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
Stochastic simulation is an important means of acquiring fluctuating wind pressures for wind induced response analyses in structural engineering. The wind pressure acting on a large-span space structure can be charact...Stochastic simulation is an important means of acquiring fluctuating wind pressures for wind induced response analyses in structural engineering. The wind pressure acting on a large-span space structure can be characterized as a stationary non-Gaussian field. This paper reviews several simulation algorithms related to the Spectral Representation Method （SRM） and the Static Transformation Method （STM）. Polynomial and Exponential transformation functions （PSTM and ESTM） are discussed. Deficiencies in current algorithms, with respect to accuracy, stability and efficiency, are analyzed, and the algorithms are improved for better practical application. In order to verify the improved algorithm, wind pressure fields on a large-span roof are simulated and compared with wind tunnel data. The simulation results fit well with the wind tunnel data, and the algorithm accuracy, stability and efficiency are shown to be better than those of current algorithms.展开更多
Wind stress impacts on ocean relatively high waves can be perfectly illustrated by a recurrent phenomenon in the Sahara desert. Indeed, on this area where the surface wind can blow without encountering major obstacle ...Wind stress impacts on ocean relatively high waves can be perfectly illustrated by a recurrent phenomenon in the Sahara desert. Indeed, on this area where the surface wind can blow without encountering major obstacle out of the sand dunes, these main targets are gradually eroded and displaced by the wind on dozens of meters. This experience highlights the action of wind on granular targets (clusters of sand or water slides) and motivates studies similar to ours, where we want to simulate impact of wind stress and breaking on the spatio-temporal evolution of the envelope of ocean relatively high waves: Impact which can inappropriately deflect the waves on ships, oil platforms or coastal infrastructures. Euler and Navier-Stokes equations allow a mathematical formulation of the gravity wave motion (ocean waves are considered in our work as a system of water particles which are held together by low surface tension) and wind acts on targets through friction forces or stress. Michel Talon stationary phase method is used to numerically solve the equations that model the impact of wind on a stationary Gaussian.展开更多
KH2PO4 （KDP） crystal with excellent optical properties is a very important element of inertial confinement fusion （ICF） device. However, KDP crystal surface micro-defects severely reduce the crystal laser damage t...KH2PO4 （KDP） crystal with excellent optical properties is a very important element of inertial confinement fusion （ICF） device. However, KDP crystal surface micro-defects severely reduce the crystal laser damage threshold, affecting the crystal service life. In this paper, Gaussian repaired pit is used to replace the crystal surface micro-defects, in order to improve the laser damage resistance of the KDP crystal with surface micro-defects. At first, the physical model of Gaussian repaired pit is built by Fourier model method, and the accuracy of the method is analyzed. It is found that the calculation error can be reduced by increasing the product of the width-period ratio and the truncation constant of the repaired pit. The calculation results about the physical model of Gaussian repaired pit show that the light intensity distribution within the crystal is symmetrical, and there are evidently enhanced light intensity regions in the crystal. Meanwhile, the maximum relative intensity inside the KDP crystal decreases gradually with the increase of the width of the Gaussian repaired pit. Secondly, the Gaussian repaired pits with different widths and the same depth of 20 μm are processed by micro-milling. Their surfaces are very smooth and present the ductile cutting state under the microscope. Finally, the laser damage threshold of the Gaussian repaired pits on the surface of the KDP crystal sample is measured by a 3 ω, 6-ns laser. The results showthat the maximum threshold of the Gaussian repaired pits is 3.12 J/cm2, which is 60% higher than the threshold of initial damage point, and the laser damage threshold increases with the increase of the width of the Gaussian repaired pit.展开更多
Aiming at the problems that the classical Gaussian mixture model is unable to detect the complete moving object, and is sensitive to the light mutation scenes and so on, an improved algorithm is proposed for moving ob...Aiming at the problems that the classical Gaussian mixture model is unable to detect the complete moving object, and is sensitive to the light mutation scenes and so on, an improved algorithm is proposed for moving object detection based on Gaussian mixture model and three-frame difference method. In the process of extracting the moving region, the improved three-frame difference method uses the dynamic segmentation threshold and edge detection technology, and it is first used to solve the problems such as the illumination mutation and the discontinuity of the target edge. Then, a new adaptive selection strategy of the number of Gaussian distributions is introduced to reduce the processing time and improve accuracy of detection. Finally, HSV color space is used to remove shadow regions, and the whole moving object is detected. Experimental results show that the proposed algorithm can detect moving objects in various situations effectively.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.
