The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and...The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.展开更多
A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order pro...A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order problems ( 1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O (hm+1) accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O (hm+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given.展开更多
We theoretically investigate the high-order harmonic generation(HHG)of defect-free solids by solving the timedependent Schr¨odinger equation(TDSE).The results show that the harmonic intensity can be enhanced,harm...We theoretically investigate the high-order harmonic generation(HHG)of defect-free solids by solving the timedependent Schr¨odinger equation(TDSE).The results show that the harmonic intensity can be enhanced,harmonic order can be extended,and modulation near the cutoff order becomes smaller for the second plateau by increasing the time delay.These effects are due to an increase of the electron population in higher energy bands,where the larger band gap allows electrons to release more energy,and the long electronic paths are suppressed.Additionally,we also investigate the HHG of defective solids by Bohmian trajectories(BT).It is found that the harmonic intensity of the second plateau can be further enhanced.Simultaneously,cutoff order is also extended due to Bohmian particles moving farther away from the defective zone.展开更多
We provide the breakdown mechanism of pressureless gases when the initial vor-ticity is zero.In other words,the maximum norm of the divergence and Ilull control the breakdown of the solution.Then we show that the solu...We provide the breakdown mechanism of pressureless gases when the initial vor-ticity is zero.In other words,the maximum norm of the divergence and Ilull control the breakdown of the solution.Then we show that the solution must blow up for certain initial data in both non-relativistic and relativistic settings.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
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
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
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
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
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
In thispaper,theexistence oftravelling frontsolution fora classofcom petition-diffu- sion system w ith high-order singular point w it = diw ixx - w αii fi(w ),x ∈R,t> 0,i= 1,2 (Ⅰ) is studied,w here di,αi>...In thispaper,theexistence oftravelling frontsolution fora classofcom petition-diffu- sion system w ith high-order singular point w it = diw ixx - w αii fi(w ),x ∈R,t> 0,i= 1,2 (Ⅰ) is studied,w here di,αi> 0 (i= 1,2) and w = (w 1(x,t),w 2(x,t)).Under the certain assum ptions on f,itis show ed thatifαi< 1 for som e i,then (Ⅰ) has no travelling frontsolution,ifαi≥1 for i= 1,2,then there isa c0,c:c0≥c> 0,w herecis called the m inim alwavespeed of(Ⅰ),such thatifc≥c0 orc= c,then (Ⅰ) has a travelling frontsolution,ifc< c,then (Ⅰ) hasno travel- ling frontsolution by using the shooting m ethod in com bination w ith a com pactness argum ent.展开更多
Continental crust is the long-term achievements of Earth's evolution across billions of years.The continental rocks could have been modified by various types of geological processes,such as metamorphism,weathering...Continental crust is the long-term achievements of Earth's evolution across billions of years.The continental rocks could have been modified by various types of geological processes,such as metamorphism,weathering,and reworking.Therefore,physical or chemical properties of rocks through time record the composite effects of geological,biological,hydrological,and climatological processes.Temporal variations in these time series datasets could provide important clues for understanding the co-evolution of different layers on Earth.However,deciphering Earth's evolution in deep time is challenged by incompleteness,singularity,and intermittence of geological records associated with extreme geological events,hindering a rigorous assessment of the underlying coupling mechanisms.Here,we applied the recently developed local singularity analysis and wavelet analysis method to deep-time U-Pb age spectra and sedimentary abundance record across the past 3.5 Gyrs.Standard cross-correlation analysis suggests that the singularity records of marine sediment accumulations and magmatism intensity at continental margin are correlated negatively(R^(2)=0.8),with a delay of~100 Myr.Specifically,wavelet coherence analysis suggests a~500-800 Myr cycle of correlation between two records,implying a coupling between the major downward processes(subduction and recycling sediments)and upward processes(magmatic events)related to the aggregation and segregation of supercontinents.The results clearly reveal the long-term cyclic feedback mechanism between sediment accumulation and magmatism intensity through aggregation of supercontinents.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
In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρ...In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.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 present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is intro...We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is introduced through the source location.The potentials for Green＇s function are derived by decomposing the partial wave solutions to Helmholtz＇s equations into upward and downward within boundaries.The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level.The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface.Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters,whereas the kernel connected with the stratified media stays unchanged.Hence,the present method can be easily applied to EM transmitting sources with little modification.The application of the proposed method to the marine controlled-source electromagnetic method（MCSEM） demonstrates its simplicity and flexibility.展开更多
Most of the current computing methods used to determine the magnetic field of a uniformly magnetized cuboid assume that the observation point is located in the upper half space without a source. However, such methods ...Most of the current computing methods used to determine the magnetic field of a uniformly magnetized cuboid assume that the observation point is located in the upper half space without a source. However, such methods may generate analytical singularities for conditions of undulating terrain. Based on basic geomagnetic field theories, in this study an improved magnetic field expression is derived using an integration method of variable substitution, and all singularity problems for the entire space without a source are discussed and solved. This integration process is simpler than that of previous methods, and final integral results with a more uniform form. AT at all points in the source-flee space can be calculated without requiring coordinate transformation; thus forward modeling is also simplified. Corresponding model tests indicate that the new magnetic field expression is more correct because there is no analytical singularity and can be used with undulating terrain.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
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
基金supported by the Guangdong Province Introduced Innovative R&D Team of Big Data-Mathematical Earth Sciences and Extreme Geological Events Team(grant number 2021ZT09H399)the National Natural Science Foundation of China(grant number 42430111,42050103).
