The proliferation of wearable biodevices has boosted the development of soft,innovative,and multifunctional materials for human health monitoring.The integration of wearable sensors with intelligent systems is an over...The proliferation of wearable biodevices has boosted the development of soft,innovative,and multifunctional materials for human health monitoring.The integration of wearable sensors with intelligent systems is an overwhelming tendency,providing powerful tools for remote health monitoring and personal health management.Among many candidates,two-dimensional(2D)materials stand out due to several exotic mechanical,electrical,optical,and chemical properties that can be efficiently integrated into atomic-thin films.While previous reviews on 2D materials for biodevices primarily focus on conventional configurations and materials like graphene,the rapid development of new 2D materials with exotic properties has opened up novel applications,particularly in smart interaction and integrated functionalities.This review aims to consolidate recent progress,highlight the unique advantages of 2D materials,and guide future research by discussing existing challenges and opportunities in applying 2D materials for smart wearable biodevices.We begin with an in-depth analysis of the advantages,sensing mechanisms,and potential applications of 2D materials in wearable biodevice fabrication.Following this,we systematically discuss state-of-the-art biodevices based on 2D materials for monitoring various physiological signals within the human body.Special attention is given to showcasing the integration of multi-functionality in 2D smart devices,mainly including self-power supply,integrated diagnosis/treatment,and human–machine interaction.Finally,the review concludes with a concise summary of existing challenges and prospective solutions concerning the utilization of2D materials for advanced biodevices.展开更多
An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions ...An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions with trigonometric and exponential terms satisfying different conditions are employed to generate a number of formulations. Performances of the new schemes are tested against well-known numerical integrators for selected test cases with quite satisfactory results. Convergence and stability issues of the new formulations are not addressed as the treatment of these aspects requires a separate work. The general approach introduced herein opens a wide vista for producing virtually unlimited number of formulations.展开更多
In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm i...In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method.To do this,these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form.By solving these systems,unknown coefficients are obtained.Also,some theorems are proved for convergence analysis.Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.展开更多
Owing to their rolling friction,two-dimensional piston pumps are highly suitable as power components for electro-hydrostatic actuators(EHAs).These pumps are particularly advantageous for applications requiring high ef...Owing to their rolling friction,two-dimensional piston pumps are highly suitable as power components for electro-hydrostatic actuators(EHAs).These pumps are particularly advantageous for applications requiring high efficiency and reliability.However,the ambiguity surrounding the output flow characteristics of individual two-dimensional pumps poses a significant challenge in achieving precise closed-loop control of the EHA positions.To address this issue,this study established a comprehensive numerical model that included gap leakage to analyze the impact of leakage on the output flow characteristics of a two-dimensional piston pump.The validity of the numerical analysis was indirectly confirmed through meticulous measurements of the leakage and volumetric efficiency,ensuring robust results.The research findings indicated that,at lower pump speeds,leakage significantly affected the output flow rate,leading to potential inefficiencies in the system.Conversely,at higher rotational speeds,the impact of leakage was less pronounced,implying that the influence of leakage on the pump outlet flow must be carefully considered and managed for EHAs to perform position servo control.Additionally,the research demonstrates that two-dimensional motion does not have a unique or additional effect on pump leakage,thus simplifying the design considerations.Finally,the study concluded that maintaining an oil-filled leakage environment is beneficial because it helps reduce the impact of leakage and enhances the overall volumetric efficiency of the pump system.展开更多
Based on the displacement discontinuity method and the discrete fracture unified pipe network model,a sequential iterative numerical method was used to build a fracturing-production integrated numerical model of shale...Based on the displacement discontinuity method and the discrete fracture unified pipe network model,a sequential iterative numerical method was used to build a fracturing-production integrated numerical model of shale gas well considering the two-phase flow of gas and water.The model accounts for the influence of natural fractures and matrix properties on the fracturing process and directly applies post-fracturing formation pressure and water saturation distribution to subsequent well shut-in and production simulation,allowing for a more accurate fracturing-production integrated simulation.The results show that the reservoir physical properties have great impacts on fracture propagation,and the reasonable prediction of formation pressure and reservoir fluid distribution after the fracturing is critical to accurately predict the gas and fluid production of the shale gas wells.Compared with the conventional method,the proposed model can more accurately simulate the water and gas production by considering the impact of fracturing on both matrix pressure and water saturation.The established model is applied to the integrated fracturing-production simulation of practical horizontal shale gas wells.The simulation results are in good agreement with the practical production data,thus verifying the accuracy of the model.展开更多
