A high order finite difference numerical scheme is developed for the shallow water equations on curvilinear meshes based on an alternative flux formulation of the weighted essentially non-oscillatory(WENO)scheme.The e...A high order finite difference numerical scheme is developed for the shallow water equations on curvilinear meshes based on an alternative flux formulation of the weighted essentially non-oscillatory(WENO)scheme.The exact C-property is investigated,and comparison with the standard finite difference WENO scheme is made.Theoretical derivation and numerical results show that the proposed finite difference WENO scheme can maintain the exact C-property on both stationarily and dynamically generalized coordinate systems.The Harten-Lax-van Leer type flux is developed on general curvilinear meshes in two dimensions and verified on a number of benchmark problems,indicating smaller errors compared with the Lax-Friedrichs solver.In addition,we propose a positivity-preserving limiter on stationary meshes such that the scheme can preserve the non-negativity of the water height without loss of mass conservation.展开更多
AIM: To compare the difference and agreement of KR- lW and iTrace for measurement of high order aberrations.METHODS: KR-1W and iTrace were respectively used in a group of healthy people (40 volunteers, 32 eyes) to...AIM: To compare the difference and agreement of KR- lW and iTrace for measurement of high order aberrations.METHODS: KR-1W and iTrace were respectively used in a group of healthy people (40 volunteers, 32 eyes) to measure the high order aberration (HOA) of corneal, internal and total ocular. The clinical difference and agreement of two instruments were respectively evaluated by paired-samples 1-test and Bland-Altman analysis. RESULTS: The paired-samples t-test showed that the corneal HOA measured by the two instruments had no statistical differences (P〉0.05); but the internal and total ocular HOA had significant statistical differences (P〈 0.05), and the mean results measured by iTrace were higher than that of KR-1W. However, Bland-Altman analysis revealed that the HOA of corneal and internal were all in 95% limits of agreement; and just one point of total ocular HOA was beyond the 95% limits of agreement. CONCLUSION: KR-1W and iTrace were consistent well in the measurement of corneal, internal and total ocular HOA, especially for the cornea.展开更多
In this paper, a numerical model is developed based on the High Order Spectral (HOS) method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident bou...In this paper, a numerical model is developed based on the High Order Spectral (HOS) method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident boundary in the HOS method. Based on the numerical model, the effects of wave parameters, such as the assumed focused amplitude, the central frequency, the frequency bandwidth, the wave amplitude distribution and the directional spreading on the surface elevation of the focused wave, the maximum generated wave crest, and the shifting of the focusing point, are numerically investigated. Especially, the effects of the wave directionality on the focused wave properties are emphasized. The numerical results show that the shifting of the focusing point and the maximum crest of the wave group are dependent on the amplitude of the focused wave, the central frequency, and the wave amplitude distribution type. The wave directionality has a definite effect on multidirectional focused waves. Generally, it can even out the difference between the simulated wave amplitude and the amplitude expected from theory and reduce the shifting of the focusing points, implying that the higher order interaction has an influence on wave focusing, especially for 2D wave. In 3D wave groups, a broader directional spreading weakens the higher nonlinear interactions.展开更多
Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process an...Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process and provided a theoretical formulation for the recurrence period in 1985 on the basis of the nonlinear cubic Schrodinger equation (NLS). However, NLS has limitations on the narrow band and the weak nonlinearity. The recurrence period is re-investigated in this paper by using a highly efficient High Order Spectral (HOS) method, which can be applied for the direct phase- resolved simulation of the nonlinear wave train evolution. It is found that the Stiassnie and Shemer's formula should be modified in the cases with most unstable initial conditions, which is important for such topics as the generation mechanisms of freak waves. A new recurrence period formula is presented and some new evolution characteristics of the Stokes wave train are also discussed in details.展开更多
