In this paper, we use a univariate multiquadric quasi-interpolation scheme to solve the one-dimensional nonlinear sine-Gordon equation that is related to many physical phenomena. We obtain a numerical scheme by using ...In this paper, we use a univariate multiquadric quasi-interpolation scheme to solve the one-dimensional nonlinear sine-Gordon equation that is related to many physical phenomena. We obtain a numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative and a difference scheme to approximate the temporal derivative. The advantage of the obtained scheme is that the algorithm is very simple so that it is very easy to implement. The results of numerical experiments are presented and compared with analytical solutions to confirm the good accuracy of the presented scheme.展开更多
A radiative heat transfer mathematical model for a one-dimensional long furnace was set up in a through-type roller-hearth furnace （TTRHF） in compact strip production （CSP）. To accurately predict the heat exchange...A radiative heat transfer mathematical model for a one-dimensional long furnace was set up in a through-type roller-hearth furnace （TTRHF） in compact strip production （CSP）. To accurately predict the heat exchange in the furnace, modeling of the complex gas energy-balance equation in volume zones was considered, and the heat transfer model of heating slabs and wall lines was coupled with the radiative heat transfer model to identify the surface zonal temperature. With numerical simulation, the temperature fields of gas, slabs, and wall lines in the furnace under one typical working condition were carefully accounted and analyzed. The fundamental theory for analyzing the thermal process in TI＇RI-IF was provided.展开更多
The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear probl...The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.展开更多
One dimensional traffic model was studied with the consideration of stochastic deceleration by using the lattice Boltzmann method. The evolution equation for vehicle density was derived, which has the form of the Bu...One dimensional traffic model was studied with the consideration of stochastic deceleration by using the lattice Boltzmann method. The evolution equation for vehicle density was derived, which has the form of the Burgers equation exhibiting the effect of viscosity corresponding to the deceleration. The simulation with the model shows that the variation of vehicle density in space tends to a periodic one, which implies the existence of kinematic waves in the 1D traffic flow and coincides with theoretical prediction.展开更多
In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian co...In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.展开更多
Singular initial value problems arise in solving one-dimensional steady transonic flow of dualmode scramjet. The existing solution method has the problems of large initial value errors in principles. This paper puts f...Singular initial value problems arise in solving one-dimensional steady transonic flow of dualmode scramjet. The existing solution method has the problems of large initial value errors in principles. This paper puts forward an improved algorithm based on variable transformation, and constructs a nonsingular one-dimensional steady transonic flow equation by defining a new variable. The improved algorithm can eliminate the singularity of the differential equation, and can solve the singular initial value problems of one-dimensional steady transonic flow of dual-mode scramjet.展开更多
In sub nanometer carbon nanotubes,water exhibits unique dynamic characteristics,and in the high-frequency region of the infrared spectrum,where the stretching vibrations of the internal oxygen-hydrogen(O-H)bonds are c...In sub nanometer carbon nanotubes,water exhibits unique dynamic characteristics,and in the high-frequency region of the infrared spectrum,where the stretching vibrations of the internal oxygen-hydrogen(O-H)bonds are closely related to the hydrogen bonds(H-bonds)network between water molecules.Therefore,it is crucial to analyze the relationship between these two aspects.In this paper,the infrared spectrum and motion characteristics of the stretching vibrations of the O-H bonds in one-dimensional confined water(1DCW)and bulk water(BW)in(6,6)single-walled carbon nanotubes(SWNT)are studied by molecular dynamics simulations.The results show that the stretching vibrations of the two O-H bonds in 1DCW exhibit different frequencies in the infrared spectrum,while the O-H bonds in BW display two identical main frequency peaks.Further analysis using the spring oscillator model reveals that the difference in the stretching amplitude of the O-H bonds is the main factor causing the change in vibration frequency,where an increase in stretching amplitude leads to a decrease in spring stiffness and,consequently,a lower vibration frequency.A more in-depth study found that the interaction of H-bonds between water molecules is the fundamental cause of the increased stretching amplitude and decreased vibration frequency of the O-H bonds.Finally,by analyzing the motion trajectory of the H atoms,the dynamic differences between 1DCW and BW are clearly revealed.These findings provide a new perspective for understanding the behavior of water molecules at the nanoscale and are of significant importance in advancing the development of infrared spectroscopy detection technology.展开更多
Based on the newly-developed element energy projection （EEP） method for computation of super-convergent results in one-dimensional finite element method （FEM）, the task of self-adaptive FEM analysis was converted ...Based on the newly-developed element energy projection （EEP） method for computation of super-convergent results in one-dimensional finite element method （FEM）, the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.展开更多
Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite ele...Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.展开更多
In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discreti...In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.展开更多
Two-dimensional(2D)transition metal sulfides(TMDs)are emerging and highly well received 2D materials,which are considered as an ideal 2D platform for studying various electronic properties and potential applications d...Two-dimensional(2D)transition metal sulfides(TMDs)are emerging and highly well received 2D materials,which are considered as an ideal 2D platform for studying various electronic properties and potential applications due to their chemical diversity.Converting 2D TMDs into one-dimensional(1D)TMDs nanotubes can not only retain some advantages of 2D nanosheets but also providing a unique direction to explore the novel properties of TMDs materials in the 1D limit.However,the controllable preparation of high-quality nanotubes remains a major challenge.It is very necessary to review the advanced development of one-dimensional transition metal dichalcogenide nanotubes from preparation to application.Here,we first summarize a series of bottom-up synthesis methods of 1D TMDs,such as template growth and metal catalyzed method.Then,top-down synthesis methods are summarized,which included selfcuring and stacking of TMDs nanosheets.In addition,we discuss some key applications that utilize the properties of 1D-TMDs nanotubes in the areas of catalyst preparation,energy storage,and electronic devices.Last but not least,we prospect the preparation methods of high-quality 1D-TMDs nanotubes,which will lay a foundation for the synthesis of high-performance optoelectronic devices,catalysts,and energy storage components.展开更多
A simple direct space-time meshless scheme,based on the radial or non-radial basis function,is proposed for the onedimensional Klein-Gordon equations.Since these equations are time-dependent,it is worthwhile to presen...A simple direct space-time meshless scheme,based on the radial or non-radial basis function,is proposed for the onedimensional Klein-Gordon equations.Since these equations are time-dependent,it is worthwhile to present two schemes for the basis functions from radial and non-radial aspects.The first scheme is fulfilled by considering time variable as normal space variable,to construct an"isotropic"space-time radial basis function.The other scheme considered a realistic relationship between space variable and time variable which is not radial.The timedependent variable is treated regularly during the whole solution process and the Klein-Gordon equations can be solved in a direct way.Numerical results show that the proposed meshless schemes are simple,accurate,stable,easy-to-program and efficient for the Klein-Gordon equations.展开更多
Recently many research works have been conducted and published regarding fractional order differential equations. There are several approaches available for numerical approximations of the solution of fractional order...Recently many research works have been conducted and published regarding fractional order differential equations. There are several approaches available for numerical approximations of the solution of fractional order diffusion equations. Spectral collocation method based on Lagrange’s basis polynomials to approximate numerical solutions of one-dimensional (1D) space fractional diffusion equations are introduced in this research paper. The proposed form of approximate solution satisfies non-zero Dirichlet’s boundary conditions on both boundaries. Collocation scheme produce a system of first order Ordinary Differential Equations (ODE) from the fractional diffusion equation. We applied this method with four different sets of collocation points to compare their performance.展开更多
We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model(n≥2)by using the cluster variation method with linear response theory.The results of this method...We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model(n≥2)by using the cluster variation method with linear response theory.The results of this method are exact in the thermodynamic limit.We present the single-site reduced densityρ^((1))(z),averages such as(z^(2)),<|z^(n)|>,and<(z_(1)-z_(2))^(2)>,the specific heat C_(v),and the static correlation functions.We analyze the scaling behavior of these quantities and obtain the exact scaling powers at the low and high temperatures.Using these results,we gauge the accuracy of the projective truncation approximation for theφ^(4)lattice model.展开更多
An efficient conformal locally one-dimensional finite-difference time-domain（LOD-CFDTD） method is presented for solving two-dimensional（2D） electromagnetic（EM） scattering problems. The formulation for the 2D tra...An efficient conformal locally one-dimensional finite-difference time-domain（LOD-CFDTD） method is presented for solving two-dimensional（2D） electromagnetic（EM） scattering problems. The formulation for the 2D transverse-electric（TE） case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit（ADI） CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field（TF/SF） boundary and the perfectly matched layer（PML）, the radar cross section（RCS） of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.展开更多
In this paper, on the basis of the heat conduction equation without consideration of the advection and turbulence effects, one-dimensional model for describing surface sea temperature ( T1), bottom sea temperature ( T...In this paper, on the basis of the heat conduction equation without consideration of the advection and turbulence effects, one-dimensional model for describing surface sea temperature ( T1), bottom sea temperature ( Tt ) and the thickness of the upper homogeneous layer ( h ) is developed in terms of the dimensionless temperature θT and depth η and self-simulation function θT - f(η) of vertical temperature profile by means of historical temperature data.The results of trial prediction with our one-dimensional model on T, Th, h , the thickness and gradient of thermocline are satisfactory to some extent.展开更多
