In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbol...In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbolic conservation laws.For the purpose of designing increasingly high-order finite difference WENO schemes,the equal-sized stencils are becoming more and more wider.The more we use wider candidate stencils,the bigger the probability of discontinuities lies in all stencils.Therefore,one innovation of these new WENO schemes is to introduce a new splitting stencil methodology to divide some fourpoint or five-point stencils into several smaller three-point stencils.By the usage of this new methodology in high-order spatial reconstruction procedure,we get different degree polynomials defined on these unequal-sized stencils,and calculate the linear weights,smoothness indicators,and nonlinear weights as specified in Jiang and Shu(J.Comput.Phys.126:202228,1996).Since the difference between the nonlinear weights and the linear weights is too big to keep the optimal order of accuracy in smooth regions,another crucial innovation is to present the new mapping functions which are used to obtain the mapped nonlinear weights and decrease the difference quantity between the mapped nonlinear weights and the linear weights,so as to keep the optimal order of accuracy in smooth regions.These new MWENO schemes can also be applied to compute some extreme examples,such as the double rarefaction wave problem,the Sedov blast wave problem,and the Leblanc problem with a normal CFL number.Extensive numerical results are provided to illustrate the good performance of the new finite difference MWENO schemes.展开更多
Efficient numerical solver for the SchrSdinger equation is very important in physics and chemistry. The finite element discrete variable representation （FE-DVR） was first proposed by Rescigno and Mc-Curdy [Phys. Rev...Efficient numerical solver for the SchrSdinger equation is very important in physics and chemistry. The finite element discrete variable representation （FE-DVR） was first proposed by Rescigno and Mc-Curdy [Phys. Rev. A 62, 032706 （2000）] for solving quantum-mechanical scattering problems. In this work, an FE-DVR method in a mapped coordinate was proposed to improve the efficiency of the original FE-DVR method. For numerical demonstration, the proposed approach is applied for solving the electronic eigenfunctions and eigenvalues of the hydrogen atom and vibrational states of the electronic state 3E＋ of the Cs2 molecule which has long-range interaction potential. The numerical results indicate that the numerical efficiency of the original FE-DVR has been improved much using our proposed mapped coordinate scheme.展开更多
The lianghui, or the annual Two Sessions of the National People＇s Congress （NPC） and the Chinese People＇s Political Consultative Conference （CPPCC） National Committee, are always a great political event in China...The lianghui, or the annual Two Sessions of the National People＇s Congress （NPC） and the Chinese People＇s Political Consultative Conference （CPPCC） National Committee, are always a great political event in China, but more so this year, with groundbreaking outcomes.展开更多
We report on the photodissociation dynamics of CO2^＋ via its A2Пu,1/2 state using the scheme of [1＋1] photon excitation that is intermediated by the mode-selected A2Hu,1/2（Vl,V2,0） vibronic states. Photodissociat...We report on the photodissociation dynamics of CO2^＋ via its A2Пu,1/2 state using the scheme of [1＋1] photon excitation that is intermediated by the mode-selected A2Hu,1/2（Vl,V2,0） vibronic states. Photodissociation fragment exciation spectrum and images of photofragment CO＋ have been measured to obtain reaction dynamics parameters such as the available energy and the average translational energy. Combining with the potential energy functions of CO2^＋, the dissociation mechanism of CO2^＋ is discussed. The conformational variation of CO2^＋ from linear to bent on the photodissociation dynamics of CO2^＋ is verified.展开更多
Despite many studies on land degradation in the Highlands of Northern Ethiopia, quantitative information regarding long-term changes in land use/cover(LUC) is rare. Hence, this study aims to investigate the LUC change...Despite many studies on land degradation in the Highlands of Northern Ethiopia, quantitative information regarding long-term changes in land use/cover(LUC) is rare. Hence, this study aims to investigate the LUC changes in the Geba catchment(5142 km2), Northern Ethiopia, over 80 years(1935–2014). Aerial photographs(APs) of the 1930 s and Google Earth(GE) images(2014) were used. The point-count technique was utilized by overlaying a grid on APs and GE images. The occurrence of cropland, forest, grassland, shrubland, bare land, built-up areas and water body was counted to compute their fractions. A multivariate adaptive regression spline was applied to identify the explanatory factors of LUC and to create fractional maps of LUC. The results indicate significant changes of most types, except for forest and cropland. In the 1930 s, shrubland(48%) was dominant, followed by cropland(39%). The fraction of cropland in 2014(42%) remained approximately the same as in the 1930 s, while shrubland significantly dropped to 37%. Forests shrank further from a meagre 6.3% in the 1930 s to 2.3% in 2014. High overall accuracies(93% and 83%) and strong Kappa coefficients(89% and 72%) for point counts and fractional maps respectively indicate the validity of the techniques used for LUC mapping.展开更多