As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely use...As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely used approaches for sensitivity analysis are based on time-consuming numerical methods, such as finite difference methods. This paper presents a semi-analytical method for calculation of the sensitivity of the stability boundary in milling. After transforming the delay-differential equation with time-periodic coefficients governing the dynamic milling process into the integral form, the Floquet transition matrix is constructed by using the numerical integration method. Then, the analytical expressions of derivatives of the Floquet transition matrix with respect to the machining parameters are obtained. Thereafter, the classical analytical expression of the sensitivity of matrix eigenvalues is employed to calculate the sensitivity of the stability lobe diagram. The two-degree-of-freedom milling example illustrates the accuracy and efficiency of the proposed method. Compared with the existing methods, the unique merit of the proposed method is that it can be used for analytically computing the sensitivity of the stability boundary in milling, without employing any finite difference methods. Therefore, the high accuracy and high efficiency are both achieved. The proposed method can serve as an effective tool for machining parameter optimization and uncertainty analysis in high-speed milling.展开更多
Finite element（FE） is a powerful tool and has been applied by investigators to real-time hybrid simulations（RTHSs）. This study focuses on the computational efficiency, including the computational time and accuracy...Finite element（FE） is a powerful tool and has been applied by investigators to real-time hybrid simulations（RTHSs）. This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time（TET） decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method（CDM）, the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ（λ = 4） method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.展开更多
Two-dimensional numerical research has been carried out on the ablation effects of titanium target irradiated by intense pulsed ion beam （IPIB） generated by TEMP Ⅱ accelerator. Temporal and spatial evolution of the...Two-dimensional numerical research has been carried out on the ablation effects of titanium target irradiated by intense pulsed ion beam （IPIB） generated by TEMP Ⅱ accelerator. Temporal and spatial evolution of the ablation process of the target during a pulse time has been simulated. We have come to the conclusion that the melting and evaporating process begin from the surface and the target is ablated layer by layer when the target is irradiated by the IPIB. Meanwhile, we also obtained the result that the average ablation velocity in target central region is about 10 m/s, which is far less than the ejection velocity of the plume plasma formed by irradiation. Different effects have been compared to the different ratio of the ions and different energy density of IPIB while the target is irradiated by pulsed beams.展开更多
In this note we consider some basic, yet unusual, issues pertaining to the accuracy and stability of numerical integration methods to follow the solution of first order and second order initial value problems (IVP). I...In this note we consider some basic, yet unusual, issues pertaining to the accuracy and stability of numerical integration methods to follow the solution of first order and second order initial value problems (IVP). Included are remarks on multiple solutions, multi-step methods, effect of initial value perturbations, as well as slowing and advancing the computed motion in second order problems.展开更多
In this paper a new ODE numerical integration method was successfully applied to solving nonlinear equations. The method is of same simplicity as fixed point iteration, but the efficiency has been significantly improv...In this paper a new ODE numerical integration method was successfully applied to solving nonlinear equations. The method is of same simplicity as fixed point iteration, but the efficiency has been significantly improved, so it is especially suitable for large scale systems. For Brown’s equations, an existing article reported that when the dimension of the equation N = 40, the subroutines they used could not give a solution, as compared with our method, we can easily solve this equation even when N = 100. Other two large equations have the dimension of N = 1000, all the existing available methods have great difficulties to handle them, however, our method proposed in this paper can deal with those tough equations without any difficulties. The sigularity and choosing initial values problems were also mentioned in this paper.展开更多
