moreover, the physical and geometrical interpretations of the computed graphs are given in detail within 2- and 3-dimensional spaces. Accordingly, the obtained approximate solutions of fractional order Airy’s ordinary differential equations and fractional order Airy’s and Airy’s type partial differential equations subjected to certain initial conditions exactly fit with exact solutions. Hence, the proposed method reveals reliability, effectiveness, efficiency, and strengthening of computed mathematical results in order to easily solve fractional order Airy’s type differential equations.

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Maczyszyn, Agnieszka. "Energy Loss Coefficients ki in a Displacement Pump and Hydraulic Motor used in Hydrostatic Drives." Polish Maritime Research 26, no. 3 (September 1, 2019): 47–55. http://dx.doi.org/10.2478/pomr-2019-0045.

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Abstract The article aims at defining and analysing the energy loss coefficients in design solutions of rotating displacement machines, with a piston machine as an example. The energy losses observed in these machines include mechanical loss, volumetric loss, and pressure loss. The scale and relations between these losses in different machines depend on machine design and manufacturing quality, and on operating parameters. The operating parameters, in turn, which affect directly or indirectly the above losses depend on whether the machine works in pump or hydraulic motor regime. The article is also a contribution to the development of a library of ki coefficients which define the losses in displacement machines, as the knowledge about these coefficients makes it possible to assess fast and easily the energy efficiency of a machine or drive system at each point of its working area.

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Пененко, А. В., and A. V. Penenko. "Numerical Algorithms for Diffusion Coefficient Identification in Problems of Tissue Engineering." Mathematical Biology and Bioinformatics 11, no. 2 (December 22, 2016): 426–44. http://dx.doi.org/10.17537/2016.11.426.

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Identification algorithms of diffusion coefficients in a specimen with tomographic images of the solution penetration dynamics are considered. With the sensitivity operator, built on the basis of adjoint equations for diffusion process model, the corresponding coefficient inverse problem is reduced to the quasilinear operator equation which is then solved by the Newton-type method with successive evaluation of r-pseudo inverse operators of increasing dimensionality. The efficiency of the constructed algorithm is tested in numerical experiments. For comparison, a gradient-based algorithm for the inverse problem solution is considered.

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Aljarrah, Hussam, Mohammad Alaroud, Anuar Ishak, and Maslina Darus. "Adaptation of Residual-Error Series Algorithm to Handle Fractional System of Partial Differential Equations." Mathematics 9, no. 22 (November 11, 2021): 2868. http://dx.doi.org/10.3390/math9222868.

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In this article, an attractive numeric–analytic algorithm, called the fractional residual power series algorithm, is implemented for predicting the approximate solutions for a certain class of fractional systems of partial differential equations in terms of Caputo fractional differentiability. The solution methodology combines the residual function and the fractional Taylor’s formula. In this context, the proposed algorithm provides the unknown coefficients of the expansion series for the governed system by a straightforward pattern as well as it presents the solutions in a systematic manner without including any restrictive conditions. To enhance the theoretical framework, some numerical examples are tested and discussed to detect the simplicity, performance, and applicability of the proposed algorithm. Numerical simulations and graphical plots are provided to check the impact of the fractional order on the geometric behavior of the fractional residual power series solutions. Moreover, the efficiency of this algorithm is discussed by comparing the obtained results with other existing methods such as Laplace Adomian decomposition and Iterative methods. Simulation of the results shows that the fractional residual power series technique is an accurate and very attractive tool to obtain the solutions for nonlinear fractional partial differential equations that occur in applied mathematics, physics, and engineering.

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ZHANG, ZE-WEI, HUI WANG, and QING-HUA QIN. "METHOD OF FUNDAMENTAL SOLUTIONS FOR NONLINEAR SKIN BIOHEAT MODEL." Journal of Mechanics in Medicine and Biology 14, no. 04 (July 3, 2014): 1450060. http://dx.doi.org/10.1142/s0219519414500602.

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In this paper, the method of fundamental solution (MFS) coupling with the dual reciprocity method (DRM) is developed to solve nonlinear steady state bioheat transfer problems. A two-dimensional nonlinear skin model with temperature-dependent blood perfusion rate is studied. Firstly, the original bioheat transfer governing equation with nonlinear term induced by temperature-dependent blood perfusion rate is linearized with the Taylor's expansion technique. Then, the linearized governing equation with specified boundary conditions is solved using a meshless approach, in which the DRM and the MFS are employed to obtain particular and homogeneous solutions, respectively. Several numerical examples involving linear, quadratic and exponential relations between temperature and blood perfusion rate are tested to verify the efficiency and accuracy of the proposed meshless model in solving nonlinear steady state bioheat transfer problems, and also the sensitivity of coefficients in the expression of temperature-dependent blood perfusion rate is analyzed for investigating the influence of blood perfusion rate to temperature distribution in skin tissues.

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Shahnazari, M. R., F. Roohi Shali, A. Saberi, and M. H. Moosavi. "A New Hybrid Method for Solving Inverse Heat Conduction Problems." International Journal of Mechanics 15 (September 6, 2021): 151–58. http://dx.doi.org/10.46300/9104.2021.15.17.

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Solving the inverse problems, especially in the field of heat transfer, is one of the challenges of engineering due to its importance in industrial applications. It is well-known that inverse heat conduction problems (IHCPs) are severely ill-posed, which means that small disturbances in the input may cause extremely large errors in the solution. This paper introduces an accurate method for solving inverse problems by combining Tikhonov's regularization and the genetic algorithm. Finding the regularization parameter as the decisive parameter is modelled by this method, a few sample problems were solved to investigate the efficiency and accuracy of the proposed method. A linear sum of fundamental solutions with unknown constant coefficients assumed as an approximated solution to the sample IHCP problem and collocation method is used to minimize residues in the collocation points. In this contribution, we use Morozov's discrepancy principle and Quasi-Optimality criterion for defining the objective function, which must be minimized to yield the value of the optimum regularization parameter.

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Li, Zhiyuan, Yepeng Xu, and Dan Huang. "Accurate solution for functionally graded beams with arbitrarily varying thicknesses resting on a two-parameter elastic foundation." Journal of Strain Analysis for Engineering Design 55, no. 7-8 (June 3, 2020): 222–36. http://dx.doi.org/10.1177/0309324720922739.

