The current study aims to investigate a suitable adhesive for primary tooth enamel. Shear bond strength(SBS)of primary teeth and the length of resin protrusion were analyzed using one-way ANOVA with Bonferroni multipl...The current study aims to investigate a suitable adhesive for primary tooth enamel. Shear bond strength(SBS)of primary teeth and the length of resin protrusion were analyzed using one-way ANOVA with Bonferroni multiple comparison tests after etching with 35% H_(3)PO_(4). SBS and marginal microleakage tests were conducted with Single Bond Universal(SBU)/Single Bond 2(SB2) adhesives with or without pre-etching using a nonparametric Kruskal-Wallis test. Clinical investigations were performed to validate the adhesive for primary teeth restoration using Chi-square tests. Results showed that the SBS and length of resin protrusion increased significantly with the etching time. Teeth in the SBU with 35% H_(3)PO_(4)pre-etching groups had higher bond strength and lower marginal microleakage than those in the SB2 groups. Mixed fractures were more common in the 35% H_(3)PO_(4)etched 30 s + SB2/SBU groups. Clinical investigations showed significant differences between the two groups in cumulative retention rates at the 6-, 12-and 18-month follow-up evaluations, as well as in marginal adaptation, discoloration, and secondary caries at the 12-and 18-month follow-up assessments.Together, pre-etching primary teeth enamel for 30 s before SBU treatment improved clinical composite resin restoration, which can provide a suitable approach for restoration of primary teeth.展开更多
The Immersed Interface Method (IIM) is derived to solve the corresponding Fokker-Planck equation of Brownian motion with pure dry friction, which is one of the simplest models of piecewise-smooth stochastic systems. T...The Immersed Interface Method (IIM) is derived to solve the corresponding Fokker-Planck equation of Brownian motion with pure dry friction, which is one of the simplest models of piecewise-smooth stochastic systems. The IIM is capable of treating a discontinuity in the drift of Fokker-Planck equation and it is readily extended to the dry and viscous friction model. Analytic results of the considered model are used to confirm the effectiveness and design accuracy of the scheme.展开更多
To ensure time stability of a seventh-order dissipative compact finite difference scheme, fourth-order boundary closures are used near domain boundaries previously. However, this would reduce the global convergence ra...To ensure time stability of a seventh-order dissipative compact finite difference scheme, fourth-order boundary closures are used near domain boundaries previously. However, this would reduce the global convergence rate to fifth-order only. In this paper, we elevate the boundary closures to sixth-order to achieve seventh-order global accuracy. To keep the improved scheme time stable, the simultaneous approximation terms (SATs) are used to impose boundary conditions weakly. Eigenvalue analysis shows that the improved scheme is time stable. Numerical experiments for linear advection equations and one-dimensional Euler equations are implemented to validate the new scheme.展开更多
A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an o...A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an optimization problem with several parameters determined by applying a generic algorithm. The optimized schemes are analyzed carefully from the aspects of the eigenvalue distribution, the ε-pseudospectra, the short time behavior, and the Fourier analysis. Numerical experiments for the Euler equations are used to show the effectiveness of the final recommended scheme.展开更多
In this work,we aim to show how to solve the continuous-time and continuous-space Krause model by using high-order finite difference(FD)schemes.Since the considered model admits solutions withδ-singularities,the FD m...In this work,we aim to show how to solve the continuous-time and continuous-space Krause model by using high-order finite difference(FD)schemes.Since the considered model admits solutions withδ-singularities,the FD method cannot be applied directly.To deal with the annoyingδ-singulariti-es,we propose to lift the solution space by introducing a spltting method,such that theδ-singularities in one spatial direction become step functions with dis-continuities.Thus the traditional shock-capturing FD schemes can be applied directly.In particular,we focus on the two dimensional case and apply a fifth-order weighted nonlinear compact scheme(WCNS)to ilustrate the validity of the proposed method.Some technical details for implementation are also presented.Numerical results show that the proposed method can captureδ-singularities well,and the obtained number of delta peaks agrees with the the-oretical prediction in the literature.展开更多
