Nonlinear wave equations have been extensively investigated in the last sev- eral decades. The Landau-Ginzburg-Higgs equation, a typical nonlinear wave equation, is studied in this paper based on the multi-symplectic ...Nonlinear wave equations have been extensively investigated in the last sev- eral decades. The Landau-Ginzburg-Higgs equation, a typical nonlinear wave equation, is studied in this paper based on the multi-symplectic theory in the Hamilton space. The multi-symplectic Runge-Kutta method is reviewed, and a semi-implicit scheme with certain discrete conservation laws is constructed to solve the first-order partial differential equations （PDEs） derived from the Landau-Ginzburg-Higgs equation. The numerical re- sults for the soliton solution of the Landau-Ginzburg-Higgs equation are reported, showing that the multi-symplectic Runge-Kutta method is an efficient algorithm with excellent long-time numerical behaviors.展开更多
A new non-invasive blood glucose measuring apparatus (NBGMA) made up of MSP430F149 SCM (single chip micyoco) was developed,which can measure blood glucose level (BGL) frequently,conveniently and painlessly. The hardwa...A new non-invasive blood glucose measuring apparatus (NBGMA) made up of MSP430F149 SCM (single chip micyoco) was developed,which can measure blood glucose level (BGL) frequently,conveniently and painlessly. The hardware and software of this apparatus were designed,and detecting algorithms based on conservation of energy method (COEM) were presented. According to the law of conservation of energy that the energy derived by human body equals energy consumed by metabolism,and the relationship between convection,evaporation,radiation and the BGL was established. The sensor module was designed. 20 healthy volunteers were involved in the clinical experiment. The BGL measured by an automatic biochemical analyzer (ABA) was set as the reference. Regression analysis was performed to compare the conservation of energy method with the biochemical method,using the 20 data points with blood glucose concentrations ranging from 680 to 1 100 mg/L. Reproducibility was measured for healthy fasting volunteers. The results show that the means of BGL detected by NBGMA and ANA are very close to each other,and the difference of standard deviation (SD) is 24.7 mg/L. The correlative coefficient is 0.807. The coefficient of variation (CV) is 4% at 921.6 mg/L. The resultant regression is evaluated by the Clarke error grid analysis (EGA) and all data points are included in the clinically acceptable regions (region A:100%,region B:0%). Accordingly,it is feasible to measure BGL with COEM.展开更多
To improve flood control efficiency and increase urban resilience to flooding,the impacts of forest type change on flood control in the upper reach of the Tingjiang River(URTR) were evaluated by a modified model based...To improve flood control efficiency and increase urban resilience to flooding,the impacts of forest type change on flood control in the upper reach of the Tingjiang River(URTR) were evaluated by a modified model based on the Soil Conservation Service curve number(SCS-CN) method. Parameters of the model were selected and determined according to the comprehensive analysis of model evaluation indexes. The first simulation of forest reconstruction scenario,namely a coniferous forest covering 59.35km^2 is replaced by a broad-leaved forest showed no significant impact on the flood reduction in the URTR. The second simulation was added with 61.75km^2 bamboo forest replaced by broad-leaved forest,the reduction of flood peak discharge and flood volume could be improved significantly. Specifically,flood peak discharge of 10-year return period event was reduced to 7-year event,and the reduction rate of small flood was 21%-28%. Moreover,the flood volume was reduced by 9%-14% and 18%-35% for moderate floods and small floods,respectively. The resultssuggest that the bamboo forest reconstruction is an effective control solution for small to moderate flood in the URTR,the effect of forest conversion on flood volume is increasingly reduced as the rainfall amount increases to more extreme magnitude. Using a hydrological model with scenarios analysis is an effective simulation approach in investigating the relationship between forest type change and flood control. This method would provide reliable support for flood control and disaster mitigation in mountainous cities.展开更多
The characteristics of the normal equation created in recovering the Earth gravity model （EGM） by least-squares （LS） adjustment from the in-situ disturbing potential is discussed in detail. It can be concluded tha...The characteristics of the normal equation created in recovering the Earth gravity model （EGM） by least-squares （LS） adjustment from the in-situ disturbing potential is discussed in detail. It can be concluded that the normal equation only depends on the orbit, and the choice of a priori gravity model has no effect on the LS solution. Therefore, the accuracy of the recovered gravity model can be accurately simulated. Starting from this point, four sets of disturbing potential along the orbit with different level of noise were simulated and were used to recover the EGM. The results show that on the current accuracy level of the accelerometer calibration, the accuracy of the EGM is not sufficient to reflect the time variability of the Earth＇s gravity field, as the dynamic method revealed.展开更多