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This work presents analytical solutions for bending deformation and stress distributions in functionally graded beams with arbitrarily and continuously variable thicknesses and resting on a two-parameter Pasternak elastic foundation. Based on two-dimensional elasticity theory directly, the general solutions of displacements and stresses which completely satisfy the differential equations governing the equilibrium for arbitrarily varying thickness functionally graded beams are derived for the first time. The undetermined coefficients in the general solution are obtained using Fourier series expansion along the upper and lower surfaces. The accuracy and efficiency of the proposed method are verified through several typical examples. The effects of mechanical and geometry parameters on the stress and displacement distributions of varying thickness functionally graded beams resting on a two-parameter Pasternak elastic foundation are discussed further.

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Guo, Tongqing, Di Zhou, and Zhiliang Lu. "A Double-Passage Shape Correction Method for Predictions of Unsteady Flow and Aeroelasticity in Turbomachinery." Advances in Applied Mathematics and Mechanics 9, no. 4 (January 18, 2017): 839–60. http://dx.doi.org/10.4208/aamm.2016.m1478.

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AbstractIn this paper, a double-passage shape correction (DPSC) method is presented for simulation of unsteady flows around vibrating blades and aeroelastic prediction. Based on the idea of phase-lagged boundary conditions, the shape correction method was proposed aimed at efficiently dealing with unsteady flow problems in turbomachinery. However, the original single-passage shape correction (SPSC) may show the disadvantage of slow convergence of unsteady solutions and even produce nonphysical oscillation. The reason is found to be related with the disturbances on the circumferential boundaries that can not be damped by numerical schemes. To overcome these difficulties, the DPSC method is adopted here, in which the Fourier coefficients are computed from flow variables at implicit boundaries instead of circumferential boundaries in the SPSC method. This treatment actually reduces the interaction between the calculation of Fourier coefficients and the update of flow variables. Therefore a faster convergence speed could be achieved and also the solution stability is improved. The present method is developed to be suitable for viscous and turbulent flows. And for real three-dimensional (3D) problems, the rotating effects are also considered. For validation, a 2D oscillating turbine cascade, a 3D oscillating flat plate cascade and a 3D practical transonic fan rotor are investigated. Comparisons with experimental data or other solutions and relevant discussions are presented in detail. Numerical results show that the solution accuracy of DPSC method is favorable and at least comparable to the SPSC method. However, fewer iteration cycles are needed to get a converged and stable unsteady solution, which greatly improves the computational efficiency.

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Kapoor, Mamta, and Varun Joshi. "Numerical approximation of coupled 1D and 2D non-linear Burgers’ equations by employing Modified Quartic Hyperbolic B-spline Differential Quadrature Method." International Journal of Mechanics 15 (April 7, 2021): 37–55. http://dx.doi.org/10.46300/9104.2021.15.5.

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In this paper, the numerical solution of coupled 1D and coupled 2D Burgers' equation is provided with the appropriate initial and boundary conditions, by implementing "modified quartic Hyperbolic B-spline DQM". In present method, the required weighting coefficients are computed using modified quartic Hyperbolic B-spline as a basis function. These coupled 1D and coupled 2D Burgers' equations got transformed into the set of ordinary differential equations, tackled by SSPRK43 scheme. Efficiency of the scheme and exactness of the obtained numerical solutions is declared with the aid of 8 numerical examples. Numerical results obtained by modified quartic Hyperbolic B-spline are efficient and it is easy to implement

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Nkemzi, Boniface, and Jake Léonard Nkeck. "A Predictor-Corrector Finite Element Method for Time-Harmonic Maxwell’s Equations in Polygonal Domains." Mathematical Problems in Engineering 2020 (February 22, 2020): 1–13. http://dx.doi.org/10.1155/2020/3502513.

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The overall efficiency and accuracy of standard finite element methods may be severely reduced if the solution of the boundary value problem entails singularities. In the particular case of time-harmonic Maxwell’s equations in nonconvex polygonal domains Ω, H1-conforming nodal finite element methods may even fail to converge to the physical solution. In this paper, we present a new nodal finite element adaptation for solving time-harmonic Maxwell’s equations with perfectly conducting electric boundary condition in general polygonal domains. The originality of the present algorithm lies in the use of explicit extraction formulas for the coefficients of the singularities to define an iterative procedure for the improvement of the finite element solutions. A priori error estimates in the energy norm and in the L2 norm show that the new algorithm exhibits the same convergence properties as it is known for problems with regular solutions in the Sobolev space H2Ω2 in convex and nonconvex domains without the use of graded mesh refinements or any other modification of the bilinear form or the finite element spaces. Numerical experiments that validate the theoretical results are presented.

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Chen, Yingxue, and Linfeng Gou. "A Boosted Particle Swarm Method for Energy Efficiency Optimization of PRO Systems." Energies 14, no. 22 (November 17, 2021): 7688. http://dx.doi.org/10.3390/en14227688.

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The analytical solutions of complex dynamic PRO systems pose challenges to ensuring that maximum power can be harvested in stable, rapid, and efficient ways in response to varying operational environments. In this paper, a boosted particle swarm optimization (BPSO) method with enhanced essential coefficients is proposed to enhance the exploration and exploitation stages in the optimization process. Moreover, several state-of-the-art techniques are utilized to evaluate the proposed BPSO of scaled-up PRO systems. The competitive results revealed that the proposed method improves power density by up to 88.9% in comparison with other algorithms, proving its ability to provide superior performance with complex and computationally intensive derivative problems. The analysis and comparison of the popular and recent metaheuristic methods in this study could provide a reference for the targeted selection method for different applications.

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Bülbül, Berna, and Mehmet Sezer. "Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/691614.

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We have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. Duffing equation and conditions are transformed into the matrix equations, which corresponds to a system of nonlinear algebraic equations with the unknown coefficients, via collocation points. Combining these matrix equations and then solving the system yield the unknown coefficients of the solution function. Numerical examples are included to demonstrate the validity and the applicability of the technique. The results show the efficiency and the accuracy of the present work. Also, the method can be easily applied to engineering and science problems.