There are such problems as convergence and stability of numerical calculations during multivariate interpolation. Moreover, it is very difficult to construct a overall multivariate numerical interpolation formula to e...There are such problems as convergence and stability of numerical calculations during multivariate interpolation. Moreover, it is very difficult to construct a overall multivariate numerical interpolation formula to ensure convergence for a set of irregular nodes. In this paper by means of an optimal binary interpolation formula given in a reproducing kernel space, a high precision overall two dimension numerical integral formula is established and its advantage is that it ensures the convergence for arbitrary irregular node set in the integral domain.展开更多
In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubi...In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.展开更多
The numerical evaluation of an integral is a frequently encountered problem in antenna analysis. A special Gauss Christoffel quadrature formula for nonclassical weight function is constructed for solving the pseu...The numerical evaluation of an integral is a frequently encountered problem in antenna analysis. A special Gauss Christoffel quadrature formula for nonclassical weight function is constructed for solving the pseudo singular integration problem arising from the analysis of thin wire antennas. High integration accuracy is obtained at comparable low computation cost by the quadrature formula constructed. This integration method can be also used in other electromagnetic integral equation problems.展开更多
A series of simulation experiments of nitrogen transportation, absorption and transformation were conducted, and the different cropping patterns of winter wheat and wastewater irrigation plans were taken into consider...A series of simulation experiments of nitrogen transportation, absorption and transformation were conducted, and the different cropping patterns of winter wheat and wastewater irrigation plans were taken into consideration. Based on the experiments, an integrated model of crop growth, roots distribution, water and nitrogen absorption by roots, water and nitrogen movement and transformation in soil-crop system by two-dimension was developed. Parameters and boundary conditions were identified and an effective computing method for optimizing watering and wastewater irrigating plans was provided.展开更多
In this work, we consider different numerical methods for the approximation of definite integrals. The three basic methods used here are the Midpoint, the Trapezoidal, and Simpson’s rules. We trace the behavior of th...In this work, we consider different numerical methods for the approximation of definite integrals. The three basic methods used here are the Midpoint, the Trapezoidal, and Simpson’s rules. We trace the behavior of the error when we refine the mesh and show that Richardson’s extrapolation improves the rate of convergence of the basic methods when the integrands are sufficiently differentiable many times. However, Richardson’s extrapolation does not work when we approximate improper integrals or even proper integrals from functions without smooth derivatives. In order to save computational resources, we construct an adaptive recursive procedure. We also show that there is a lower limit to the error during computations with floating point arithmetic.展开更多
The recent result of an orbit continuation algorithm has provided a rigorous method for long-term numerical integration of an orbit on the unstable manifold of a periodic solution.This algorithm is matrix-free and emp...The recent result of an orbit continuation algorithm has provided a rigorous method for long-term numerical integration of an orbit on the unstable manifold of a periodic solution.This algorithm is matrix-free and employs a combination of the Newton-Raphson method and the Krylov subspace method.Moreover,the algorithm adopts a multiple shooting method to address the problem of orbital instability due to long-term numerical integration.The algorithm is described through computing the extension of unstable manifold of a recomputed Nagata′s lowerbranch steady solution of plane Couette flow,which is an example of an exact coherent state that has recently been studied in subcritical transition to turbulence.展开更多
With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and re...With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.展开更多
In reference [1], for large scale nonlinear equations , a new ODE solving method was given. This paper is a continuous work. Here has gradient structure i.e. , is a scalar function. The eigenvalues of the Jacobian of;...In reference [1], for large scale nonlinear equations , a new ODE solving method was given. This paper is a continuous work. Here has gradient structure i.e. , is a scalar function. The eigenvalues of the Jacobian of;or the Hessian of , are all real number. So the new method is very suitable for this structure. For quadratic function the convergence was proved and the spectral radius of iteration matrix was given and compared with traditional method. Examples show for large scale problems (dimension ) the new method is very efficient.展开更多
This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equ...This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equations. Numerical method for modelling the short waves is investigated in detail. The forces, such as Coriolis forces, wind stress, atmosphere and bottom friction, are considered. A two-dimensional implicit difference scheme of Boussinesq equations is proposed. The low-reflection outflow open boundary is suggested. By means of this model,both velocity fields of circulation current in a channel with step expansion and the wave diffraction behind a semi-infinite breakwater are computed, and the results are satisfactory.展开更多
