We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground...We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.展开更多
In actual power systems,most of the high-voltage buses of the transformers are zero injection buses without load or generation.Power injections into these buses are strictly 0,so based on Kirchhoff's current law(K...In actual power systems,most of the high-voltage buses of the transformers are zero injection buses without load or generation.Power injections into these buses are strictly 0,so based on Kirchhoff's current law(KCL),equality constraints should be used to handle these buses in a state estimation model.It is a challenge to ensure that these zero injection constraints can be strictly satisfied without losing computational efficiency.展开更多
In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian co...In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.展开更多
In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discreti...In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.展开更多
A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous H...A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.展开更多
For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （...For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.展开更多
Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator （IEO） method to solving the energy spectrmn of the three-mo...Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator （IEO） method to solving the energy spectrmn of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1, X2] = [X2, X3]=[X3, X1] = iθ, and this method seems effective and concise.展开更多
Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved ...Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.展开更多
Bond valence method illustrates the relation between valence and length of a particular bond type. This theory has been used to predict structure information, but the effect is very limited. In this paper, two indexes...Bond valence method illustrates the relation between valence and length of a particular bond type. This theory has been used to predict structure information, but the effect is very limited. In this paper, two indexes, i.e., global instability index（GII） and bond strain index（BSI）, are adopted as a judgment of a search-match program for prediction. The results show that with GII and BSI combined as judgment, the predicted atom positions are very close to real ones. The mechanism and validity of this searching program are also discussed. The GII ＆ BSI distribution contour map reveals that the predicted function is a reflection of exponential feature of bond valence formula. This combined searching method may be integrated with other structure-determination method, and may be helpful in refining and testifying light atom positions.展开更多
A new numerical approach, called the “subdomain Chebyshev spectral method” is presented for calculation of the spatial derivatives in a curved coordinate system, which may be employed for numerical solutions of part...A new numerical approach, called the “subdomain Chebyshev spectral method” is presented for calculation of the spatial derivatives in a curved coordinate system, which may be employed for numerical solutions of partial differential equations defined in a 2D or 3D geological model. The new approach refers to a “strong version” against the “weak version” of the subspace spectral method based on the variational principle or Galerkin’s weighting scheme. We incorporate local nonlinear transformations and global spline interpolations in a curved coordinate system and make the discrete grid exactly matches geometry of the model so that it is achieved to convert the global domain into subdomains and apply Chebyshev points to locally sampling physical quantities and globally computing the spatial derivatives. This new approach not only remains exponential convergence of the standard spectral method in subdomains, but also yields a sparse assembled matrix when applied for the global domain simulations. We conducted 2D and 3D synthetic experiments and compared accuracies of the numerical differentiations with traditional finite difference approaches. The results show that as the points of differentiation vector are larger than five, the subdomain Chebyshev spectral method significantly improve the accuracies of the finite difference approaches.展开更多
This paper presents an array pattern synthesis algorithm for arbitrary arrays based on coordinate descent method (CDM). With this algorithm, the complex element weights are found to minimize a weighted L2 norm of the ...This paper presents an array pattern synthesis algorithm for arbitrary arrays based on coordinate descent method (CDM). With this algorithm, the complex element weights are found to minimize a weighted L2 norm of the difference between desired and achieved pattern. Compared with traditional optimization techniques, CDM is easy to implement and efficient to reach the optimum solutions. Main advantage is the flexibility. CDM is suitable for linear and planar array with arbitrary array elements on arbitrary positions. With this method, we can configure arbitrary beam pattern, which gives it the ability to solve variety of beam forming problem, e.g. focused beam, shaped beam, nulls at arbitrary direction and with arbitrary beam width. CDM is applicable for phase-only and amplitude-only arrays as well, and furthermore, it is a suitable method to treat the problem of array with element failures.展开更多
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
Dirac's method which itself is for constrained Boson fields and particle systems is followed and developed to treat Dirac fields in light-front coordinates.