The bsd-pg（bundle sheath defective pale green） mutant is a novel maize mutation, controlled by a single recessive gene, which was isolated from offspring of maize plantlets regenerated from tissue callus of the maiz...The bsd-pg（bundle sheath defective pale green） mutant is a novel maize mutation, controlled by a single recessive gene, which was isolated from offspring of maize plantlets regenerated from tissue callus of the maize inbred line 501. The characterization was that the biogenesis and development of the chloroplasts was mainly interfered in bundle sheath cells rather than in mesophyll cells. For mapping the bsd-pg, an F2 population was derived from a cross between the mutant bsd-pg and an inbred line Xianzao 17. Using specific locus amplified fragment sequencing（SLAF-Seq） technology, a total of 5 783 polymorphic SLAFs were analysed with 1 771 homozygous alleles between maternal and paternal parents. There were 49 SLAFs, which had a ratio of paternal to maternal alleles of 2：1 in bulked normal lines, and three trait-related candidate regions were obtained on chromosome 1 with a size of 3.945 Mb. For the fine mapping, new simple sequence repeats（SSRs） markers were designed by utilizing information of the B73 genome and the candidate regions were localized a size of 850 934 bp on chromosome 1 between umc1603 and umc1395, including 35 candidate genes. These results provide a foundation for the cloning of bsd-pg by map-based strategy, which is essential for revealing the functional differentiation and coordination of the two cell types, and helps to elucidate a comprehensive understanding of the C4 photosynthesis pathway and related processes in maize leaves.展开更多
The displacement discontinuity method(DDM) is a kind of boundary element method aiming at modeling two-dimensional linear elastic crack problems. The singularity around the crack tip prevents the DDM from optimally co...The displacement discontinuity method(DDM) is a kind of boundary element method aiming at modeling two-dimensional linear elastic crack problems. The singularity around the crack tip prevents the DDM from optimally converging when the basis functions are polynomials of first order or higher. To overcome this issue,enlightened by the mapped finite element method(FEM) proposed in Ref. [13], we present an optimally convergent mapped DDM in this work, called the mapped DDM(MDDM). It is essentially based on approximating a much smoother function obtained by reformulating the problem with an appropriate auxiliary map. Two numerical examples of crack problems are presented in comparison with the conventional DDM. The results show that the proposed method improves the accuracy of the DDM; moreover, it yields an optimal convergence rate for quadratic interpolating polynomials.展开更多
This article designs a new fifth-order finite volume mapped unequal-sized weighted essentially non-oscillatory scheme(MUS-WENO)for solving hyperbolic conservation laws on structured meshes.One advantage is that the ne...This article designs a new fifth-order finite volume mapped unequal-sized weighted essentially non-oscillatory scheme(MUS-WENO)for solving hyperbolic conservation laws on structured meshes.One advantage is that the new mapped WENOtype spatial reconstruction is a convex combination of a quartic polynomial with two linear polynomials defined on unequal-sized central or biased spatial stencils.Then we propose the new mapped nonlinear weights and new mapping function to decrease the difference between the linear weights and nonlinear weights.This method has the characteristics of small truncation errors and high-order accuracy.And it could give optimal fifth-order convergence with a very tiny#even near critical points in smooth regions while suppressing spurious oscillations near strong discontinuities.Compared with the classical finite volume WENO schemes and mapped WENO(MWENO)schemes,the linear weights can be any positive numbers on the condition that their summation is one,which greatly reduces the calculation cost.Finally,we propose a new modified positivity-preserving method for solving some low density,low pressure,or low energy problems.Extensive numerical examples including some unsteadystate problems,steady-state problems,and extreme problems are used to testify to the efficiency of this new finite volume MUS-WENO scheme.展开更多
