The Lagrangian integral time scale(LITS)is a crucial characteristic for investigating the changes in fluid dynamics induced by the chaotic nature,and the finitetime Lyapunov exponent(FTLE)serves as a key measure in th...The Lagrangian integral time scale(LITS)is a crucial characteristic for investigating the changes in fluid dynamics induced by the chaotic nature,and the finitetime Lyapunov exponent(FTLE)serves as a key measure in the analysis of chaos.In this study,a new LITS model with an explicit theoretical basis and broad applicability is proposed based on the FTLE,along with a verification and evaluation criterion grounded in the Lagrangian velocity correlation coefficient.The model is used to cavitating the flow around a Clark-Y hydrofoil,and the LITS is investigated.It leads to the determination of model constants applicable to cavitating flow.The model is evaluated by the Lagrangian velocity correlation coefficient in comparison with other solution methods.All the results show that the LITS model can offer a new perspective and a new approach for studying the changes in fluid dynamics from a Lagrangian viewpoint.展开更多
We present a comprehensive extension of the integral of first passage times(IFS)method to investigate the adsorption kinetics of polymers with multiple binding sites on planar surfaces.While effective for single-point...We present a comprehensive extension of the integral of first passage times(IFS)method to investigate the adsorption kinetics of polymers with multiple binding sites on planar surfaces.While effective for single-point adsorption,the original IFS method was limited in capturing the complex kinetics of multi-point adsorption due to inadequate reaction coordinates and theoretical frameworks.Our approach introduces a center-of-mass-based reaction coordinate and a generalized kinetic model that accounts for multi-barrier free energy landscapes characteristic of collective polymer diffusion and binding.This theoretical advancement,implemented using the adaptive bias force method for efficient sampling,enables prediction of adsorption kinetics across timescales from nanoseconds to seconds.Our results demonstrate that adsorption behavior is governed by two key factors:the number of binding monomers primarily controls desorption barriers and long-term stability,while the configuration of pre-adsorbed layers significantly modulates both adsorption and desorption rates.Polymers with three or more binding sites exhibit effectively irreversible adsorption due to exponentially increasing desorption barriers,whereas different adsorbed layer configurations lead to distinct equilibrium coverages and kinetic profiles.This extended IFS framework provides critical insights for designing functional surfaces in nanoscale sensing,macromolecular recognition,and tailored polymeric coatings where precise control over adsorption kinetics is essential.展开更多
To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of...To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of the memorial dynamics. Stability criteria of the scheme for an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its RT scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog (LF) difference scheme.展开更多
Due to the widespread application of the PID controller in industrial control systems, it is desirable to know the complete set of all the stabilizing PID controllers for a given plant before the controller design and...Due to the widespread application of the PID controller in industrial control systems, it is desirable to know the complete set of all the stabilizing PID controllers for a given plant before the controller design and tuning. In this paper, the stabilization problems of the classical proportionalintegral-derivative （PID） controller and the singleparameter PID controller （containing only one adjustable parameter） for integral processes with time delay are investigated, respectively. The complete set of stabilizing parameters of the classical PID controller is determined using a version of the Hermite-Biehler Theorem applicable to quasipolynomials. Since the stabilization problem of the singie-parameter PID controller cannot be treated by the Hermite-Biehler Theorem, a simple method called duallocus diagram is employed to derive the stabilizing range of the single-parameter PID controller. These results provide insight into the tuning of the PID controllers.展开更多
A fast Time Domain Integral Equation(TDIE) solver is presented for analysis of transient scattering from electrically large conducting complex objects.The numerical process of Marching-On-in-Time(MOT) method based TDI...A fast Time Domain Integral Equation(TDIE) solver is presented for analysis of transient scattering from electrically large conducting complex objects.The numerical process of Marching-On-in-Time(MOT) method based TDIE encounters high computational cost and exorbitant memory requirements.A group-style accelerated method-Plane Wave Time Domain(PWTD) algorithm,which permits rapid evaluation of transient wave field generated by temporally bandlimited sources,is employed to reduce the computational cost of MOT-based TDIE solvers.An efficient compressed storage technique for sparse matrix is adopted to decrease the enormous memory requirements of MOT.The scheme of the Multi-Level PWTD(MLPWTD)-enhanced MOT with compressed storage for sparse matrix is presented for analysis of transient scattering from electrically large complex objects in this paper.The numerical simulation results demonstrate the validity and efficiency of the presented scheme.展开更多
