In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(...In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(Δt 4+Δx 4) It can be easily solved by double sweeping method.展开更多
In this paper,we construct a new two-dimensional convergent scheme to solve Cauchy problem of following two-dimensional scalar conservation law{ tu ＋ xf（u） ＋ yg（u） = 0,u（x,y,0） = u0（x,y）.In which initial dat...In this paper,we construct a new two-dimensional convergent scheme to solve Cauchy problem of following two-dimensional scalar conservation law{ tu ＋ xf（u） ＋ yg（u） = 0,u（x,y,0） = u0（x,y）.In which initial data can be unbounded.Although the existence and uniqueness of the weak entropy solution are obtained,little is known about how to investigate two-dimensional or higher dimensional conservation law by the schemes based on wave interaction of 2D Riemann solutions and their estimation.So we construct such scheme in our paper and get some new results.展开更多
A new numerical method named as basic function method is proposed. It can directly discretize differential operators on unstructured grids. By expanding the basic function to approach the exact function, the central a...A new numerical method named as basic function method is proposed. It can directly discretize differential operators on unstructured grids. By expanding the basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as a basic function and applying the flux splitting method and the combination of central and upwind schemes to suppress non-physical fluctuation near shock waves, a second-order basic function scheme of polynomial type is proposed to solve inviscid compressible flows numerically. Numerical results of typical examples for two-dimensional inviscid compressible transonic and supersonic steady flows indicate that the new scheme has high accuracy and high resolution for shock waves. Combined with the adaptive remeshing technique, satisfactory results can be obtained.展开更多
In this paper. a three explicit difference shcemes with high order accuracy for solving the equations of two-dimensional parabolic type is proposed. The stability condition is r=△t/△x￣ 2=△t/△y￣2≤1/4 and the...In this paper. a three explicit difference shcemes with high order accuracy for solving the equations of two-dimensional parabolic type is proposed. The stability condition is r=△t/△x￣ 2=△t/△y￣2≤1/4 and the truncation error is O (△t￣2 + △x￣4 ).展开更多
Firstly data standardization technology and combined classification method have been applied to carry out classification of kinematic behaviors and mechanisms in the mapping field between the kinematic behavior level ...Firstly data standardization technology and combined classification method have been applied to carry out classification of kinematic behaviors and mechanisms in the mapping field between the kinematic behavior level and the mechanism level of conceptual design.The principle of computer coding and storing have been built to give a fast and broad selection of mechanisms that meets the requirements of basic motion characters.Then on the basis of mentioned above,the heuristic matching propagation principle (HMPP) of kinematic behaviors and its true table serves as a guide to perform mechanism types selection.Finally an application is given to indicate its practicability and effectiveness.展开更多
This paper proposed several new types of finite-difference methods for the shallow water equation in absolute coordinate system and put forward an effective two-step predictor-corrector method, a compact and iterative...This paper proposed several new types of finite-difference methods for the shallow water equation in absolute coordinate system and put forward an effective two-step predictor-corrector method, a compact and iterative algorithm for five diagonal matrix. Then the iterative method was used for a multi-grid procedure for shallow water equation. A t last, an initial-boundary value problem was considered, and the numerical results show that the linear sinusoidal wave would successively evolve into conoidal wave.展开更多
TiO2 nanoparticles were prepared using the hydrothermal method and modified with CgN to syn-thesize a Type-Ⅱheterojunction semiconductor photocatalyst,TiO2-C;Na.In addition,a carbon layerwas coated onto the TiO2 nano...TiO2 nanoparticles were prepared using the hydrothermal method and modified with CgN to syn-thesize a Type-Ⅱheterojunction semiconductor photocatalyst,TiO2-C;Na.In addition,a carbon layerwas coated onto the TiO2 nanoparticles and the obtained material was uniformly covered on thesurface of CaNa to form an all-solid-state Z-scheme semiconductor photocatalyst,TiO2-C-C3N4,Through characterization by XRD,XPS,SEM,TEM,BET,photoelectrochemical experiments,UV-visible diffuse reflection,and PL spectroscopy,the charge transfer mechanism and band gappositions for the composite photocatalysts were analyzed.The Type-Ⅱand all-solid-state Z-schemeheterojunction structures were compared.By combining microscopic internal mechanisms withmacroscopic experimental phenomena,the relationship between performance and structure wasverified.Experimental methods were used to explore the adaptation degree of different photocata-lytic mechanisms using the same degradation system.This study highlights effective photocatalystdesign to meet the requirements for specific degradation conditions.展开更多