Senior high school is an important stage for students to learn and a key time for students to enter the desired university. For junior high school knowledge, the difficulty of senior high school knowledge also rises s...Senior high school is an important stage for students to learn and a key time for students to enter the desired university. For junior high school knowledge, the difficulty of senior high school knowledge also rises sharply compared with junior high school. All subjects require stronger logical thinking and divergent thinking. As an important subject in senior high school, chemistry is very comprehensive and experimental. For high school students, they are facing great pressure from the college entrance examination and their studies. Therefore, excellent problem-solving skills can help students to learn more efficiently, and can also promote the cultivation of logical thinking ability, eventually forming a virtuous circle, making learning easier. As a common method in chemical problem solving, conservation method can greatly save students' time and improve the correct rate of problem solving, thus improving learning efficiency. This paper gives a brief introduction to the application of conservation method in high school chemistry problem solving, hoping to be helpful to the students.展开更多
Drainage canals are engineering structures widely used for debris flow mitigation.When passing through a drainage canal,debris flow usually scours the gully bed at the back of the rib sill of the drainage canal,which ...Drainage canals are engineering structures widely used for debris flow mitigation.When passing through a drainage canal,debris flow usually scours the gully bed at the back of the rib sill of the drainage canal,which leads to failure of the rib sill.Therefore,the scour depth at the back of the rib sill is an important design problem and it is related to the economic benefits of engineering and service years.To explore the law of the depth of the scour pit after debris flow through drainage canal ribs,we first proposed a formula for the calculation of the maximum scour depth at the back of a rib sill based on energy conservation.We then conducted a series of simulation experiments to test the proposed formula.The experimental results show that the scour depth,trench slope and the distance between ribs all increase with a decrease in debris flow density.We then compared the results of experiments and formula calculations.Through the testing analysis,we found that the calculation results of the conductedformula correspond with the experimental results better.Finally,taking Qipan Gully as an example,we designed the ultimate depth of a drainage canal for debris flow using the calculation formula.展开更多
Firstly, the Earth＇s gravitational field from the past Challenging Minisatellite Payload （CHAMP） mission is determined using the energy conservation principle, the combined error model of the cumulative geoid heigh...Firstly, the Earth＇s gravitational field from the past Challenging Minisatellite Payload （CHAMP） mission is determined using the energy conservation principle, the combined error model of the cumulative geoid height influenced by three instrument errors from the current Gravity Recovery and Climate Experiment （GRACE） and future GRACE Follow-On missions is established based on the semi-analytical method, and the Earth＇s gravitational field from the executed Gravity Field and Steady-State Ocean Circulation Explorer （GOCE） mission is recovered by the space-time-wise approach. Secondly, the cumulative geoid height errors are 1.727 × 10^-1 m, 1.839 × 10^-1 m and 9.025 × 10^ -2 m at degrees 70,120 and 250 from the implemented three-stage satellite gravity missions consisting of CHAMP, GRACE and GOCE, which preferably accord with those from the existing earth gravity field models involving EIGEN-CHAMP03S, EICEN-GRACE02S and GO_CONS GCF 2 DIR R1. The cumulative geoid height error is 6.847 × 10 ^-2 m at degree 250 from the future GRACE Follow-On mission. Finally, the complementarity among the four-stage satellite gravity missions including CHAMP, GRACE, GOCE and GRACE Follow-On is demonstrated contrastively.展开更多
This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order...This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.展开更多
A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid.Two kinds of moments(i.e.,point values(PV moment) at cell interface...A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid.Two kinds of moments(i.e.,point values(PV moment) at cell interfaces and volume integrated average(VIA moment) value) are defined within a single cell.The PV moment is updated by a conventional semi-Lagrangian method,while the VIA moment is cast by the flux form formulation to assure the exact numerical conservation.Different from the spatial approximation used in the CSL2(conservative semi-Lagrangian scheme with second order polynomial function) scheme,a monotonic rational function which can effectively remove non-physical oscillations is reconstructed within a single cell by the PV moments and VIA moment.To achieve exactly positive-definite preserving,two kinds of corrections are made on the original conservative semi-Lagrangian with rational function(CSLR)scheme.The resulting scheme is inherently conservative,non-negative,and allows a Courant number larger than one.Moreover,the spatial reconstruction can be performed within a single cell,which is very efficient and economical for practical implementation.In addition,a dimension-splitting approach coupled with multi-moment finite volume scheme is adopted on cubed-sphere geometry,which benefitsthe implementation of the 1 D CSLR solver with large Courant number.The proposed model is evaluated by several widely used benchmark tests on cubed-sphere geometry.Numerical results show that the proposed transport model can effectively remove nonphysical oscillations and preserve the numerical nonnegativity,and it has the potential to transport the tracers accurately in a real atmospheric model.展开更多
We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-or...We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.展开更多
In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solut...In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solution element scheme for conservative hyperbolic governing equations with source terms is given. A modified ghost fluid method is proposed for the treatment of the boundary conditions. Numerical simulations of the Taylor bar problem and the ricochet phenomenon of a sphere impacting a plate target at an angle of 60~ are carried out. The numerical results are in good agreement with the corresponding experimental observations. It is proved that our computational technique is feasible for analyzing 3D high-velocity impact problems.展开更多