We develop in this paper a lifting method for Fokker-Planck equations with drift-admitting jumps,such that high-order finite difference schemes.can be constructed directly based on grids with pure solution points.To i...We develop in this paper a lifting method for Fokker-Planck equations with drift-admitting jumps,such that high-order finite difference schemes.can be constructed directly based on grids with pure solution points.To illustrate the idea,we present as an example the construction of a fifth-order finite difference scheme.The validity of the scheme is demonstrated by conducting numerical experiments for the cases with drift admitting one jump and two jumps,respectively.Additionally,by introducing a splitting technique,we show that the lifting method can be extended to high dimensions.In particular,a two-dimensional case is studied in details to show the effectiveness of the extension.展开更多
It is well known that developing well-balanced schemes for the balance laws is useful for reducing numerical errors.In this paper,a well-balanced weighted compact nonlinear scheme(WCNS)is proposed for shallow water eq...It is well known that developing well-balanced schemes for the balance laws is useful for reducing numerical errors.In this paper,a well-balanced weighted compact nonlinear scheme(WCNS)is proposed for shallow water equations in prebalanced forms.The scheme is proved to be well-balanced provided that the source term is treated appropriately as the advection term.Some numerical examples in oneand two-dimensions are also presented to demonstrate the well-balanced property,high order accuracy and good shock capturing capability of the proposed scheme.展开更多
In this paper,we develop a multi-symplectic wavelet collocation method for three-dimensional(3-D)Maxwell’s equations.For the multi-symplectic formulation of the equations,wavelet collocation method based on autocorre...In this paper,we develop a multi-symplectic wavelet collocation method for three-dimensional(3-D)Maxwell’s equations.For the multi-symplectic formulation of the equations,wavelet collocation method based on autocorrelation functions is applied for spatial discretization and appropriate symplectic scheme is employed for time integration.Theoretical analysis shows that the proposed method is multi-symplectic,unconditionally stable and energy-preserving under periodic boundary conditions.The numerical dispersion relation is investigated.Combined with splitting scheme,an explicit splitting symplectic wavelet collocation method is also constructed.Numerical experiments illustrate that the proposed methods are efficient,have high spatial accuracy and can preserve energy conservation laws exactly.展开更多
In this paper,we propose two new explicit multi-symplectic splitting methods for the nonlinear Dirac(NLD)equation.Based on its multi-symplectic formulation,the NLD equation is split into one linear multi-symplectic sy...In this paper,we propose two new explicit multi-symplectic splitting methods for the nonlinear Dirac(NLD)equation.Based on its multi-symplectic formulation,the NLD equation is split into one linear multi-symplectic system and one nonlinear infinite Hamiltonian system.Then multi-symplectic Fourier pseudospectral method and multi-symplectic Preissmann scheme are employed to discretize the linear subproblem,respectively.And the nonlinear subsystem is solved by a symplectic scheme.Finally,a composition method is applied to obtain the final schemes for the NLD equation.We find that the two proposed schemes preserve the total symplecticity and can be solved explicitly.Numerical experiments are presented to show the effectiveness of the proposed methods.展开更多
In this paper,we propose a wavelet collocation splitting(WCS)method,and a Fourier pseudospectral splitting(FPSS)method as comparison,for solving onedimensional and two-dimensional Schrödinger equations with varia...In this paper,we propose a wavelet collocation splitting(WCS)method,and a Fourier pseudospectral splitting(FPSS)method as comparison,for solving onedimensional and two-dimensional Schrödinger equations with variable coefficients in quantum mechanics.The two methods can preserve the intrinsic properties of original problems as much as possible.The splitting technique increases the computational efficiency.Meanwhile,the error estimation and some conservative properties are investigated.It is proved to preserve the charge conservation exactly.The global energy and momentum conservation laws can be preserved under several conditions.Numerical experiments are conducted during long time computations to show the performances of the proposed methods and verify the theoretical analysis.展开更多