In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study diffusion-type traffic flow model based on exponential velocity density relation, which prov...In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study diffusion-type traffic flow model based on exponential velocity density relation, which provides a non-linear second-order parabolic partial differential equation. The analytical solution of the diffusion-type traffic flow model is very complicated to approximate the initial density of the Cauchy problem as a function of x from given data and it may cause a huge error. For the complexity of the analytical solution, the numerical solution is performed by implementing an explicit upwind, explicitly centered, and second-order Lax-Wendroff scheme for the numerical solution. From the comparison of relative error among these three schemes, it is observed that Lax-Wendroff scheme gives less error than the explicit upwind and explicit centered difference scheme. The numerical, analytical analysis and comparative result discussion bring out the fact that the Lax-Wendroff scheme with exponential velocity-density relation of diffusion type traffic flow model is suitable for the congested area and shows a better fit in traffic-congested regions.展开更多
This paper studies the strong convergence of the quantum lattice Boltzmann(QLB)scheme for the nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.The initial data for the scheme are assumed to be converg...This paper studies the strong convergence of the quantum lattice Boltzmann(QLB)scheme for the nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.The initial data for the scheme are assumed to be convergent in L^(2).Then for any T≥0 the corresponding solutions for the quantum lattice Boltzmann scheme are shown to be convergent in C([0,T];L^(2)(R^(1)))to the strong solution to the nonlinear Dirac equations as the mesh sizes converge to zero.In the proof,at first a Glimm type functional is introduced to establish the stability estimates for the difference between two solutions for the corresponding quantum lattice Boltzmann scheme,which leads to the compactness of the set of the solutions for the quantum lattice Boltzmann scheme.Finally the limit of any convergent subsequence of the solutions for the quantum lattice Boltzmann scheme is shown to coincide with the strong solution to a Cauchy problem for the nonlinear Dirac equations.展开更多
This paper presents an explicit difference scheme with accuracy and branching stability for solving onedimensional parabolic type equation by the method of undetermined parameters and its truncation error is O(△t4+△...This paper presents an explicit difference scheme with accuracy and branching stability for solving onedimensional parabolic type equation by the method of undetermined parameters and its truncation error is O(△t4+△x4). The stability condition is r=a△t/△x2<1/2.展开更多
目的:探讨新型帐篷医院系统手术模块展开与撤收的标准化操作方案。方法:从队员分工、操作顺序、操作技巧、注意事项等方面总结出一套手术模块展开与撤收的标准化操作方案并进行实施。记录方案实施前后各5次展开与撤收的操作时间、操作...目的:探讨新型帐篷医院系统手术模块展开与撤收的标准化操作方案。方法:从队员分工、操作顺序、操作技巧、注意事项等方面总结出一套手术模块展开与撤收的标准化操作方案并进行实施。记录方案实施前后各5次展开与撤收的操作时间、操作失误次数、装备损坏次数,并记录方案实施后队员操作结束后的即刻心率、个人最大心率百分比、主观体力感觉等级(rating of perceived exercise,RPE)评分。采用SPSS 26.0软件对数据进行统计分析。结果:实施标准化操作方案后,手术模块的展开、撤收时间分别为(58.23±8.513)min、(48.92±7.129)min,短于方案实施前[(85.15±11.430)min、(65.36±9.369)min],差异有统计学意义(P<0.05);方案实施后的操作失误次数、装备损坏次数均低于实施前;操作结束后队员的即刻心率为43~157次/min,平均为151.1次/min,个人最大心率百分比为75%~87%,平均为81.1%,RPE评分为14~17分,平均为15.3分,均属于中等作业强度。结论:标准化操作方案可实现手术模块的快速、高质量展开与撤收,能够满足实战及训练考核的需要,可在装备该新型帐篷医院系统手术模块的卫勤机构中推广应用。展开更多
A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the v...A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.展开更多
文摘In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(Δt 4+Δx 4) It can be easily solved by double sweeping method.
文摘In this paper,we construct a new two-dimensional convergent scheme to solve Cauchy problem of following two-dimensional scalar conservation law{ tu ＋ xf（u） ＋ yg（u） = 0,u（x,y,0） = u0（x,y）.In which initial data can be unbounded.Although the existence and uniqueness of the weak entropy solution are obtained,little is known about how to investigate two-dimensional or higher dimensional conservation law by the schemes based on wave interaction of 2D Riemann solutions and their estimation.So we construct such scheme in our paper and get some new results.
基金supported by the National Natural Science Foundation of China (No. 19889210)
文摘A new numerical method named as basic function method is proposed. It can directly discretize differential operators on unstructured grids. By expanding the basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as a basic function and applying the flux splitting method and the combination of central and upwind schemes to suppress non-physical fluctuation near shock waves, a second-order basic function scheme of polynomial type is proposed to solve inviscid compressible flows numerically. Numerical results of typical examples for two-dimensional inviscid compressible transonic and supersonic steady flows indicate that the new scheme has high accuracy and high resolution for shock waves. Combined with the adaptive remeshing technique, satisfactory results can be obtained.
文摘In this paper. a three explicit difference shcemes with high order accuracy for solving the equations of two-dimensional parabolic type is proposed. The stability condition is r=△t/△x￣ 2=△t/△y￣2≤1/4 and the truncation error is O (△t￣2 + △x￣4 ).
基金Sponsored by the Chinese National Foundation of Science Na 59875058.
文摘Firstly data standardization technology and combined classification method have been applied to carry out classification of kinematic behaviors and mechanisms in the mapping field between the kinematic behavior level and the mechanism level of conceptual design.The principle of computer coding and storing have been built to give a fast and broad selection of mechanisms that meets the requirements of basic motion characters.Then on the basis of mentioned above,the heuristic matching propagation principle (HMPP) of kinematic behaviors and its true table serves as a guide to perform mechanism types selection.Finally an application is given to indicate its practicability and effectiveness.
