The work is devoted to a new semi-analytical method, to treat the classical dual integral equation of the lifting surface theory. The method operates with the initial form of the integral equation, and no preliminary ...
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The work is devoted to a new semi-analytical method, to treat the classical dual integral equation of the lifting surface theory. The method operates with the initial form of the integral equation, and no preliminary transformation is needed for the applied efficient approach. (C) 2018 Elsevier Ltd. All rights reserved.
A new algorithm is proposed to calculate the behavior of non-linear equations with multiple solutions. Use of this algorithm is demonstrated by calculation of compositions in an adsorbed layer for a vapor that exhibit...
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A new algorithm is proposed to calculate the behavior of non-linear equations with multiple solutions. Use of this algorithm is demonstrated by calculation of compositions in an adsorbed layer for a vapor that exhibits two-dimensional condensation. (C) 1998 Elsevier Science Ltd. All rights reserved.
A simple numerical algorithm for the design of a rectangular directional coupler (RDC) with arbitrary couplings is proposed. The performance of a designed RDC is also described. It is seen that the measured data agree...
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A simple numerical algorithm for the design of a rectangular directional coupler (RDC) with arbitrary couplings is proposed. The performance of a designed RDC is also described. It is seen that the measured data agree well with the results predicted by using the proposed algorithm.
The paper investigates the finite-time stability (FTS) analysis of a very general class of nonlinear time-varying systems. The FTS of the considered system, whose vector field consists of a nonlinear part which can be...
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The paper investigates the finite-time stability (FTS) analysis of a very general class of nonlinear time-varying systems. The FTS of the considered system, whose vector field consists of a nonlinear part which can be sublinear or superlinear, and a linear part which can be time-varying, has not been fully studied before. By estimating the bound of the norm of the considered system's states with the generalised Gronwall-Bellman inequality, a sufficient criterion is established to guarantee the FTS of the considered system. To facilitate checking the criterion in practice, a novel numerical algorithm is proposed by numerically solving certain differential equations. Therefore, the FTS of the considered class of nonlinear time-varying systems can be easily analysed by the numerical algorithm. Further considering the numerical errors in the practical numerical computation, we strictly prove the credibility and programmability of the numerical algorithm in theory. Finally, three numerical examples are provided to illustrate the effectiveness the proposed results.
Though considerable efforts have been made to improve the precision of numerical algorithms for obtaining more accurate chatter stability prediction in milling process, a calculation boundary vulnerability, existing g...
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Though considerable efforts have been made to improve the precision of numerical algorithms for obtaining more accurate chatter stability prediction in milling process, a calculation boundary vulnerability, existing generally in numerical predictive methods, is usually ignored, which can significantly reduce accuracy of chatter stability prediction in certain calculated step lengths. Starting from the numerical solution of delay differential equation, this paper first gives a detailed mathematical derivation to demonstrate the beingness of the numerical calculation errors at the crucial step for two equal interval calculation methods of cutting force coefficients, and then discusses the impact of the errors on the convergence effect and prediction accuracy. Afterwards, the methods seeking and repairing the discrete number of time period with vulnerability are proposed, which are verified by the classic milling models. The presented technique could prevent this undesirable boundary vulnerability happening in numerical prediction of milling stability, and help the path planers obtain more accurate parameters which can achieve chatter free in the manufacturing process.
In this work, a matrix form of numerical algorithm for spectral shift is presented based on the novel nonequilibrium solvation model that is established by introducing the constrained equilibrium manipulation. This fo...
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In this work, a matrix form of numerical algorithm for spectral shift is presented based on the novel nonequilibrium solvation model that is established by introducing the constrained equilibrium manipulation. This form is convenient for the development of codes for numerical solution. By means of the integral equation formulation polarizable continuum model (IEF-PCM), a subroutine has been implemented to compute spectral shift numerically. Here, the spectral shifts of absorption spectra for several popular chromophores, N,N-diethyl-p-nitroaniline (DEPNA), methylenecyclopropene (MCP), acrolein (ACL) and p-nitroaniline (PNA) were investigated in different solvents with various polarities. The computed spectral shifts can explain the available experimental findings reasonably. Discussions were made on the contributions of solute geometry distortion, electrostatic polarization and other non-electrostatic interactions to spectral shift. (C) 2017 Elsevier B.V. All rights reserved.