To clarify the influence of the hydrofoil characteristic thickness on the distribution characteristics and mechanisms of clearance cavitation erosion risk,a large eddy simulation(LES)is conducted to study the clearanc...To clarify the influence of the hydrofoil characteristic thickness on the distribution characteristics and mechanisms of clearance cavitation erosion risk,a large eddy simulation(LES)is conducted to study the clearance cavitating flow around NACA0012 and NACA0024 hydrofoils under identical conditions.The study predicts cavitation erosion risk using three methods:The erosive power method(EPM),the improved gray level method(IGLM)and the energy conservation method(ECM).The numerical results are in good agreement with the experiment data and the ECM is applied due to its simplicity in parameter adjustment and low sensitivity.The results indicate that the characteristic thickness significantly influences the flow field,leading to variations in the position and intensity of cavitation collapse,ultimately resulting in notable differences in cavitation erosion risk distribution.The high cavitation erosion risk region on the clearance surface of NACA0012 is concentrated around the midsection,while it is concentrated in the upstream region for the NACA0024,with a lower frequency of extreme events.Tip separation vortex(TSV)cavitation is the main cause of the differences in cavitation erosion risk distribution.On the clearance surface of the NACA0012,TSV cavitation primarily collapses in the central region,whereas for the NACA0024 hydrofoil,TSV cavitation occurs only in the upstream region of the clearance surface and exhibits more stability.The differences in vorticity distribution near the clearance surface partially influence the distribution of TSV cavitation,thereby affecting the characteristics of cavitation erosion risk distribution.The larger characteristic thickness of the NACA0024 reduces the effects of the stretching term and the baroclinic torque term,weakening the effect of vorticity on TSV cavitation,resulting in more stable patterns of the TSV cavitation.展开更多
The purpose of this article is to summarize our recent progress in high-order and high accurate CFD methods for flow problems with complex grids as well as to discuss the engineering prospects in using these methods.D...The purpose of this article is to summarize our recent progress in high-order and high accurate CFD methods for flow problems with complex grids as well as to discuss the engineering prospects in using these methods.Despite the rapid development of high-order algorithms in CFD,the applications of high-order and high accurate methods on complex configurations are still limited.One of the main reasons which hinder the widely applications of thesemethods is the complexity of grids.Many aspects which can be neglected for low-order schemes must be treated carefully for high-order ones when the configurations are complex.In order to implement highorder finite difference schemes on complex multi-block grids,the geometric conservation lawand block-interface conditions are discussed.A conservativemetricmethod is applied to calculate the grid derivatives,and a characteristic-based interface condition is employed to fulfil high-order multi-block computing.The fifth-order WCNS-E-5 proposed by Deng[9,10]is applied to simulate flows with complex grids,including a double-delta wing,a transonic airplane configuration,and a hypersonic X-38 configuration.The results in this paper and the references show pleasant prospects in engineering-oriented applications of high-order schemes.展开更多
We construct and analyze conservative local discontinuous Galerkin(LDG)methods for the Generalized Korteweg-de-Vries equation.LDG methods are designed by writing the equation as a system and performing separate approx...We construct and analyze conservative local discontinuous Galerkin(LDG)methods for the Generalized Korteweg-de-Vries equation.LDG methods are designed by writing the equation as a system and performing separate approximations to the spatial derivatives.The main focus is on the development of conservative methods which can preserve discrete versions of the first two invariants of the continuous solution,and a posteriori error estimates for a fully discrete approximation that is based on the idea of dispersive reconstruction.Numerical experiments are provided to verify the theoretical estimates.展开更多
Under harsh conditions （such as high temperature, high pressure, and millisecond lifetime chemical reaction）, a long-standing challenge remains to accurately predict the growth characteristics of nanosize spherical ...Under harsh conditions （such as high temperature, high pressure, and millisecond lifetime chemical reaction）, a long-standing challenge remains to accurately predict the growth characteristics of nanosize spherical particles and to determine the rapid chemical reaction flow field characteristics, The growth characteristics of similar spherical oxide nanoparticles are further studied by successfully introducing the space-time conservation element-solution element （CE/SE） algorithm with the monodisperse Kruis model. This approach overcomes the nanosize particle rapid growth limit set and successfully captures the characteristics of the rapid gaseous chemical reaction process. The results show that this approach quantitatively captures the characteristics of the rapid chemical reaction, nanosize particle growth and size distribution. To reveal the growth mechanism for numerous types of oxide nanoparticles, it is very important to choose a rational numerical method and particle physics model.展开更多
