The Gaussian weighted trajectory method （GWTM） is a practical implementation of classical S matrix theory （CSMT） in the random phase approximation, CSMT being the first and simplest semi-classical approach of mole...The Gaussian weighted trajectory method （GWTM） is a practical implementation of classical S matrix theory （CSMT） in the random phase approximation, CSMT being the first and simplest semi-classical approach of molecular collisions, developped in the early seventies. Though very close in spirit to the purely classical description, GWTM accounts to some extent for the quantization of the different degrees-of-freedom involved in the processes. While CSMT may give diverging final state distributions, in relation to the rainbow effect of elastic scattering theory, GWTM has never led to such a mathematical catastrophe. The goal of the present note is to explain this finding.展开更多
The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficu...The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.展开更多
A current based hybrid method （HM） is proposed which combines the method of moment （MOM） with the Kirchhoff approximation （KA） for the analysis of scattering interaction between a two-dimensional （2D） infinite...A current based hybrid method （HM） is proposed which combines the method of moment （MOM） with the Kirchhoff approximation （KA） for the analysis of scattering interaction between a two-dimensional （2D） infinitely long conducting target with arbitrary cross section and a one-dimensional （1D） Gaussian rough surface. The electromagnetic scattering region in the HM is split into KA region and MOM region. The electric field integral equation （EFIE） in MOM region （target） is derived, the computational time of the HM depends mainly on the number of unknowns of the target. The bistatic scattering coefficient for the infinitely long cylinder above the rough surface with Gaussian roughness spectrum is calculated, and the numerical results are compared and verified with those obtained by the conventional MOM, which shows the high efficiency of the HM. Finally, the influence of the size, location of the target, the rms height and correlation length of the rough surface on the bistatic scattering coefficient with different polarizations is discussed in detail.展开更多
Knowledge-Based Engineering （KBE） is introduced into the ship structural design in this paper. From the implementation of KBE, the design solutions for both Rules Design Method （RDM） and Interpolation Design Meth...Knowledge-Based Engineering （KBE） is introduced into the ship structural design in this paper. From the implementation of KBE, the design solutions for both Rules Design Method （RDM） and Interpolation Design Method （IDM） are generated. The corresponding Finite Element （FE） models are generated. Topological design of the longitudinal structures is studied where the Gaussian Process （GP） is employed to build the surrogate model for FE analysis. Multi-objective optimization methods inspired by Pareto Front are used to reduce the design tank weight and outer surface area simultaneously. Additionally, an enhanced Level Set Method （LSM） which employs implicit algorithm is applied to the topological design of typical bracket plate which is used extensively in ship structures. Two different sets of boundary conditions are considered. The proposed methods show satisfactory efficiency and accuracy.展开更多
The energy distribution model of motion blurred star point is analyzed.The distribution of the star point approximates to a two-dimensional(2 D) Gaussian distribution under degeneration.Two multi-parameter nonlinear G...The energy distribution model of motion blurred star point is analyzed.The distribution of the star point approximates to a two-dimensional(2 D) Gaussian distribution under degeneration.Two multi-parameter nonlinear Gaussian fitting methods(GFMs) are proposed,and the relationship between fitting parameters and motion blur parameters is analyzed.Estimation of the parameters of motion blur by fitting parameters is calculated to realize the error compensation of the motion blur.The simulation results show the effectiveness and accuracy.展开更多
A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the ba...A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the basic property of fGn and related fractional Brownian motion （iBm） are briefly introduced. Then, the averaged fractional stochastic differential equations （SDEs） for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well.展开更多
文摘The Gaussian weighted trajectory method （GWTM） is a practical implementation of classical S matrix theory （CSMT） in the random phase approximation, CSMT being the first and simplest semi-classical approach of molecular collisions, developped in the early seventies. Though very close in spirit to the purely classical description, GWTM accounts to some extent for the quantization of the different degrees-of-freedom involved in the processes. While CSMT may give diverging final state distributions, in relation to the rainbow effect of elastic scattering theory, GWTM has never led to such a mathematical catastrophe. The goal of the present note is to explain this finding.
基金financial support from Hunan Provincial Natura1 Science Foundation of China,Grant Number:02JJY2085,for this study
文摘The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.
基金Project supported by the National Natural Science Foundation of China (Grant No 60571058)the Specialized Research Fund for the Doctoral Program of Higher Education, China
文摘A current based hybrid method （HM） is proposed which combines the method of moment （MOM） with the Kirchhoff approximation （KA） for the analysis of scattering interaction between a two-dimensional （2D） infinitely long conducting target with arbitrary cross section and a one-dimensional （1D） Gaussian rough surface. The electromagnetic scattering region in the HM is split into KA region and MOM region. The electric field integral equation （EFIE） in MOM region （target） is derived, the computational time of the HM depends mainly on the number of unknowns of the target. The bistatic scattering coefficient for the infinitely long cylinder above the rough surface with Gaussian roughness spectrum is calculated, and the numerical results are compared and verified with those obtained by the conventional MOM, which shows the high efficiency of the HM. Finally, the influence of the size, location of the target, the rms height and correlation length of the rough surface on the bistatic scattering coefficient with different polarizations is discussed in detail.
基金financially supported by the Project of Ministry of Education and Finance of China(Grant Nos.200512 and 201335)the Project of the State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University(Grant No.GKZD010053-10)
文摘Knowledge-Based Engineering （KBE） is introduced into the ship structural design in this paper. From the implementation of KBE, the design solutions for both Rules Design Method （RDM） and Interpolation Design Method （IDM） are generated. The corresponding Finite Element （FE） models are generated. Topological design of the longitudinal structures is studied where the Gaussian Process （GP） is employed to build the surrogate model for FE analysis. Multi-objective optimization methods inspired by Pareto Front are used to reduce the design tank weight and outer surface area simultaneously. Additionally, an enhanced Level Set Method （LSM） which employs implicit algorithm is applied to the topological design of typical bracket plate which is used extensively in ship structures. Two different sets of boundary conditions are considered. The proposed methods show satisfactory efficiency and accuracy.
文摘The energy distribution model of motion blurred star point is analyzed.The distribution of the star point approximates to a two-dimensional(2 D) Gaussian distribution under degeneration.Two multi-parameter nonlinear Gaussian fitting methods(GFMs) are proposed,and the relationship between fitting parameters and motion blur parameters is analyzed.Estimation of the parameters of motion blur by fitting parameters is calculated to realize the error compensation of the motion blur.The simulation results show the effectiveness and accuracy.
基金supported by the National Natural Science Foundation of China under grants nos.:11272279,11321202 and 11432012
文摘A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the basic property of fGn and related fractional Brownian motion （iBm） are briefly introduced. Then, the averaged fractional stochastic differential equations （SDEs） for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well.
