In this paper,the zero-temperature string method and the nudged elastic band method for computing the transition paths and transition rates between metastable states are investigated.The stability,accuracy as well as ...In this paper,the zero-temperature string method and the nudged elastic band method for computing the transition paths and transition rates between metastable states are investigated.The stability,accuracy as well as computational cost of the two methods are discussed.The results are verified by numerical experiments.展开更多
We present an efficient algorithm for calculating the minimum energy path(MEP)and energy barriers between local minima on a multidimensional potential energy surface(PES).Such paths play a central role in the understa...We present an efficient algorithm for calculating the minimum energy path(MEP)and energy barriers between local minima on a multidimensional potential energy surface(PES).Such paths play a central role in the understanding of transition pathways between metastable states.Our method relies on the original formulation of the string method[Phys.Rev.B,66,052301(2002)],i.e.to evolve a smooth curve along a direction normal to the curve.The algorithm works by performing minimization steps on hyperplanes normal to the curve.Therefore the problem of finding MEP on the PES is remodeled as a set of constrained minimization problems.This provides the flexibility of using minimization algorithms faster than the steepest descent method used in the simplified string method[J.Chem.Phys.,126(16),164103(2007)].At the same time,it provides a more direct analog of the finite temperature string method.The applicability of the algorithm is demonstrated using various examples.展开更多
To investigate the principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string,the method of multiple scales is applied directly to the nonlinear partial differentia...To investigate the principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string,the method of multiple scales is applied directly to the nonlinear partial differential equation that governs the transverse vibration of the string.To derive the governing equation,Newton's second law,Lagrangean strain,and Kelvin's model are respectively used to account the dynamical relation,geometric nonlinearity and the viscoelasticity of the string material. Based on the solvability condition of eliminating the secular terms,closed form solutions are obtained for the amplitude and the existence conditions of nontrivial steady-state response of the principal parametric resonance.The Lyapunov linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions in the principal parametric resonance.Some numerical examples are presented to show the effects of the mean transport speed,the amplitude and the frequency of speed variation.展开更多
The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear...The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.展开更多
A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is ...A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is applied to discretize the state variables, and the Runge- Kutta method is applied to solve the resulting differential-integral equation system. A linear iterative process is designed to compute the integral terms at each time step, which makes the numerical method more efficient and accurate. As examples, nonlinear parametric vibrations of an axially moving viscoelastic string are analyzed.展开更多
The notion of string stability of a countably infinite interconnection of a class of nonlinear system was introduced. Intuitively, string stability implies uniform boundedness of all the stares of the interconnected s...The notion of string stability of a countably infinite interconnection of a class of nonlinear system was introduced. Intuitively, string stability implies uniform boundedness of all the stares of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. Vector V-function method used to judge the stability is generalized for infinite interconnected system and sufficient conditions which guarantee the asymptotic string stability of a class of interconnected system are given. The stability regions obtained here are much larger than those in previous papers. The method given here overcomes some difficulties to deal with stability of infinite nonlinear interconnected system in previous papers.展开更多
Three-dimensional nonlinear analysis of drill string structure in annulus of curvedwellbore is done by using the theory of finite element and Newton-Raphson method.According to the characteristics of its deformation,...Three-dimensional nonlinear analysis of drill string structure in annulus of curvedwellbore is done by using the theory of finite element and Newton-Raphson method.According to the characteristics of its deformation,a method of the description andcomputation of taking different forms of elements for different parameters is advanced.The penalty function method is applied for finding the unknown boundary .the nonlinear effects of curvature of wellbore on the side forces on bit ae shown by thecomputation.展开更多
Under the consideration of harmonic fluctuations of initial tension and axially velocity, a nonlinear governing equation for transverse vibration of an axially accelerating string is set up by using the equation of mo...Under the consideration of harmonic fluctuations of initial tension and axially velocity, a nonlinear governing equation for transverse vibration of an axially accelerating string is set up by using the equation of motion for a 3-dimensional deformable body with initial stresses. The Kelvin model is used to describe viscoelastic behaviors of the material. The basis function of the complex-mode Galerkin method for axially accelerating nonlinear strings is constructed by using the modal function of linear moving strings with constant axially transport velocity. By the constructed basis functions, the application of the complex-mode Galerkin method in nonlinear vibration analysis of an axially accelerating viscoelastic string is investigated. Numerical results show that the convergence velocity of the complex-mode Galerkin method is higher than that of the real-mode Galerkin method for a variable coefficient gyroscopic system.展开更多
基金supported by the National Science Foundation of China under the grant 10425105the National Basic Research Program under the grant 2005CB321704.
