A new oxidative N-heterocyclic carbene(NHC)-catalyzed high-order[7+3]annulation reaction ofγ-indolyl phenols as 1,7-dinucleophiles andα,β-alkynals with the aid of Sc(OTf)_(3)is reported,enabling the highly regiosel...A new oxidative N-heterocyclic carbene(NHC)-catalyzed high-order[7+3]annulation reaction ofγ-indolyl phenols as 1,7-dinucleophiles andα,β-alkynals with the aid of Sc(OTf)_(3)is reported,enabling the highly regioselective access to unprecedented polyarene-fused ten-membered lactams bearing a bridged aryl-aryl-indole scaffold in moderate to good yields.This protocol demonstrates a broad substrate scope,good compatibility with substituents and complete regioselectivity,providing an organocatalytic modular synthetic strategy for creating medium-sized lactams.展开更多
The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the ...The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.展开更多
We investigate theoretically the effects of chirped laser pulses on high-order harmonic generation(HHG)from solids.We find that the harmonic spectra display redshifts for the driving laser pulses with negative chirp a...We investigate theoretically the effects of chirped laser pulses on high-order harmonic generation(HHG)from solids.We find that the harmonic spectra display redshifts for the driving laser pulses with negative chirp and blueshifts for those with positive chirp,which is due to the change in the instantaneous frequency of the driving laser for different chirped pulses.The analysis of crystal-momentum-resolved(k-resolved)HHG reveals that the frequency shifts are equal for the harmonics generated by different crystal momentum channels.The frequency shifts in the cutoff region are larger than those in the plateau region.With the increase of the absolute value of the chirp parameters,the frequency shifts of HHG become more significant,leading to the shifts from odd-to even-order harmonics.We also demonstrate that the frequency shifts of harmonic spectra are related to the duration of the chirped laser field,but are insensitive to the laser intensity and dephasing time.展开更多
Thermal expansion is crucial for various industrial processes and is increasingly the focus of research endeavors aimed at improving material performance.However,it is the continuous advancements in first-principles c...Thermal expansion is crucial for various industrial processes and is increasingly the focus of research endeavors aimed at improving material performance.However,it is the continuous advancements in first-principles calculations that have enabled researchers to understand the microscopic origins of thermal expansion.In this study,we propose a coefficient of thermal expansion(CTE)calculation scheme based on self-consistent phonon theory,incorporating the fourth-order anharmonicity.We selected four structures(Si,CaZrF_(6),SrTiO_(3),NaBr)to investigate high-order anharmonicity’s impact on their CTEs,based on bonding types.The results indicate that our method goes beyond the second-order quasi-harmonic approximation and the third-order perturbation theory,aligning closely with experimental data.Furthermore,we observed that an increase in the ionicity of the structures leads to a more pronounced influence of high-order anharmonicity on CTE,with this effect primarily manifesting in variations of the Grüneisen parameter.Our research provides a theoretical foundation for accurately predicting and regulating the thermal expansion behavior of materials.展开更多
An efficient and accurate scalar auxiliary variable(SAV)scheme for numerically solving nonlinear parabolic integro-differential equation(PIDE)is developed in this paper.The original equation is first transformed into ...An efficient and accurate scalar auxiliary variable(SAV)scheme for numerically solving nonlinear parabolic integro-differential equation(PIDE)is developed in this paper.The original equation is first transformed into an equivalent system,and the k-order backward differentiation formula(BDF k)and central difference formula are used to discretize the temporal and spatial derivatives,respectively.Different from the traditional discrete method that adopts full implicit or full explicit for the nonlinear integral terms,the proposed scheme is based on the SAV idea and can be treated semi-implicitly,taking into account both accuracy and effectiveness.Numerical results are presented to demonstrate the high-order convergence(up to fourth-order)of the developed schemes and it is computationally efficient in long-time computations.展开更多
With the availability of high-performance computing technology and the development of advanced numerical simulation methods, Computational Fluid Dynamics (CFD) is becoming more and more practical and efficient in engi...With the availability of high-performance computing technology and the development of advanced numerical simulation methods, Computational Fluid Dynamics (CFD) is becoming more and more practical and efficient in engineering. As one of the high-precision representative algorithms, the high-order Discontinuous Galerkin Method (DGM) has not only attracted widespread attention from scholars in the CFD research community, but also received strong development. However, when DGM is extended to high-speed aerodynamic flow field calculations, non-physical numerical Gibbs oscillations near shock waves often significantly affect the numerical accuracy and even cause calculation failure. Data driven approaches based on machine learning techniques can be used to