In the traditional radar unmanned aerial vehicle(UAV)detection process,coherent integration and micro-Doppler(m-D)parameter estimation are carried out separately.The target discrimination process needs to obtain the p...In the traditional radar unmanned aerial vehicle(UAV)detection process,coherent integration and micro-Doppler(m-D)parameter estimation are carried out separately.The target discrimination process needs to obtain the position information of the target,which will lose energy.In this paper,a long time integration method of radar signal based on rotating target radon Fourier transform(RTRFT)is proposed.This method modifies the distance and frequency terms in the traditional generalized radon Fourier transform(GRFT),and adds the frequency sinusoidal modulation term.Then,based on the cardinality balanced multi-target multi-Bernoulli(CBMeMBer)filter,the position of the target is detected in the high-dimensional space obtained by RTRFT.This method can combine coherent integration and micro-motion parameter estimation.Simulation experiments show that the proposed method can estimate the main translational parameters and rotational micro-motion parameters of the target while detecting the target,and the target detection performance is improved.展开更多
Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA ...Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA structure statistical mechanical model,and time complexity and precision were analyzed on the calculated results.展开更多
An efficient data-driven numerical framework is developed for transient heat conduction analysis in thin-walled structures.The proposed approach integrates spectral time discretization with neural network approximatio...An efficient data-driven numerical framework is developed for transient heat conduction analysis in thin-walled structures.The proposed approach integrates spectral time discretization with neural network approximation,forming a spectral-integrated neural network(SINN)scheme tailored for problems characterized by long-time evolution.Temporal derivatives are treated through a spectral integration strategy based on orthogonal polynomial expansions,which significantly alleviates stability constraints associated with conventional time-marching schemes.A fully connected neural network is employed to approximate the temperature-related variables,while governing equa-tions and boundary conditions are enforced through a physics-informed loss formulation.Numerical investigations demonstrate that the proposed method maintains high accuracy even when large time steps are adopted,where standard numerical solvers often suffer from instability or excessive computational cost.Moreover,the framework exhibits strong robustness for ultrathin configurations with extreme aspect ratios,achieving relative errors on the order of 10−5 or lower.These results indicate that the SINN framework provides a reliable and efficient alternative for transient thermal analysis of thin-walled structures under challenging computational conditions.展开更多
The micro- and macro-time scales in two-phase turbulent channel flows are investigated using the direct nu- merical simulation and the Lagrangian particle trajectory methods for the fluid- and the particle-phases, res...The micro- and macro-time scales in two-phase turbulent channel flows are investigated using the direct nu- merical simulation and the Lagrangian particle trajectory methods for the fluid- and the particle-phases, respectively. Lagrangian and Eulerian time scales of both phases are cal- culated using velocity correlation functions. Due to flow anisotropy, micro-time scales are not the same with the theo- retical estimations in large Reynolds number （isotropic） tur- bulence. Lagrangian macro-time scales of particle-phase and of fluid-phase seen by particles are both dependent on particle Stokes number. The fluid-phase Lagrangian inte- gral time scales increase with distance from the wall, longer than those time scales seen by particles. The Eulerian inte- gral macro-time scales increase in near-wall regions but de- crease in out-layer regions. The moving Eulerian time scales are also investigated and compared with Lagrangian integral time scales, and in good agreement with previous measure- ments and numerical predictions. For the fluid particles the micro Eulerian time scales are longer than the Lagrangian ones in the near wall regions, while away from the walls the micro Lagrangian time scales are longer. The Lagrangian integral time scales are longer than the Eulerian ones. The results are useful for further understanding two-phase flow physics and especially for constructing accurate prediction models of inertial particle dispersion.展开更多
There are two models in use today to analyze structural responses when subjected to earthquake ground motions,the Displacement Input Model(DIM)and the Acceleration Input Model(AIM).The time steps used in direct integr...There are two models in use today to analyze structural responses when subjected to earthquake ground motions,the Displacement Input Model(DIM)and the Acceleration Input Model(AIM).The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM.Numerical results are presented and show that the time-step for DIM is about the same as for AIM,and achieves the same accuracy.This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading,and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation.It is shown in this paper that DIM is as accurate and suitable as,if not more than,AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.展开更多
The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficu...The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.展开更多
In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