The analysis and calculating method of dynamic errors of CMMs during probing are discussed.To relate the dynamic displacement errors with the dynamic rotational errors a method for obtaining the displacement errors at...The analysis and calculating method of dynamic errors of CMMs during probing are discussed.To relate the dynamic displacement errors with the dynamic rotational errors a method for obtaining the displacement errors at the probing position from dynamic rotational errors is presented.It is pointed out that the finite element method might be used for modeling dynamic errors.However,dynamic errors are difficult to be modeled so a combined practical and theoretical approach is needed.In addition,the dynamic errors are measured with inductive position sensors.展开更多
A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution f...A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into the modified lattice Boltzmann equation which could recover the Navier–Stokes equations, including contribution of chemical reaction, via the Chapman–Enskog expansion.For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium in the highly symmetric case. The internal kinetic energies in different degrees of freedom around the detonation front do not coincide. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed.展开更多
Based on the analysis of the advantages and disadvantages of some vertical coordinates applied in the calculation of the Changjiang diluted water （CDW）, a new hybrid vertical coordinate is designed, which uses σ co...Based on the analysis of the advantages and disadvantages of some vertical coordinates applied in the calculation of the Changjiang diluted water （CDW）, a new hybrid vertical coordinate is designed, which uses σ coordinate for current and σ-z coordinate for salinity. To combine the current and salinity, the Eulerian-Lagrangian method is used for the salinity calculation, and the baroclinic pressure gradient （BPG） is calculated on the salinity sited layers. The new hybrid vertical coordinate is introduced to the widely used model of POM （Princeton Ocean Model） to make a new model of POM-σ-z. The BPG calculations of an ideal case show that POM-σ-z model brings smaller error than POM model does. The simulations of CDW also show that POM-σ-z model is better than POM model on simulating the salinity and its front.展开更多
A simple and fast route for the synthesis of metal-organic framework（MOF） particles was presented.Cu 3（BTC） 2（HKUST-1,BTC=1,3,5-benzenetricarboxylate）,one of the most well-known MOFs,was synthesized at room temp...A simple and fast route for the synthesis of metal-organic framework（MOF） particles was presented.Cu 3（BTC） 2（HKUST-1,BTC=1,3,5-benzenetricarboxylate）,one of the most well-known MOFs,was synthesized at room temperature via coordination modulation method.By adding different modulators（monocarboxylic acids） into the reaction system,the morphologies of HKUST-1 crystals were tuned from nano spheres to micro octahedrons at room temperature without any complex equipment.X-Ray diffractions and gas sorption measurements revealed highly crystalline particles with large Brunauer-Emmett-Teller（BET） surface areas（1116―1273 m^ 2 /g） and total pore volumes（0.62―0.73 cm^ 3 /g）.The significantly small particle sizes and high capacity of gas sorption are considered advantageous for envisaged application in practical industrial process.展开更多
Three types of spatial function zoning is an effective measure for regional environmental protection and orderly development.For ecological and economic coordinated development, spatial function zones should be divide...Three types of spatial function zoning is an effective measure for regional environmental protection and orderly development.For ecological and economic coordinated development, spatial function zones should be divided scientifically to clear its direction of development and protection. Therefore, based on ecological constraints, a beneficial discussion would be about the key ecological function areas adopting the concept of ecological protection restriction and supporting socioeconomic development for spatial function zoning. In this paper, the researchers, taking Tacheng Basin, Xinjiang of China as an example, choose township as basic research unit and set up an evaluation index system from three aspects, namely, ecological protection suitability, agricultural production suitability, and urban development suitability, which are analyzed by using spatial analysis functions and exclusive matrix method. The results showed that: 1) This paper formed a set of multilevel evaluation index systems for three types of spatial function zoning of the key ecological function areas based on a novel perspective by scientifically dividing Tacheng Basin into ecological space, agricultural space, and urban space,which realized the integration and scientific orientation for spatial function at the township scale. 2) Under the guidance of three types of spatial pattern, the functional orientation and suggestions of development and protection was clearly defined for ecological protection zones,ecological economic zones, agricultural production zones, and urban development zones. 3) A new idea of space governance is provided to promote the coordinated and sustainable development between ecology and economy, which can break the traditional mode of thinking about regional economic development, and offers a scientific basis and reference for macro decision-making.展开更多