learn the characteristics of Gibbs noise, which motivates us to use it in high-speed DG applications. To achieve this goal, labeled data need to be generated in order to train the machine learning models. This paper proposes a new method for denoising modeling of Gibbs phenomenon using a machine learning technique, the zero-shot learning strategy, to eliminate acquiring large amounts of CFD data. The model adopts a graph convolutional network combined with graph attention mechanism to learn the denoising paradigm from synthetic Gibbs noise data and generalize to DGM numerical simulation data. Numerical simulation results show that the Gibbs denoising model proposed in this paper can suppress the numerical oscillation near shock waves in the high-order DGM. Our work automates the extension of DGM to high-speed aerodynamic flow field calculations with higher generalization and lower cost.展开更多
We present a comprehensive study on the role of various excited states in high-order harmonic generation of hydrogen atoms driven by a long-wavelength(1500 nm)laser field.By numerically solving the time-dependent Schr...We present a comprehensive study on the role of various excited states in high-order harmonic generation of hydrogen atoms driven by a long-wavelength(1500 nm)laser field.By numerically solving the time-dependent Schrodinger equation(TDSE)and performing a time-frequency analysis,we investigate the influence of individual excited states on the harmonic spectrum.Our results reveal that the 2s excited state primarily contributes to the enhancement of high-energy harmonic yields by facilitating long electron trajectories,while the 2p excited state predominantly suppresses harmonic yields in the lower-energy region(20th-50th orders)by altering the contributions of electron trajectories.Our results highlight the critical role of the excited states in the HHG process,even at longer laser wavelengths.展开更多
In the field of discretization-based meshfree/meshless methods,the improvements in the higher-order consistency,stability,and computational efficiency are of great concerns in computational science and numerical solut...In the field of discretization-based meshfree/meshless methods,the improvements in the higher-order consistency,stability,and computational efficiency are of great concerns in computational science and numerical solutions to partial differential equations.Various alternative numerical methods of the finite particle method(FPM)frame have been extended from mathematical theories to numerical applications separately.As a comprehensive numerical scheme,this study suggests a unified resolved program for numerically investigating their accuracy,stability,consistency,computational efficiency,and practical applicability in industrial engineering contexts.The high-order finite particle method(HFPM)and corrected methods based on the multivariate Taylor series expansion are constructed and analyzed to investigate the whole applicability in different benchmarks of computational fluid dynamics.Specifically,four benchmarks are designed purposefully from statical exact solutions to multifaceted hydrodynamic tests,which possess different numerical performances on the particle consistency,numerical discretized forms,particle distributions,and transient time evolutional stabilities.This study offers a numerical reference for the current unified resolved program.展开更多
We performed real-time and real-space numerical simulations of high-order harmonic generation in the threedimensional structured molecule methane(CH_(4)) using time-dependent density functional theory. By irradiating ...We performed real-time and real-space numerical simulations of high-order harmonic generation in the threedimensional structured molecule methane(CH_(4)) using time-dependent density functional theory. By irradiating the methane molecule with an elliptically polarized laser pulse polarized in the x–y plane, we observed significant even-order harmonic emission in the z-direction. By analyzing the electron dynamics in the electric field and the multi-orbital effects of the molecule, we revealed that electron recombination near specific atoms in methane is the primary source of highorder harmonic generation in the z-direction. Furthermore, we identified the dominant molecular orbitals responsible for the enhancement of harmonics in this direction and demonstrated the critical role played by multi-orbital effects in this process.展开更多
A high-order Lagrangian cell-centered conservative gas dynamics scheme is presented on unstructured meshes. A high-order piecewise pressure of the cell is intro- duced. With the high-order piecewise pressure of the ce...A high-order Lagrangian cell-centered conservative gas dynamics scheme is presented on unstructured meshes. A high-order piecewise pressure of the cell is intro- duced. With the high-order piecewise pressure of the cell, the high-order spatial discretiza- tion fluxes are constructed. The time discretization of the spatial fluxes is performed by means of the Taylor expansions of the spatial discretization fluxes. The vertex velocities are evaluated in a consistent manner due to an original solver located at the nodes by means of momentum conservation. Many numerical tests are presented to demonstrate the robustness and the accuracy of the scheme.展开更多