A novel class of weighted essentially nonoscillatory (WENO) schemes based on Hermite polynomi- als, termed as HWENO schemes, is developed and applied as limiters for high order discontinuous Galerkin (DG) method o...A novel class of weighted essentially nonoscillatory (WENO) schemes based on Hermite polynomi- als, termed as HWENO schemes, is developed and applied as limiters for high order discontinuous Galerkin (DG) method on triangular grids. The developed HWENO methodology utilizes high-order derivative information to keep WENO re- construction stencils in the von Neumann neighborhood. A simple and efficient technique is also proposed to enhance the smoothness of the existing stencils, making higher-order scheme stable and simplifying the reconstruction process at the same time. The resulting HWENO-based limiters are as compact as the underlying DG schemes and therefore easy to implement. Numerical results for a wide range of flow conditions demonstrate that for DG schemes of up to fourth order of accuracy, the designed HWENO limiters can simul- taneously obtain uniform high order accuracy and sharp, es- sentially non-oscillatory shock transition.展开更多
In this article,we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrodinger type operator(—Δ)^2+V%2 in R%n(n≥5)with V being a nonnegat...In this article,we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrodinger type operator(—Δ)^2+V%2 in R%n(n≥5)with V being a nonnegative potential satisfying the reverse Holder inequality.Furt her more,we prove the boundedness of the variation operators on associated Morrey spaces.In the proof of the main results,we always make use of the variation inequalities associated with the hea t semigroup genera ted by the biharmonic operator(-Δ)2.展开更多
An optimal design approach of high order FIR digital filter is developed based on the algorithm of neural networks with cosine basis function . The main idea is to minimize the sum of the square errors between the amp...An optimal design approach of high order FIR digital filter is developed based on the algorithm of neural networks with cosine basis function . The main idea is to minimize the sum of the square errors between the amplitude response of the desired FIR filter and that of the designed by training the weights of neural networks, then obtains the impulse response of FIR digital filter . The convergence theorem of the neural networks algorithm is presented and proved, and the optimal design method is introduced by designing four kinds of FIR digital filters , i.e., low-pass, high-pass, bandpass , and band-stop FIR digital filter. The results of the amplitude responses show that attenuation in stop-bands is more than 60 dB with no ripple and pulse existing in pass-bands, and cutoff frequency of passband and stop-band is easily controlled precisely .The presented optimal design approach of high order FIR digital filter is significantly effective.展开更多
The transient thermal response of a thick orthotropic hollow cylinder with finite length is studied by a high order shell theory. The radial and axial displacements are assumed to have quadratic and cubic variations t...The transient thermal response of a thick orthotropic hollow cylinder with finite length is studied by a high order shell theory. The radial and axial displacements are assumed to have quadratic and cubic variations through the thickness, respectively. It is important that the radial stress is approximated by a cubic expansion satisfying the boundary conditions at the inner and outer surfaces, and the corresponding strain should be least-squares compatible with the strain derived from the strain-displacement relation. The equations of motion are derived from the integration of the equilibrium equations of stresses, which are solved by precise integration method (PIM). Numerical results are.obtained, and compared with FE simulations and dynamic thermo-elasticity solutions, which indicates that the high order shell theory is capable of predicting the transient thermal response of an orthotropic (or isotropic) thick hollow cylinder efficiently, and for the detonation tube of actual pulse detonation engines (PDE) heated continuously, the thermal stresses will become too large to be neglected, which are not like those in the one time experiments with very short time.展开更多
In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary unde...In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.展开更多
Variational principle for non-vortex, non-linear wave theories is established in this paper. By using this variational principle and related functional minimum condition, the fifth and sixth order Stokes Vaves are giv...Variational principle for non-vortex, non-linear wave theories is established in this paper. By using this variational principle and related functional minimum condition, the fifth and sixth order Stokes Vaves are given as an example and the results are compared with those in Reference (Skjel-breia, 1961).展开更多
The Besov spaces B_p^(α,4)(Γ)and Triebel-Lizorkin spaces F_p^(α,4)(Γ)with high order x∈R on a Lipschitz curve Γ are defind,when 1≤p≤∞,1≤q≤∞.To compare to the classical case.a difference characterization of...The Besov spaces B_p^(α,4)(Γ)and Triebel-Lizorkin spaces F_p^(α,4)(Γ)with high order x∈R on a Lipschitz curve Γ are defind,when 1≤p≤∞,1≤q≤∞.To compare to the classical case.a difference characterization of such spaces in the case|x|<1 is given also.展开更多
