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Communications in Computational Physics 2009年第7期6卷 231-246页

作者： F.Y.Hansen H.Taub Department of Chemistry Technical University of DenmarkIK 207 DTUDK-2800 LyngbyDenmark Department of Physics and Astronomy and the University of Missouri Research Reactor University of MissouriColumbiaMissouri 65211USA

The motion of the atoms in a molecule may be described as a superposition of translational motion of the molecular center-of-mass,rotational motion about the principal molecular axes,and an intramolecular motion that may be associated with vibrations and librations as well as molecular conformational changes.We have constructed projection operators that use the atomic coordinates and velocities at any two times,t=0 and a later time t,to determine the molecular center-of-mass,rotational,and intramolecular motions in a molecular dynamics simulation.This model-independent technique facilitates characterization of the atomic motions within a system of complex molecules and is important for the interpretation of experiments that rely on time correlation functions of atomic and molecular positions and velocities.The application of the projection operator technique is illustrated for the inelastic neutron scattering functions and for the translational and rotational velocity autocorrelation functions.

关键词： Molecular dynamics projection operator correlation functions scattering functions translational motion rotational motion intramolecular motion

DOMAIN DECOMPOSITION WITH NONMATCHING GRIDS FOR EXTERIOR TRANSMISSION PROBLEMS VIA FEM AND DTN MAPPING

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Journal of Computational Mathematics 2006年第3期24卷 323-342页

作者： Ju-e Yang De-hao Yu LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

In this paper, we are concerned with a non-overlapping domain decomposition method （DDM） for exterior transmission problems in the plane. Based on the natural boundary integral operator, we combine the DDM with a Dirichlet-to-Neumann （DtN） mapping and provide the numerical analysis with nonmatching grids. The weak continuity of the approximation solutions on the interface is imposed by a dual basis multiplier. We show that this multiplier space can generate optimal error estimate and obtain the corresponding rate of convergence. Finally, several numerical examples confirm the theoretical results.

关键词： Domain decomposition Nature boundary element Nonmatching grids Weakcontinuity D-N alternating Dual basis projection operator Error estimate.

Decomposition and Approximation of Multivariate Functions on the Cube

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Acta Mathematica Sinica,English Series 2013年第1期29卷 119-136页

作者： Zhi Hua ZHANG College of Global Change and Earth System Science Beijing Normal University

In this paper, we present a decomposition method of multivariate functions. This method shows that any multivariate function f on [0, 1]d is a finite sum of the form ∑jФjψj, where each Фj can be extended to a smooth periodic function, each ψj is an algebraic polynomial, and each Фjψj is a product of separated variable type and its smoothness is same as f. Since any smooth periodic function can be approximated well by trigonometric polynomials, using our decomposition method, we find that any smooth multivariate function on [0, 1]d can be approximated well by a combination of algebraic polynomials and trigonometric polynomials. Meanwhile, we give a precise estimate of the approximation error.

关键词： Decomposition of multivariate functions approximation of multivariate functions fundamental polynomial projection operator classification of boundary points

ERROR ESTIMATE FOR INFLUENCE OF MODEL REDUCTION OF NONLINEAR DISSIPATIVE AUTONOMOUS DYNAMICAL SYSTEM ON LONG-TERM BEHAVIOURS

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Applied Mathematics and Mechanics(English Edition) 2005年第7期26卷 938-943页

作者：张家忠刘雁陈党民 School of Energy and Power Engineering Xi’an Jiaotong University Xi’an 710049 P.R.China Department of Mechanical Engineering Northwestern Polytechnical University Xi’an 710072 P.R.China

From viewpoint of nonlinear dynamics, the model reduction and its influence on the long-term behaviours of a class of nonlinear dissipative autonomous dynamical system with higher dimension are investigated theoretically under some assumptions. The system is analyzed in the state space with an introduction of a distance definition which can be used to describe the distance between the full system and the reduced system, and the solution of the full system is then projected onto the complete space spanned by the eigenvectors of the linear operator of the governing equations. As a result, the influence of mode series truncation on the long-term behaviours and the error estimate are derived, showing that the error is dependent on the first products of frequencies and damping ratios in the subspace spanned by the eigenvectors with higher modal damping. Furthermore, the fundamental understanding for the topological change of the solution due to the application of different model reduction is interpreted in a mathematically precise way, using the qualitative theory of nonlinear dynamics.

关键词： nonlinear dynamical system dissipative system projection operator long-term behaviour

The Second-Order Differential Equation System with the Feedback Controls for Solving Convex Programming

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Open Journal of Applied Sciences 2022年第6期12卷 977-989页

作者： Xingxu Chen Li Wang Juhe Sun Yanhong Yuan School of Science Shenyang Aerospace University Shenyang China College of Economics and Management Taiyuan University of Technology Taiyuan China

In this paper, we establish the second-order differential equation system with the feedback controls for solving the problem of convex programming. Using Lagrange function and projection operator, the equivalent operator equations for the convex programming problems under the certain conditions are obtained. Then a second-order differential equation system with the feedback controls is constructed on the basis of operator equation. We prove that any accumulation point of the trajectory of the second-order differential equation system with the feedback controls is a solution to the convex programming problem. In the end, two examples using this differential equation system are solved. The numerical results are reported to verify the effectiveness of the second-order differential equation system with the feedback controls for solving the convex programming problem.

关键词： Convex Programming Lagrange Function projection operator Second-Order Differential Equation

Feynman propagator for an arbitrary half—integral spin

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Chinese Physics B 2003年第7期12卷 721-731页

作者：黄时中张鹏飞阮图南祝玉灿郑志鹏 DepartmentofModernPhysicsandNationalSynchrotronRadiationLaboratory UniversityofScienceandTechnologyofChinaHefei230027China ChinaCenterofAdvancedScienceandTechnology(WorldLaboratory) Beijing100080China InstituteofHighEnergyPhysics ChineseAcademyofScienceBeijing100039China

Based on the solution to Bargmann-Wigner equation for a particle with arbitrary half-integral spin, a directderivation of the projection operator and propagator for a particle with arbitrary half-integral spin is worked out. Theprojection operator constructed by Behrends and Fronsdal is re-deduced and confirmed and simplified, the generalcommutation rules and Feynman propagator with additional non-covariant terms for a free particle with arbitraryhalf-integral spin are derived, and explicit expressions for the propagators for spins 3/2, 5/2 and 7/2 are provided.

关键词： half-integral spin projection operator commutation rule Feynman propagator