基金supported by the Technology Development Fund of Nanjing Medical University(Grants No.NMUB2016115 and NMUB2020117)。
文摘The current study aims to investigate a suitable adhesive for primary tooth enamel. Shear bond strength(SBS)of primary teeth and the length of resin protrusion were analyzed using one-way ANOVA with Bonferroni multiple comparison tests after etching with 35% H_(3)PO_(4). SBS and marginal microleakage tests were conducted with Single Bond Universal(SBU)/Single Bond 2(SB2) adhesives with or without pre-etching using a nonparametric Kruskal-Wallis test. Clinical investigations were performed to validate the adhesive for primary teeth restoration using Chi-square tests. Results showed that the SBS and length of resin protrusion increased significantly with the etching time. Teeth in the SBU with 35% H_(3)PO_(4)pre-etching groups had higher bond strength and lower marginal microleakage than those in the SB2 groups. Mixed fractures were more common in the 35% H_(3)PO_(4)etched 30 s + SB2/SBU groups. Clinical investigations showed significant differences between the two groups in cumulative retention rates at the 6-, 12-and 18-month follow-up evaluations, as well as in marginal adaptation, discoloration, and secondary caries at the 12-and 18-month follow-up assessments.Together, pre-etching primary teeth enamel for 30 s before SBU treatment improved clinical composite resin restoration, which can provide a suitable approach for restoration of primary teeth.
文摘The Immersed Interface Method (IIM) is derived to solve the corresponding Fokker-Planck equation of Brownian motion with pure dry friction, which is one of the simplest models of piecewise-smooth stochastic systems. The IIM is capable of treating a discontinuity in the drift of Fokker-Planck equation and it is readily extended to the dry and viscous friction model. Analytic results of the considered model are used to confirm the effectiveness and design accuracy of the scheme.
基金supported by the National Natural Science Foundation of China(No.11601517)the Basic Research Foundation of National University of Defense Technology(No.ZDYYJ-CYJ20140101)
文摘To ensure time stability of a seventh-order dissipative compact finite difference scheme, fourth-order boundary closures are used near domain boundaries previously. However, this would reduce the global convergence rate to fifth-order only. In this paper, we elevate the boundary closures to sixth-order to achieve seventh-order global accuracy. To keep the improved scheme time stable, the simultaneous approximation terms (SATs) are used to impose boundary conditions weakly. Eigenvalue analysis shows that the improved scheme is time stable. Numerical experiments for linear advection equations and one-dimensional Euler equations are implemented to validate the new scheme.
基金Project supported by the National Natural Science Foundation of China(Nos.11601517,11502296,61772542,and 61561146395)the Basic Research Foundation of National University of Defense Technology(No.ZDYYJ-CYJ20140101)
文摘A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an optimization problem with several parameters determined by applying a generic algorithm. The optimized schemes are analyzed carefully from the aspects of the eigenvalue distribution, the ε-pseudospectra, the short time behavior, and the Fourier analysis. Numerical experiments for the Euler equations are used to show the effectiveness of the final recommended scheme.
基金the National Natural Science Foundation(Grant No.11972370)the National Key Project(Grant No.GJXM92579)of China.
文摘In this work,we aim to show how to solve the continuous-time and continuous-space Krause model by using high-order finite difference(FD)schemes.Since the considered model admits solutions withδ-singularities,the FD method cannot be applied directly.To deal with the annoyingδ-singulariti-es,we propose to lift the solution space by introducing a spltting method,such that theδ-singularities in one spatial direction become step functions with dis-continuities.Thus the traditional shock-capturing FD schemes can be applied directly.In particular,we focus on the two dimensional case and apply a fifth-order weighted nonlinear compact scheme(WCNS)to ilustrate the validity of the proposed method.Some technical details for implementation are also presented.Numerical results show that the proposed method can captureδ-singularities well,and the obtained number of delta peaks agrees with the the-oretical prediction in the literature.
基金supported by the National Natural Science Foundation of China(Grant 11972370)the National Key Project of China(Grant GJXM92579).