The paper reports new software developments for symmetrical components estimation. Nonrecursive Newton-type algorithm is extended with the second stage algorithm for symmetrical components calculation from the estimat...
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The paper reports new software developments for symmetrical components estimation. Nonrecursive Newton-type algorithm is extended with the second stage algorithm for symmetrical components calculation from the estimated fundamental phasors of three-phase signals (arbitrary voltages or currents). The algorithm is not sensitive to power system frequency changes and to the harmonic distortion of input signals. The algorithm is tested through computer simulations and by using laboratory obtained input signals and those recorded in the real distribution network.
Let C be a real plane algebraic curve defined by the resultant of two polynomials (resp. by the discriminant of a polynomial). Geometrically such a curve is the projection of the intersection of the surfaces P (x, y, ...
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Let C be a real plane algebraic curve defined by the resultant of two polynomials (resp. by the discriminant of a polynomial). Geometrically such a curve is the projection of the intersection of the surfaces P (x, y, z) = Q (x, y, z) = 0 (resp. P(x, y, z) = az (x, y, z) = 0), and generically its singularities are nodes (resp. nodes and ordinary cusps). State-of-the-art numerical algorithms compute the topology of smooth curves but usually fail to certify the topology of singular ones. The main challenge is to find practical numerical criteria that guarantee the existence and the uniqueness of a singularity inside a given box B, while ensuring that B does not contain any closed loop of C. We solve this problem by first providing a square deflation system, based on subresultants, that can be used to certify numerically whether B contains a unique singularity p or not. Then we introduce a numeric adaptive separation criterion based on interval arithmetic to ensure that the topology of C in B is homeomorphic to the local topology at p. Our algorithms are implemented and experiments show their efficiency compared to state-of-the-art symbolic or homotopic methods. (C) 2016 Elsevier Ltd. All rights reserved.
In this paper, a numerical algorithm based on a new kind of tension B-spline, named hyperbolic-trigonometric tension B-spline method, is applied for solving Burgers-Huxley equation. This method is generated over the s...
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In this paper, a numerical algorithm based on a new kind of tension B-spline, named hyperbolic-trigonometric tension B-spline method, is applied for solving Burgers-Huxley equation. This method is generated over the space span {sin(tau t), cos(tau t), sinh(tau t), cosh(tau t), 1, t, ..., t(n-5)}, n >= 5, where tau is the tension parameter. Properties of it are the same in most of the properties of the usual polynomial B-splines and benefit from some other advantages, as well. Therefore, in this paper, we apply three methods consisting of trigonometric method, hyperbolic tension B-spline method, and our new hyperbolic-trigonometric tension B-spline method, to solve Burgers-Huxley equation. The convergence analysis is discussed. Then, we use some numerical examples to illustrate the accuracy and implementation of the proposed algorithm.
In the preceding companion paper (Bazant and Li, 1997), the solution of an aging viscoelastic structure containing a cohesive crack with a rate-dependent stress-displacement softening law was reduced to a system of on...
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In the preceding companion paper (Bazant and Li, 1997), the solution of an aging viscoelastic structure containing a cohesive crack with a rate-dependent stress-displacement softening law was reduced to a system of one-dimensional integro-differential equations involving compliance functions for points on the crack faces and the load point. An effective numerical algorithm for solving these equations, which dramatically reduces the computer time compared to the general two-dimensional finite element solution, is presented. The behavior of the model for various loading conditions is studied. It is shown that the model can closely reproduce the available experimental data from fracture tests with different loading rates spanning several orders of magnitude, and tests with sudden changes of the loading rate. Influence of the loading rate on the size effect and brittleness is also analyzed and is shown to agree with experiments.
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