The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody sys...The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody systems. However, the formulation has so many principles in choosing the generalized coordinates that it hinders the implementation of modeling automation, A first order direct sensitivity analysis approach to multibody systems formulated with novel natural coordinates is presented. Firstly, a new selection method for natural coordinate is developed. The method introduces 12 coordinates to describe the position and orientation of a spatial object. On the basis of the proposed natural coordinates, rigid constraint conditions, the basic constraint elements as well as the initial conditions for the governing equations are derived. Considering the characteristics of the governing equations, the newly proposed generalized-ct integration method is used and the corresponding algorithm flowchart is discussed. The objective function, the detailed analysis process of first order direct sensitivity analysis and related solving strategy are provided based on the previous modeling system Finally, in order to verify the validity and accuracy of the method presented, the sensitivity analysis of a planar spinner-slider mechanism and a spatial crank-slider mechanism are conducted. The test results agree well with that of the finite difference method, and the maximum absolute deviation of the results is less than 3%. The proposed approach is not only convenient for automatic modeling, but also helpful for the reduction of the complexity of sensitivity analysis, which provides a practical and effective way to obtain sensitivity for the optimization problems of multibody systems.展开更多
A reconstructed edge-based smoothed triangular element, which is incorporated with the discrete shear gap (DSG) method, is formulated based on the global coordinate for analysis of Reissner-Mindlin plates. A symbolic ...A reconstructed edge-based smoothed triangular element, which is incorporated with the discrete shear gap (DSG) method, is formulated based on the global coordinate for analysis of Reissner-Mindlin plates. A symbolic integration combined with the smoothing technique is implemented to calculate the smoothed finite element matrices, which is integrated along the boundaries of each smoothing cell. Numerical results show that the proposed element is free from shear locking, and its results are in good agreement with the exact solutions, even for very thin plates with extremely distorted elements. The proposed element gives more accurate results than the original DSG element without smoothing, and it can be taken as an alternative element for analysis of Reissner-Mindlin plates. The prominent feature of the present element is that the integration scheme is unified in the smoothed form for all of the finite element matrices.展开更多
基金supported by the National Key R&D Program of China(No.2023YFA1606701)the National Natural Science Foundation of China(Nos.12175042,11890710,11890714,12047514,12147101,and 12347106)+1 种基金Guangdong Major Project of Basic and Applied Basic Research(No.2020B0301030008)China National Key R&D Program(No.2022YFA1602402).
文摘We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.
文摘In actual power systems,most of the high-voltage buses of the transformers are zero injection buses without load or generation.Power injections into these buses are strictly 0,so based on Kirchhoff's current law(KCL),equality constraints should be used to handle these buses in a state estimation model.It is a challenge to ensure that these zero injection constraints can be strictly satisfied without losing computational efficiency.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035 and 11171038)the Science Research Foundation of the Institute of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2012MS0102)
文摘In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035,11171038,and 10771019)the Science Reaearch Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region,China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region,China (Grant No. 2012MS0102)
文摘In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.
文摘A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant No.10874174)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20070358009)
文摘For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.
基金the President Foundation of the Chinese Academy of Sciencesthe Specialized Research Fund for the Doctoral Program of Higher Education
文摘Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator （IEO） method to solving the energy spectrmn of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1, X2] = [X2, X3]=[X3, X1] = iθ, and this method seems effective and concise.
基金support of this work by the National Natural Science Foundation of China(No.51405096)the Fundamental Research Funds for the Central Universities(HEUCF210710).
文摘Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.
基金Project supported by the National Natural Science Foundation of China(Grant No.51272027)
文摘Bond valence method illustrates the relation between valence and length of a particular bond type. This theory has been used to predict structure information, but the effect is very limited. In this paper, two indexes, i.e., global instability index（GII） and bond strain index（BSI）, are adopted as a judgment of a search-match program for prediction. The results show that with GII and BSI combined as judgment, the predicted atom positions are very close to real ones. The mechanism and validity of this searching program are also discussed. The GII ＆ BSI distribution contour map reveals that the predicted function is a reflection of exponential feature of bond valence formula. This combined searching method may be integrated with other structure-determination method, and may be helpful in refining and testifying light atom positions.