Using the Bose-Fermi mapping method,we obtain the exact ground state wavefunction of one-dimensional(1D)Bose gas with the zero-range dipolar interaction in the strongly repulsive contact interaction limit.Its ground s...Using the Bose-Fermi mapping method,we obtain the exact ground state wavefunction of one-dimensional(1D)Bose gas with the zero-range dipolar interaction in the strongly repulsive contact interaction limit.Its ground state density distributions for both repulsive and attractive dipole interactions are exhibited.It is shown that in the case of the finite dipole interaction the density profiles do not change obviously with the increase of dipole interaction and display the typical shell structure of Tonks-Girardeau gases.As the repulsive dipole interaction is greatly strong,the density decreases at the center of the trap and displays a sunken valley.As the attractive dipole interaction increases,the density displays more oscillations and sharp peaks appear in the strong attraction limit,which mainly originate from the atoms occupying the low single particle levels.展开更多
Adjustable or programmable metamaterials offer versatile functions,while the complex multi-dimensional regulation increases workload,and hinders their applications in practical scenarios.To address these challenges,we...Adjustable or programmable metamaterials offer versatile functions,while the complex multi-dimensional regulation increases workload,and hinders their applications in practical scenarios.To address these challenges,we present a mechanically programmable acoustic metamaterial for real-time focal tuning via one-dimensional phase-gradient modulation in this paper.The device integrates a phase gradient structure with concave cavity channels and an x-shaped telescopic mechanical framework,enabling dynamic adjustment of inter-unit spacing(1 mm-3 mm)through a microcontroller-driven motor.By modulating the spacing between adjacent channels,the phase gradient is precisely controlled,allowing continuous focal shift from 50 mm to 300 mm along the x-axis at 7500 Hz.Broadband focusing is also discussed in the range6800 Hz-8100 Hz,with transmission coefficients exceeding 0.5,ensuring high efficiency and robust performance.Experimental results align closely with simulations,validating the design's effectiveness and adaptability.Unlike conventional programmable metamaterials requiring multi-dimensional parameter optimization,this approach simplifies real-time control through single-axis mechanical adjustment,significantly reducing operational complexity.Due to the advantages of broadband focusing,simple control mode,real-time monitoring,and so on,the device may have extensive applications in the fields of acoustic imaging,nondestructive testing,ultrasound medical treatment,etc.展开更多
In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al...In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.展开更多
The oxygen evolution reaction(OER),a critical half-reaction in water electrolysis,has garnered significant attention.However,sluggish OER kinetics has emerged as a major impediment to efficient electrochemical energy c...The oxygen evolution reaction(OER),a critical half-reaction in water electrolysis,has garnered significant attention.However,sluggish OER kinetics has emerged as a major impediment to efficient electrochemical energy conversion.There is an urgent need to design novel electrocatalysts with optimized OER kinetics and enhanced intrinsic activity to improve overall OER performance.Herein,one-dimensional(1D)nanocomposites with high electrocatalytic activity were developed through the deposition of CoFePBA nanocubes onto the surface of MnO_(2) nanowires.The electronic structure of the nanocomposite surface was modified,and the synergistic effects between transition metals were leveraged to enhance catalytic activity through the deposition of Prussian blue analog(PBA)nanocubes on manganese dioxide nanowires.Specifically,CoFePBA featured an open crystal structure that offiered numerous electrochemical active sites and efficient charge transfer pathways.Additionally,the synergistic interactions between Co and Fe significantly reduced the OER overpotential.Additionally,the 1D rigid MnO_(2) acted as protective armor,ensuring the stability of active sites within CoFePBA during the OER.The synthesized MnO_(2)@CoFePBA achieved an overpotential of 1.614 V at 10 mA/cm^(2) and a small Tafel slope of 94 mV/dec and demonstrated stable performance for over 200 h.This work offers new insights into the rational design of various PBA-based nanocomposites with high activity and stability.展开更多
基金supported by the State Key Development Program for Basic Research of China (Grant No 2006CB303102)Science and Technology Commission of Shanghai Municipality,China (Grant No 09DZ2272900)
文摘In this paper, we use a univariate multiquadric quasi-interpolation scheme to solve the one-dimensional nonlinear sine-Gordon equation that is related to many physical phenomena. We obtain a numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative and a difference scheme to approximate the temporal derivative. The advantage of the obtained scheme is that the algorithm is very simple so that it is very easy to implement. The results of numerical experiments are presented and compared with analytical solutions to confirm the good accuracy of the presented scheme.