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Ribeiro, Filipe, Pedro Albuquerque, Pedro Gamboa, and Kouamana Bousson. "Use of Multiquadric Functions for Multivariable Representation of the Aerodynamic Coefficients of Airfoils." Mathematical Problems in Engineering 2021 (April 23, 2021): 1–21. http://dx.doi.org/10.1155/2021/6615601.

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Given an array (or matrix) of values for a function of one or more variables, it is often desired to find a value between two given points. Multivariable interpolation and approximation by radial basis functions are important subjects in approximation theory that have many applications in Science and Engineering fields. During the last decades, radial basis functions (RBFs) have found increasingly widespread use for functional approximation of scattered data. This research work aims at benchmarking two different approaches: an approximation by radial basis functions and a piecewise linear multivariable interpolation in terms of their effectiveness and efficiency in order to conclude about the advantages and disadvantages of each approach in approximating the aerodynamic coefficients of airfoils. The main focus of this article is to study the main factors that affect the accuracy of the multiquadric functions, including the location and quantity of centers and the choice of the form factor. It also benchmarks them against piecewise linear multivariable interpolation regarding their precision throughout the selected domain and the computational cost required to accomplish a given amount of solutions associated with the aerodynamic coefficients of lift, drag and pitching moment. The approximation functions are applied to two different multidimensional cases: two independent variables, where the aerodynamic coefficients depend on the Reynolds number (Re) and the angle-of-attack (α), and four independent variables, where the aerodynamic coefficients depend on Re, α, flap chord ratio (cflap), and flap deflection (δflap).

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Ahmed, Hazem A., Hamed Salah, Joerg Robert, and Albert Heuberger. "A Closed-Form Solution for ALOHA Frame Length Optimizing Multiple Collision Recovery Coefficients’ Reading Efficiency." IEEE Systems Journal 12, no. 1 (March 2018): 1047–50. http://dx.doi.org/10.1109/jsyst.2016.2539380.

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Qian, Mengqi, Yuwei Zuo, Zhihao Chen, Xiaoshuang Yin, Ying Liu, Wenzhong Yang, and Yun Chen. "Crystallization of CaCO3 in Aqueous Solutions with Extremely High Concentrations of NaCl." Crystals 9, no. 12 (December 6, 2019): 647. http://dx.doi.org/10.3390/cryst9120647.

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The effect of NaCl at extremely high concentrations from 3.5 to 14 wt. % on the crystallization of CaCO3 was investigated in depth. The static test experiment verified that the Ca2+ retention efficiency (η) of NaCl on CaCO3 scale increased from 31.06% (3.5 wt. %) to 41.56% (14 wt. %). Based on the calculation of supersaturation rations, the high concentration of NaCl could reduce the activity coefficients of [Ca2+] and [CO32−], thus reducing the actual concentration of CaCO3. The CaCO3 deposition rate constants (k) showed that NaCl slowed down the rate of CaCO3 crystallization. The X–ray diffraction (XRD) testing disclosed that the growth of (1 0 4) and (1 1 0) faces from calcite was impeded, while the formation of (1 1 1) face from aragonite was induced by the increasing concentration of NaCl. The inductively coupled plasma optical emission spectrometry (ICP–OES) results indicated that Na+ could be doped into CaCO3, leading to the one–dimensional crystal growth. It was further proved that NaCl heightens the efficiency of the typical phosphate inhibitors (2–phosphonobutane–1,2,4–tricarboxylic acid (PBTCA) and 1–hydroxyethane–1,1–diphosphonic acid (HEDP)) on prohibiting the scale of CaCO3.

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Thomazelli, Rodolfo, and Stelamaris Bertoli. "An experimental study on the optimization of the production and efficiency of tunable Helmholtz absorbers for the modal control of small rooms." Building Acoustics 26, no. 2 (February 24, 2019): 69–91. http://dx.doi.org/10.1177/1351010x19829870.

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Helmholtz absorbers are a common solution for controlling the low-frequency modes found in small rooms. These devices only perform in a narrow spectrum range with the tuning depending on each room’s geometrical configurations. Consequently, their development still operates on a case-by-case basis. A possible alternative to optimize the production of these acoustic solutions is the development of a tunable Helmholtz absorber capable of changing its geometrical configurations according to each room’s acoustic needs. The present work shares the results of tests performed on varied samples of different configurations of absorbers. The samples were chosen aiming the control of the three first modes of each direction in rooms with volume ranging from 20 to 60 m3. The research revealed that the use of a single tunable absorber has the potential to produce sound absorption coefficients higher than 0.8 in almost the entirety of the frequency spectrum considered.

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Lee, Sen Yung, and Yee Hsiung Kuo. "Exact Solutions for the Analysis of General Elastically Restrained Nonuniform Beams." Journal of Applied Mechanics 59, no. 2S (June 1, 1992): S205—S212. http://dx.doi.org/10.1115/1.2899490.

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The exact solutions for the problems governed by a general self-adjoint fourth-order nonhomogeneous ordinary differential equation with arbitrarily polynomial varying coefficients and general elastic boundary conditions are derived in Green’s function form. To illustrate the analysis, the static deflection and dynamic analysis of a general eiastically end restrained Bernoulli-Euler beam with polynomial varying bending rigidity, applied axial and force, and elastic foundation modulus along the beam, subjected to an arbitrary transverse force are presented. The Green’s function is concisely expressed in terms of the four normalized fundamental solutions of the system and these fundamental solutions are given in power series forms. The characteristic equations for elastic stability and free vibrational analysis of the beam can be obtained by setting the denominator of the corresponding Green’s function equal to zero. Finally, examples are given to illustrate the accuracy and efficiency of the analysis.

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Sun, Yanhong, Yi Qiu, Lianyun Liu, and Xu Zheng. "Three-Dimensional Acoustic Analysis of a Rectangular Duct with Gradient Cross-Sections in High-Speed Trains: A Theoretical Derivation." Applied Sciences 12, no. 11 (May 24, 2022): 5307. http://dx.doi.org/10.3390/app12115307.