基金National Natural Science Foundation of China under Grant Nos.51278160,51478155,51378147
文摘Stochastic simulation is an important means of acquiring fluctuating wind pressures for wind induced response analyses in structural engineering. The wind pressure acting on a large-span space structure can be characterized as a stationary non-Gaussian field. This paper reviews several simulation algorithms related to the Spectral Representation Method （SRM） and the Static Transformation Method （STM）. Polynomial and Exponential transformation functions （PSTM and ESTM） are discussed. Deficiencies in current algorithms, with respect to accuracy, stability and efficiency, are analyzed, and the algorithms are improved for better practical application. In order to verify the improved algorithm, wind pressure fields on a large-span roof are simulated and compared with wind tunnel data. The simulation results fit well with the wind tunnel data, and the algorithm accuracy, stability and efficiency are shown to be better than those of current algorithms.
文摘Wind stress impacts on ocean relatively high waves can be perfectly illustrated by a recurrent phenomenon in the Sahara desert. Indeed, on this area where the surface wind can blow without encountering major obstacle out of the sand dunes, these main targets are gradually eroded and displaced by the wind on dozens of meters. This experience highlights the action of wind on granular targets (clusters of sand or water slides) and motivates studies similar to ours, where we want to simulate impact of wind stress and breaking on the spatio-temporal evolution of the envelope of ocean relatively high waves: Impact which can inappropriately deflect the waves on ships, oil platforms or coastal infrastructures. Euler and Navier-Stokes equations allow a mathematical formulation of the gravity wave motion (ocean waves are considered in our work as a system of water particles which are held together by low surface tension) and wind acts on targets through friction forces or stress. Michel Talon stationary phase method is used to numerically solve the equations that model the impact of wind on a stationary Gaussian.
基金Project support by the National Natural Science Foundation of China(Grant No.51275113)the National Science and Technology Major Project of China(Grant No.2013ZX04006011-215)
文摘KH2PO4 （KDP） crystal with excellent optical properties is a very important element of inertial confinement fusion （ICF） device. However, KDP crystal surface micro-defects severely reduce the crystal laser damage threshold, affecting the crystal service life. In this paper, Gaussian repaired pit is used to replace the crystal surface micro-defects, in order to improve the laser damage resistance of the KDP crystal with surface micro-defects. At first, the physical model of Gaussian repaired pit is built by Fourier model method, and the accuracy of the method is analyzed. It is found that the calculation error can be reduced by increasing the product of the width-period ratio and the truncation constant of the repaired pit. The calculation results about the physical model of Gaussian repaired pit show that the light intensity distribution within the crystal is symmetrical, and there are evidently enhanced light intensity regions in the crystal. Meanwhile, the maximum relative intensity inside the KDP crystal decreases gradually with the increase of the width of the Gaussian repaired pit. Secondly, the Gaussian repaired pits with different widths and the same depth of 20 μm are processed by micro-milling. Their surfaces are very smooth and present the ductile cutting state under the microscope. Finally, the laser damage threshold of the Gaussian repaired pits on the surface of the KDP crystal sample is measured by a 3 ω, 6-ns laser. The results showthat the maximum threshold of the Gaussian repaired pits is 3.12 J/cm2, which is 60% higher than the threshold of initial damage point, and the laser damage threshold increases with the increase of the width of the Gaussian repaired pit.
文摘Aiming at the problems that the classical Gaussian mixture model is unable to detect the complete moving object, and is sensitive to the light mutation scenes and so on, an improved algorithm is proposed for moving object detection based on Gaussian mixture model and three-frame difference method. In the process of extracting the moving region, the improved three-frame difference method uses the dynamic segmentation threshold and edge detection technology, and it is first used to solve the problems such as the illumination mutation and the discontinuity of the target edge. Then, a new adaptive selection strategy of the number of Gaussian distributions is introduced to reduce the processing time and improve accuracy of detection. Finally, HSV color space is used to remove shadow regions, and the whole moving object is detected. Experimental results show that the proposed algorithm can detect moving objects in various situations effectively.