文摘We develop in this paper a lifting method for Fokker-Planck equations with drift-admitting jumps,such that high-order finite difference schemes.can be constructed directly based on grids with pure solution points.To illustrate the idea,we present as an example the construction of a fifth-order finite difference scheme.The validity of the scheme is demonstrated by conducting numerical experiments for the cases with drift admitting one jump and two jumps,respectively.Additionally,by introducing a splitting technique,we show that the lifting method can be extended to high dimensions.In particular,a two-dimensional case is studied in details to show the effectiveness of the extension.
基金The work is supported by the Basic Research Foundation of the National NumericalWind Tunnel Project(Grant No.NNW2018-ZT4A08)the National Natural Science Foundation(Grant No.11972370)the National Key Project(Grant No.GJXM92579)of China.
文摘It is well known that developing well-balanced schemes for the balance laws is useful for reducing numerical errors.In this paper,a well-balanced weighted compact nonlinear scheme(WCNS)is proposed for shallow water equations in prebalanced forms.The scheme is proved to be well-balanced provided that the source term is treated appropriately as the advection term.Some numerical examples in oneand two-dimensions are also presented to demonstrate the well-balanced property,high order accuracy and good shock capturing capability of the proposed scheme.
基金This research was partially supported by the Natural Science Foundation of China(Grant No.10971226 and No.11001270)the 973 Project of China(Grant No.2009CB723802-4).
文摘In this paper,we develop a multi-symplectic wavelet collocation method for three-dimensional(3-D)Maxwell’s equations.For the multi-symplectic formulation of the equations,wavelet collocation method based on autocorrelation functions is applied for spatial discretization and appropriate symplectic scheme is employed for time integration.Theoretical analysis shows that the proposed method is multi-symplectic,unconditionally stable and energy-preserving under periodic boundary conditions.The numerical dispersion relation is investigated.Combined with splitting scheme,an explicit splitting symplectic wavelet collocation method is also constructed.Numerical experiments illustrate that the proposed methods are efficient,have high spatial accuracy and can preserve energy conservation laws exactly.
基金the open foundations of State Key Laboratory of High Performance Computing and State Key Laboratory of Aerodynamics.Y.C.gratefully acknowledges support from NUDT’s Innovation Foundation(Grant No.B110205)H.Z.was supported by the Natural Science Foundation of China(Grant No.11301525).
文摘In this paper,we propose two new explicit multi-symplectic splitting methods for the nonlinear Dirac(NLD)equation.Based on its multi-symplectic formulation,the NLD equation is split into one linear multi-symplectic system and one nonlinear infinite Hamiltonian system.Then multi-symplectic Fourier pseudospectral method and multi-symplectic Preissmann scheme are employed to discretize the linear subproblem,respectively.And the nonlinear subsystem is solved by a symplectic scheme.Finally,a composition method is applied to obtain the final schemes for the NLD equation.We find that the two proposed schemes preserve the total symplecticity and can be solved explicitly.Numerical experiments are presented to show the effectiveness of the proposed methods.
基金supported by the National Natural Science Foundation of China(Grant Nos.91130013,10971226,and 11001270)Hunan Provincial Innovation Foundation(Grant Nos.CX2011B011,and CX2012B010)+1 种基金the Innovation Fund of NUDT(Grant No.B120205)Chinese Scholarship Council.
文摘In this paper,we propose a wavelet collocation splitting(WCS)method,and a Fourier pseudospectral splitting(FPSS)method as comparison,for solving onedimensional and two-dimensional Schrödinger equations with variable coefficients in quantum mechanics.The two methods can preserve the intrinsic properties of original problems as much as possible.The splitting technique increases the computational efficiency.Meanwhile,the error estimation and some conservative properties are investigated.It is proved to preserve the charge conservation exactly.The global energy and momentum conservation laws can be preserved under several conditions.Numerical experiments are conducted during long time computations to show the performances of the proposed methods and verify the theoretical analysis.