A component-based model integration framework for computer numerical control system design and development is presented.The model integrates modeling,simulation,verification and implementation in a uniform environment...A component-based model integration framework for computer numerical control system design and development is presented.The model integrates modeling,simulation,verification and implementation in a uniform environment.The computer numerical control(CNC) modeling language with well defined syntax and unambiguous semantics is developed.Using the proposed CNC model integration method,a three axis milling system model is developed in the case study.The approach is an attempt to create an infrastructure to support the CNC system design in an efficient way,while at the same time guarantees the function and performance requirements with advanced capability of the system such as modularity,flexibility,reusability,etc.展开更多
基金the support from the National Natural Science Foundation of China(22272004,62272041)the Fundamental Research Funds for the Central Universities(YWF-22-L-1256)+1 种基金the National Key R&D Program of China(2023YFC3402600)the Beijing Institute of Technology Research Fund Program for Young Scholars(No.1870011182126)。
文摘The proliferation of wearable biodevices has boosted the development of soft,innovative,and multifunctional materials for human health monitoring.The integration of wearable sensors with intelligent systems is an overwhelming tendency,providing powerful tools for remote health monitoring and personal health management.Among many candidates,two-dimensional(2D)materials stand out due to several exotic mechanical,electrical,optical,and chemical properties that can be efficiently integrated into atomic-thin films.While previous reviews on 2D materials for biodevices primarily focus on conventional configurations and materials like graphene,the rapid development of new 2D materials with exotic properties has opened up novel applications,particularly in smart interaction and integrated functionalities.This review aims to consolidate recent progress,highlight the unique advantages of 2D materials,and guide future research by discussing existing challenges and opportunities in applying 2D materials for smart wearable biodevices.We begin with an in-depth analysis of the advantages,sensing mechanisms,and potential applications of 2D materials in wearable biodevice fabrication.Following this,we systematically discuss state-of-the-art biodevices based on 2D materials for monitoring various physiological signals within the human body.Special attention is given to showcasing the integration of multi-functionality in 2D smart devices,mainly including self-power supply,integrated diagnosis/treatment,and human–machine interaction.Finally,the review concludes with a concise summary of existing challenges and prospective solutions concerning the utilization of2D materials for advanced biodevices.
文摘An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions with trigonometric and exponential terms satisfying different conditions are employed to generate a number of formulations. Performances of the new schemes are tested against well-known numerical integrators for selected test cases with quite satisfactory results. Convergence and stability issues of the new formulations are not addressed as the treatment of these aspects requires a separate work. The general approach introduced herein opens a wide vista for producing virtually unlimited number of formulations.
文摘In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method.To do this,these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form.By solving these systems,unknown coefficients are obtained.Also,some theorems are proved for convergence analysis.Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.
基金Supported by National Natural Science Foundation of China(Grant No.52205072).
文摘Owing to their rolling friction,two-dimensional piston pumps are highly suitable as power components for electro-hydrostatic actuators(EHAs).These pumps are particularly advantageous for applications requiring high efficiency and reliability.However,the ambiguity surrounding the output flow characteristics of individual two-dimensional pumps poses a significant challenge in achieving precise closed-loop control of the EHA positions.To address this issue,this study established a comprehensive numerical model that included gap leakage to analyze the impact of leakage on the output flow characteristics of a two-dimensional piston pump.The validity of the numerical analysis was indirectly confirmed through meticulous measurements of the leakage and volumetric efficiency,ensuring robust results.The research findings indicated that,at lower pump speeds,leakage significantly affected the output flow rate,leading to potential inefficiencies in the system.Conversely,at higher rotational speeds,the impact of leakage was less pronounced,implying that the influence of leakage on the pump outlet flow must be carefully considered and managed for EHAs to perform position servo control.Additionally,the research demonstrates that two-dimensional motion does not have a unique or additional effect on pump leakage,thus simplifying the design considerations.Finally,the study concluded that maintaining an oil-filled leakage environment is beneficial because it helps reduce the impact of leakage and enhances the overall volumetric efficiency of the pump system.
