The performance of the so-called superconvergent quantum perturbation theory （Wenhua Hal et al2000 Phys. Rev. A 61 052105） is investigated for the case of the ground-state energy of the helium-like ions. The scaling...The performance of the so-called superconvergent quantum perturbation theory （Wenhua Hal et al2000 Phys. Rev. A 61 052105） is investigated for the case of the ground-state energy of the helium-like ions. The scaling transformation τ → τ/Z applied to the Hamiltonian of a two-electron atomic ion with a nuclear charge Z （in atomic units）. Using the improved Rayleigh-SchrSdinger perturbation theory based on the integral equation to helium-like ions in the ground states and treating the electron correlations as perturbations, we have performed a third-order perturbation calculation and obtained the second-order corrected wavefunctions consisting of a few terms and third-order energy corrections. We find that third-order and higher-order energy corrections are improved with decreasing nuclear charge. This result means that the former is quadratically integrable and the latter is physically meaningful. The improved quantum perturbation theory fits the higher-order perturbation case. This work shows that it is a development on the quantum perturbation problem of helium-like systems.展开更多
A frozen orbit is beneficial for observation owing to its stationary apsidal line.The traditional gravitational field model of frozen orbits only considers the main zonal harmonic terms J_(2) and limited high-order te...A frozen orbit is beneficial for observation owing to its stationary apsidal line.The traditional gravitational field model of frozen orbits only considers the main zonal harmonic terms J_(2) and limited high-order terms,which cannot meet the stringent demands of all missions.In this study,the gravitational field is expanded to J_(15) terms and the Hamiltonian canonical form described by the Delaunay variables is used.The zonal harmonic coefficients of the Earth are chosen as the sample.Short-periodic terms are eliminated based on the Hori-Lie transformation.An algorithm is developed to solve all equilibrium points of the Hamiltonian function.A stable frozen orbit with an argument of perigee that equals neither 90°nor 270°is first reported in this paper.The local stability and topology of the equilibrium points are obtained from their eigenvalues.The bifurcations of the equilibrium points are presented by drawing their global long-term evolution of frozen orbits and their orbital periods.The relationship between the terms of the gravitational field and number of frozen points is addressed to explain why only limited frozen orbits are found in the low-order term case.The analytical results can be applied to other Earth-like planets and asteroids.展开更多
A singularly perturbed eigenvalue Robin problem with turning point of higher order is studied, which can describe some heat conduction phenomena. Using the method of Langer transformation, the uniformly asymptotic sol...A singularly perturbed eigenvalue Robin problem with turning point of higher order is studied, which can describe some heat conduction phenomena. Using the method of Langer transformation, the uniformly asymptotic solution of the equation is obtained, which is expressed by Bessel function, and the eigenvalue and eigenfunction of the problem are given, and then the known result is generalized.展开更多
To begin with, in this paper, the displacement governing equations and the boundary conditions of nonsymmetrical large deflection problem of circular thin plates are derived. By using the transformation and the pertur...To begin with, in this paper, the displacement governing equations and the boundary conditions of nonsymmetrical large deflection problem of circular thin plates are derived. By using the transformation and the perturbation method, the nonlinear displacement equations are linearized, and the approximate boundary value problems are obtained. As an example, the nonlinear bending problem of circular thin plates subjected to comparatively complex loads is studied.展开更多
In this paper, with the application of the Delauney variables, according to the Hamilton equations, the influence on the perturbation of a satellite exerted by the gravitational force of the earth through canonical tr...In this paper, with the application of the Delauney variables, according to the Hamilton equations, the influence on the perturbation of a satellite exerted by the gravitational force of the earth through canonical transformation has been found out. As a result, the equation about how the position and velocity of the satellite vary with time is deduced.展开更多
In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean engineering.This equation will be reduced to the Korteweg-de Vries...In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean engineering.This equation will be reduced to the Korteweg-de Vries equation via using the perturbation analysis.We derive the corresponding vectors,symmetry reduction and explicit solutions for this equation.We readily obtain Bäcklund transformation associated with truncated Painlevéexpansion.We also examine the related conservation laws of this equation via using the multiplier method.Moreover,we investigate the reciprocal Bäcklund transformations of the derived conservation laws for the first time.展开更多
There are two kinds of definitions of perturbation of physical quantities in the framework of general relativity： one is direct, the other is geometrical. Correspondingly, there are two types of gauge transformation ...There are two kinds of definitions of perturbation of physical quantities in the framework of general relativity： one is direct, the other is geometrical. Correspondingly, there are two types of gauge transformation related with these two definitions. The passive approach is based on the property of general covariance, and the active one is through the action of Lie-derivative. Although under a proper coordinate choice, the two approaches seem to agree with each other, they are different in nature. The geometrical definition of relativistic perturbation and the active approach for gauge transformation are more rigorous in mathematics and less confusing in physical explanation. The direct definition, however, seems to be plagued with difficulties in physical meaning, and the passive approach is more awkward to use, especially for high-order gauge transformations.展开更多
基金supported by the National Natural Science Foundation of China (Grant No 10575034)the Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics of China (Grant No T152504)the Foundation of the Education Committee of Hunan Province of China
文摘The performance of the so-called superconvergent quantum perturbation theory （Wenhua Hal et al2000 Phys. Rev. A 61 052105） is investigated for the case of the ground-state energy of the helium-like ions. The scaling transformation τ → τ/Z applied to the Hamiltonian of a two-electron atomic ion with a nuclear charge Z （in atomic units）. Using the improved Rayleigh-SchrSdinger perturbation theory based on the integral equation to helium-like ions in the ground states and treating the electron correlations as perturbations, we have performed a third-order perturbation calculation and obtained the second-order corrected wavefunctions consisting of a few terms and third-order energy corrections. We find that third-order and higher-order energy corrections are improved with decreasing nuclear charge. This result means that the former is quadratically integrable and the latter is physically meaningful. The improved quantum perturbation theory fits the higher-order perturbation case. This work shows that it is a development on the quantum perturbation problem of helium-like systems.