High-order ghost imaging with thermal light consisting of N different frequencies is investigated. The high-order intensity correlation and intrinsic correlation functions are derived for such N-colour light. It is fo...High-order ghost imaging with thermal light consisting of N different frequencies is investigated. The high-order intensity correlation and intrinsic correlation functions are derived for such N-colour light. It is found that they are similar in form to those for the monochromatic case, thus most of the conclusions we obtained previously for monochromatic Nth-order ghost imaging are still applicable. However, we find that the visibility of the N-colour ghost image depends strongly on the wavelength used to illuminate the object, and increases as this wavelength increases when the test arm is fixed. On the contrary, changes of wavelength in the reference arms do not lead to any change of the visibility.展开更多
In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered gri...In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.展开更多
In this paper, we consider the Cauchy numbers and polynomials of order k and give some relation between Cauchy polynomials of order k and special polynomials by using generating functions and the Riordan matrix method...In this paper, we consider the Cauchy numbers and polynomials of order k and give some relation between Cauchy polynomials of order k and special polynomials by using generating functions and the Riordan matrix methods. In addition, we establish some new equalities and relations involving high-order Cauchy numbers and polynomials, high-order Daehee numbers and polynomials, the generalized Bell polynomials, the Bernoulli numbers and polynomials, high-order Changhee polynomials, high-order Changhee-Genocchi polynomials, the combinatorial numbers, Lah numbers and Stirling numbers, etc.展开更多
The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and ...The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.展开更多
This paper presents a detailed investigation, via field experiment, into the mechanism of high-order polygonal wear of wheels of a new type of high-speed train. The investigation was carried out during the performance...This paper presents a detailed investigation, via field experiment, into the mechanism of high-order polygonal wear of wheels of a new type of high-speed train. The investigation was carried out during the performance acceptance test of the train and its initial commercial operation. The investigation covered the performance acceptance test of 150 000 km and the commercial operation of about 150 000 km. In the performance acceptance test of the first stage of about 70 000 km, at 200-250 km/h with full loading and sometimes overloading by 30%, the serious polygonal wear of 23-order took place on all the wheels of the train, and was measured and analyzed in detail. All the potygonized wheels were re-profiled because the polygonal wear had caused strong vibration and damage to the train parts. After re-profiling, the vibration of the train and track and the wear status of the wheels were measured and analyzed at different test mileages according to the polygonal wear situation of the wheels. The measured vibration of the train includes the accelerations at different positions of a motor car and a trail car. The vibration modes of the key parts of the bogies of the two cars were calculated. Meanwhile, the track resonant frequencies were investigated at the site. The purpose of the above tests and analysis is try to find the frequency of work mode matching the passing frequency of the high-order wheel polygon. The present investigation shows that one of the working models causes the formation and development of the high-order wheel polygonal wear. The growth of this wear was effectively reduced through the frequent changing of the running speed of the train operating on the way back and forth every day.展开更多
The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order differ...The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme （WCNS-E-5） is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression comers at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris＇ and Shur＇s compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris＇ modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.展开更多
Abstract Based on the Reynolds-averaged Navier--Stokes （RANS） equations and structured grid technology, the calibration and validation of Y-Reo transition model is preformed with fifth-order weighted compact nonline...Abstract Based on the Reynolds-averaged Navier--Stokes （RANS） equations and structured grid technology, the calibration and validation of Y-Reo transition model is preformed with fifth-order weighted compact nonlinear scheme （WCNS）, and the purpose of the present work is to improve the numerical accuracy for aerodynamic characteristics simulation of low-speed flow with transition model on the basis of high-order numerical method study. Firstly, the empirical correlation functions involved in the Y-Reo transition model are modified and calibrated with experimental data of turbulent flat plates. Then, the grid convergence is studied on NLR-7301 two-element airfoil with the modified empirical correlation. At last, the modified empirical correlation is validated with NLR-7301 two-element airfoil and high-lift trapezoidal wing from transition location, velocity pro- file in boundary layer, surface pressure coefficient and aerodynamic characteristics. The numerical results illustrate that the numerical accuracy of transition length and skin friction behind transition location are improved with modified empirical correlation function, and obviously increases the numerical accuracy of aerodynamic characteristics prediction for typical transport configurations in low-speed range.展开更多