In this paper,we propose a newly designed fifth-order finite difference well-balanced mapped unequal-sized weighted essentially non-oscillatory(WBMUSWENO)scheme for simulating the shallow water systems on multi-dimens...In this paper,we propose a newly designed fifth-order finite difference well-balanced mapped unequal-sized weighted essentially non-oscillatory(WBMUSWENO)scheme for simulating the shallow water systems on multi-dimensional structured meshes.We design new non-linear weights and a new mapping function,so that the WBMUS-WENO scheme can maintain fifth-order accuracy with a small#even nearby the extreme points in smooth regions.The truncation errors of the scheme is smaller and it has better convergence in simulating some steady-state problems.Unlike the traditional well-balanced WENO-XS scheme[29],this new WBMUS-WENO scheme uses three unequal-sized stencils,denotes the linear weights to be any positive numbers on condition that their summation is one.By incorporating a quartic polynomial on the whole big stencil into WENO reconstruction,the WBMUS-WENO scheme is simple and efficient.Extensive examples are performed to testify the exact C-property,absolute convergence property,and good representations of this new WBMUS-WENO scheme.展开更多
In this paper,the boundary mapped collocation(BMC)approach is presented for the analysis of heat conduction problems involving heat generation and non-homogeneous thermal conductivity.The proposed methodology is intro...In this paper,the boundary mapped collocation(BMC)approach is presented for the analysis of heat conduction problems involving heat generation and non-homogeneous thermal conductivity.The proposed methodology is introduced to produce the numerical solutions of the temperature field within the framework of the BMC method,a novel boundary meshless method,without resorting to requiring any integral calculation,neither in the domain nor at the boundary.In particular,the arrangement of discrete nodes is restricted to the axis,which brings the spatial dimension down by one.The technique also reduced the traditional complex shape functions to succinct one-dimensional boundary shape functions by using one-dimensional basis functions and weight functions for two-and three-dimensional approximation implementation.In addition,four numerical applications and comparisons with the outcomes of the finite element approach and another meshfree method are used to demonstrate the correctness,convergence,and stability of the BMC method.展开更多
An innovative meshless method is proposed in this paper for the bending problem of arbitrary Kirchhoff plates subjected to external force with various shapes and different boundary conditions.Without using a numerical...An innovative meshless method is proposed in this paper for the bending problem of arbitrary Kirchhoff plates subjected to external force with various shapes and different boundary conditions.Without using a numerical integral,the deflection of the thin plate is approximated by using the boundary mapped collocation approach.Moreover,the computational domain discretization is just dependent on discretized nodes on the axis,while tensor product nodes have been mapped in the domain automatically.Hence,in the boundary mapped collocation implementation,the approximation functions are derived by employing the one-dimensional moving least squares technique for two-dimensional and higher-dimensional problems.Further,the virtual boundary technique is introduced to enforce the boundary conditions in the proposed method.Additionally,four numerical experiments are presented to illustrate the excellent convergence and high precision of the proposed approach.展开更多
Existing mapped WENO schemes can hardly prevent spurious oscillations while preserving high resolutions at long output times.We reveal in this paper the essential reason of such phenomena.It is actually caused by that...Existing mapped WENO schemes can hardly prevent spurious oscillations while preserving high resolutions at long output times.We reveal in this paper the essential reason of such phenomena.It is actually caused by that the mapping function in these schemes can not preserve the order of the nonlinear weights of the stencils.The nonlinear weights may be increased for non-smooth stencils and be decreased for smooth stencils.It is then indicated to require the set of mapping functions to be order-preserving in mapped WENO schemes.Therefore,we propose a new mapped WENO scheme with a set of mapping functions to be order-preserving which exhibits a remarkable advantage over the mapped WENO schemes in references.For long output time simulations of the one-dimensional linear advection equation,the new scheme has the capacity to attain high resolutions and avoid spurious oscillations near discontinuities meanwhile.In addition,for the two-dimensional Euler problems with strong shock waves,the new scheme can significantly reduce the numerical oscillations.展开更多
基金the NSFC grant 11872210 and the Science Challenge Project,No.TZ2016002the NSFC Grant 11926103 when he visited Tianyuan Mathematical Center in Southeast China,Xiamen 361005,Fujian,Chinathe NSFC Grant 12071392 and the Science Challenge Project,No.TZ2016002.