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Rectangular ducts used in the air-conditioning system of a high-speed train should be carefully designed to achieve optimal acoustic and flow performance. However, the theoretical analysis of the rectangular ducts with gradient cross-sections (RDGC) at frequencies higher than the one-dimensional cut-off frequency is rarely published. This paper has developed the three-dimensional analytical solutions to the wave equations of the expanding and shrinking RDGCs. Firstly, a homogeneous second-order variable coefficient differential equation is derived from the wave equations. Two coefficients of the solution to the differential equation are set to zero to ensure convergence. Secondly, the transfer matrices of the duct systems composed of multiple RDGCs are derived from the three-dimensional solutions. The transmission losses of the duct systems are then calculated from the transfer matrices and validated with the measurement. Finally, the acoustic performance and flow efficiency of the RDGCs with different geometries are discussed. The results show that the REC with double baffles distributed transversely has good performance in both acoustic attenuation and flow efficiency. This study shall provide a helpful guide for designing rectangular ducts used in high-speed trains.

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Amiri, Fatemeh, Mansooreh Dehghani, Zeinab Amiri, Saeed Yousefinejad, and Aboolfazl Azhdarpoor. "Photocatalytic degradation of 2,4-dichlorophenoxyacetic acid from aqueous solutions by Ag3PO4/TiO2 nanoparticles under visible light: kinetic and thermodynamic studies." Water Science and Technology 83, no. 12 (May 21, 2021): 3110–22. http://dx.doi.org/10.2166/wst.2021.193.

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Abstract Between the countless chemical substances applied in agriculture, 2,4-dichlorophenoxyacetic acid (2,4-D) herbicide is considered as a toxic and carcinogenic pollutant which is difficult to remove from water due to its biological and chemical stability and high solubility. The goal of this study was photocatalytic degradation of 2,4-D, using Ag3PO4/TiO2 nanoparticles under visible light. The Ag3PO4/TiO2 nanoparticles were characterized using XRD, FESEM and EDS analysis to investigate its crystal structure and elemental compounds. The effect of operating parameters such as pH, contact time, catalyst dose, and initial concentration of herbicide on the efficiency of the process was studied. Increasing the pH and initial concentration of herbicide led to the reduction of the efficiency of removing the herbicide, while increasing contact time and catalyst dose increased the efficiency. The best result (98.4% removal efficiency) was achieved at pH = 3, 1 g/L catalyst dose, 60 min contact time, and 10 mg/L initial concentration of 2,4-D. According to the results, 2,4-D removal efficiency with Ag3PO4/TiO2 photocatalyst reached 96.1% from 98.4% after 5 cycles of reaction. The pseudo-first-order kinetics was the best fit for the 2,4-D degradation by Ag3PO4/TiO2 with correlation coefficients (R2 = 0.9945). The results demonstrated that the photocatalytic process using Ag3PO4/TiO2 nanoparticles in the presence of visible light had a relatively good efficiency in removing 2,4-D. Moreover, Ag3PO4/TiO2 can be used as a reusable photocatalyst for the degradation of such toxins from polluted water and wastewater.

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Liu, Qingxin, Ni Li, Heming Jia, Qi Qi, Laith Abualigah, and Yuxiang Liu. "A Hybrid Arithmetic Optimization and Golden Sine Algorithm for Solving Industrial Engineering Design Problems." Mathematics 10, no. 9 (May 6, 2022): 1567. http://dx.doi.org/10.3390/math10091567.

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Анотація:

Arithmetic Optimization Algorithm (AOA) is a physically inspired optimization algorithm that mimics arithmetic operators in mathematical calculation. Although the AOA has an acceptable exploration and exploitation ability, it also has some shortcomings such as low population diversity, premature convergence, and easy stagnation into local optimal solutions. The Golden Sine Algorithm (Gold-SA) has strong local searchability and fewer coefficients. To alleviate the above issues and improve the performance of AOA, in this paper, we present a hybrid AOA with Gold-SA called HAGSA for solving industrial engineering design problems. We divide the whole population into two subgroups and optimize them using AOA and Gold-SA during the searching process. By dividing these two subgroups, we can exchange and share profitable information and utilize their advantages to find a satisfactory global optimal solution. Furthermore, we used the Levy flight and proposed a new strategy called Brownian mutation to enhance the searchability of the hybrid algorithm. To evaluate the efficiency of the proposed work, HAGSA, we selected the CEC 2014 competition test suite as a benchmark function and compared HAGSA against other well-known algorithms. Moreover, five industrial engineering design problems were introduced to verify the ability of algorithms to solve real-world problems. The experimental results demonstrate that the proposed work HAGSA is significantly better than original AOA, Gold-SA, and other compared algorithms in terms of optimization accuracy and convergence speed.

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Chung, Eric, Hyea-Hyun Kim, Ming-Fai Lam, and Lina Zhao. "Learning Adaptive Coarse Spaces of BDDC Algorithms for Stochastic Elliptic Problems with Oscillatory and High Contrast Coefficients." Mathematical and Computational Applications 26, no. 2 (June 6, 2021): 44. http://dx.doi.org/10.3390/mca26020044.

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In this paper, we consider the balancing domain decomposition by constraints (BDDC) algorithm with adaptive coarse spaces for a class of stochastic elliptic problems. The key ingredient in the construction of the coarse space is the solutions of local spectral problems, which depend on the coefficient of the PDE. This poses a significant challenge for stochastic coefficients as it is computationally expensive to solve the local spectral problems for every realization of the coefficient. To tackle this computational burden, we propose a machine learning approach. Our method is based on the use of a deep neural network (DNN) to approximate the relation between the stochastic coefficients and the coarse spaces. For the input of the DNN, we apply the Karhunen–Loève expansion and use the first few dominant terms in the expansion. The output of the DNN is the resulting coarse space, which is then applied with the standard adaptive BDDC algorithm. We will present some numerical results with oscillatory and high contrast coefficients to show the efficiency and robustness of the proposed scheme.

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30

Ramadan, Mohamed A., Heba S. Osheba, and Adel R. Hadhoud. "A Highly Efficient and Accurate Finite Iterative Method for Solving Linear Two-Dimensional Fredholm Fuzzy Integral Equations of the Second Kind Using Triangular Functions." Mathematical Problems in Engineering 2020 (August 29, 2020): 1–16. http://dx.doi.org/10.1155/2020/2028763.