This paper presents an engineering-oriented UGKS solver package developed in China Aerodynamics Research and Development Center(CARDC).The solver is programmed in Fortran language and uses structured body-fitted mesh,...This paper presents an engineering-oriented UGKS solver package developed in China Aerodynamics Research and Development Center(CARDC).The solver is programmed in Fortran language and uses structured body-fitted mesh,aiming for predicting aerodynamic and aerothermodynamics characteristics in flows covering various regimes on complex three-dimensional configurations.The conservative discrete ordinate method and implicit implementation are incorporated.Meanwhile,a local mesh refinement technique in the velocity space is developed.The parallel strategies include MPI and OpenMP.Test cases include a wedge,a cylinder,a 2D blunt cone,a sphere,and a X38-like vehicle.Good agreements with experimental or DSMC results have been achieved.展开更多
Two-quasiparticle bands and low-lying excited high-K four-, six-, and eight-quasiparticle bands in the doubly-odd 174, 176Lu are analyzed by using the cranked shell model （CSM） with the pairing correlations treated ...Two-quasiparticle bands and low-lying excited high-K four-, six-, and eight-quasiparticle bands in the doubly-odd 174, 176Lu are analyzed by using the cranked shell model （CSM） with the pairing correlations treated by a particle-number conserving （PNC） method, in which the blocking effects are taken into account exactly. The proton and neutron Nilsson level schemes for 174, 176Lu are taken from the adjacent odd-A Lu and Hf isotopes, which are adopted to reproduce the experimental bandhead energies of the one-quasiproton and one-quasineutron bands of these odd-A Lu and Hf nuclei, respectively. Once the quasiparticle configurations are determined, the experimental bandhead energies and the moments of inertia of these two- and multi-quasiparticle bands are well reproduced by PNC-CSM calculations. The Coriolis mixing of the low-K （K=｜Ω1-Ω2｜） two-quasiparticle band of the Gallagher-Moszkowski doublet with one nucleon in the Ω = 1/2 orbital is analyzed.展开更多
We present a newly developed global magnetohydrodynamic(MHD) model to study the responses of the Earth's magnetosphere to the solar wind. The model is established by using the space-time conservation element and s...We present a newly developed global magnetohydrodynamic(MHD) model to study the responses of the Earth's magnetosphere to the solar wind. The model is established by using the space-time conservation element and solution element(CESE) method in general curvilinear coordinates on a six-component grid system. As a preliminary study, this paper is to present the model's numerical results of the quasi-steady state and the dynamics of the Earth's magnetosphere under steady solar wind flow with due northward interplanetary magnetic field(IMF). The model results are found to be in good agreement with those published by other numerical magnetospheric models.展开更多
The recently observed two high-spin rotational bands in the proton emitter ^113Cs are investigated using the cranked shell model with pairing correlations treated by a particle-number conserving method, in which the P...The recently observed two high-spin rotational bands in the proton emitter ^113Cs are investigated using the cranked shell model with pairing correlations treated by a particle-number conserving method, in which the Pauli blocking effects are taken into account exactly. By using the configuration assignments of band 1 [π3/2^＋[422]（g7/2）, α =-1/2] and band 2 [π1/2^＋[420]（d5/2）, α=1/2], the experimental moments of inertia and quasiparticle alignments can be reproduced much better by the present calculations than those using the configuration assginment of π1/2^-[550]（h11/2）, which in turn may support these configuration assignments. Furthermore, by analyzing the occupation probability nμ of each cranked Nilsson level near the Fermi surface and the contribution of each orbital to the angular momentum alignments, the backbending mechanism of these two bands is also investigated.展开更多
The experimentally observed ten rotational bands in 179Re are analyzed with the particle-number conserving method for treating the cranked shell model with pairing interaction, in which the blocking effects are taken ...The experimentally observed ten rotational bands in 179Re are analyzed with the particle-number conserving method for treating the cranked shell model with pairing interaction, in which the blocking effects are taken into account exactly. The experimental moments of inertia of these bands are reproduced quite well by our calculations with no free parameter and the deformation driving effects are discussed. The bandhead energies and the variation in the occupation probability of each cranked orbital are also analyzed.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10772147 and10632030)the Ph. D. Program Foundation of Ministry of Education of China (No. 20070699028)+2 种基金the Natural Science Foundation of Shaanxi Province of China (No. 2006A07)the Open Foundationof State Key Laboratory of Structural Analysis of Industrial Equipment (No. GZ0802)the Foundation for Fundamental Research of Northwestern Polytechnical University
文摘Nonlinear wave equations have been extensively investigated in the last sev- eral decades. The Landau-Ginzburg-Higgs equation, a typical nonlinear wave equation, is studied in this paper based on the multi-symplectic theory in the Hamilton space. The multi-symplectic Runge-Kutta method is reviewed, and a semi-implicit scheme with certain discrete conservation laws is constructed to solve the first-order partial differential equations （PDEs） derived from the Landau-Ginzburg-Higgs equation. The numerical re- sults for the soliton solution of the Landau-Ginzburg-Higgs equation are reported, showing that the multi-symplectic Runge-Kutta method is an efficient algorithm with excellent long-time numerical behaviors.