This paper introduces a correlation-polarization potential with high order terms for vibrational excitation in electron-molecule scattering. The new polarization potential generalizes the two-term approximation so tha...This paper introduces a correlation-polarization potential with high order terms for vibrational excitation in electron-molecule scattering. The new polarization potential generalizes the two-term approximation so that it can better reflect the dependence of correlation and polarization effects on the position coordinate of the scattering electron. It applies the new potential on the vibrational excitation scattering from N2 in an energy range which includes the ^2Ⅱg shape resonance. The good agreement of theoretical resonant peaks with experiments shows that polarization potentials with high order terms are important and should be included in vibrational excitation scattering.展开更多
In this paper, we consider two extended systems. When using them for the two parameter bifurcation problems, the simple bifurcation point with regard to lambda on turn into the simple turning point with. regard to mu....In this paper, we consider two extended systems. When using them for the two parameter bifurcation problems, the simple bifurcation point with regard to lambda on turn into the simple turning point with. regard to mu. Simple high orde bifurcation point is first studied without using the symmetry condition.展开更多
In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equatio...In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equation method. The numerical approximate schemes for both problems on a bounded or unbounded domain in R3 are proposed and their prior error estimates are obtained.展开更多
The exit wave function including zero and high order Laue zones has been simulated by both multi-slice method and electron dynamic diffraction analytical expression. Coincidence of the simulations by these two methods...The exit wave function including zero and high order Laue zones has been simulated by both multi-slice method and electron dynamic diffraction analytical expression. Coincidence of the simulations by these two methods was achieved. The calculated results showed that the exit wave function highly dominated by zero order Laue zone, while high order ones modify the exit wave function to some extent depending on the situation. High order Laue zone effects become important for the following cases: sample consists of light elements, the thickness is very thin, lattice planar spacing perpendicular to the direction of the incident beam is large, and the electron beam has long wavelength. In these cases the exit wave function should be corrected by adding high order Laue zone effects. The analytical expression is effective and convenient for dealing with high order Laue zone effects.展开更多
Based on the precise integration method (PIM), a coupling technique of the high order multiplication perturbation method (HOMPM) and the reduction method is proposed to solve variable coefficient singularly pertur...Based on the precise integration method (PIM), a coupling technique of the high order multiplication perturbation method (HOMPM) and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems (TPBVPs) with one boundary layer. First, the inhomogeneous ordinary differential equations (ODEs) are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.展开更多
In this paper,three tuning methods of the integer order proportional integral derivative(IOPID)controller,the fuzzy proportional integral derivative(FPID)controller and the fractional order proportional integral deriv...In this paper,three tuning methods of the integer order proportional integral derivative(IOPID)controller,the fuzzy proportional integral derivative(FPID)controller and the fractional order proportional integral derivative(FOPID)controller for high order system are presented respectively.Both IOPID controller and FOPID controller designed by the two tuning methods can satisfy all the three specifications proposed,which can guarantee the desired control performance and the robustness of the high order system to the loop gain variations.From the simulation results,the three controllers meet the dynamic performance requirements of high order system.Moreover,the FOPID controller,with the shortest overshoot and adjustment time,outperforms the IOPID controller and the FPID controller for the high order system.展开更多
We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integratio...We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integration is in the strip 0<Rez<aπ.展开更多
This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singula...This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations (ODEs) are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.展开更多
In this paper, we consider multi-symplectic Fourier pseudospectral method for a high order integrable equation of KdV type, which describes many important physical phenomena. The multi-symplectic structure are constru...In this paper, we consider multi-symplectic Fourier pseudospectral method for a high order integrable equation of KdV type, which describes many important physical phenomena. The multi-symplectic structure are constructed for the equation, and the conservation laws of the continuous equation are presented. The multisymplectic discretization of each formulation is exemplified by the multi-symplectic Fourier pseudospectral scheme. The numerical experiments are given, and the results verify the efficiency of the Fourier pseudospectral method.展开更多
基金the National Natural Science Foundation of China(11901555,11871448,12001009).