文摘A radiative heat transfer mathematical model for a one-dimensional long furnace was set up in a through-type roller-hearth furnace （TTRHF） in compact strip production （CSP）. To accurately predict the heat exchange in the furnace, modeling of the complex gas energy-balance equation in volume zones was considered, and the heat transfer model of heating slabs and wall lines was coupled with the radiative heat transfer model to identify the surface zonal temperature. With numerical simulation, the temperature fields of gas, slabs, and wall lines in the furnace under one typical working condition were carefully accounted and analyzed. The fundamental theory for analyzing the thermal process in TI＇RI-IF was provided.
基金supported by the National Natural Science Foundation of China(Nos.51378293,51078199,50678093,and 50278046)the Program for Changjiang Scholars and the Innovative Research Team in University of China(No.IRT00736)
文摘The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.
文摘One dimensional traffic model was studied with the consideration of stochastic deceleration by using the lattice Boltzmann method. The evolution equation for vehicle density was derived, which has the form of the Burgers equation exhibiting the effect of viscosity corresponding to the deceleration. The simulation with the model shows that the variation of vehicle density in space tends to a periodic one, which implies the existence of kinematic waves in the 1D traffic flow and coincides with theoretical prediction.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035 and 11171038)the Science Research Foundation of the Institute of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2012MS0102)
文摘In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.
基金Hi TechResearchandDevelopmentProgramofChina(2002AA723011),OutstandingYouthFoundationofHeilongjiang Province
文摘Singular initial value problems arise in solving one-dimensional steady transonic flow of dualmode scramjet. The existing solution method has the problems of large initial value errors in principles. This paper puts forward an improved algorithm based on variable transformation, and constructs a nonsingular one-dimensional steady transonic flow equation by defining a new variable. The improved algorithm can eliminate the singularity of the differential equation, and can solve the singular initial value problems of one-dimensional steady transonic flow of dual-mode scramjet.
基金Supported by the Natural Science Foundation of China(51705326,52075339)。
文摘In sub nanometer carbon nanotubes,water exhibits unique dynamic characteristics,and in the high-frequency region of the infrared spectrum,where the stretching vibrations of the internal oxygen-hydrogen(O-H)bonds are closely related to the hydrogen bonds(H-bonds)network between water molecules.Therefore,it is crucial to analyze the relationship between these two aspects.In this paper,the infrared spectrum and motion characteristics of the stretching vibrations of the O-H bonds in one-dimensional confined water(1DCW)and bulk water(BW)in(6,6)single-walled carbon nanotubes(SWNT)are studied by molecular dynamics simulations.The results show that the stretching vibrations of the two O-H bonds in 1DCW exhibit different frequencies in the infrared spectrum,while the O-H bonds in BW display two identical main frequency peaks.Further analysis using the spring oscillator model reveals that the difference in the stretching amplitude of the O-H bonds is the main factor causing the change in vibration frequency,where an increase in stretching amplitude leads to a decrease in spring stiffness and,consequently,a lower vibration frequency.A more in-depth study found that the interaction of H-bonds between water molecules is the fundamental cause of the increased stretching amplitude and decreased vibration frequency of the O-H bonds.Finally,by analyzing the motion trajectory of the H atoms,the dynamic differences between 1DCW and BW are clearly revealed.These findings provide a new perspective for understanding the behavior of water molecules at the nanoscale and are of significant importance in advancing the development of infrared spectroscopy detection technology.