基金Project(07JJ6133) supported by the Natural Science Foundation of Hunan Province, China
文摘A new non-invasive blood glucose measuring apparatus (NBGMA) made up of MSP430F149 SCM (single chip micyoco) was developed,which can measure blood glucose level (BGL) frequently,conveniently and painlessly. The hardware and software of this apparatus were designed,and detecting algorithms based on conservation of energy method (COEM) were presented. According to the law of conservation of energy that the energy derived by human body equals energy consumed by metabolism,and the relationship between convection,evaporation,radiation and the BGL was established. The sensor module was designed. 20 healthy volunteers were involved in the clinical experiment. The BGL measured by an automatic biochemical analyzer (ABA) was set as the reference. Regression analysis was performed to compare the conservation of energy method with the biochemical method,using the 20 data points with blood glucose concentrations ranging from 680 to 1 100 mg/L. Reproducibility was measured for healthy fasting volunteers. The results show that the means of BGL detected by NBGMA and ANA are very close to each other,and the difference of standard deviation (SD) is 24.7 mg/L. The correlative coefficient is 0.807. The coefficient of variation (CV) is 4% at 921.6 mg/L. The resultant regression is evaluated by the Clarke error grid analysis (EGA) and all data points are included in the clinically acceptable regions (region A:100%,region B:0%). Accordingly,it is feasible to measure BGL with COEM.
基金funded by the National Natural Science Foundation of China (Grants No.51278239)
文摘To improve flood control efficiency and increase urban resilience to flooding,the impacts of forest type change on flood control in the upper reach of the Tingjiang River(URTR) were evaluated by a modified model based on the Soil Conservation Service curve number(SCS-CN) method. Parameters of the model were selected and determined according to the comprehensive analysis of model evaluation indexes. The first simulation of forest reconstruction scenario,namely a coniferous forest covering 59.35km^2 is replaced by a broad-leaved forest showed no significant impact on the flood reduction in the URTR. The second simulation was added with 61.75km^2 bamboo forest replaced by broad-leaved forest,the reduction of flood peak discharge and flood volume could be improved significantly. Specifically,flood peak discharge of 10-year return period event was reduced to 7-year event,and the reduction rate of small flood was 21%-28%. Moreover,the flood volume was reduced by 9%-14% and 18%-35% for moderate floods and small floods,respectively. The resultssuggest that the bamboo forest reconstruction is an effective control solution for small to moderate flood in the URTR,the effect of forest conversion on flood volume is increasingly reduced as the rainfall amount increases to more extreme magnitude. Using a hydrological model with scenarios analysis is an effective simulation approach in investigating the relationship between forest type change and flood control. This method would provide reliable support for flood control and disaster mitigation in mountainous cities.
基金Funded by the National Natural Science Foundation of China （No.40274004）, and the Open Fund of Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, China （No. 06-09）. The authors are grateful to Prof. CHAO Dingbo for his critical comments and also thank Dr. Dadzie very much for his proof-reading.
文摘The characteristics of the normal equation created in recovering the Earth gravity model （EGM） by least-squares （LS） adjustment from the in-situ disturbing potential is discussed in detail. It can be concluded that the normal equation only depends on the orbit, and the choice of a priori gravity model has no effect on the LS solution. Therefore, the accuracy of the recovered gravity model can be accurately simulated. Starting from this point, four sets of disturbing potential along the orbit with different level of noise were simulated and were used to recover the EGM. The results show that on the current accuracy level of the accelerometer calibration, the accuracy of the EGM is not sufficient to reflect the time variability of the Earth＇s gravity field, as the dynamic method revealed.
文摘Senior high school is an important stage for students to learn and a key time for students to enter the desired university. For junior high school knowledge, the difficulty of senior high school knowledge also rises sharply compared with junior high school. All subjects require stronger logical thinking and divergent thinking. As an important subject in senior high school, chemistry is very comprehensive and experimental. For high school students, they are facing great pressure from the college entrance examination and their studies. Therefore, excellent problem-solving skills can help students to learn more efficiently, and can also promote the cultivation of logical thinking ability, eventually forming a virtuous circle, making learning easier. As a common method in chemical problem solving, conservation method can greatly save students' time and improve the correct rate of problem solving, thus improving learning efficiency. This paper gives a brief introduction to the application of conservation method in high school chemistry problem solving, hoping to be helpful to the students.