Time delay and integration （TDI） charge coupled device （CCD） noise sets a fundamental limit on image sensor performance, especially under low illumination in remote sensing applications. After introducing the comp...Time delay and integration （TDI） charge coupled device （CCD） noise sets a fundamental limit on image sensor performance, especially under low illumination in remote sensing applications. After introducing the complete sources of CCD noise, we study the effects of TDI operation mode on noise, and the relationship between different types of noise and number of the TDI stage. Then we propose a new technique to identify and measure sources of TDI CCD noise employing mathematical statistics theory, where theoretical analysis shows that noise estimated formulation converges well. Finally, we establish a testing platform to carry out experiments, and a standard TDI CCD is calibrated by using the proposed method. The experimental results show that the noise analysis and measurement methods presented in this paper are useful for modeling TDI CCDs.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
This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditiona...This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.展开更多
The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integ...The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integration schemes derived by the singlepoint precise integration method given in this paper are proved unconditionally stable.Comparisons between the schemes derived by the finite difference method and theschemes by the method employed in the present paper are made for diffusion andconvective-diffusion equations. Nunierical examples show the superiority of the singlepoint integration method.展开更多
This paper explores pole placement techniques for the 4th order C1 DC-to-DC Buck converter focusing on optimizing various performance metrics. Refinements were made to existing ITAE (Integral of Time-weighted Absolute...This paper explores pole placement techniques for the 4th order C1 DC-to-DC Buck converter focusing on optimizing various performance metrics. Refinements were made to existing ITAE (Integral of Time-weighted Absolute Error) polynomials. Additionally, metrics such as IAE (Integral Absolute Error), ISE (Integral of Square Error), ITSE (Integral of Time Squared Error), a MaxMin metric as well as LQR (Linear Quadratic Regulator) were evaluated. PSO (Particle Swarm Optimization) was employed for metric optimization. Time domain response to a step disturbance input was evaluated. The design which optimized the ISE metric proved to be the best performing, followed by IAE and MaxMin (with equivalent results) and then LQR.展开更多
This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order...This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.展开更多
The computational uncertainty principle states that the numerical computation of nonlinear ordinary differential equations（ODEs） should use appropriately sized time steps to obtain reliable solutions.However,the int...The computational uncertainty principle states that the numerical computation of nonlinear ordinary differential equations（ODEs） should use appropriately sized time steps to obtain reliable solutions.However,the interval of effective step size（IES） has not been thoroughly explored theoretically.In this paper,by using a general estimation for the total error of the numerical solutions of ODEs,a method is proposed for determining an approximate IES by translating the functions for truncation and rounding errors.It also illustrates this process with an example.Moreover,the relationship between the IES and its approximation is found,and the relative error of the approximation with respect to the IES is given.In addition,variation in the IES with increasing integration time is studied,which can provide an explanation for the observed numerical results.The findings contribute to computational step-size choice for reliable numerical solutions.展开更多
In this article,the mode superposition method is combined with a time integration method like the trapezoidal rule to improve solution accuracy for linear dynamic systems.In this combination strategy,the essential thi...In this article,the mode superposition method is combined with a time integration method like the trapezoidal rule to improve solution accuracy for linear dynamic systems.In this combination strategy,the essential thing is to decompose a dynamic system into two sub-systems,a small-scale low-frequency system and a high-frequency system.The former can be analytically and efficiently solved with the mode superposition method,and the latter is dealt with through a time integration method such as the Newmark method.The summation of the responses of these two sub-systems is the responses of the original dynamic system.It is concluded that,with little sacrifice of efficiency,the combination method based on the strategy is more accurate than the combined time integration method,but it has the same accuracy order as that of the combined method.Numerical experiments validate the effectiveness of the proposed strategy.展开更多
基金Project supported by the Key Project of the National Natural Science Foundation of China(No.52336001)the Natural Science Foundation of Zhejiang Province of China(No.LR20E090001)。
文摘The Lagrangian integral time scale(LITS)is a crucial characteristic for investigating the changes in fluid dynamics induced by the chaotic nature,and the finitetime Lyapunov exponent(FTLE)serves as a key measure in the analysis of chaos.In this study,a new LITS model with an explicit theoretical basis and broad applicability is proposed based on the FTLE,along with a verification and evaluation criterion grounded in the Lagrangian velocity correlation coefficient.The model is used to cavitating the flow around a Clark-Y hydrofoil,and the LITS is investigated.It leads to the determination of model constants applicable to cavitating flow.The model is evaluated by the Lagrangian velocity correlation coefficient in comparison with other solution methods.All the results show that the LITS model can offer a new perspective and a new approach for studying the changes in fluid dynamics from a Lagrangian viewpoint.