基金Supported by the National Natural Science Foundation of China(52374043)Key Program of the National Natural Science Foundation of China(52234003).
文摘Based on the displacement discontinuity method and the discrete fracture unified pipe network model,a sequential iterative numerical method was used to build a fracturing-production integrated numerical model of shale gas well considering the two-phase flow of gas and water.The model accounts for the influence of natural fractures and matrix properties on the fracturing process and directly applies post-fracturing formation pressure and water saturation distribution to subsequent well shut-in and production simulation,allowing for a more accurate fracturing-production integrated simulation.The results show that the reservoir physical properties have great impacts on fracture propagation,and the reasonable prediction of formation pressure and reservoir fluid distribution after the fracturing is critical to accurately predict the gas and fluid production of the shale gas wells.Compared with the conventional method,the proposed model can more accurately simulate the water and gas production by considering the impact of fracturing on both matrix pressure and water saturation.The established model is applied to the integrated fracturing-production simulation of practical horizontal shale gas wells.The simulation results are in good agreement with the practical production data,thus verifying the accuracy of the model.
基金supported by National Key Basic Research Program (973 Program, Grant No. 2011CB706804)National Natural Science Foundation of China (Grant No. 50805093)Science & Technology Commission of Shanghai Municipality, China (Grant No. 09QH1401500)
文摘As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely used approaches for sensitivity analysis are based on time-consuming numerical methods, such as finite difference methods. This paper presents a semi-analytical method for calculation of the sensitivity of the stability boundary in milling. After transforming the delay-differential equation with time-periodic coefficients governing the dynamic milling process into the integral form, the Floquet transition matrix is constructed by using the numerical integration method. Then, the analytical expressions of derivatives of the Floquet transition matrix with respect to the machining parameters are obtained. Thereafter, the classical analytical expression of the sensitivity of matrix eigenvalues is employed to calculate the sensitivity of the stability lobe diagram. The two-degree-of-freedom milling example illustrates the accuracy and efficiency of the proposed method. Compared with the existing methods, the unique merit of the proposed method is that it can be used for analytically computing the sensitivity of the stability boundary in milling, without employing any finite difference methods. Therefore, the high accuracy and high efficiency are both achieved. The proposed method can serve as an effective tool for machining parameter optimization and uncertainty analysis in high-speed milling.
基金National Natural Science Foundation of China under Grant Nos.51639006 and 51725901
文摘Finite element（FE） is a powerful tool and has been applied by investigators to real-time hybrid simulations（RTHSs）. This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time（TET） decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method（CDM）, the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ（λ = 4） method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.
文摘Two-dimensional numerical research has been carried out on the ablation effects of titanium target irradiated by intense pulsed ion beam （IPIB） generated by TEMP Ⅱ accelerator. Temporal and spatial evolution of the ablation process of the target during a pulse time has been simulated. We have come to the conclusion that the melting and evaporating process begin from the surface and the target is ablated layer by layer when the target is irradiated by the IPIB. Meanwhile, we also obtained the result that the average ablation velocity in target central region is about 10 m/s, which is far less than the ejection velocity of the plume plasma formed by irradiation. Different effects have been compared to the different ratio of the ions and different energy density of IPIB while the target is irradiated by pulsed beams.
文摘In this note we consider some basic, yet unusual, issues pertaining to the accuracy and stability of numerical integration methods to follow the solution of first order and second order initial value problems (IVP). Included are remarks on multiple solutions, multi-step methods, effect of initial value perturbations, as well as slowing and advancing the computed motion in second order problems.
文摘In this paper a new ODE numerical integration method was successfully applied to solving nonlinear equations. The method is of same simplicity as fixed point iteration, but the efficiency has been significantly improved, so it is especially suitable for large scale systems. For Brown’s equations, an existing article reported that when the dimension of the equation N = 40, the subroutines they used could not give a solution, as compared with our method, we can easily solve this equation even when N = 100. Other two large equations have the dimension of N = 1000, all the existing available methods have great difficulties to handle them, however, our method proposed in this paper can deal with those tough equations without any difficulties. The sigularity and choosing initial values problems were also mentioned in this paper.