文摘In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbolic conservation laws.For the purpose of designing increasingly high-order finite difference WENO schemes,the equal-sized stencils are becoming more and more wider.The more we use wider candidate stencils,the bigger the probability of discontinuities lies in all stencils.Therefore,one innovation of these new WENO schemes is to introduce a new splitting stencil methodology to divide some fourpoint or five-point stencils into several smaller three-point stencils.By the usage of this new methodology in high-order spatial reconstruction procedure,we get different degree polynomials defined on these unequal-sized stencils,and calculate the linear weights,smoothness indicators,and nonlinear weights as specified in Jiang and Shu(J.Comput.Phys.126:202228,1996).Since the difference between the nonlinear weights and the linear weights is too big to keep the optimal order of accuracy in smooth regions,another crucial innovation is to present the new mapping functions which are used to obtain the mapped nonlinear weights and decrease the difference quantity between the mapped nonlinear weights and the linear weights,so as to keep the optimal order of accuracy in smooth regions.These new MWENO schemes can also be applied to compute some extreme examples,such as the double rarefaction wave problem,the Sedov blast wave problem,and the Leblanc problem with a normal CFL number.Extensive numerical results are provided to illustrate the good performance of the new finite difference MWENO schemes.
文摘Efficient numerical solver for the SchrSdinger equation is very important in physics and chemistry. The finite element discrete variable representation （FE-DVR） was first proposed by Rescigno and Mc-Curdy [Phys. Rev. A 62, 032706 （2000）] for solving quantum-mechanical scattering problems. In this work, an FE-DVR method in a mapped coordinate was proposed to improve the efficiency of the original FE-DVR method. For numerical demonstration, the proposed approach is applied for solving the electronic eigenfunctions and eigenvalues of the hydrogen atom and vibrational states of the electronic state 3E＋ of the Cs2 molecule which has long-range interaction potential. The numerical results indicate that the numerical efficiency of the original FE-DVR has been improved much using our proposed mapped coordinate scheme.
文摘The lianghui, or the annual Two Sessions of the National People＇s Congress （NPC） and the Chinese People＇s Political Consultative Conference （CPPCC） National Committee, are always a great political event in China, but more so this year, with groundbreaking outcomes.
基金This work was supported by the Natural Science Foundation of Changzhou Institute of Technology （No.YN1507）, Undergraduate Training Program for Innovation of Changzhou Institute of Technology （No.J150245）, the China Postdoctoral Science Foundation （No.2013M531506）, the National Natural Science Foundation of China （No.21273212）.
文摘We report on the photodissociation dynamics of CO2^＋ via its A2Пu,1/2 state using the scheme of [1＋1] photon excitation that is intermediated by the mode-selected A2Hu,1/2（Vl,V2,0） vibronic states. Photodissociation fragment exciation spectrum and images of photofragment CO＋ have been measured to obtain reaction dynamics parameters such as the available energy and the average translational energy. Combining with the potential energy functions of CO2^＋, the dissociation mechanism of CO2^＋ is discussed. The conformational variation of CO2^＋ from linear to bent on the photodissociation dynamics of CO2^＋ is verified.
基金a scholarship of the Special Research Fund (BOF) obtained from Ghent University, Belgiumpartially covered by the RIP-MU (VLIR, Belgium) project
文摘Despite many studies on land degradation in the Highlands of Northern Ethiopia, quantitative information regarding long-term changes in land use/cover(LUC) is rare. Hence, this study aims to investigate the LUC changes in the Geba catchment(5142 km2), Northern Ethiopia, over 80 years(1935–2014). Aerial photographs(APs) of the 1930 s and Google Earth(GE) images(2014) were used. The point-count technique was utilized by overlaying a grid on APs and GE images. The occurrence of cropland, forest, grassland, shrubland, bare land, built-up areas and water body was counted to compute their fractions. A multivariate adaptive regression spline was applied to identify the explanatory factors of LUC and to create fractional maps of LUC. The results indicate significant changes of most types, except for forest and cropland. In the 1930 s, shrubland(48%) was dominant, followed by cropland(39%). The fraction of cropland in 2014(42%) remained approximately the same as in the 1930 s, while shrubland significantly dropped to 37%. Forests shrank further from a meagre 6.3% in the 1930 s to 2.3% in 2014. High overall accuracies(93% and 83%) and strong Kappa coefficients(89% and 72%) for point counts and fractional maps respectively indicate the validity of the techniques used for LUC mapping.