基金financially supported by the National Natural Science Foundation of China(No.12374207)the Natural Science Foundation of Jiangsu Province(No.BK20233001)supported by the Big Data Computing Center of Southeast University。
文摘We present a comprehensive extension of the integral of first passage times(IFS)method to investigate the adsorption kinetics of polymers with multiple binding sites on planar surfaces.While effective for single-point adsorption,the original IFS method was limited in capturing the complex kinetics of multi-point adsorption due to inadequate reaction coordinates and theoretical frameworks.Our approach introduces a center-of-mass-based reaction coordinate and a generalized kinetic model that accounts for multi-barrier free energy landscapes characteristic of collective polymer diffusion and binding.This theoretical advancement,implemented using the adaptive bias force method for efficient sampling,enables prediction of adsorption kinetics across timescales from nanoseconds to seconds.Our results demonstrate that adsorption behavior is governed by two key factors:the number of binding monomers primarily controls desorption barriers and long-term stability,while the configuration of pre-adsorbed layers significantly modulates both adsorption and desorption rates.Polymers with three or more binding sites exhibit effectively irreversible adsorption due to exponentially increasing desorption barriers,whereas different adsorbed layer configurations lead to distinct equilibrium coverages and kinetic profiles.This extended IFS framework provides critical insights for designing functional surfaces in nanoscale sensing,macromolecular recognition,and tailored polymeric coatings where precise control over adsorption kinetics is essential.
基金The project supported by the National Key Program for Developing Basic Sciences (G1999043408 and G1998040901-1)the National Natural Sciences Foundation of China (40175024 and 40035010)
文摘To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of the memorial dynamics. Stability criteria of the scheme for an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its RT scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog (LF) difference scheme.
基金National Science Foundation of China （60274032） SRFDP （20030248040） SRSP （04QMH1405）
文摘Due to the widespread application of the PID controller in industrial control systems, it is desirable to know the complete set of all the stabilizing PID controllers for a given plant before the controller design and tuning. In this paper, the stabilization problems of the classical proportionalintegral-derivative （PID） controller and the singleparameter PID controller （containing only one adjustable parameter） for integral processes with time delay are investigated, respectively. The complete set of stabilizing parameters of the classical PID controller is determined using a version of the Hermite-Biehler Theorem applicable to quasipolynomials. Since the stabilization problem of the singie-parameter PID controller cannot be treated by the Hermite-Biehler Theorem, a simple method called duallocus diagram is employed to derive the stabilizing range of the single-parameter PID controller. These results provide insight into the tuning of the PID controllers.
文摘A fast Time Domain Integral Equation(TDIE) solver is presented for analysis of transient scattering from electrically large conducting complex objects.The numerical process of Marching-On-in-Time(MOT) method based TDIE encounters high computational cost and exorbitant memory requirements.A group-style accelerated method-Plane Wave Time Domain(PWTD) algorithm,which permits rapid evaluation of transient wave field generated by temporally bandlimited sources,is employed to reduce the computational cost of MOT-based TDIE solvers.An efficient compressed storage technique for sparse matrix is adopted to decrease the enormous memory requirements of MOT.The scheme of the Multi-Level PWTD(MLPWTD)-enhanced MOT with compressed storage for sparse matrix is presented for analysis of transient scattering from electrically large complex objects in this paper.The numerical simulation results demonstrate the validity and efficiency of the presented scheme.
文摘In the traditional radar unmanned aerial vehicle(UAV)detection process,coherent integration and micro-Doppler(m-D)parameter estimation are carried out separately.The target discrimination process needs to obtain the position information of the target,which will lose energy.In this paper,a long time integration method of radar signal based on rotating target radon Fourier transform(RTRFT)is proposed.This method modifies the distance and frequency terms in the traditional generalized radon Fourier transform(GRFT),and adds the frequency sinusoidal modulation term.Then,based on the cardinality balanced multi-target multi-Bernoulli(CBMeMBer)filter,the position of the target is detected in the high-dimensional space obtained by RTRFT.This method can combine coherent integration and micro-motion parameter estimation.Simulation experiments show that the proposed method can estimate the main translational parameters and rotational micro-motion parameters of the target while detecting the target,and the target detection performance is improved.