文摘The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.
文摘A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order problems ( 1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O (hm+1) accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O (hm+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given.
基金supported by the Natural Science Foundation of Jilin Province of China(Grant No.20230101014JC)the Fundamental Research Funds for the Central Universities(Grant No.2572021BC05)the National Natural Science Foundation of China(Grant No.12374265)。
文摘We theoretically investigate the high-order harmonic generation(HHG)of defect-free solids by solving the timedependent Schr¨odinger equation(TDSE).The results show that the harmonic intensity can be enhanced,harmonic order can be extended,and modulation near the cutoff order becomes smaller for the second plateau by increasing the time delay.These effects are due to an increase of the electron population in higher energy bands,where the larger band gap allows electrons to release more energy,and the long electronic paths are suppressed.Additionally,we also investigate the HHG of defective solids by Bohmian trajectories(BT).It is found that the harmonic intensity of the second plateau can be further enhanced.Simultaneously,cutoff order is also extended due to Bohmian particles moving farther away from the defective zone.
基金supported by the National Key R&D Program of China(2021YFA1001700)the NSFC(12071360)the Fundamental Research Funds for the Central Universities in China.
文摘We provide the breakdown mechanism of pressureless gases when the initial vor-ticity is zero.In other words,the maximum norm of the divergence and Ilull control the breakdown of the solution.Then we show that the solution must blow up for certain initial data in both non-relativistic and relativistic settings.
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 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.
文摘In thispaper,theexistence oftravelling frontsolution fora classofcom petition-diffu- sion system w ith high-order singular point w it = diw ixx - w αii fi(w ),x ∈R,t> 0,i= 1,2 (Ⅰ) is studied,w here di,αi> 0 (i= 1,2) and w = (w 1(x,t),w 2(x,t)).Under the certain assum ptions on f,itis show ed thatifαi< 1 for som e i,then (Ⅰ) has no travelling frontsolution,ifαi≥1 for i= 1,2,then there isa c0,c:c0≥c> 0,w herecis called the m inim alwavespeed of(Ⅰ),such thatifc≥c0 orc= c,then (Ⅰ) has a travelling frontsolution,ifc< c,then (Ⅰ) hasno travel- ling frontsolution by using the shooting m ethod in com bination w ith a com pactness argum ent.
基金supported by the National Natural Science Foundation of China(No.42050103)。
文摘Continental crust is the long-term achievements of Earth's evolution across billions of years.The continental rocks could have been modified by various types of geological processes,such as metamorphism,weathering,and reworking.Therefore,physical or chemical properties of rocks through time record the composite effects of geological,biological,hydrological,and climatological processes.Temporal variations in these time series datasets could provide important clues for understanding the co-evolution of different layers on Earth.However,deciphering Earth's evolution in deep time is challenged by incompleteness,singularity,and intermittence of geological records associated with extreme geological events,hindering a rigorous assessment of the underlying coupling mechanisms.Here,we applied the recently developed local singularity analysis and wavelet analysis method to deep-time U-Pb age spectra and sedimentary abundance record across the past 3.5 Gyrs.Standard cross-correlation analysis suggests that the singularity records of marine sediment accumulations and magmatism intensity at continental margin are correlated negatively(R^(2)=0.8),with a delay of~100 Myr.Specifically,wavelet coherence analysis suggests a~500-800 Myr cycle of correlation between two records,implying a coupling between the major downward processes(subduction and recycling sediments)and upward processes(magmatic events)related to the aggregation and segregation of supercontinents.The results clearly reveal the long-term cyclic feedback mechanism between sediment accumulation and magmatism intensity through aggregation of supercontinents.
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 Technological Innovation Talents in Universities and Colleges in Henan Province(No.21HASTIT025)the Natural Science Foundation of Henan Province(No.222300420449)the Innovative Research Team of Henan Polytechnic University(No.T2022-7)。
文摘In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.
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supported by CNSF(Granted No.40874050)Chinese High Technology Project(Granted No.2011YQ05006010)
文摘We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is introduced through the source location.The potentials for Green＇s function are derived by decomposing the partial wave solutions to Helmholtz＇s equations into upward and downward within boundaries.The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level.The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface.Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters,whereas the kernel connected with the stratified media stays unchanged.Hence,the present method can be easily applied to EM transmitting sources with little modification.The application of the proposed method to the marine controlled-source electromagnetic method（MCSEM） demonstrates its simplicity and flexibility.
基金supported by China Geological Survey Northeastern Tarim Aeromagnetic and Aerogravity comprehensive survey project(No.12120115039401)
文摘Most of the current computing methods used to determine the magnetic field of a uniformly magnetized cuboid assume that the observation point is located in the upper half space without a source. However, such methods may generate analytical singularities for conditions of undulating terrain. Based on basic geomagnetic field theories, in this study an improved magnetic field expression is derived using an integration method of variable substitution, and all singularity problems for the entire space without a source are discussed and solved. This integration process is simpler than that of previous methods, and final integral results with a more uniform form. AT at all points in the source-flee space can be calculated without requiring coordinate transformation; thus forward modeling is also simplified. Corresponding model tests indicate that the new magnetic field expression is more correct because there is no analytical singularity and can be used with undulating terrain.
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.
