In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradi...In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradient optimization(CCR-GO).The main strength of the CCR-GO method is that it does not require manual adjustment of optimization parameters in the wave function;instead,a mathematically well-defined optimization path can be followed.Our method is proven to be very efficient in searching resonant positions and widths over a variety of few-body atomic systems,and can significantly improve the accuracy of the results.As a special case,the CCR-GO method is equally capable of dealing with bound-state problems with high accuracy,which is traditionally achieved through the usual extreme conditions of energy itself.展开更多
By considering the characteristics of deformation of rotationally periodic structures under rotationally periodic loads, the periodic structure is divided into some identical substructures in this study. The degrees-o...By considering the characteristics of deformation of rotationally periodic structures under rotationally periodic loads, the periodic structure is divided into some identical substructures in this study. The degrees-of-freedom (DOFs) of joint nodes between the neighboring substructures are classified as master and slave ones. The stress and strain conditions of the whole structure are obtained by solving the elastic static equations for only one substructure by introducing the displacement constraints between master and slave DOFs. The complex constraint method is used to get the bifurcation buckling load and mode for the whole rotationally periodic structure by solving the eigenvalue problem for only one substructure without introducing any additional approximation. The finite element (FE) formulation of shell element of relative degrees of freedom (SERDF) in the buckling analysis is derived. Different measures of tackling internal degrees of freedom for different kinds of buckling problems and different stages of numerical analysis are presented. Some numerical examples are given to illustrate the high efficiency and validity of this method.展开更多
In this work,the Fukui functions of the two ~2P resonance states of Be,a ~2P resonance state of Mg~–,and a ~2D resonance state of Ca~– have been determined.The trajectories of these resonance states,in conjunction w...In this work,the Fukui functions of the two ~2P resonance states of Be,a ~2P resonance state of Mg~–,and a ~2D resonance state of Ca~– have been determined.The trajectories of these resonance states,in conjunction with the complex rotation of the Hamiltonian,were used to determine their wave functions.The electron densities,Fukui functions,and values of the hyper-radius<r^2>were computed from these wave functions.The Fukui functions have negative regions in the valence shell in addition to the inner shell regions,indicating screening effects of the outer temporary electron.Selected configuration interactions with up to quadruple excitations were used along the trajectories and for computing the final wave function.Based on this data,the densities,Fukui functions,and<r^2>were calculated.展开更多
By applying rotated complex empirical orthogonal function (RCEOF) analysis on 1880-1999 summer rainfall at 28 selected stations over the east part of China, the spatio-temporal variations of China summer rainfall are ...By applying rotated complex empirical orthogonal function (RCEOF) analysis on 1880-1999 summer rainfall at 28 selected stations over the east part of China, the spatio-temporal variations of China summer rainfall are investigated. Six divisions are identified, showing strong temporal variability, the middle and lower reaches of the Yangtze River, the Huaihe River, Southeast China, North China, Southwest China, and Northeast China. The locations of all divisions except Southwest China are in a good agreement with those of the rainband which moves northward from Southeast China to Northeast China from June-August. The phase relationship revealed by the RCEOF analysis suggests that rainfall anomalies in the middle and lower reaches of the Yangtze River, Southeast China, and Northeast China are all characterized by a stationary wave, while a traveling wave is more pronounced in the Huaihe River division, North China, and Southwest China. The fourth RCEOF mode indicates that rainfall anomalies can propagate from south of Northeast China across lower reaches of the Huanghe River and the Huaihe River to the lower reaches of the Yangtze River. A 20-25-year oscillation is found at the middle and lower reaches of the Yangtze River, the Huaihe River valley, North China, and Northeast China. The middle and lower reaches of the Yangtze River and Northeast China also show an approximately-60-year oscillation. Northeast China and the Huaihe River division are dominated by a 36-year and a 70-80-year oscillation, respectively. An 11-year oscillation is also evident in North China, with a periodicity similar to sunspot activity. The interdecadal variability in the middle and lower reaches of the Yangtze River, the Huaihe River valley, and North China shows a significant positive correlation with the solar activity.展开更多
Based on the ab initio/6-31Gcalculation, the potential barrier to internal rotation in mol-ecule HN--BHhas been studed by means of PD/LSF atomic charge model and Buckingham（exp--6-1）energy partition method. The resu...Based on the ab initio/6-31Gcalculation, the potential barrier to internal rotation in mol-ecule HN--BHhas been studed by means of PD/LSF atomic charge model and Buckingham（exp--6-1）energy partition method. The results indicate that the order of the contributions of the componentsto the total energy barrier △E is |△V|（electrostatic） >|△V| （charge transfer）>|△V| （exchangerepulsion）>|△V| （dispersion）. For △Vthere are maxima at θ= 30°and 90°, and a saddle atθ= 60°. There are good linear relationships for the total barrier △E, △Vand △Vwith cos3θrespectively, and the same for the dipole moment from PD/LSF model (μ) and that from abinitio calculation (μ) vs. cos3θ respectively.展开更多
In this paper,a new diagnostic method,the rotated complex empirical orthogonal function (RCEOF)analysis is developed.The general principle and the mathematical foundation of RCEOF are discussed.