基金Project supported by the National Natural Science Foundation of China (No.50278046)
文摘Based on the newly-developed element energy projection （EEP） method for computation of super-convergent results in one-dimensional finite element method （FEM）, the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.
基金the National Natural Science Foundation of China(No.50678093)Program for Changjiang Scholars and Innovative Research Team in University(No.IRT00736)
文摘Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035,11171038,and 10771019)the Science Reaearch Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region,China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region,China (Grant No. 2012MS0102)
文摘In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.
基金supported by the National Natural Science Foundation of China(No.22202065).
文摘Two-dimensional(2D)transition metal sulfides(TMDs)are emerging and highly well received 2D materials,which are considered as an ideal 2D platform for studying various electronic properties and potential applications due to their chemical diversity.Converting 2D TMDs into one-dimensional(1D)TMDs nanotubes can not only retain some advantages of 2D nanosheets but also providing a unique direction to explore the novel properties of TMDs materials in the 1D limit.However,the controllable preparation of high-quality nanotubes remains a major challenge.It is very necessary to review the advanced development of one-dimensional transition metal dichalcogenide nanotubes from preparation to application.Here,we first summarize a series of bottom-up synthesis methods of 1D TMDs,such as template growth and metal catalyzed method.Then,top-down synthesis methods are summarized,which included selfcuring and stacking of TMDs nanosheets.In addition,we discuss some key applications that utilize the properties of 1D-TMDs nanotubes in the areas of catalyst preparation,energy storage,and electronic devices.Last but not least,we prospect the preparation methods of high-quality 1D-TMDs nanotubes,which will lay a foundation for the synthesis of high-performance optoelectronic devices,catalysts,and energy storage components.
基金Supported by Anhui Provincial Natural Science Foundation(1908085QA09)
文摘A simple direct space-time meshless scheme,based on the radial or non-radial basis function,is proposed for the onedimensional Klein-Gordon equations.Since these equations are time-dependent,it is worthwhile to present two schemes for the basis functions from radial and non-radial aspects.The first scheme is fulfilled by considering time variable as normal space variable,to construct an"isotropic"space-time radial basis function.The other scheme considered a realistic relationship between space variable and time variable which is not radial.The timedependent variable is treated regularly during the whole solution process and the Klein-Gordon equations can be solved in a direct way.Numerical results show that the proposed meshless schemes are simple,accurate,stable,easy-to-program and efficient for the Klein-Gordon equations.
文摘Recently many research works have been conducted and published regarding fractional order differential equations. There are several approaches available for numerical approximations of the solution of fractional order diffusion equations. Spectral collocation method based on Lagrange’s basis polynomials to approximate numerical solutions of one-dimensional (1D) space fractional diffusion equations are introduced in this research paper. The proposed form of approximate solution satisfies non-zero Dirichlet’s boundary conditions on both boundaries. Collocation scheme produce a system of first order Ordinary Differential Equations (ODE) from the fractional diffusion equation. We applied this method with four different sets of collocation points to compare their performance.
基金supported by the National Natural Science Foundation of China(Grant No.11974420).
文摘We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model(n≥2)by using the cluster variation method with linear response theory.The results of this method are exact in the thermodynamic limit.We present the single-site reduced densityρ^((1))(z),averages such as(z^(2)),<|z^(n)|>,and<(z_(1)-z_(2))^(2)>,the specific heat C_(v),and the static correlation functions.We analyze the scaling behavior of these quantities and obtain the exact scaling powers at the low and high temperatures.Using these results,we gauge the accuracy of the projective truncation approximation for theφ^(4)lattice model.
基金supported by the National Natural Science Foundation of China(Grant Nos.61331007 and 61471105)
文摘An efficient conformal locally one-dimensional finite-difference time-domain（LOD-CFDTD） method is presented for solving two-dimensional（2D） electromagnetic（EM） scattering problems. The formulation for the 2D transverse-electric（TE） case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit（ADI） CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field（TF/SF） boundary and the perfectly matched layer（PML）, the radar cross section（RCS） of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.