文摘In this paper,the zero-temperature string method and the nudged elastic band method for computing the transition paths and transition rates between metastable states are investigated.The stability,accuracy as well as computational cost of the two methods are discussed.The results are verified by numerical experiments.
基金support by the Department of Energy under Grant No.DE-SC0002623.
文摘We present an efficient algorithm for calculating the minimum energy path(MEP)and energy barriers between local minima on a multidimensional potential energy surface(PES).Such paths play a central role in the understanding of transition pathways between metastable states.Our method relies on the original formulation of the string method[Phys.Rev.B,66,052301(2002)],i.e.to evolve a smooth curve along a direction normal to the curve.The algorithm works by performing minimization steps on hyperplanes normal to the curve.Therefore the problem of finding MEP on the PES is remodeled as a set of constrained minimization problems.This provides the flexibility of using minimization algorithms faster than the steepest descent method used in the simplified string method[J.Chem.Phys.,126(16),164103(2007)].At the same time,it provides a more direct analog of the finite temperature string method.The applicability of the algorithm is demonstrated using various examples.
基金The project supported by the National Natural Science Foundation of China (10172056)
文摘To investigate the principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string,the method of multiple scales is applied directly to the nonlinear partial differential equation that governs the transverse vibration of the string.To derive the governing equation,Newton's second law,Lagrangean strain,and Kelvin's model are respectively used to account the dynamical relation,geometric nonlinearity and the viscoelasticity of the string material. Based on the solvability condition of eliminating the secular terms,closed form solutions are obtained for the amplitude and the existence conditions of nontrivial steady-state response of the principal parametric resonance.The Lyapunov linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions in the principal parametric resonance.Some numerical examples are presented to show the effects of the mean transport speed,the amplitude and the frequency of speed variation.
文摘The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.
基金supported by the National Outstanding Young Scientists Fund of China (No. 10725209)the National ScienceFoundation of China (No. 10672092)+1 种基金Shanghai Municipal Education Commission Scientific Research Project (No. 07ZZ07)Shanghai Leading Academic Discipline Project (No. Y0103).
文摘A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is applied to discretize the state variables, and the Runge- Kutta method is applied to solve the resulting differential-integral equation system. A linear iterative process is designed to compute the integral terms at each time step, which makes the numerical method more efficient and accurate. As examples, nonlinear parametric vibrations of an axially moving viscoelastic string are analyzed.
文摘The notion of string stability of a countably infinite interconnection of a class of nonlinear system was introduced. Intuitively, string stability implies uniform boundedness of all the stares of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. Vector V-function method used to judge the stability is generalized for infinite interconnected system and sufficient conditions which guarantee the asymptotic string stability of a class of interconnected system are given. The stability regions obtained here are much larger than those in previous papers. The method given here overcomes some difficulties to deal with stability of infinite nonlinear interconnected system in previous papers.
文摘Three-dimensional nonlinear analysis of drill string structure in annulus of curvedwellbore is done by using the theory of finite element and Newton-Raphson method.According to the characteristics of its deformation,a method of the description andcomputation of taking different forms of elements for different parameters is advanced.The penalty function method is applied for finding the unknown boundary .the nonlinear effects of curvature of wellbore on the side forces on bit ae shown by thecomputation.
基金Project supported by the National Natural Science Foundation of China (No. 10472060)Shanghai Leading Academic Discipline Project (No.Y0103)the Natural Science Foundation of Shanghai (No.04ZR14058)the Outstanding Youth Program of Shanghai Municipal Commission of Educatio(No.04YQHB088)
文摘Under the consideration of harmonic fluctuations of initial tension and axially velocity, a nonlinear governing equation for transverse vibration of an axially accelerating string is set up by using the equation of motion for a 3-dimensional deformable body with initial stresses. The Kelvin model is used to describe viscoelastic behaviors of the material. The basis function of the complex-mode Galerkin method for axially accelerating nonlinear strings is constructed by using the modal function of linear moving strings with constant axially transport velocity. By the constructed basis functions, the application of the complex-mode Galerkin method in nonlinear vibration analysis of an axially accelerating viscoelastic string is investigated. Numerical results show that the convergence velocity of the complex-mode Galerkin method is higher than that of the real-mode Galerkin method for a variable coefficient gyroscopic system.