In this paper, iterative learning control （ILC） design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models （HOLM）. An HOlM formulated as...In this paper, iterative learning control （ILC） design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models （HOLM）. An HOlM formulated as a polynomial operator between consecutive iterations describes the changes of desired trajectories in the iteration domain and makes the iterative learning problem become iteration varying. The classical ILC for tracking iteration-invariant reference trajectories, on the other hand, is a special case of HOlM where the polynomial renders to a unity coefficient or a special first-order internal model. By inserting the HOlM into P-type ILC, the tracking performance along the iteration axis is investigated for a class of continuous-time nonlinear systems. Time-weighted norm method is utilized to guarantee validity of proposed algorithm in a sense of data-driven control.展开更多
A novel high-order sliding mode control strategy is proposed for the attitude control problem of reentry vehicles in the presence of parametric uncertainties and external disturbances, which results in the robust and ...A novel high-order sliding mode control strategy is proposed for the attitude control problem of reentry vehicles in the presence of parametric uncertainties and external disturbances, which results in the robust and accurate tracking of the aerodynamic angle commands with the finite time convergence. The proposed control strategy is developed on the basis of integral sliding mode philosophy, which combines conventional sliding mode control and a linear quadratic regulator over a finite time interval with a free-final-state and allows the finite-time establishment of a high-order sliding mode. Firstly, a second-order sliding mode attitude controller is designed in the proposed high-order siding mode control framework. Then, to address the control chattering problem, a virtual control is introduced in the control design and hence a third-order sliding mode attitude controller is developed, leading to the chattering reduction as well as the control accuracy improvement. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.展开更多
Linear and nonlinear evolutions of TS wave and high-order harmonic waves in boundary layers are studied based on the parabolic stability equation （PSE）. Initial conditions are derived by the local method with the La...Linear and nonlinear evolutions of TS wave and high-order harmonic waves in boundary layers are studied based on the parabolic stability equation （PSE）. Initial conditions are derived by the local method with the Landau expansion. The evolution process and characteristics of the disturbance amplitude and the velocity profile, etc. , especially stronger nonlinear effects, are computed by an efficient numerical method. Effects and regulations of different initial amplitudes, frequencies and pressure gradients on the evolution of disturbances are explored, which are directly relative to the stability and the transition in boundary layers. Simulation results are in good agreement with the data of the accuracy direct numerical simulation （DNS） using full Navier-Stokes equations.展开更多
基金National Natural Science Foundation of China(Nos.21971090 and 22271123)the NSF of Jiangsu Province(No.BK20230201)+1 种基金the Natural Science Foundation of Jiangsu Education Committee(No.22KJB150024)the Natural Science Foundation of Jiangsu Normal University(No.21XSRX010)。
文摘A new oxidative N-heterocyclic carbene(NHC)-catalyzed high-order[7+3]annulation reaction ofγ-indolyl phenols as 1,7-dinucleophiles andα,β-alkynals with the aid of Sc(OTf)_(3)is reported,enabling the highly regioselective access to unprecedented polyarene-fused ten-membered lactams bearing a bridged aryl-aryl-indole scaffold in moderate to good yields.This protocol demonstrates a broad substrate scope,good compatibility with substituents and complete regioselectivity,providing an organocatalytic modular synthetic strategy for creating medium-sized lactams.
基金supported by the National Natural Science Foundation of China under Grant No.12072090.
文摘The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.
基金Project supported by the Natural Science Foundation of Jilin Province of China(Grant No.20230101014JC)the National Natural Science Foundation of China(Grant No.12374265)。
文摘We investigate theoretically the effects of chirped laser pulses on high-order harmonic generation(HHG)from solids.We find that the harmonic spectra display redshifts for the driving laser pulses with negative chirp and blueshifts for those with positive chirp,which is due to the change in the instantaneous frequency of the driving laser for different chirped pulses.The analysis of crystal-momentum-resolved(k-resolved)HHG reveals that the frequency shifts are equal for the harmonics generated by different crystal momentum channels.The frequency shifts in the cutoff region are larger than those in the plateau region.With the increase of the absolute value of the chirp parameters,the frequency shifts of HHG become more significant,leading to the shifts from odd-to even-order harmonics.We also demonstrate that the frequency shifts of harmonic spectra are related to the duration of the chirped laser field,but are insensitive to the laser intensity and dephasing time.
