By employing the improved moving least-square （IMLS） approximation, the improved element-free Galerkin （IEFG） method is presented for the unsteady Schrodinger equation. In the IEFG method, the two-dimensional （2D...By employing the improved moving least-square （IMLS） approximation, the improved element-free Galerkin （IEFG） method is presented for the unsteady Schrodinger equation. In the IEFG method, the two-dimensional （2D） trial function is approximated by the IMLS approximation, the variation method is used to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. Because the number of coefficients in the IMLS approximation is less than in the moving least-square （MLS） approximation, fewer nodes are needed in the entire domain when the IMLS approximation is used than when the MLS approximation is adopted. Then the IEFG method has high computational efficiency and accuracy. Several numerical examples are given to verify the accuracy and efficiency of the IEFG method in this paper.展开更多
The South China Sea （SCS） is a hot spot for oceanic internal solitary waves due to many factors, such as the complexity of the terrain environment. The internal solitary waves in the northern SCS mainly originate in...The South China Sea （SCS） is a hot spot for oceanic internal solitary waves due to many factors, such as the complexity of the terrain environment. The internal solitary waves in the northern SCS mainly originate in the Luzon Strait. The generation mechanism of the internal solitary waves in the Luzon Strait is discussed using a modulation instability. The energy gain of the modulation instability is derived based on the fully nonlinear Schr6dinger equation. The peak value of the gain is calculated under different conditions of stratification, wavelength and the initial amplitude of an internal tidal wave. The characteristics of the modulation instability in the Luzon Strait are investigated. The conditions that make the internal tidal wave evolve into an internal solitary wave in the Luzon strait are also obtained. The results show that the internal tide waves can generate the modulation instability in the Luzon Strait and that the maximum gain occur at the eastern sill of the Luzon Strait, where the internal tide waves start to break up into internal solitary trains. The magnitude and the scope of the peak gain are relevant to the stratification and the initial conditions of the internal tide waves. The numerical simulation results are consistent with the in-situ data.展开更多
Nonlinear mechanics for a super-thin elastic rod with the biological background of DNA super-coiling macromolecules is an interdisciplinary research area of classical mechanics and molecular biology. It is also a subj...Nonlinear mechanics for a super-thin elastic rod with the biological background of DNA super-coiling macromolecules is an interdisciplinary research area of classical mechanics and molecular biology. It is also a subject of dynamics and elasticity because elastic bodies are analyzed via the theory of dynamics. It is in frontiers of general mechanics （dynamics and control）. This dissertation is devoted to model a constrained super-thin elastic rod and analyze its stability in equilibrium. The existing research results are summarized. Analytical mechanics is systematically applied to model the elastic rod. The Schroedinger equation for complex curvatures or complex bending moments is, respectively, extended from the case of circular crosssections to that of non-circular ones. The equilibrium of a rod constrained on a surface is investigated.展开更多
We study the spherical quantum pseudodots in the Schr6dinger equation by using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite en...We study the spherical quantum pseudodots in the Schr6dinger equation by using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite energy levels and the wave functions are calculated. Furthermore, the behavior of the essential thermodynamic quantities such as, the free energy, the mean energy, the entropy, the specific heat, the magnetization, the magnetic susceptibility, and the persistent currents are also studied by using the characteristic function. Our analytical results are found to be in good agreement with the other works. The numerical results on the energy levels as well as the thermodynamic quantities have also been given.展开更多
The functionality of the plasma antenna has been narrowed to types and brand names only. The physics of its operation has been neglected and has stagnated technological innovations. The magnetic field in the sheath an...The functionality of the plasma antenna has been narrowed to types and brand names only. The physics of its operation has been neglected and has stagnated technological innovations. The magnetic field in the sheath and plasma were investigated. Notable specifications were worked out in the proposed improved cylindrical monopole plasma antenna. The occurrence of femto spin demagnetization was discovered between the duration of switch on and switch off of the antenna. This phenomenon seems transient because magnetization is highest at the switch on/off point.展开更多
We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue a...We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties corresponding effective potentials for several mass functions, for the system with PDM are also discussed. We give the the systems with such potentials are isospectral to the usual harmonic oscillator.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11171208)the Natural Science Foundation of Zhejiang Province,China(Grant No.LY15A020007)+1 种基金the Natural Science Foundation of Ningbo City(Grant No.2014A610028)the K.C.Wong Magna Fund in Ningbo University,China
文摘By employing the improved moving least-square （IMLS） approximation, the improved element-free Galerkin （IEFG） method is presented for the unsteady Schrodinger equation. In the IEFG method, the two-dimensional （2D） trial function is approximated by the IMLS approximation, the variation method is used to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. Because the number of coefficients in the IMLS approximation is less than in the moving least-square （MLS） approximation, fewer nodes are needed in the entire domain when the IMLS approximation is used than when the MLS approximation is adopted. Then the IEFG method has high computational efficiency and accuracy. Several numerical examples are given to verify the accuracy and efficiency of the IEFG method in this paper.