文摘A high order finite difference numerical scheme is developed for the shallow water equations on curvilinear meshes based on an alternative flux formulation of the weighted essentially non-oscillatory(WENO)scheme.The exact C-property is investigated,and comparison with the standard finite difference WENO scheme is made.Theoretical derivation and numerical results show that the proposed finite difference WENO scheme can maintain the exact C-property on both stationarily and dynamically generalized coordinate systems.The Harten-Lax-van Leer type flux is developed on general curvilinear meshes in two dimensions and verified on a number of benchmark problems,indicating smaller errors compared with the Lax-Friedrichs solver.In addition,we propose a positivity-preserving limiter on stationary meshes such that the scheme can preserve the non-negativity of the water height without loss of mass conservation.
文摘AIM: To compare the difference and agreement of KR- lW and iTrace for measurement of high order aberrations.METHODS: KR-1W and iTrace were respectively used in a group of healthy people (40 volunteers, 32 eyes) to measure the high order aberration (HOA) of corneal, internal and total ocular. The clinical difference and agreement of two instruments were respectively evaluated by paired-samples 1-test and Bland-Altman analysis. RESULTS: The paired-samples t-test showed that the corneal HOA measured by the two instruments had no statistical differences (P〉0.05); but the internal and total ocular HOA had significant statistical differences (P〈 0.05), and the mean results measured by iTrace were higher than that of KR-1W. However, Bland-Altman analysis revealed that the HOA of corneal and internal were all in 95% limits of agreement; and just one point of total ocular HOA was beyond the 95% limits of agreement. CONCLUSION: KR-1W and iTrace were consistent well in the measurement of corneal, internal and total ocular HOA, especially for the cornea.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51309050 and 51221961)the National Basic Research Program of China(973 Program,Grant Nos.2013CB036101 and 2011CB013703)
文摘In this paper, a numerical model is developed based on the High Order Spectral (HOS) method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident boundary in the HOS method. Based on the numerical model, the effects of wave parameters, such as the assumed focused amplitude, the central frequency, the frequency bandwidth, the wave amplitude distribution and the directional spreading on the surface elevation of the focused wave, the maximum generated wave crest, and the shifting of the focusing point, are numerically investigated. Especially, the effects of the wave directionality on the focused wave properties are emphasized. The numerical results show that the shifting of the focusing point and the maximum crest of the wave group are dependent on the amplitude of the focused wave, the central frequency, and the wave amplitude distribution type. The wave directionality has a definite effect on multidirectional focused waves. Generally, it can even out the difference between the simulated wave amplitude and the amplitude expected from theory and reduce the shifting of the focusing points, implying that the higher order interaction has an influence on wave focusing, especially for 2D wave. In 3D wave groups, a broader directional spreading weakens the higher nonlinear interactions.
基金supported by the National Natural Science Foundation of China (Grant No. 41106001)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100094110016)+1 种基金the Special Research Funding of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (Grant No. 2009585812)the Priority Academic Program Development of Jiangsu Higher Education Institutions (Coastal Development and Conservancy)
文摘Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process and provided a theoretical formulation for the recurrence period in 1985 on the basis of the nonlinear cubic Schrodinger equation (NLS). However, NLS has limitations on the narrow band and the weak nonlinearity. The recurrence period is re-investigated in this paper by using a highly efficient High Order Spectral (HOS) method, which can be applied for the direct phase- resolved simulation of the nonlinear wave train evolution. It is found that the Stiassnie and Shemer's formula should be modified in the cases with most unstable initial conditions, which is important for such topics as the generation mechanisms of freak waves. A new recurrence period formula is presented and some new evolution characteristics of the Stokes wave train are also discussed in details.