基金Project supported by the National Natural Science Foundation of China(Grant No.62125402).
文摘Thermal expansion is crucial for various industrial processes and is increasingly the focus of research endeavors aimed at improving material performance.However,it is the continuous advancements in first-principles calculations that have enabled researchers to understand the microscopic origins of thermal expansion.In this study,we propose a coefficient of thermal expansion(CTE)calculation scheme based on self-consistent phonon theory,incorporating the fourth-order anharmonicity.We selected four structures(Si,CaZrF_(6),SrTiO_(3),NaBr)to investigate high-order anharmonicity’s impact on their CTEs,based on bonding types.The results indicate that our method goes beyond the second-order quasi-harmonic approximation and the third-order perturbation theory,aligning closely with experimental data.Furthermore,we observed that an increase in the ionicity of the structures leads to a more pronounced influence of high-order anharmonicity on CTE,with this effect primarily manifesting in variations of the Grüneisen parameter.Our research provides a theoretical foundation for accurately predicting and regulating the thermal expansion behavior of materials.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12001210 and 12261103)the Natural Science Foundation of Henan(Grant No.252300420308)the Yunnan Fundamental Research Projects(Grant No.202301AT070117).
文摘An efficient and accurate scalar auxiliary variable(SAV)scheme for numerically solving nonlinear parabolic integro-differential equation(PIDE)is developed in this paper.The original equation is first transformed into an equivalent system,and the k-order backward differentiation formula(BDF k)and central difference formula are used to discretize the temporal and spatial derivatives,respectively.Different from the traditional discrete method that adopts full implicit or full explicit for the nonlinear integral terms,the proposed scheme is based on the SAV idea and can be treated semi-implicitly,taking into account both accuracy and effectiveness.Numerical results are presented to demonstrate the high-order convergence(up to fourth-order)of the developed schemes and it is computationally efficient in long-time computations.
基金co-supported by the Aeronautical Science Foundation of China(Nos.2018ZA52002,2019ZA052011).
文摘With the availability of high-performance computing technology and the development of advanced numerical simulation methods, Computational Fluid Dynamics (CFD) is becoming more and more practical and efficient in engineering. As one of the high-precision representative algorithms, the high-order Discontinuous Galerkin Method (DGM) has not only attracted widespread attention from scholars in the CFD research community, but also received strong development. However, when DGM is extended to high-speed aerodynamic flow field calculations, non-physical numerical Gibbs oscillations near shock waves often significantly affect the numerical accuracy and even cause calculation failure. Data driven approaches based on machine learning techniques can be used to learn the characteristics of Gibbs noise, which motivates us to use it in high-speed DG applications. To achieve this goal, labeled data need to be generated in order to train the machine learning models. This paper proposes a new method for denoising modeling of Gibbs phenomenon using a machine learning technique, the zero-shot learning strategy, to eliminate acquiring large amounts of CFD data. The model adopts a graph convolutional network combined with graph attention mechanism to learn the denoising paradigm from synthetic Gibbs noise data and generalize to DGM numerical simulation data. Numerical simulation results show that the Gibbs denoising model proposed in this paper can suppress the numerical oscillation near shock waves in the high-order DGM. Our work automates the extension of DGM to high-speed aerodynamic flow field calculations with higher generalization and lower cost.
基金supported by the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi。
文摘We present a comprehensive study on the role of various excited states in high-order harmonic generation of hydrogen atoms driven by a long-wavelength(1500 nm)laser field.By numerically solving the time-dependent Schrodinger equation(TDSE)and performing a time-frequency analysis,we investigate the influence of individual excited states on the harmonic spectrum.Our results reveal that the 2s excited state primarily contributes to the enhancement of high-energy harmonic yields by facilitating long electron trajectories,while the 2p excited state predominantly suppresses harmonic yields in the lower-energy region(20th-50th orders)by altering the contributions of electron trajectories.Our results highlight the critical role of the excited states in the HHG process,even at longer laser wavelengths.