The numerical solving and the program designing of the rotated complex empirical orthogonal function(RCEOF)are discussed.Some examples of RCEOF are also presented.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.91636216,11974382,and 11474316)the Chinese Academy of Sciences Strategic Priority Research Program(Grant No.XDB21020200)+1 种基金by the YIPA Programthe support of NSERC,SHARCnet,ACEnet of Canada。
文摘In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradient optimization(CCR-GO).The main strength of the CCR-GO method is that it does not require manual adjustment of optimization parameters in the wave function;instead,a mathematically well-defined optimization path can be followed.Our method is proven to be very efficient in searching resonant positions and widths over a variety of few-body atomic systems,and can significantly improve the accuracy of the results.As a special case,the CCR-GO method is equally capable of dealing with bound-state problems with high accuracy,which is traditionally achieved through the usual extreme conditions of energy itself.
文摘By considering the characteristics of deformation of rotationally periodic structures under rotationally periodic loads, the periodic structure is divided into some identical substructures in this study. The degrees-of-freedom (DOFs) of joint nodes between the neighboring substructures are classified as master and slave ones. The stress and strain conditions of the whole structure are obtained by solving the elastic static equations for only one substructure by introducing the displacement constraints between master and slave DOFs. The complex constraint method is used to get the bifurcation buckling load and mode for the whole rotationally periodic structure by solving the eigenvalue problem for only one substructure without introducing any additional approximation. The finite element (FE) formulation of shell element of relative degrees of freedom (SERDF) in the buckling analysis is derived. Different measures of tackling internal degrees of freedom for different kinds of buckling problems and different stages of numerical analysis are presented. Some numerical examples are given to illustrate the high efficiency and validity of this method.
文摘In this work,the Fukui functions of the two ~2P resonance states of Be,a ~2P resonance state of Mg~–,and a ~2D resonance state of Ca~– have been determined.The trajectories of these resonance states,in conjunction with the complex rotation of the Hamiltonian,were used to determine their wave functions.The electron densities,Fukui functions,and values of the hyper-radius<r^2>were computed from these wave functions.The Fukui functions have negative regions in the valence shell in addition to the inner shell regions,indicating screening effects of the outer temporary electron.Selected configuration interactions with up to quadruple excitations were used along the trajectories and for computing the final wave function.Based on this data,the densities,Fukui functions,and<r^2>were calculated.
基金The authors wish to thank Professor Wang Shaowu from the Department of AtmosphericSciences of Peking University, who generously provided the China Summer Rainfall Station Data used in this study. This research was supported by the National Key Program
文摘By applying rotated complex empirical orthogonal function (RCEOF) analysis on 1880-1999 summer rainfall at 28 selected stations over the east part of China, the spatio-temporal variations of China summer rainfall are investigated. Six divisions are identified, showing strong temporal variability, the middle and lower reaches of the Yangtze River, the Huaihe River, Southeast China, North China, Southwest China, and Northeast China. The locations of all divisions except Southwest China are in a good agreement with those of the rainband which moves northward from Southeast China to Northeast China from June-August. The phase relationship revealed by the RCEOF analysis suggests that rainfall anomalies in the middle and lower reaches of the Yangtze River, Southeast China, and Northeast China are all characterized by a stationary wave, while a traveling wave is more pronounced in the Huaihe River division, North China, and Southwest China. The fourth RCEOF mode indicates that rainfall anomalies can propagate from south of Northeast China across lower reaches of the Huanghe River and the Huaihe River to the lower reaches of the Yangtze River. A 20-25-year oscillation is found at the middle and lower reaches of the Yangtze River, the Huaihe River valley, North China, and Northeast China. The middle and lower reaches of the Yangtze River and Northeast China also show an approximately-60-year oscillation. Northeast China and the Huaihe River division are dominated by a 36-year and a 70-80-year oscillation, respectively. An 11-year oscillation is also evident in North China, with a periodicity similar to sunspot activity. The interdecadal variability in the middle and lower reaches of the Yangtze River, the Huaihe River valley, and North China shows a significant positive correlation with the solar activity.
基金the National Natural Science Foundation of China.
文摘Based on the ab initio/6-31Gcalculation, the potential barrier to internal rotation in mol-ecule HN--BHhas been studed by means of PD/LSF atomic charge model and Buckingham（exp--6-1）energy partition method. The results indicate that the order of the contributions of the componentsto the total energy barrier △E is |△V|（electrostatic） >|△V| （charge transfer）>|△V| （exchangerepulsion）>|△V| （dispersion）. For △Vthere are maxima at θ= 30°and 90°, and a saddle atθ= 60°. There are good linear relationships for the total barrier △E, △Vand △Vwith cos3θrespectively, and the same for the dipole moment from PD/LSF model (μ) and that from abinitio calculation (μ) vs. cos3θ respectively.
基金National 9th Five-Year Project under Grant 95-11.
文摘In this paper,a new diagnostic method,the rotated complex empirical orthogonal function (RCEOF)analysis is developed.The general principle and the mathematical foundation of RCEOF are discussed.
基金Supported by the National 9th Five-Year Project under Grant 95-11.
文摘The numerical solving and the program designing of the rotated complex empirical orthogonal function(RCEOF)are discussed.Some examples of RCEOF are also presented.