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This work introduces a computational method for solving the linear two-dimensional fuzzy Fredholm integral equation of the second form (2D-FFIE-2) based on triangular basis functions. We have used the parametric form of fuzzy functions and transformed a 2D-FFIE-2 with three variables in crisp case to a linear Fredholm integral equation of the second kind. First, a method based on the use of two m-sets of orthogonal functions of triangular form is implemented on the integral equation under study to be changed to coupled algebraic equation system. In order to solve these two schemes, a finite iterative algorithm is then applied to evaluate the coefficients that provided the approximate solution of the integral problems. Three examples are given to clarify the efficiency and accuracy of the method. The obtained numerical results are compared with other direct and exact solutions.

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31

Bataineh, Malik, Mohammad Alaroud, Shrideh Al-Omari, and Praveen Agarwal. "Series Representations for Uncertain Fractional IVPs in the Fuzzy Conformable Fractional Sense." Entropy 23, no. 12 (December 7, 2021): 1646. http://dx.doi.org/10.3390/e23121646.

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Fuzzy differential equations provide a crucial tool for modeling numerous phenomena and uncertainties that potentially arise in various applications across physics, applied sciences and engineering. Reliable and effective analytical methods are necessary to obtain the required solutions, as it is very difficult to obtain accurate solutions for certain fuzzy differential equations. In this paper, certain fuzzy approximate solutions are constructed and analyzed by means of a residual power series (RPS) technique involving some class of fuzzy fractional differential equations. The considered methodology for finding the fuzzy solutions relies on converting the target equations into two fractional crisp systems in terms of ρ-cut representations. The residual power series therefore gives solutions for the converted systems by combining fractional residual functions and fractional Taylor expansions to obtain values of the coefficients of the fractional power series. To validate the efficiency and the applicability of our proposed approach we derive solutions of the fuzzy fractional initial value problem by testing two attractive applications. The compatibility of the behavior of the solutions is determined via some graphical and numerical analysis of the proposed results. Moreover, the comparative results point out that the proposed method is more accurate compared to the other existing methods. Finally, the results attained in this article emphasize that the residual power series technique is easy, efficient, and fast for predicting solutions of the uncertain models arising in real physical phenomena.

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Abbasbandy, S., and J. Hajishafieiha. "Numerical solution to the Falkner-Skan equation: a novel numerical approach through the new rational a-polynomials." Applied Mathematics and Mechanics 42, no. 10 (September 29, 2021): 1449–60. http://dx.doi.org/10.1007/s10483-021-2777-5.

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Анотація:

AbstractThe new rational a-polynomials are used to solve the Falkner-Skan equation. These polynomials are equipped with an auxiliary parameter. The approximated solution to the Falkner-Skan equation is obtained by the new rational a-polynomials with unknown coefficients. To find the unknown coefficients and the auxiliary parameter contained in the polynomials, the collocation method with Chebyshev-Gauss points is used. The numerical examples show the efficiency of this method.

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Li, Fenglan, Tianshun Yan, and Liyun Su. "Solution of an Integral-Differential Equation Arising in Oscillating Magnetic Fields Using Local Polynomial Regression." Advances in Mechanical Engineering 6 (January 1, 2014): 101230. http://dx.doi.org/10.1155/2014/101230.

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An integrodifferential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The local polynomial regression method (LPR) is used to solve this equation. The reliability of this method and the reduction in the size of computational domain give this method a wider applicability. Several representative examples are given to reconfirm the efficiency of these algorithms. The results of applying this theory to the integro-differential equation with time-periodic coefficients reveal that LPR method possesses very high accuracy, adaptability, and efficiency.

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Petrovic, Marija, Tatjana Sostaric, Lato Pezo, Slavka Stankovic, Caslav Lacnjevac, Jelena Milojkovic, and Mirjana Stojanovic. "Usefulness of ANN-based model for copper removal from aqueous solutions using agro industrial waste materials." Chemical Industry and Chemical Engineering Quarterly 21, no. 2 (2015): 249–59. http://dx.doi.org/10.2298/ciceq140510023p.

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The purpose of this study was to investigate the adsorption properties of locally available lignocelluloses biomaterials as biosorbents for the removal of copper ions from aqueous solution. Materials are generated from juice production (apricot stones) and from the corn milling process (corn cob). Such solid wastes have little or no economic value and very often present a disposal problem. Using batch adsorption techniques the effects of initial Cu(II) ions concentration (Ci), amount of biomass (m) and volume of metal solution (V), on biosorption efficiency and capacity were studied for both materials, without any pre-treatments. The optimal parameters for both biosorbents were selected depending on a highest sorption capability of biosorbent, in removal of Cu(II). Experimental data were compared with second order polynomial regression models (SOPs) and artificial neural networks (ANNs). SOPs showed acceptable coefficients of determination (0.842 - 0.997), while ANNs performed high prediction accuracy (0.980-0.986) in comparison to experimental results.

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35

Chang, Feng, Weiqiang Wang, Yan Liu, and Yanpeng Qu. "A Fortran implementation of isogeometric analysis for thin plate problems with the penalty method." Engineering Computations 33, no. 7 (October 3, 2016): 2149–64. http://dx.doi.org/10.1108/ec-10-2015-0306.

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Purpose As one of the earliest high-level programming languages, Fortran with easy accessibility and computational efficiency is widely used in the engineering field. The purpose of this paper is to present a Fortran implementation of isogeometric analysis (IGA) for thin plate problems. Design/methodology/approach IGA based on non-uniform rational B-splines (NURBS) offers exact geometries and is more accurate than finite element analysis (FEA). Unlike the basis functions in FEA, NURBS basis functions are non-interpolated. Hence, the penalty method is used to enforce boundary conditions. Findings Several thin plate examples based on the Kirchhoff-Love theory were illustrated to demonstrate the accuracy of the implementation in contrast with analytical solutions, and the efficiency was validated in comparison with another open method. Originality/value A Fortran implementation of NURBS-based IGA was developed to solve Kirchhoff-Love plate problems. It easily obtained high-continuity basis functions, which are necessary for Kirchhoff formulation. In comparison with theoretical solutions, the numerical examples demonstrated higher accuracy and faster convergence of the Fortran implementation. The Fortran implementation can well solve the time-consuming problem, and it was validated by the time-consumption comparison with the Matlab implementation. Due to the non-interpolation of NURBS, the penalty method was used to impose boundary conditions. A suggestion of the selection of penalty coefficients was given.