基金supported by the National Natural Science Foundation of China(No.12002290)。
文摘In the field of discretization-based meshfree/meshless methods,the improvements in the higher-order consistency,stability,and computational efficiency are of great concerns in computational science and numerical solutions to partial differential equations.Various alternative numerical methods of the finite particle method(FPM)frame have been extended from mathematical theories to numerical applications separately.As a comprehensive numerical scheme,this study suggests a unified resolved program for numerically investigating their accuracy,stability,consistency,computational efficiency,and practical applicability in industrial engineering contexts.The high-order finite particle method(HFPM)and corrected methods based on the multivariate Taylor series expansion are constructed and analyzed to investigate the whole applicability in different benchmarks of computational fluid dynamics.Specifically,four benchmarks are designed purposefully from statical exact solutions to multifaceted hydrodynamic tests,which possess different numerical performances on the particle consistency,numerical discretized forms,particle distributions,and transient time evolutional stabilities.This study offers a numerical reference for the current unified resolved program.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12204214)the National Key Research and Development Program of China (Grant No. 2022YFE0134200)+1 种基金the Fundamental Research Funds for the Central Universities (Grant No. GK202207012), QCYRCXM-2022-241the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2025A1515011117)。
文摘We performed real-time and real-space numerical simulations of high-order harmonic generation in the threedimensional structured molecule methane(CH_(4)) using time-dependent density functional theory. By irradiating the methane molecule with an elliptically polarized laser pulse polarized in the x–y plane, we observed significant even-order harmonic emission in the z-direction. By analyzing the electron dynamics in the electric field and the multi-orbital effects of the molecule, we revealed that electron recombination near specific atoms in methane is the primary source of highorder harmonic generation in the z-direction. Furthermore, we identified the dominant molecular orbitals responsible for the enhancement of harmonics in this direction and demonstrated the critical role played by multi-orbital effects in this process.
基金supported by the National Natural Science Foundation of China(Nos.11172050,11372051,and 11001027)
文摘A high-order Lagrangian cell-centered conservative gas dynamics scheme is presented on unstructured meshes. A high-order piecewise pressure of the cell is intro- duced. With the high-order piecewise pressure of the cell, the high-order spatial discretiza- tion fluxes are constructed. The time discretization of the spatial fluxes is performed by means of the Taylor expansions of the spatial discretization fluxes. The vertex velocities are evaluated in a consistent manner due to an original solver located at the nodes by means of momentum conservation. Many numerical tests are presented to demonstrate the robustness and the accuracy of the scheme.
基金supported by the National Natural Science Foundation of China (Grant No. 60978002)the National Fundamental Research Programme of China (Grant Nos. 2006CB921107 and 2010CB922904)
文摘High-order ghost imaging with thermal light consisting of N different frequencies is investigated. The high-order intensity correlation and intrinsic correlation functions are derived for such N-colour light. It is found that they are similar in form to those for the monochromatic case, thus most of the conclusions we obtained previously for monochromatic Nth-order ghost imaging are still applicable. However, we find that the visibility of the N-colour ghost image depends strongly on the wavelength used to illuminate the object, and increases as this wavelength increases when the test arm is fixed. On the contrary, changes of wavelength in the reference arms do not lead to any change of the visibility.
基金supported by the National Natural Science Foundation of China(NSFC)(Grant No. 41074100)the Program for New Century Excellent Talents in University of Ministry of Education of China(Grant No. NCET-10-0812)
文摘In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.
文摘In this paper, we consider the Cauchy numbers and polynomials of order k and give some relation between Cauchy polynomials of order k and special polynomials by using generating functions and the Riordan matrix methods. In addition, we establish some new equalities and relations involving high-order Cauchy numbers and polynomials, high-order Daehee numbers and polynomials, the generalized Bell polynomials, the Bernoulli numbers and polynomials, high-order Changhee polynomials, high-order Changhee-Genocchi polynomials, the combinatorial numbers, Lah numbers and Stirling numbers, etc.
文摘The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.
基金Project supported by the National Natural Science Foundation of China （No. U 1134202）
文摘This paper presents a detailed investigation, via field experiment, into the mechanism of high-order polygonal wear of wheels of a new type of high-speed train. The investigation was carried out during the performance acceptance test of the train and its initial commercial operation. The investigation covered the performance acceptance test of 150 000 km and the commercial operation of about 150 000 km. In the performance acceptance test of the first stage of about 70 000 km, at 200-250 km/h with full loading and sometimes overloading by 30%, the serious polygonal wear of 23-order took place on all the wheels of the train, and was measured and analyzed in detail. All the potygonized wheels were re-profiled because the polygonal wear had caused strong vibration and damage to the train parts. After re-profiling, the vibration of the train and track and the wear status of the wheels were measured and analyzed at different test mileages according to the polygonal wear situation of the wheels. The measured vibration of the train includes the accelerations at different positions of a motor car and a trail car. The vibration modes of the key parts of the bogies of the two cars were calculated. Meanwhile, the track resonant frequencies were investigated at the site. The purpose of the above tests and analysis is try to find the frequency of work mode matching the passing frequency of the high-order wheel polygon. The present investigation shows that one of the working models causes the formation and development of the high-order wheel polygonal wear. The growth of this wear was effectively reduced through the frequent changing of the running speed of the train operating on the way back and forth every day.