基金The National Natural Science Foundation of China under contract No.61171161
文摘The South China Sea （SCS） is a hot spot for oceanic internal solitary waves due to many factors, such as the complexity of the terrain environment. The internal solitary waves in the northern SCS mainly originate in the Luzon Strait. The generation mechanism of the internal solitary waves in the Luzon Strait is discussed using a modulation instability. The energy gain of the modulation instability is derived based on the fully nonlinear Schr6dinger equation. The peak value of the gain is calculated under different conditions of stratification, wavelength and the initial amplitude of an internal tidal wave. The characteristics of the modulation instability in the Luzon Strait are investigated. The conditions that make the internal tidal wave evolve into an internal solitary wave in the Luzon strait are also obtained. The results show that the internal tide waves can generate the modulation instability in the Luzon Strait and that the maximum gain occur at the eastern sill of the Luzon Strait, where the internal tide waves start to break up into internal solitary trains. The magnitude and the scope of the peak gain are relevant to the stratification and the initial conditions of the internal tide waves. The numerical simulation results are consistent with the in-situ data.
文摘Nonlinear mechanics for a super-thin elastic rod with the biological background of DNA super-coiling macromolecules is an interdisciplinary research area of classical mechanics and molecular biology. It is also a subject of dynamics and elasticity because elastic bodies are analyzed via the theory of dynamics. It is in frontiers of general mechanics （dynamics and control）. This dissertation is devoted to model a constrained super-thin elastic rod and analyze its stability in equilibrium. The existing research results are summarized. Analytical mechanics is systematically applied to model the elastic rod. The Schroedinger equation for complex curvatures or complex bending moments is, respectively, extended from the case of circular crosssections to that of non-circular ones. The equilibrium of a rod constrained on a surface is investigated.
文摘We study the spherical quantum pseudodots in the Schr6dinger equation by using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite energy levels and the wave functions are calculated. Furthermore, the behavior of the essential thermodynamic quantities such as, the free energy, the mean energy, the entropy, the specific heat, the magnetization, the magnetic susceptibility, and the persistent currents are also studied by using the characteristic function. Our analytical results are found to be in good agreement with the other works. The numerical results on the energy levels as well as the thermodynamic quantities have also been given.
文摘The functionality of the plasma antenna has been narrowed to types and brand names only. The physics of its operation has been neglected and has stagnated technological innovations. The magnetic field in the sheath and plasma were investigated. Notable specifications were worked out in the proposed improved cylindrical monopole plasma antenna. The occurrence of femto spin demagnetization was discovered between the duration of switch on and switch off of the antenna. This phenomenon seems transient because magnetization is highest at the switch on/off point.
基金supported by the National Natural Science Foundation of China under Grant Nos.10125521 and 60371013the 973 National Basic Pesearch and Development Program of China under Contract No.G2000077400
文摘We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties corresponding effective potentials for several mass functions, for the system with PDM are also discussed. We give the the systems with such potentials are isospectral to the usual harmonic oscillator.