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Mossaiby, Farshid, Majid Bazrpach, and Arman Shojaei. "Extending the method of exponential basis functions to problems with singularities." Engineering Computations 32, no. 2 (April 20, 2015): 406–23. http://dx.doi.org/10.1108/ec-01-2014-0019.

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Анотація:

Purpose – The purpose of this paper is to aim at extending the method of exponential basis functions (EBF) to solve a class of problems with singularities. Design/methodology/approach – In the procedure of EBF a summation of EBF satisfying the governing differential equation with unknown constant coefficients is considered for the solution. These coefficients are determined by the satisfaction of prescribed boundary conditions through a collocation approach. The applied basis functions are available in the case of linear partial differential equations (PDEs) with constant coefficients. Moreover, the method contributes to yield highly accurate results with ultra convergence rates for problems with smooth solution. This leads EBF to offer many advantages for a variety of engineering problems. However, owing to the global and smooth nature of the bases, the performance of EBF deteriorates in problems with singularities. In the present study, some exponential-like influence functions are developed, and a few of them are added to original bases. Findings – The new bases are capable of forming the constitutive terms of the asymptotic solution near the singularity points and alleviate the aforementioned limitation. The appealing feature of this method is that all the advantages of EBF such as its simplicity and efficiency are completely preserved. Research limitations/implications – In its current form, EBF can only solve PDEs with constant coefficients. Originality/value – Application of the method to some benchmark problems demonstrates its robustness over some other boundary approximation methods. This research may pave the road for future investigations corresponding to a wide range of practical engineering problems.

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Taparcevska, Julija, Liljana Markovska, Bogdana Koumanova, and Vera Meshko. "Diffusion models for adsorption kinetics of Zn2+ , Cd2+ and Pb2+ onto natural zeolite." Water Science and Technology 62, no. 5 (September 1, 2010): 1136–42. http://dx.doi.org/10.2166/wst.2010.918.

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The kinetics of zinc, cadmium, and lead ions removal by natural zeolite-clinoptilolite has been investigated using an agitated batch adsorber. Batch experiments at constant temperature have been performed. The influence of agitation speed, initial heavy metals concentration and particle size of the sorbent on the removal efficiency of heavy metals from liquid phase have been studied. A decrease in the initial heavy metals concentration in aqueous solutions prolongs the time needed for equilibrium. Two kinetics models according to the Vermeulen's approximation and the parabolic diffusion model have been tested with the experimental data for adsorption of heavy metals onto natural zeolite. For the systems examined, the fit of the proposed models with the experimental data was shown to be equally good using both models. The diffusion coefficients are calculated from kinetic models of heavy metal ions and they are of the order from 10−5 to 10−6 cm2/min. The diffusion coefficients depend on initial concentration for both models.

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38

Boudana, Marwa, Samir Ladaci та Jean-Jacques Loiseau. "Fractional Order PIλDµ Control Design for a Class of Cyber-Physical Systems with Fractional Order Time-Delay models". International Journal of Cyber-Physical Systems 1, № 2 (липень 2019): 1–18. http://dx.doi.org/10.4018/ijcps.2019070101.

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The control of cyber-physical systems (CPS) is a great challenge for researchers in control theory and engineering mainly because of delays induced by merging computation, communication, and control of physical processes. Consequently, control solutions for time-delay systems can be applied efficiently for many CPS system configurations. In this article, a fractional order PIλ and PIλDµ control design is investigated for a class of fractional order time-delay systems. The proposed control design approach is simple and efficient. The controller parameter's adjustment is achieved in two steps: first, the relay approach is used to compute satisfactory classical PID coefficients, namely kp, Ti and Td. Then, the fractional orders λ and µ are optimized using performance criteria. Simulation results show the efficiency of the proposed design technique and its ability to enhance the PID control performance.

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39

Shevchenko, Viktor, Bohdan Pakhaliuk, Janis Zakis, Oleksandr Veligorskyi, Jaroslaw Luszcz, Oleksandr Husev, Oleksandr Lytvyn, and Oleksandr Matiushkin. "Closed-Loop Control System Design for Wireless Charging of Low-Voltage EV Batteries with Time-Delay Constraints." Energies 14, no. 13 (June 30, 2021): 3934. http://dx.doi.org/10.3390/en14133934.

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This paper presents an inductive power transfer system on the basis of a double single-phase three-level T-type inverter and two split transmitting coils for constant current and constant voltage wireless charging of low-voltage light electric vehicle batteries with closed-loop control, considering time-delay communication constraints. An optimal control structure and a modified control strategy were chosen and implemented to the wireless power transfer system as a result of a review and analysis of existing solutions. The control system analysis and adjustment of the coefficients of the regulator using Laplace transform were performed. Our study addressed the behavior of the control system with different time delays as well as the dynamic response of the system. The detecting algorithm of a secondary coil was proposed, which ensured efficient system operation and increased the functionality, safety and usability of the device. The efficiency of energy transfer of 90% was reached at the transmitted power of 110 W, which is at the level of existing solutions considered in the article and opens the way to the commercialization of the proposed solution. Therefore, the feasibility of using a nonclassical multilevel inverter, together with split transmitting coils for wireless charging was confirmed.

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Yuan, Si, Kangsheng Ye, Yongliang Wang, David Kennedy, and Frederic W. Williams. "Adaptive finite element method for eigensolutions of regular second and fourth order Sturm-Liouville problems via the element energy projection technique." Engineering Computations 34, no. 8 (November 6, 2017): 2862–76. http://dx.doi.org/10.1108/ec-03-2017-0090.