基金Foundation items： National Basic Research Program of China （2009CB723801） National Natural Science Foundation of China （11072259）
文摘The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme （WCNS-E-5） is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression comers at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris＇ and Shur＇s compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris＇ modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.
基金supported by the National Basic Research Program of China(No.2014CB744803)
文摘Abstract Based on the Reynolds-averaged Navier--Stokes （RANS） equations and structured grid technology, the calibration and validation of Y-Reo transition model is preformed with fifth-order weighted compact nonlinear scheme （WCNS）, and the purpose of the present work is to improve the numerical accuracy for aerodynamic characteristics simulation of low-speed flow with transition model on the basis of high-order numerical method study. Firstly, the empirical correlation functions involved in the Y-Reo transition model are modified and calibrated with experimental data of turbulent flat plates. Then, the grid convergence is studied on NLR-7301 two-element airfoil with the modified empirical correlation. At last, the modified empirical correlation is validated with NLR-7301 two-element airfoil and high-lift trapezoidal wing from transition location, velocity pro- file in boundary layer, surface pressure coefficient and aerodynamic characteristics. The numerical results illustrate that the numerical accuracy of transition length and skin friction behind transition location are improved with modified empirical correlation function, and obviously increases the numerical accuracy of aerodynamic characteristics prediction for typical transport configurations in low-speed range.
基金supported by the General Program (No.60774022)the State Key Program of National Natural Science Foundation of China(No.60834001)the State Key Laboratory of Rail Traffic Control and Safety,Beijing Jiaotong University (No.RCS2009ZT011)
文摘In this paper, iterative learning control （ILC） design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models （HOLM）. An HOlM formulated as a polynomial operator between consecutive iterations describes the changes of desired trajectories in the iteration domain and makes the iterative learning problem become iteration varying. The classical ILC for tracking iteration-invariant reference trajectories, on the other hand, is a special case of HOlM where the polynomial renders to a unity coefficient or a special first-order internal model. By inserting the HOlM into P-type ILC, the tracking performance along the iteration axis is investigated for a class of continuous-time nonlinear systems. Time-weighted norm method is utilized to guarantee validity of proposed algorithm in a sense of data-driven control.
基金supported by Major State Basic Research Development Program(2012CB720000)National Natural Science Foundation of China(11372034)Innovative Research Team of Beijing Institute of Technology
文摘A novel high-order sliding mode control strategy is proposed for the attitude control problem of reentry vehicles in the presence of parametric uncertainties and external disturbances, which results in the robust and accurate tracking of the aerodynamic angle commands with the finite time convergence. The proposed control strategy is developed on the basis of integral sliding mode philosophy, which combines conventional sliding mode control and a linear quadratic regulator over a finite time interval with a free-final-state and allows the finite-time establishment of a high-order sliding mode. Firstly, a second-order sliding mode attitude controller is designed in the proposed high-order siding mode control framework. Then, to address the control chattering problem, a virtual control is introduced in the control design and hence a third-order sliding mode attitude controller is developed, leading to the chattering reduction as well as the control accuracy improvement. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.
文摘Linear and nonlinear evolutions of TS wave and high-order harmonic waves in boundary layers are studied based on the parabolic stability equation （PSE）. Initial conditions are derived by the local method with the Landau expansion. The evolution process and characteristics of the disturbance amplitude and the velocity profile, etc. , especially stronger nonlinear effects, are computed by an efficient numerical method. Effects and regulations of different initial amplitudes, frequencies and pressure gradients on the evolution of disturbances are explored, which are directly relative to the stability and the transition in boundary layers. Simulation results are in good agreement with the data of the accuracy direct numerical simulation （DNS） using full Navier-Stokes equations.