基金supported in part by the National Natural Science Foundation of China(Nos.11772024 and 11432001)Qian Xuesen Youth Innovation Foundation of China Aerospace Science and Technology Corporation.
文摘A frozen orbit is beneficial for observation owing to its stationary apsidal line.The traditional gravitational field model of frozen orbits only considers the main zonal harmonic terms J_(2) and limited high-order terms,which cannot meet the stringent demands of all missions.In this study,the gravitational field is expanded to J_(15) terms and the Hamiltonian canonical form described by the Delaunay variables is used.The zonal harmonic coefficients of the Earth are chosen as the sample.Short-periodic terms are eliminated based on the Hori-Lie transformation.An algorithm is developed to solve all equilibrium points of the Hamiltonian function.A stable frozen orbit with an argument of perigee that equals neither 90°nor 270°is first reported in this paper.The local stability and topology of the equilibrium points are obtained from their eigenvalues.The bifurcations of the equilibrium points are presented by drawing their global long-term evolution of frozen orbits and their orbital periods.The relationship between the terms of the gravitational field and number of frozen points is addressed to explain why only limited frozen orbits are found in the low-order term case.The analytical results can be applied to other Earth-like planets and asteroids.
基金Supported by the Projects of the National Natural Science Foundation of China (10471039)the Natural Science Foundation of Zhejiang Province (102009).
文摘A singularly perturbed eigenvalue Robin problem with turning point of higher order is studied, which can describe some heat conduction phenomena. Using the method of Langer transformation, the uniformly asymptotic solution of the equation is obtained, which is expressed by Bessel function, and the eigenvalue and eigenfunction of the problem are given, and then the known result is generalized.
基金Project supported by the National Natural Science Foundation of China
文摘To begin with, in this paper, the displacement governing equations and the boundary conditions of nonsymmetrical large deflection problem of circular thin plates are derived. By using the transformation and the perturbation method, the nonlinear displacement equations are linearized, and the approximate boundary value problems are obtained. As an example, the nonlinear bending problem of circular thin plates subjected to comparatively complex loads is studied.
文摘In this paper, with the application of the Delauney variables, according to the Hamilton equations, the influence on the perturbation of a satellite exerted by the gravitational force of the earth through canonical transformation has been found out. As a result, the equation about how the position and velocity of the satellite vary with time is deduced.
基金supported by Natural Science Foundation of Hebei Province,China(Grant No.A2018207030)Youth Key Program of Hebei University of Economics and Business(2018QZ07)+2 种基金Key Program of Hebei University of Economics and Business(2020ZD11)Youth Team Support Program of Hebei University of Economics and BusinessNational Natural Science Foundation of China(Grant No.11801133)。
文摘In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean engineering.This equation will be reduced to the Korteweg-de Vries equation via using the perturbation analysis.We derive the corresponding vectors,symmetry reduction and explicit solutions for this equation.We readily obtain Bäcklund transformation associated with truncated Painlevéexpansion.We also examine the related conservation laws of this equation via using the multiplier method.Moreover,we investigate the reciprocal Bäcklund transformations of the derived conservation laws for the first time.
基金supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,the Ministry of Educationthe Chinese Academy of Sciences under Grant No.KJCX3-SYW-N2
文摘There are two kinds of definitions of perturbation of physical quantities in the framework of general relativity： one is direct, the other is geometrical. Correspondingly, there are two types of gauge transformation related with these two definitions. The passive approach is based on the property of general covariance, and the active one is through the action of Lie-derivative. Although under a proper coordinate choice, the two approaches seem to agree with each other, they are different in nature. The geometrical definition of relativistic perturbation and the active approach for gauge transformation are more rigorous in mathematics and less confusing in physical explanation. The direct definition, however, seems to be plagued with difficulties in physical meaning, and the passive approach is more awkward to use, especially for high-order gauge transformations.