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Purpose The purpose of this paper is to present a numerically adaptive finite element (FE) method for accurate, efficient and reliable eigensolutions of regular second- and fourth-order Sturm–Liouville (SL) problems with variable coefficients. Design/methodology/approach After the conventional FE solution for an eigenpair (i.e. eigenvalue and eigenfunction) of a particular order has been obtained on a given mesh, a novel strategy is introduced, in which the FE solution of the eigenproblem is equivalently viewed as the FE solution of an associated linear problem. This strategy allows the element energy projection (EEP) technique for linear problems to calculate the super-convergent FE solutions for eigenfunctions anywhere on any element. These EEP super-convergent solutions are used to estimate the FE solution errors and to guide mesh refinements, until the accuracy matches user-preset error tolerance on both eigenvalues and eigenfunctions. Findings Numerical results for a number of representative and challenging SL problems are presented to demonstrate the effectiveness, efficiency, accuracy and reliability of the proposed method. Research limitations/implications The method is limited to regular SL problems, but it can also solve some singular SL problems in an indirect way. Originality/value Comprehensive utilization of the EEP technique yields a simple, efficient and reliable adaptive FE procedure that finds sufficiently fine meshes for preset error tolerances on eigenvalues and eigenfunctions to be achieved, even on problems which proved troublesome to competing methods. The method can readily be extended to vector SL problems.

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Liu, Mei Lin, Ren Man Ruan, Jian Kang Wen, and Dian Zuo Wang. "Investigation of Viscosity and Thermodynamic Properties on the Bioleaching Solution with and without Mesophilic Bacteria." Advanced Materials Research 20-21 (July 2007): 149–51. http://dx.doi.org/10.4028/www.scientific.net/amr.20-21.149.

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In this study, the viscosities and conductivities of bioleaching solution were determined by Ubbelohde viscometer and conductivity meter, respectively. The mean ionic activity coefficients, relative partial molar free energies of copper bioleaching solution at above experimental temperatures ranging from 298 K to 313 K have been calculated. Simultaneously, these characters of copper bioleaching solution were compared with and without mesophilic bacteria. The experimental data showed that the viscosities and thermodynamic properties for bioleaching solution would be crucial to minimize the third phase formation so as to increase extraction efficiency.

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Pietrzyk, Maciej, Jan Kusiak, Danuta Szeliga, Łukasz Rauch, Łukasz Sztangret, and Grzegorz Górecki. "Application of Metamodels to Identification of Metallic Materials Models." Advances in Materials Science and Engineering 2016 (2016): 1–20. http://dx.doi.org/10.1155/2016/2357534.

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Improvement of the efficiency of the inverse analysis (IA) for various material tests was the objective of the paper. Flow stress models and microstructure evolution models of various complexity of mathematical formulation were considered. Different types of experiments were performed and the results were used for the identification of models. Sensitivity analysis was performed for all the models and the importance of parameters in these models was evaluated. Metamodels based on artificial neural network were proposed to simulate experiments in the inverse solution. Performed analysis has shown that significant decrease of the computing times could be achieved when metamodels substitute finite element model in the inverse analysis, which is the case in the identification of flow stress models. Application of metamodels gave good results for flow stress models based on closed form equations accounting for an influence of temperature, strain, and strain rate (4 coefficients) and additionally for softening due to recrystallization (5 coefficients) and for softening and saturation (7 coefficients). Good accuracy and high efficiency of the IA were confirmed. On the contrary, identification of microstructure evolution models, including phase transformation models, did not give noticeable reduction of the computing time.

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Li, Chao, De-Long Xu, Wen-Quan Xie, Xian-Hui Zhang, and Si-Ze Yang. "Increasing the ⋅OH radical concentration synergistically with plasma electrolysis and ultrasound in aqueous DMSO solution." Chinese Physics B 31, no. 4 (March 1, 2022): 048706. http://dx.doi.org/10.1088/1674-1056/ac523d.

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Анотація:

In recent years, significant increases in waste processing and material engineering have been seen by using advanced oxidation processes. The treatment results and energy yields of these processes are largely determined by the generation and retention of reactive oxygen species (ROS). However, increasing the amount of ROS remains a key challenge because of the unavailability of performance- and energy-efficient techniques. In this study, plasma electrolysis, ultrasound, and plasma electrolysis combined with ultrasound were used to treat dimethyl sulfoxide (DMSO) solutions, and the results showed that the two methods can synergistically convert filament discharge into spark discharge, and the conversion of the discharge mode can significantly increase the concentration of OH radicals and effectively improve the efficiency of DMSO degradation. We verified the rationality of the results by analyzing the mass transfer path of ROS based on the reaction coefficients and found that the ⋅OH radicals in aqueous solution were mainly derived from the decomposition of hydrogen peroxide. These findings indicated that the synergistic action of plasma electrolysis and ultrasound can enhance the production of chemically reactive species, and provide new insights and guiding principles for the future translation of this combined strategy into real-life applications. Our results demonstrated that the synergistic strategy of ultrasound and plasma electrolysis is feasible in the switching mode and increasing the ROS, and may open new routes for materials engineering and pollutant degradation.

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Feng, Fei Long, Jian Zhong Shen, Jing Jun Deng, and Qiu Ping Wang. "Analytical Solution of Lamb Wave Scattering at Plate End." Advanced Materials Research 199-200 (February 2011): 949–52. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.949.

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An analytical solution based on modal decomposition is presented to investigate Lamb wave scattering at plate end. Take boundary condition into biorthogonality relation, a matrix equation is established with all matrix elements have analytical expressions. The scattering feature is then expressed in matrix form, named as reflection matrix, which has explicit expression composed of those matrixes. Calculation examples have be implemented when antisymmetric modes are reflected. Scattering coefficients are figured out in a range when frequency-thickness product vary from 0 to 8kHzm, to prove the calculation efficiency. The calculation precision is very close to the least square method based on model discretization.

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Zhao, Jian, Haiyang Li, Xiangyue He, Yuechen Huang, and Jianghui Liu. "Uncertainty Analysis for Return Trajectory of Vertical Takeoff and Vertical Landing Reusable Launch Vehicle." Mathematical Problems in Engineering 2020 (July 11, 2020): 1–18. http://dx.doi.org/10.1155/2020/4313758.