文摘There are such problems as convergence and stability of numerical calculations during multivariate interpolation. Moreover, it is very difficult to construct a overall multivariate numerical interpolation formula to ensure convergence for a set of irregular nodes. In this paper by means of an optimal binary interpolation formula given in a reproducing kernel space, a high precision overall two dimension numerical integral formula is established and its advantage is that it ensures the convergence for arbitrary irregular node set in the integral domain.
文摘In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.
文摘The numerical evaluation of an integral is a frequently encountered problem in antenna analysis. A special Gauss Christoffel quadrature formula for nonclassical weight function is constructed for solving the pseudo singular integration problem arising from the analysis of thin wire antennas. High integration accuracy is obtained at comparable low computation cost by the quadrature formula constructed. This integration method can be also used in other electromagnetic integral equation problems.
文摘A series of simulation experiments of nitrogen transportation, absorption and transformation were conducted, and the different cropping patterns of winter wheat and wastewater irrigation plans were taken into consideration. Based on the experiments, an integrated model of crop growth, roots distribution, water and nitrogen absorption by roots, water and nitrogen movement and transformation in soil-crop system by two-dimension was developed. Parameters and boundary conditions were identified and an effective computing method for optimizing watering and wastewater irrigating plans was provided.
文摘In this work, we consider different numerical methods for the approximation of definite integrals. The three basic methods used here are the Midpoint, the Trapezoidal, and Simpson’s rules. We trace the behavior of the error when we refine the mesh and show that Richardson’s extrapolation improves the rate of convergence of the basic methods when the integrands are sufficiently differentiable many times. However, Richardson’s extrapolation does not work when we approximate improper integrals or even proper integrals from functions without smooth derivatives. In order to save computational resources, we construct an adaptive recursive procedure. We also show that there is a lower limit to the error during computations with floating point arithmetic.
文摘The recent result of an orbit continuation algorithm has provided a rigorous method for long-term numerical integration of an orbit on the unstable manifold of a periodic solution.This algorithm is matrix-free and employs a combination of the Newton-Raphson method and the Krylov subspace method.Moreover,the algorithm adopts a multiple shooting method to address the problem of orbital instability due to long-term numerical integration.The algorithm is described through computing the extension of unstable manifold of a recomputed Nagata′s lowerbranch steady solution of plane Couette flow,which is an example of an exact coherent state that has recently been studied in subcritical transition to turbulence.
文摘With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.
文摘In reference [1], for large scale nonlinear equations , a new ODE solving method was given. This paper is a continuous work. Here has gradient structure i.e. , is a scalar function. The eigenvalues of the Jacobian of;or the Hessian of , are all real number. So the new method is very suitable for this structure. For quadratic function the convergence was proved and the spectral radius of iteration matrix was given and compared with traditional method. Examples show for large scale problems (dimension ) the new method is very efficient.
基金Supported by the Fund of National Nature Sciences of China
文摘This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equations. Numerical method for modelling the short waves is investigated in detail. The forces, such as Coriolis forces, wind stress, atmosphere and bottom friction, are considered. A two-dimensional implicit difference scheme of Boussinesq equations is proposed. The low-reflection outflow open boundary is suggested. By means of this model,both velocity fields of circulation current in a channel with step expansion and the wave diffraction behind a semi-infinite breakwater are computed, and the results are satisfactory.
基金the National Natural Science Foundation of China (Nos. 50575075 and 50875090)
文摘A component-based model integration framework for computer numerical control system design and development is presented.The model integrates modeling,simulation,verification and implementation in a uniform environment.The computer numerical control(CNC) modeling language with well defined syntax and unambiguous semantics is developed.Using the proposed CNC model integration method,a three axis milling system model is developed in the case study.The approach is an attempt to create an infrastructure to support the CNC system design in an efficient way,while at the same time guarantees the function and performance requirements with advanced capability of the system such as modularity,flexibility,reusability,etc.