基金supported by the National Natural Science Foundation of China (30700476 and 31071057)the Beijing Natural Science Foundation, China (5083021)
文摘The bsd-pg（bundle sheath defective pale green） mutant is a novel maize mutation, controlled by a single recessive gene, which was isolated from offspring of maize plantlets regenerated from tissue callus of the maize inbred line 501. The characterization was that the biogenesis and development of the chloroplasts was mainly interfered in bundle sheath cells rather than in mesophyll cells. For mapping the bsd-pg, an F2 population was derived from a cross between the mutant bsd-pg and an inbred line Xianzao 17. Using specific locus amplified fragment sequencing（SLAF-Seq） technology, a total of 5 783 polymorphic SLAFs were analysed with 1 771 homozygous alleles between maternal and paternal parents. There were 49 SLAFs, which had a ratio of paternal to maternal alleles of 2：1 in bulked normal lines, and three trait-related candidate regions were obtained on chromosome 1 with a size of 3.945 Mb. For the fine mapping, new simple sequence repeats（SSRs） markers were designed by utilizing information of the B73 genome and the candidate regions were localized a size of 850 934 bp on chromosome 1 between umc1603 and umc1395, including 35 candidate genes. These results provide a foundation for the cloning of bsd-pg by map-based strategy, which is essential for revealing the functional differentiation and coordination of the two cell types, and helps to elucidate a comprehensive understanding of the C4 photosynthesis pathway and related processes in maize leaves.
基金the National Natural Science Foundation of China(No.11402146)the Young 1000 Talent Program of China
文摘The displacement discontinuity method(DDM) is a kind of boundary element method aiming at modeling two-dimensional linear elastic crack problems. The singularity around the crack tip prevents the DDM from optimally converging when the basis functions are polynomials of first order or higher. To overcome this issue,enlightened by the mapped finite element method(FEM) proposed in Ref. [13], we present an optimally convergent mapped DDM in this work, called the mapped DDM(MDDM). It is essentially based on approximating a much smoother function obtained by reformulating the problem with an appropriate auxiliary map. Two numerical examples of crack problems are presented in comparison with the conventional DDM. The results show that the proposed method improves the accuracy of the DDM; moreover, it yields an optimal convergence rate for quadratic interpolating polynomials.
基金supported by National Natural Science Foundation of China(NSFC)grant No.11872210supported by National Natural Science Foundation of China(NSFC)grant No.11872210 and Grant No.MCMS-I-0120G01.
文摘This article designs a new fifth-order finite volume mapped unequal-sized weighted essentially non-oscillatory scheme(MUS-WENO)for solving hyperbolic conservation laws on structured meshes.One advantage is that the new mapped WENOtype spatial reconstruction is a convex combination of a quartic polynomial with two linear polynomials defined on unequal-sized central or biased spatial stencils.Then we propose the new mapped nonlinear weights and new mapping function to decrease the difference between the linear weights and nonlinear weights.This method has the characteristics of small truncation errors and high-order accuracy.And it could give optimal fifth-order convergence with a very tiny#even near critical points in smooth regions while suppressing spurious oscillations near strong discontinuities.Compared with the classical finite volume WENO schemes and mapped WENO(MWENO)schemes,the linear weights can be any positive numbers on the condition that their summation is one,which greatly reduces the calculation cost.Finally,we propose a new modified positivity-preserving method for solving some low density,low pressure,or low energy problems.Extensive numerical examples including some unsteadystate problems,steady-state problems,and extreme problems are used to testify to the efficiency of this new finite volume MUS-WENO scheme.