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The uncertainties during the return trajectory of vertical takeoff and vertical landing reusable launch vehicle weaken the ability of precision landing and make the return process more challenging. This paper is devoted to quantifying the probability uncertainty of return trajectory with uncertain parameters. The uncertainty model of return multi-flight-phase under the uncertainties of initial flight path angle, axial aerodynamic coefficient, and atmospheric density is established using the generalized polynomial chaos expansion method. By parameterizing random uncertainties and introducing random parameters into the uncertainty model, the uncertainty analysis problem of return trajectory is transformed into stochastic trajectory approximation problem. The coefficients of the polynomial basis function are solved by the stochastic collocation method. Then state solutions, statistical properties, and global sensitivity with Sobol index are established based on coefficients. The simulation results show the efficiency and accuracy of this method compared with the Monte Carlo method, the evolution process of main output parameters under random parameters, and relative importance for random parameters. Through the uncertainty analysis of the return trajectory, the robustness of return trajectory can be quantified, which is contributed to improving the safety, reliability, and robustness of recovery and landing mission.

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Hussain, Nadia, Salam Alwan, Hassan Alshamsi, and Ibrahim Sahib. "Green Synthesis of S- and N-Codoped Carbon Nanospheres and Application as Adsorbent of Pb (II) from Aqueous Solution." International Journal of Chemical Engineering 2020 (March 16, 2020): 1–13. http://dx.doi.org/10.1155/2020/9068358.

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In this paper, green and facile synthesis of sulfur- and nitrogen-codoped carbon nanospheres (CNs) was prepared from the extract of Hibiscus sabdariffa L by a direct hydrothermal method. Finally, sulfur-carbon nanospheres (CNs) were used as the adsorbent to remove Pb+2 ions from aqueous solutions because of the high surface area of S-CNs from CNs and N-CNs. The synthesized nanospheres were examined by Fourier transform infrared (FTIR) spectroscopy, X-ray diffraction (XRD), field emission scanning electron microscopy, transmission electron microscopy (TEM), and nitrogen adsorption-desorption isotherms. The results show spherical shapes have a particle size of up to 65 nm with a high surface area capable of absorbing lead ions efficiently. Additionally, the factors affecting the process of adsorption that include equilibrium time, temperature, pH solution, ionic intensity, and adsorbent dose were studied. The equilibrium removal efficiency was studied employing Langmuir, Freundlich, and Temkin isotherm forms. The kinetic data were analyzed with two different kinetic models, and both apply to the adsorption process depending on the values of correlation coefficients. The thermodynamic parameters including Gibbs free energy (ΔG°), standard enthalpy change (ΔH°), and standard entropy change (ΔS°) were calculated for the adsorption process.

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Tchier, Fairouz, Ioannis Dassios, Ferdous Tawfiq, and Lakhdar Ragoub. "On the Approximate Solution of Partial Integro-Differential Equations Using the Pseudospectral Method Based on Chebyshev Cardinal Functions." Mathematics 9, no. 3 (February 1, 2021): 286. http://dx.doi.org/10.3390/math9030286.

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Анотація:

In this paper, we apply the pseudospectral method based on the Chebyshev cardinal function to solve the parabolic partial integro-differential equations (PIDEs). Since these equations play a key role in mathematics, physics, and engineering, finding an appropriate solution is important. We use an efficient method to solve PIDEs, especially for the integral part. Unlike when using Chebyshev functions, when using Chebyshev cardinal functions it is no longer necessary to integrate to find expansion coefficients of a given function. This reduces the computation. The convergence analysis is investigated and some numerical examples guarantee our theoretical results. We compare the presented method with others. The results confirm the efficiency and accuracy of the method.

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Wang, Cheng, and Bin Yang. "The Super-Exponential Algorithm of Blind Equalization for Time-Varying Channel Based on Basis Expansion Model." Advanced Materials Research 756-759 (September 2013): 3125–30. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.3125.

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Existing algorithms of blind equalization for time-varying channels are slow in convergence, easily interfered, and hard to pinpoint the location of pulsation in the frequency domain. In this paper we present a new blind equalization method that addresses the aforementioned issues. The new solution combines super-exponential algorithm with carrier frequency-offset estimation for time-varying channels. The time-varying channel taps described by the complex exponential basis expansion model (CE-BEM) are expressed as a superposition of time-varying complex exponential bases with time-invariant coefficients. We first employ a super-exponential algorithm to remove the inter-symbol interference caused by time-invariant coefficients. Then we estimate channel pulsation from equalized signals with a carrier frequency-offset estimation algorithm. Compared with existing ones, our solution converges faster with lower inter-symbol interference and easier specification of the pulsation in frequency domain. Simulation results prove the efficiency of the proposed algorithm.

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Ujlayan, Amit, and Ajay Dixit. "Hybrid Method for Solution of Fractional Order Linear Differential Equation with Variable Coefficients." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 6 (September 25, 2018): 621–26. http://dx.doi.org/10.1515/ijnsns-2017-0167.

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AbstractIn this paper, we proposed a new analytical hybrid methods for the solution of conformable fractional differential equations (CFDE), which are based on the recently proposed conformable fractional derivative (CFD) in R. Khalil, M. Al Horani, A. Yusuf and M. Sababhed, A New definition of fractional derivative, J. Comput. Appl. 264 (2014). Moreover, we use the method of variation of parameters and reduction of order based on CFD, for the CFDE. Furthermore, to show the efficiency of the proposed analytical hybrid method, some examples are also presented.

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50

Adibi, Hojatollah, and Pouria Assari. "Chebyshev Wavelet Method for Numerical Solution of Fredholm Integral Equations of the First Kind." Mathematical Problems in Engineering 2010 (2010): 1–17. http://dx.doi.org/10.1155/2010/138408.

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A computational method for solving Fredholm integral equations of the first kind is presented. The method utilizes Chebyshev wavelets constructed on the unit interval as basis in Galerkin method and reduces solving the integral equation to solving a system of algebraic equations. The properties of Chebyshev wavelets are used to make the wavelet coefficient matrices sparse which eventually leads to the sparsity of the coefficients matrix of obtained system. Finally, numerical examples are presented to show the validity and efficiency of the technique.

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