基金supported by the National Basic Research Program of China (2009CB724104)the National Natural Science Foundation of China (90716010)
文摘A novel class of weighted essentially nonoscillatory (WENO) schemes based on Hermite polynomi- als, termed as HWENO schemes, is developed and applied as limiters for high order discontinuous Galerkin (DG) method on triangular grids. The developed HWENO methodology utilizes high-order derivative information to keep WENO re- construction stencils in the von Neumann neighborhood. A simple and efficient technique is also proposed to enhance the smoothness of the existing stencils, making higher-order scheme stable and simplifying the reconstruction process at the same time. The resulting HWENO-based limiters are as compact as the underlying DG schemes and therefore easy to implement. Numerical results for a wide range of flow conditions demonstrate that for DG schemes of up to fourth order of accuracy, the designed HWENO limiters can simul- taneously obtain uniform high order accuracy and sharp, es- sentially non-oscillatory shock transition.
基金supported by the National Natural Science Foundation of China(11701453)Fundamental Research Funds for the Central Universities(31020180QD05)+2 种基金The second author was supported by the National Natural Science Foundation of China(11971431,11401525)the Natural Science Foundation of Zhejiang Province(LY18A010006)and the first Class Discipline of Zhejiang-A(Zhejiang Gongshang University-Statistics).
文摘In this article,we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrodinger type operator(—Δ)^2+V%2 in R%n(n≥5)with V being a nonnegative potential satisfying the reverse Holder inequality.Furt her more,we prove the boundedness of the variation operators on associated Morrey spaces.In the proof of the main results,we always make use of the variation inequalities associated with the hea t semigroup genera ted by the biharmonic operator(-Δ)2.
基金This project was supported by the National Natural Science Foundation of China (50277010)Doctoral Special Fund of Ministry of Education (20020532016) and Fund of Outstanding Young Scientist of Hunan University.
文摘An optimal design approach of high order FIR digital filter is developed based on the algorithm of neural networks with cosine basis function . The main idea is to minimize the sum of the square errors between the amplitude response of the desired FIR filter and that of the designed by training the weights of neural networks, then obtains the impulse response of FIR digital filter . The convergence theorem of the neural networks algorithm is presented and proved, and the optimal design method is introduced by designing four kinds of FIR digital filters , i.e., low-pass, high-pass, bandpass , and band-stop FIR digital filter. The results of the amplitude responses show that attenuation in stop-bands is more than 60 dB with no ripple and pulse existing in pass-bands, and cutoff frequency of passband and stop-band is easily controlled precisely .The presented optimal design approach of high order FIR digital filter is significantly effective.
基金supported by the National Basic Research Program of China (No.2006CB 601202)NPU Foundation for Fundamental Research, the Doctorate Foundation of Northwestern Polytechnical University (No.CX200810)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (No.GZ0802)
文摘The transient thermal response of a thick orthotropic hollow cylinder with finite length is studied by a high order shell theory. The radial and axial displacements are assumed to have quadratic and cubic variations through the thickness, respectively. It is important that the radial stress is approximated by a cubic expansion satisfying the boundary conditions at the inner and outer surfaces, and the corresponding strain should be least-squares compatible with the strain derived from the strain-displacement relation. The equations of motion are derived from the integration of the equilibrium equations of stresses, which are solved by precise integration method (PIM). Numerical results are.obtained, and compared with FE simulations and dynamic thermo-elasticity solutions, which indicates that the high order shell theory is capable of predicting the transient thermal response of an orthotropic (or isotropic) thick hollow cylinder efficiently, and for the detonation tube of actual pulse detonation engines (PDE) heated continuously, the thermal stresses will become too large to be neglected, which are not like those in the one time experiments with very short time.
基金Project supported by the National Natural Science Foundation of China (Nos. 11901555, 11901213,11871448, and 11732016)the National Numerical Windtunnel Project (No. NNW2019ZT4-B10)。
文摘In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.
文摘Variational principle for non-vortex, non-linear wave theories is established in this paper. By using this variational principle and related functional minimum condition, the fifth and sixth order Stokes Vaves are given as an example and the results are compared with those in Reference (Skjel-breia, 1961).