基金financially supported by the key Projects of the Chinese Academy of Sciences (Grant No.KZZD-EW-05-01-04)the National Science and Technology Support Program (Grant No.2012BAC06B02)the sub-program of Science and technology research and development plan from China Railway (Grant No.2014G004-A-5)
文摘Drainage canals are engineering structures widely used for debris flow mitigation.When passing through a drainage canal,debris flow usually scours the gully bed at the back of the rib sill of the drainage canal,which leads to failure of the rib sill.Therefore,the scour depth at the back of the rib sill is an important design problem and it is related to the economic benefits of engineering and service years.To explore the law of the depth of the scour pit after debris flow through drainage canal ribs,we first proposed a formula for the calculation of the maximum scour depth at the back of a rib sill based on energy conservation.We then conducted a series of simulation experiments to test the proposed formula.The experimental results show that the scour depth,trench slope and the distance between ribs all increase with a decrease in debris flow density.We then compared the results of experiments and formula calculations.Through the testing analysis,we found that the calculation results of the conductedformula correspond with the experimental results better.Finally,taking Qipan Gully as an example,we designed the ultimate depth of a drainage canal for debris flow using the calculation formula.
基金supported by the Main Direction Program of Knowledge Innovation of Chinese Academy of Sciences for Distinguished Young Scholar(KZCX2-EW-QN114)the National Natural Science Foundation of China(41004006,41131067,11173049 and 41274041)+7 种基金the Merit-based Scientific Research Foundation of the State Ministry of Human Resources and Social Security of China for Returned Overseas Chinese Scholars(Z01101)the Open Research Fund Program of the Key Laboratory of Geospace Environment and Geodesy,Ministry of Education,China(11-01-02)the Open Research Fund Program of the Key Laboratory of Geo-Informatics of National Administration of Surveying,Mapping and Geoinformation of China(201322)the Open Research Fund Program of the State Key Laboratory of Geoinformation Engineering,China(SKLGIE2013-M-1-5)the Main Direction Program of Institute of Geodesy and Geophysics,Chinese Academy of Sciences(Y309451045)the Research Fund Program of State Key Laboratory of Geodesy and Earth's Dynamics,China(Y309491050)the Research Fund of the National Civilian Space Infrastructure Project(Y419341034)the Research Fund of the Lu Jiaxi Young Talent and the Youth Innovation Promotion Association of Chinese Academy of Science(Y305171017)
文摘Firstly, the Earth＇s gravitational field from the past Challenging Minisatellite Payload （CHAMP） mission is determined using the energy conservation principle, the combined error model of the cumulative geoid height influenced by three instrument errors from the current Gravity Recovery and Climate Experiment （GRACE） and future GRACE Follow-On missions is established based on the semi-analytical method, and the Earth＇s gravitational field from the executed Gravity Field and Steady-State Ocean Circulation Explorer （GOCE） mission is recovered by the space-time-wise approach. Secondly, the cumulative geoid height errors are 1.727 × 10^-1 m, 1.839 × 10^-1 m and 9.025 × 10^ -2 m at degrees 70,120 and 250 from the implemented three-stage satellite gravity missions consisting of CHAMP, GRACE and GOCE, which preferably accord with those from the existing earth gravity field models involving EIGEN-CHAMP03S, EICEN-GRACE02S and GO_CONS GCF 2 DIR R1. The cumulative geoid height error is 6.847 × 10 ^-2 m at degree 250 from the future GRACE Follow-On mission. Finally, the complementarity among the four-stage satellite gravity missions including CHAMP, GRACE, GOCE and GRACE Follow-On is demonstrated contrastively.
基金supported by the National Natural Science Foun-dation of China (11172334)
文摘This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.
基金supported by the National Key Research and Development Program of China (Grant Nos.2017YFC1501901 and 2017YFA0603901)the Beijing Natural Science Foundation (Grant No.JQ18001)。
文摘A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid.Two kinds of moments(i.e.,point values(PV moment) at cell interfaces and volume integrated average(VIA moment) value) are defined within a single cell.The PV moment is updated by a conventional semi-Lagrangian method,while the VIA moment is cast by the flux form formulation to assure the exact numerical conservation.Different from the spatial approximation used in the CSL2(conservative semi-Lagrangian scheme with second order polynomial function) scheme,a monotonic rational function which can effectively remove non-physical oscillations is reconstructed within a single cell by the PV moments and VIA moment.To achieve exactly positive-definite preserving,two kinds of corrections are made on the original conservative semi-Lagrangian with rational function(CSLR)scheme.The resulting scheme is inherently conservative,non-negative,and allows a Courant number larger than one.Moreover,the spatial reconstruction can be performed within a single cell,which is very efficient and economical for practical implementation.In addition,a dimension-splitting approach coupled with multi-moment finite volume scheme is adopted on cubed-sphere geometry,which benefitsthe implementation of the 1 D CSLR solver with large Courant number.The proposed model is evaluated by several widely used benchmark tests on cubed-sphere geometry.Numerical results show that the proposed transport model can effectively remove nonphysical oscillations and preserve the numerical nonnegativity,and it has the potential to transport the tracers accurately in a real atmospheric model.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11571366 and 11501570the Open Foundation of State Key Laboratory of High Performance Computing of China+1 种基金the Research Fund of National University of Defense Technology under Grant No JC15-02-02the Fund from HPCL
文摘We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10732010,10972010,and 11332002)
文摘In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solution element scheme for conservative hyperbolic governing equations with source terms is given. A modified ghost fluid method is proposed for the treatment of the boundary conditions. Numerical simulations of the Taylor bar problem and the ricochet phenomenon of a sphere impacting a plate target at an angle of 60~ are carried out. The numerical results are in good agreement with the corresponding experimental observations. It is proved that our computational technique is feasible for analyzing 3D high-velocity impact problems.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.52479085,12472245).