文摘In this paper, on the basis of the heat conduction equation without consideration of the advection and turbulence effects, one-dimensional model for describing surface sea temperature ( T1), bottom sea temperature ( Tt ) and the thickness of the upper homogeneous layer ( h ) is developed in terms of the dimensionless temperature θT and depth η and self-simulation function θT - f(η) of vertical temperature profile by means of historical temperature data.The results of trial prediction with our one-dimensional model on T, Th, h , the thickness and gradient of thermocline are satisfactory to some extent.
基金Project supported by the National Natural Science Foundation of China(Grant No.11174026)。
文摘Using the Bose-Fermi mapping method,we obtain the exact ground state wavefunction of one-dimensional(1D)Bose gas with the zero-range dipolar interaction in the strongly repulsive contact interaction limit.Its ground state density distributions for both repulsive and attractive dipole interactions are exhibited.It is shown that in the case of the finite dipole interaction the density profiles do not change obviously with the increase of dipole interaction and display the typical shell structure of Tonks-Girardeau gases.As the repulsive dipole interaction is greatly strong,the density decreases at the center of the trap and displays a sunken valley.As the attractive dipole interaction increases,the density displays more oscillations and sharp peaks appear in the strong attraction limit,which mainly originate from the atoms occupying the low single particle levels.
基金supported by the National Natural Science Foundation of China(Grant No.12374416)。
文摘Adjustable or programmable metamaterials offer versatile functions,while the complex multi-dimensional regulation increases workload,and hinders their applications in practical scenarios.To address these challenges,we present a mechanically programmable acoustic metamaterial for real-time focal tuning via one-dimensional phase-gradient modulation in this paper.The device integrates a phase gradient structure with concave cavity channels and an x-shaped telescopic mechanical framework,enabling dynamic adjustment of inter-unit spacing(1 mm-3 mm)through a microcontroller-driven motor.By modulating the spacing between adjacent channels,the phase gradient is precisely controlled,allowing continuous focal shift from 50 mm to 300 mm along the x-axis at 7500 Hz.Broadband focusing is also discussed in the range6800 Hz-8100 Hz,with transmission coefficients exceeding 0.5,ensuring high efficiency and robust performance.Experimental results align closely with simulations,validating the design's effectiveness and adaptability.Unlike conventional programmable metamaterials requiring multi-dimensional parameter optimization,this approach simplifies real-time control through single-axis mechanical adjustment,significantly reducing operational complexity.Due to the advantages of broadband focusing,simple control mode,real-time monitoring,and so on,the device may have extensive applications in the fields of acoustic imaging,nondestructive testing,ultrasound medical treatment,etc.
基金supported by the National Science Foundation grant DMS-1818998.
文摘In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.
基金supported by the National Natural Science Foundation of China(No.52371240)the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘The oxygen evolution reaction(OER),a critical half-reaction in water electrolysis,has garnered significant attention.However,sluggish OER kinetics has emerged as a major impediment to efficient electrochemical energy conversion.There is an urgent need to design novel electrocatalysts with optimized OER kinetics and enhanced intrinsic activity to improve overall OER performance.Herein,one-dimensional(1D)nanocomposites with high electrocatalytic activity were developed through the deposition of CoFePBA nanocubes onto the surface of MnO_(2) nanowires.The electronic structure of the nanocomposite surface was modified,and the synergistic effects between transition metals were leveraged to enhance catalytic activity through the deposition of Prussian blue analog(PBA)nanocubes on manganese dioxide nanowires.Specifically,CoFePBA featured an open crystal structure that offiered numerous electrochemical active sites and efficient charge transfer pathways.Additionally,the synergistic interactions between Co and Fe significantly reduced the OER overpotential.Additionally,the 1D rigid MnO_(2) acted as protective armor,ensuring the stability of active sites within CoFePBA during the OER.The synthesized MnO_(2)@CoFePBA achieved an overpotential of 1.614 V at 10 mA/cm^(2) and a small Tafel slope of 94 mV/dec and demonstrated stable performance for over 200 h.This work offers new insights into the rational design of various PBA-based nanocomposites with high activity and stability.