基金supported by the National Natural Science Foundation of China(Grant Nos.11872210 and 11971070)supported by the Natural Science Foundation of Jiangsu Province(No.BK20230868)the Jiangsu Funding Program for Excellent Postdoctoral Talent(No.2023ZB080).
文摘In this paper,we propose a newly designed fifth-order finite difference well-balanced mapped unequal-sized weighted essentially non-oscillatory(WBMUSWENO)scheme for simulating the shallow water systems on multi-dimensional structured meshes.We design new non-linear weights and a new mapping function,so that the WBMUS-WENO scheme can maintain fifth-order accuracy with a small#even nearby the extreme points in smooth regions.The truncation errors of the scheme is smaller and it has better convergence in simulating some steady-state problems.Unlike the traditional well-balanced WENO-XS scheme[29],this new WBMUS-WENO scheme uses three unequal-sized stencils,denotes the linear weights to be any positive numbers on condition that their summation is one.By incorporating a quartic polynomial on the whole big stencil into WENO reconstruction,the WBMUS-WENO scheme is simple and efficient.Extensive examples are performed to testify the exact C-property,absolute convergence property,and good representations of this new WBMUS-WENO scheme.
基金supported by GuangDong Basic and Applied Basic Research Foundation(No.2021A1515110807)the PhD Starting Foundation of Nanchang Hangkong University(No.EA202411285)+1 种基金the Program for Guangdong Introducing Innovative and Entrepreneurial Teams(No.2019ZT08G315)National Natural Science Foundation of China(No.U19A2098).
文摘In this paper,the boundary mapped collocation(BMC)approach is presented for the analysis of heat conduction problems involving heat generation and non-homogeneous thermal conductivity.The proposed methodology is introduced to produce the numerical solutions of the temperature field within the framework of the BMC method,a novel boundary meshless method,without resorting to requiring any integral calculation,neither in the domain nor at the boundary.In particular,the arrangement of discrete nodes is restricted to the axis,which brings the spatial dimension down by one.The technique also reduced the traditional complex shape functions to succinct one-dimensional boundary shape functions by using one-dimensional basis functions and weight functions for two-and three-dimensional approximation implementation.In addition,four numerical applications and comparisons with the outcomes of the finite element approach and another meshfree method are used to demonstrate the correctness,convergence,and stability of the BMC method.
基金supported by GuangDong Basic and Applied Basic Research Foundation(No.2021A1515110807)the PhD Starting Foundation of Nanchang Hangkong University(No.EA202411285)+1 种基金the Program for Guangdong Introducing Innovative and Entrepreneurial Teams(No.2019ZT08G315)National Natural Science Foundation of China(No.U19A2098).
文摘An innovative meshless method is proposed in this paper for the bending problem of arbitrary Kirchhoff plates subjected to external force with various shapes and different boundary conditions.Without using a numerical integral,the deflection of the thin plate is approximated by using the boundary mapped collocation approach.Moreover,the computational domain discretization is just dependent on discretized nodes on the axis,while tensor product nodes have been mapped in the domain automatically.Hence,in the boundary mapped collocation implementation,the approximation functions are derived by employing the one-dimensional moving least squares technique for two-dimensional and higher-dimensional problems.Further,the virtual boundary technique is introduced to enforce the boundary conditions in the proposed method.Additionally,four numerical experiments are presented to illustrate the excellent convergence and high precision of the proposed approach.
文摘Existing mapped WENO schemes can hardly prevent spurious oscillations while preserving high resolutions at long output times.We reveal in this paper the essential reason of such phenomena.It is actually caused by that the mapping function in these schemes can not preserve the order of the nonlinear weights of the stencils.The nonlinear weights may be increased for non-smooth stencils and be decreased for smooth stencils.It is then indicated to require the set of mapping functions to be order-preserving in mapped WENO schemes.Therefore,we propose a new mapped WENO scheme with a set of mapping functions to be order-preserving which exhibits a remarkable advantage over the mapped WENO schemes in references.For long output time simulations of the one-dimensional linear advection equation,the new scheme has the capacity to attain high resolutions and avoid spurious oscillations near discontinuities meanwhile.In addition,for the two-dimensional Euler problems with strong shock waves,the new scheme can significantly reduce the numerical oscillations.
