The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise w...The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.展开更多
The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference.The phase equations for single-channel states and th...The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference.The phase equations for single-channel states and the coupled equations of multi-channel scattering are solved numerically using the 5^(th) order Runge-kutta method.We employ a piece-wise smooth reference potential comprising three Morse functions as the initial input.Leveraging a machine learning-based genetic algorithm,we optimize the model parameters to minimize the mean-squared error between simulated and anticipated phase shifts.Our approach yields inverse potentials for both single and multichannel scattering,achieving convergence to a mean-squared error≤10^(-3).The resulting scattering lengths"a_(0)"and effective ranges"r"for ^(3)S_(1) and ^(1)S_(0) states,expressed as[a_(0),r],are found to be[5.445(5.424),1.770(1.760)]and[–23.741(–23.749),2.63(2.81)],respectively;these values are in excellent agreement with experimental ones.Furthermore,the calculated total scattering cross-sections are highly consistent with their experimental counterparts,having a percentage error of less than 1%.This computational approach can be easily extended to obtain interaction potentials for charged particle scattering.展开更多
In this work,the(2+1)-dimensional Date–Jimbo–Kashiwara–Miwa(DJKM)equation is studied by means of the ■-dressing method.A new ■ problem has been constructed by analyzing the characteristic function and the Green’...In this work,the(2+1)-dimensional Date–Jimbo–Kashiwara–Miwa(DJKM)equation is studied by means of the ■-dressing method.A new ■ problem has been constructed by analyzing the characteristic function and the Green’s function of its Lax representation.Based on solving the ■ equation and choosing the proper spectral transformation,the solution of the DJKM equation is constructed.Furthermore,the more general solution of the DJKM equation can be also obtained by ensuring the evolution of the time spectral data.展开更多
We consider an inverse quadratic programming （IQP） problem in which the parameters in the objective function of a given quadratic programming （QP） problem are adjusted as little as possible so that a known feasibl...We consider an inverse quadratic programming （IQP） problem in which the parameters in the objective function of a given quadratic programming （QP） problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. This problem can be formulated as a minimization problem with a positive semidefinite cone constraint and its dual （denoted IQD（A, b）） is a semismoothly differentiable （SC^1） convex programming problem with fewer variables than the original one. In this paper a smoothing Newton method is used for getting a Karush-Kuhn-Tucker point of IQD（A, b）. The proposed method needs to solve only one linear system per iteration and achieves quadratic convergence. Numerical experiments are reported to show that the smoothing Newton method is effective for solving this class of inverse quadratic programming problems.展开更多
Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustr...Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustrate theoretical conclusions. Alternative methods of identification of obstacles are mentioned： the Support Function Method （SFM） and the Modified Rayleigh Conjecture （MRC） method.展开更多
文摘The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.
基金Support provided by Department of Science and Technology(DST),Government of India vide Grant No.DST/INSPIRE Fellowship/2020/IF200538。
文摘The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference.The phase equations for single-channel states and the coupled equations of multi-channel scattering are solved numerically using the 5^(th) order Runge-kutta method.We employ a piece-wise smooth reference potential comprising three Morse functions as the initial input.Leveraging a machine learning-based genetic algorithm,we optimize the model parameters to minimize the mean-squared error between simulated and anticipated phase shifts.Our approach yields inverse potentials for both single and multichannel scattering,achieving convergence to a mean-squared error≤10^(-3).The resulting scattering lengths"a_(0)"and effective ranges"r"for ^(3)S_(1) and ^(1)S_(0) states,expressed as[a_(0),r],are found to be[5.445(5.424),1.770(1.760)]and[–23.741(–23.749),2.63(2.81)],respectively;these values are in excellent agreement with experimental ones.Furthermore,the calculated total scattering cross-sections are highly consistent with their experimental counterparts,having a percentage error of less than 1%.This computational approach can be easily extended to obtain interaction potentials for charged particle scattering.
基金supported by National Natural Science Foundation of China under Grant Nos.12175111,11975131K C Wong Magna Fund in Ningbo University。
文摘In this work,the(2+1)-dimensional Date–Jimbo–Kashiwara–Miwa(DJKM)equation is studied by means of the ■-dressing method.A new ■ problem has been constructed by analyzing the characteristic function and the Green’s function of its Lax representation.Based on solving the ■ equation and choosing the proper spectral transformation,the solution of the DJKM equation is constructed.Furthermore,the more general solution of the DJKM equation can be also obtained by ensuring the evolution of the time spectral data.
基金supported by the National Natural Science Foundation of China under project No. 10771026by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China
文摘We consider an inverse quadratic programming （IQP） problem in which the parameters in the objective function of a given quadratic programming （QP） problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. This problem can be formulated as a minimization problem with a positive semidefinite cone constraint and its dual （denoted IQD（A, b）） is a semismoothly differentiable （SC^1） convex programming problem with fewer variables than the original one. In this paper a smoothing Newton method is used for getting a Karush-Kuhn-Tucker point of IQD（A, b）. The proposed method needs to solve only one linear system per iteration and achieves quadratic convergence. Numerical experiments are reported to show that the smoothing Newton method is effective for solving this class of inverse quadratic programming problems.
文摘Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustrate theoretical conclusions. Alternative methods of identification of obstacles are mentioned： the Support Function Method （SFM） and the Modified Rayleigh Conjecture （MRC） method.