文摘This paper proposed several new types of finite-difference methods for the shallow water equation in absolute coordinate system and put forward an effective two-step predictor-corrector method, a compact and iterative algorithm for five diagonal matrix. Then the iterative method was used for a multi-grid procedure for shallow water equation. A t last, an initial-boundary value problem was considered, and the numerical results show that the linear sinusoidal wave would successively evolve into conoidal wave.
文摘TiO2 nanoparticles were prepared using the hydrothermal method and modified with CgN to syn-thesize a Type-Ⅱheterojunction semiconductor photocatalyst,TiO2-C;Na.In addition,a carbon layerwas coated onto the TiO2 nanoparticles and the obtained material was uniformly covered on thesurface of CaNa to form an all-solid-state Z-scheme semiconductor photocatalyst,TiO2-C-C3N4,Through characterization by XRD,XPS,SEM,TEM,BET,photoelectrochemical experiments,UV-visible diffuse reflection,and PL spectroscopy,the charge transfer mechanism and band gappositions for the composite photocatalysts were analyzed.The Type-Ⅱand all-solid-state Z-schemeheterojunction structures were compared.By combining microscopic internal mechanisms withmacroscopic experimental phenomena,the relationship between performance and structure wasverified.Experimental methods were used to explore the adaptation degree of different photocata-lytic mechanisms using the same degradation system.This study highlights effective photocatalystdesign to meet the requirements for specific degradation conditions.
文摘In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study diffusion-type traffic flow model based on exponential velocity density relation, which provides a non-linear second-order parabolic partial differential equation. The analytical solution of the diffusion-type traffic flow model is very complicated to approximate the initial density of the Cauchy problem as a function of x from given data and it may cause a huge error. For the complexity of the analytical solution, the numerical solution is performed by implementing an explicit upwind, explicitly centered, and second-order Lax-Wendroff scheme for the numerical solution. From the comparison of relative error among these three schemes, it is observed that Lax-Wendroff scheme gives less error than the explicit upwind and explicit centered difference scheme. The numerical, analytical analysis and comparative result discussion bring out the fact that the Lax-Wendroff scheme with exponential velocity-density relation of diffusion type traffic flow model is suitable for the congested area and shows a better fit in traffic-congested regions.
基金partially supported by the NSFC(11421061,12271507)the Natural Science Foundation of Shanghai(15ZR1403900)。
文摘This paper studies the strong convergence of the quantum lattice Boltzmann(QLB)scheme for the nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.The initial data for the scheme are assumed to be convergent in L^(2).Then for any T≥0 the corresponding solutions for the quantum lattice Boltzmann scheme are shown to be convergent in C([0,T];L^(2)(R^(1)))to the strong solution to the nonlinear Dirac equations as the mesh sizes converge to zero.In the proof,at first a Glimm type functional is introduced to establish the stability estimates for the difference between two solutions for the corresponding quantum lattice Boltzmann scheme,which leads to the compactness of the set of the solutions for the quantum lattice Boltzmann scheme.Finally the limit of any convergent subsequence of the solutions for the quantum lattice Boltzmann scheme is shown to coincide with the strong solution to a Cauchy problem for the nonlinear Dirac equations.
文摘This paper presents an explicit difference scheme with accuracy and branching stability for solving onedimensional parabolic type equation by the method of undetermined parameters and its truncation error is O(△t4+△x4). The stability condition is r=a△t/△x2<1/2.
文摘目的:探讨新型帐篷医院系统手术模块展开与撤收的标准化操作方案。方法:从队员分工、操作顺序、操作技巧、注意事项等方面总结出一套手术模块展开与撤收的标准化操作方案并进行实施。记录方案实施前后各5次展开与撤收的操作时间、操作失误次数、装备损坏次数,并记录方案实施后队员操作结束后的即刻心率、个人最大心率百分比、主观体力感觉等级(rating of perceived exercise,RPE)评分。采用SPSS 26.0软件对数据进行统计分析。结果:实施标准化操作方案后,手术模块的展开、撤收时间分别为(58.23±8.513)min、(48.92±7.129)min,短于方案实施前[(85.15±11.430)min、(65.36±9.369)min],差异有统计学意义(P<0.05);方案实施后的操作失误次数、装备损坏次数均低于实施前;操作结束后队员的即刻心率为43~157次/min,平均为151.1次/min,个人最大心率百分比为75%~87%,平均为81.1%,RPE评分为14~17分,平均为15.3分,均属于中等作业强度。结论:标准化操作方案可实现手术模块的快速、高质量展开与撤收,能够满足实战及训练考核的需要,可在装备该新型帐篷医院系统手术模块的卫勤机构中推广应用。
基金supported by the National Natural Science Foundation of China (Nos. 10971203 and 11271340)the Research Fund for the Doctoral Program of Higher Education of China (No. 20094101110006)
文摘A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.