文摘To clarify the influence of the hydrofoil characteristic thickness on the distribution characteristics and mechanisms of clearance cavitation erosion risk,a large eddy simulation(LES)is conducted to study the clearance cavitating flow around NACA0012 and NACA0024 hydrofoils under identical conditions.The study predicts cavitation erosion risk using three methods:The erosive power method(EPM),the improved gray level method(IGLM)and the energy conservation method(ECM).The numerical results are in good agreement with the experiment data and the ECM is applied due to its simplicity in parameter adjustment and low sensitivity.The results indicate that the characteristic thickness significantly influences the flow field,leading to variations in the position and intensity of cavitation collapse,ultimately resulting in notable differences in cavitation erosion risk distribution.The high cavitation erosion risk region on the clearance surface of NACA0012 is concentrated around the midsection,while it is concentrated in the upstream region for the NACA0024,with a lower frequency of extreme events.Tip separation vortex(TSV)cavitation is the main cause of the differences in cavitation erosion risk distribution.On the clearance surface of the NACA0012,TSV cavitation primarily collapses in the central region,whereas for the NACA0024 hydrofoil,TSV cavitation occurs only in the upstream region of the clearance surface and exhibits more stability.The differences in vorticity distribution near the clearance surface partially influence the distribution of TSV cavitation,thereby affecting the characteristics of cavitation erosion risk distribution.The larger characteristic thickness of the NACA0024 reduces the effects of the stretching term and the baroclinic torque term,weakening the effect of vorticity on TSV cavitation,resulting in more stable patterns of the TSV cavitation.
基金This studywas supported by the project of National Natural Science Foundation of China(Grant 11072259 and 10621062)National Basic Research Program of China(Grant No.2009CB723800).The authors would like to thank Dr.Huayong Liu,and Assistant Researcher GuangxueWang of State Key Laboratory of Aerodynamics for their contributions.
文摘The purpose of this article is to summarize our recent progress in high-order and high accurate CFD methods for flow problems with complex grids as well as to discuss the engineering prospects in using these methods.Despite the rapid development of high-order algorithms in CFD,the applications of high-order and high accurate methods on complex configurations are still limited.One of the main reasons which hinder the widely applications of thesemethods is the complexity of grids.Many aspects which can be neglected for low-order schemes must be treated carefully for high-order ones when the configurations are complex.In order to implement highorder finite difference schemes on complex multi-block grids,the geometric conservation lawand block-interface conditions are discussed.A conservativemetricmethod is applied to calculate the grid derivatives,and a characteristic-based interface condition is employed to fulfil high-order multi-block computing.The fifth-order WCNS-E-5 proposed by Deng[9,10]is applied to simulate flows with complex grids,including a double-delta wing,a transonic airplane configuration,and a hypersonic X-38 configuration.The results in this paper and the references show pleasant prospects in engineering-oriented applications of high-order schemes.
基金The research of O.Karakashian was partially supported by National Science Foundation grant DMS-1216740The research of Y.Xing was partially supported by National Science Foundation grants DMS-1216454 and DMS-1621111.
文摘We construct and analyze conservative local discontinuous Galerkin(LDG)methods for the Generalized Korteweg-de-Vries equation.LDG methods are designed by writing the equation as a system and performing separate approximations to the spatial derivatives.The main focus is on the development of conservative methods which can preserve discrete versions of the first two invariants of the continuous solution,and a posteriori error estimates for a fully discrete approximation that is based on the idea of dispersive reconstruction.Numerical experiments are provided to verify the theoretical estimates.
基金This research was financially supported by the National Natural Science Foundation of China （No. 11502282）, the China Scholarship Council Fund （No. 201506425040）, the Natural Science Foundation of Jiangsu Province （No. BK20140178）.