文摘A new numerical approach, called the “subdomain Chebyshev spectral method” is presented for calculation of the spatial derivatives in a curved coordinate system, which may be employed for numerical solutions of partial differential equations defined in a 2D or 3D geological model. The new approach refers to a “strong version” against the “weak version” of the subspace spectral method based on the variational principle or Galerkin’s weighting scheme. We incorporate local nonlinear transformations and global spline interpolations in a curved coordinate system and make the discrete grid exactly matches geometry of the model so that it is achieved to convert the global domain into subdomains and apply Chebyshev points to locally sampling physical quantities and globally computing the spatial derivatives. This new approach not only remains exponential convergence of the standard spectral method in subdomains, but also yields a sparse assembled matrix when applied for the global domain simulations. We conducted 2D and 3D synthetic experiments and compared accuracies of the numerical differentiations with traditional finite difference approaches. The results show that as the points of differentiation vector are larger than five, the subdomain Chebyshev spectral method significantly improve the accuracies of the finite difference approaches.
文摘This paper presents an array pattern synthesis algorithm for arbitrary arrays based on coordinate descent method (CDM). With this algorithm, the complex element weights are found to minimize a weighted L2 norm of the difference between desired and achieved pattern. Compared with traditional optimization techniques, CDM is easy to implement and efficient to reach the optimum solutions. Main advantage is the flexibility. CDM is suitable for linear and planar array with arbitrary array elements on arbitrary positions. With this method, we can configure arbitrary beam pattern, which gives it the ability to solve variety of beam forming problem, e.g. focused beam, shaped beam, nulls at arbitrary direction and with arbitrary beam width. CDM is applicable for phase-only and amplitude-only arrays as well, and furthermore, it is a suitable method to treat the problem of array with element failures.
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Dirac's method which itself is for constrained Boson fields and particle systems is followed and developed to treat Dirac fields in light-front coordinates.
文摘The analysis and calculating method of dynamic errors of CMMs during probing are discussed.To relate the dynamic displacement errors with the dynamic rotational errors a method for obtaining the displacement errors at the probing position from dynamic rotational errors is presented.It is pointed out that the finite element method might be used for modeling dynamic errors.However,dynamic errors are difficult to be modeled so a combined practical and theoretical approach is needed.In addition,the dynamic errors are measured with inductive position sensors.
基金support of the Science Foundations of National Key Laboratory of Computational Physics,National Natural Science Foundation of China under Grant No.11202003the opening project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) under Grant No.KFJJ14-1M.YL +1 种基金support of National Natural Science Foundation of China under Grant Nos.11074300 and 41472130National Basic Research Program of China under Grant No.2013CBA01504
文摘A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into the modified lattice Boltzmann equation which could recover the Navier–Stokes equations, including contribution of chemical reaction, via the Chapman–Enskog expansion.For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium in the highly symmetric case. The internal kinetic energies in different degrees of freedom around the detonation front do not coincide. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed.
文摘Based on the analysis of the advantages and disadvantages of some vertical coordinates applied in the calculation of the Changjiang diluted water （CDW）, a new hybrid vertical coordinate is designed, which uses σ coordinate for current and σ-z coordinate for salinity. To combine the current and salinity, the Eulerian-Lagrangian method is used for the salinity calculation, and the baroclinic pressure gradient （BPG） is calculated on the salinity sited layers. The new hybrid vertical coordinate is introduced to the widely used model of POM （Princeton Ocean Model） to make a new model of POM-σ-z. The BPG calculations of an ideal case show that POM-σ-z model brings smaller error than POM model does. The simulations of CDW also show that POM-σ-z model is better than POM model on simulating the salinity and its front.
基金Supported by the National Natural Science Foundation of China(Nos.21173034,20907006)
文摘A simple and fast route for the synthesis of metal-organic framework（MOF） particles was presented.Cu 3（BTC） 2（HKUST-1,BTC=1,3,5-benzenetricarboxylate）,one of the most well-known MOFs,was synthesized at room temperature via coordination modulation method.By adding different modulators（monocarboxylic acids） into the reaction system,the morphologies of HKUST-1 crystals were tuned from nano spheres to micro octahedrons at room temperature without any complex equipment.X-Ray diffractions and gas sorption measurements revealed highly crystalline particles with large Brunauer-Emmett-Teller（BET） surface areas（1116―1273 m^ 2 /g） and total pore volumes（0.62―0.73 cm^ 3 /g）.The significantly small particle sizes and high capacity of gas sorption are considered advantageous for envisaged application in practical industrial process.