基金The author is supported in part by the Foundation of Zhongshan University Advanced Research Centre and NSF of China.
文摘The Besov spaces B_p^(α,4)(Γ)and Triebel-Lizorkin spaces F_p^(α,4)(Γ)with high order x∈R on a Lipschitz curve Γ are defind,when 1≤p≤∞,1≤q≤∞.To compare to the classical case.a difference characterization of such spaces in the case|x|<1 is given also.
基金Project supported by National Natural Science Foundation of China (Grant Nos 10504022 and 10774105)
文摘This paper introduces a correlation-polarization potential with high order terms for vibrational excitation in electron-molecule scattering. The new polarization potential generalizes the two-term approximation so that it can better reflect the dependence of correlation and polarization effects on the position coordinate of the scattering electron. It applies the new potential on the vibrational excitation scattering from N2 in an energy range which includes the ^2Ⅱg shape resonance. The good agreement of theoretical resonant peaks with experiments shows that polarization potentials with high order terms are important and should be included in vibrational excitation scattering.
文摘In this paper, we consider two extended systems. When using them for the two parameter bifurcation problems, the simple bifurcation point with regard to lambda on turn into the simple turning point with. regard to mu. Simple high orde bifurcation point is first studied without using the symmetry condition.
基金This research was supported by the National Natural Science Foundation of China
文摘In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equation method. The numerical approximate schemes for both problems on a bounded or unbounded domain in R3 are proposed and their prior error estimates are obtained.
基金National Natural Science Foundation of China(No.10374077)the Key Foundation of Education Department of Hunan Province 01A003the Scientific Fund of Education Department of Hunan Province 03C187
文摘The exit wave function including zero and high order Laue zones has been simulated by both multi-slice method and electron dynamic diffraction analytical expression. Coincidence of the simulations by these two methods was achieved. The calculated results showed that the exit wave function highly dominated by zero order Laue zone, while high order ones modify the exit wave function to some extent depending on the situation. High order Laue zone effects become important for the following cases: sample consists of light elements, the thickness is very thin, lattice planar spacing perpendicular to the direction of the incident beam is large, and the electron beam has long wavelength. In these cases the exit wave function should be corrected by adding high order Laue zone effects. The analytical expression is effective and convenient for dealing with high order Laue zone effects.
基金Project supported by the National Natural Science Foundation of China(Key Program)(Nos.11132004 and 51078145)
文摘Based on the precise integration method (PIM), a coupling technique of the high order multiplication perturbation method (HOMPM) and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems (TPBVPs) with one boundary layer. First, the inhomogeneous ordinary differential equations (ODEs) are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.
基金Sponsored by the Foundation of Jilin Educational Committee(Grant No.22201-2221010195)
文摘In this paper,three tuning methods of the integer order proportional integral derivative(IOPID)controller,the fuzzy proportional integral derivative(FPID)controller and the fractional order proportional integral derivative(FOPID)controller for high order system are presented respectively.Both IOPID controller and FOPID controller designed by the two tuning methods can satisfy all the three specifications proposed,which can guarantee the desired control performance and the robustness of the high order system to the loop gain variations.From the simulation results,the three controllers meet the dynamic performance requirements of high order system.Moreover,the FOPID controller,with the shortest overshoot and adjustment time,outperforms the IOPID controller and the FPID controller for the high order system.
基金Supported by the National Natural Science Foundation of China(19971064 10161009)
文摘We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integration is in the strip 0<Rez<aπ.
基金supported by the National Natural Science Foundation of China(Key Program)(Nos.11132004 and 51078145)
文摘This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations (ODEs) are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.
文摘In this paper, we consider multi-symplectic Fourier pseudospectral method for a high order integrable equation of KdV type, which describes many important physical phenomena. The multi-symplectic structure are constructed for the equation, and the conservation laws of the continuous equation are presented. The multisymplectic discretization of each formulation is exemplified by the multi-symplectic Fourier pseudospectral scheme. The numerical experiments are given, and the results verify the efficiency of the Fourier pseudospectral method.