文摘Under harsh conditions （such as high temperature, high pressure, and millisecond lifetime chemical reaction）, a long-standing challenge remains to accurately predict the growth characteristics of nanosize spherical particles and to determine the rapid chemical reaction flow field characteristics, The growth characteristics of similar spherical oxide nanoparticles are further studied by successfully introducing the space-time conservation element-solution element （CE/SE） algorithm with the monodisperse Kruis model. This approach overcomes the nanosize particle rapid growth limit set and successfully captures the characteristics of the rapid gaseous chemical reaction process. The results show that this approach quantitatively captures the characteristics of the rapid chemical reaction, nanosize particle growth and size distribution. To reveal the growth mechanism for numerous types of oxide nanoparticles, it is very important to choose a rational numerical method and particle physics model.
基金This work was supported by the National Natural Science Foundation of China(11402287 and 11372342).
文摘This paper presents an engineering-oriented UGKS solver package developed in China Aerodynamics Research and Development Center(CARDC).The solver is programmed in Fortran language and uses structured body-fitted mesh,aiming for predicting aerodynamic and aerothermodynamics characteristics in flows covering various regimes on complex three-dimensional configurations.The conservative discrete ordinate method and implicit implementation are incorporated.Meanwhile,a local mesh refinement technique in the velocity space is developed.The parallel strategies include MPI and OpenMP.Test cases include a wedge,a cylinder,a 2D blunt cone,a sphere,and a X38-like vehicle.Good agreements with experimental or DSMC results have been achieved.
基金Supported by NSFC(10875157, 10979066)MOST(973 Project 2007CB815000)CAS(KJCX2-EW-N01, KJCX2-YW-N32)
文摘Two-quasiparticle bands and low-lying excited high-K four-, six-, and eight-quasiparticle bands in the doubly-odd 174, 176Lu are analyzed by using the cranked shell model （CSM） with the pairing correlations treated by a particle-number conserving （PNC） method, in which the blocking effects are taken into account exactly. The proton and neutron Nilsson level schemes for 174, 176Lu are taken from the adjacent odd-A Lu and Hf isotopes, which are adopted to reproduce the experimental bandhead energies of the one-quasiproton and one-quasineutron bands of these odd-A Lu and Hf nuclei, respectively. Once the quasiparticle configurations are determined, the experimental bandhead energies and the moments of inertia of these two- and multi-quasiparticle bands are well reproduced by PNC-CSM calculations. The Coriolis mixing of the low-K （K=｜Ω1-Ω2｜） two-quasiparticle band of the Gallagher-Moszkowski doublet with one nucleon in the Ω = 1/2 orbital is analyzed.
基金supported by the National Basic Research Program of China(Grant Nos.2012CB825601,2014CB845903,2012CB825604)the National Natural Science Foundation of China(Grant Nos.41031066,41231068,41274192,41074121,41204127,41174122)+1 种基金the Knowledge Innovation Program of the Chinese Academy of Sciences(Grant No.KZZD-EW-01-4)the Specialized Research Fund for State Key Laboratories
文摘We present a newly developed global magnetohydrodynamic(MHD) model to study the responses of the Earth's magnetosphere to the solar wind. The model is established by using the space-time conservation element and solution element(CESE) method in general curvilinear coordinates on a six-component grid system. As a preliminary study, this paper is to present the model's numerical results of the quasi-steady state and the dynamics of the Earth's magnetosphere under steady solar wind flow with due northward interplanetary magnetic field(IMF). The model results are found to be in good agreement with those published by other numerical magnetospheric models.
基金Supported by National Natural Science Foundation of China(11275098,11275248,11505058)Fundamental Research Funds for the Central Universities(2015QN21)
文摘The recently observed two high-spin rotational bands in the proton emitter ^113Cs are investigated using the cranked shell model with pairing correlations treated by a particle-number conserving method, in which the Pauli blocking effects are taken into account exactly. By using the configuration assignments of band 1 [π3/2^＋[422]（g7/2）, α =-1/2] and band 2 [π1/2^＋[420]（d5/2）, α=1/2], the experimental moments of inertia and quasiparticle alignments can be reproduced much better by the present calculations than those using the configuration assginment of π1/2^-[550]（h11/2）, which in turn may support these configuration assignments. Furthermore, by analyzing the occupation probability nμ of each cranked Nilsson level near the Fermi surface and the contribution of each orbital to the angular momentum alignments, the backbending mechanism of these two bands is also investigated.
基金Supported by NSFC (10775012, 10875157, 10979066)MOST (973 project 2007CB815000)KIP of CAS (KJCX3-SYW-N02, KJCX2-YW-N32)
文摘The experimentally observed ten rotational bands in 179Re are analyzed with the particle-number conserving method for treating the cranked shell model with pairing interaction, in which the blocking effects are taken into account exactly. The experimental moments of inertia of these bands are reproduced quite well by our calculations with no free parameter and the deformation driving effects are discussed. The bandhead energies and the variation in the occupation probability of each cranked orbital are also analyzed.