基金Under the auspices of Grant Program of Clean Development Mechanism Fund of China(CDMF)(No.2014092)Task 2 of Key Service Project 5 for the Characteristic Institute of Chinese Academy of Sciences(No.TSS-2015-014-FW-5-2)+2 种基金National Natural Science Foundation of China(No.41571159)The Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDA20010301)Jiangsu Natural Science Foundation(No.BK20181105)
文摘Three types of spatial function zoning is an effective measure for regional environmental protection and orderly development.For ecological and economic coordinated development, spatial function zones should be divided scientifically to clear its direction of development and protection. Therefore, based on ecological constraints, a beneficial discussion would be about the key ecological function areas adopting the concept of ecological protection restriction and supporting socioeconomic development for spatial function zoning. In this paper, the researchers, taking Tacheng Basin, Xinjiang of China as an example, choose township as basic research unit and set up an evaluation index system from three aspects, namely, ecological protection suitability, agricultural production suitability, and urban development suitability, which are analyzed by using spatial analysis functions and exclusive matrix method. The results showed that: 1) This paper formed a set of multilevel evaluation index systems for three types of spatial function zoning of the key ecological function areas based on a novel perspective by scientifically dividing Tacheng Basin into ecological space, agricultural space, and urban space,which realized the integration and scientific orientation for spatial function at the township scale. 2) Under the guidance of three types of spatial pattern, the functional orientation and suggestions of development and protection was clearly defined for ecological protection zones,ecological economic zones, agricultural production zones, and urban development zones. 3) A new idea of space governance is provided to promote the coordinated and sustainable development between ecology and economy, which can break the traditional mode of thinking about regional economic development, and offers a scientific basis and reference for macro decision-making.
基金supported by National Defense Pre-research Foundation of China during the 12th Five-Year Plan Period(Grant No.51036050107)
文摘The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody systems. However, the formulation has so many principles in choosing the generalized coordinates that it hinders the implementation of modeling automation, A first order direct sensitivity analysis approach to multibody systems formulated with novel natural coordinates is presented. Firstly, a new selection method for natural coordinate is developed. The method introduces 12 coordinates to describe the position and orientation of a spatial object. On the basis of the proposed natural coordinates, rigid constraint conditions, the basic constraint elements as well as the initial conditions for the governing equations are derived. Considering the characteristics of the governing equations, the newly proposed generalized-ct integration method is used and the corresponding algorithm flowchart is discussed. The objective function, the detailed analysis process of first order direct sensitivity analysis and related solving strategy are provided based on the previous modeling system Finally, in order to verify the validity and accuracy of the method presented, the sensitivity analysis of a planar spinner-slider mechanism and a spatial crank-slider mechanism are conducted. The test results agree well with that of the finite difference method, and the maximum absolute deviation of the results is less than 3%. The proposed approach is not only convenient for automatic modeling, but also helpful for the reduction of the complexity of sensitivity analysis, which provides a practical and effective way to obtain sensitivity for the optimization problems of multibody systems.
基金supported by the National Natural Science Foundation of China (Grants 11272118, 11372106)Fundamental Research Fund of the Central Universities (Grant 227201401203)
文摘A reconstructed edge-based smoothed triangular element, which is incorporated with the discrete shear gap (DSG) method, is formulated based on the global coordinate for analysis of Reissner-Mindlin plates. A symbolic integration combined with the smoothing technique is implemented to calculate the smoothed finite element matrices, which is integrated along the boundaries of each smoothing cell. Numerical results show that the proposed element is free from shear locking, and its results are in good agreement with the exact solutions, even for very thin plates with extremely distorted elements. The proposed element gives more accurate results than the original DSG element without smoothing, and it can be taken as an alternative element for analysis of Reissner-Mindlin plates. The prominent feature of the present element is that the integration scheme is unified in the smoothed form for all of the finite element matrices.