基金Supported by Inner Mongolia Natural Science Foundation(200711020112)Innovation Fundation of Inner Mongolia University of Science and Technology (2009NC064)~~
文摘Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA structure statistical mechanical model,and time complexity and precision were analyzed on the calculated results.
基金supported by the National Natural Science Foundation of China(Nos.12422207 and 12372199).
文摘An efficient data-driven numerical framework is developed for transient heat conduction analysis in thin-walled structures.The proposed approach integrates spectral time discretization with neural network approximation,forming a spectral-integrated neural network(SINN)scheme tailored for problems characterized by long-time evolution.Temporal derivatives are treated through a spectral integration strategy based on orthogonal polynomial expansions,which significantly alleviates stability constraints associated with conventional time-marching schemes.A fully connected neural network is employed to approximate the temperature-related variables,while governing equa-tions and boundary conditions are enforced through a physics-informed loss formulation.Numerical investigations demonstrate that the proposed method maintains high accuracy even when large time steps are adopted,where standard numerical solvers often suffer from instability or excessive computational cost.Moreover,the framework exhibits strong robustness for ultrathin configurations with extreme aspect ratios,achieving relative errors on the order of 10−5 or lower.These results indicate that the SINN framework provides a reliable and efficient alternative for transient thermal analysis of thin-walled structures under challenging computational conditions.
基金supported by the National Natural Science Foundation of China (11132005 and 50706021)
文摘The micro- and macro-time scales in two-phase turbulent channel flows are investigated using the direct nu- merical simulation and the Lagrangian particle trajectory methods for the fluid- and the particle-phases, respectively. Lagrangian and Eulerian time scales of both phases are cal- culated using velocity correlation functions. Due to flow anisotropy, micro-time scales are not the same with the theo- retical estimations in large Reynolds number （isotropic） tur- bulence. Lagrangian macro-time scales of particle-phase and of fluid-phase seen by particles are both dependent on particle Stokes number. The fluid-phase Lagrangian inte- gral time scales increase with distance from the wall, longer than those time scales seen by particles. The Eulerian inte- gral macro-time scales increase in near-wall regions but de- crease in out-layer regions. The moving Eulerian time scales are also investigated and compared with Lagrangian integral time scales, and in good agreement with previous measure- ments and numerical predictions. For the fluid particles the micro Eulerian time scales are longer than the Lagrangian ones in the near wall regions, while away from the walls the micro Lagrangian time scales are longer. The Lagrangian integral time scales are longer than the Eulerian ones. The results are useful for further understanding two-phase flow physics and especially for constructing accurate prediction models of inertial particle dispersion.
文摘There are two models in use today to analyze structural responses when subjected to earthquake ground motions,the Displacement Input Model(DIM)and the Acceleration Input Model(AIM).The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM.Numerical results are presented and show that the time-step for DIM is about the same as for AIM,and achieves the same accuracy.This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading,and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation.It is shown in this paper that DIM is as accurate and suitable as,if not more than,AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.
基金financial support from Hunan Provincial Natura1 Science Foundation of China,Grant Number:02JJY2085,for this study
文摘The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.
文摘In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
基金Project supported by the National High Technology Research and Development Program of China (Grant No. 2006AA06A208)
文摘Time delay and integration （TDI） charge coupled device （CCD） noise sets a fundamental limit on image sensor performance, especially under low illumination in remote sensing applications. After introducing the complete sources of CCD noise, we study the effects of TDI operation mode on noise, and the relationship between different types of noise and number of the TDI stage. Then we propose a new technique to identify and measure sources of TDI CCD noise employing mathematical statistics theory, where theoretical analysis shows that noise estimated formulation converges well. Finally, we establish a testing platform to carry out experiments, and a standard TDI CCD is calibrated by using the proposed method. The experimental results show that the noise analysis and measurement methods presented in this paper are useful for modeling TDI CCDs.
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.
基金The project supported by the National Key Basic Research and Development Foundation of the Ministry of Science and Technology of China （G2000048702, 2003CB716707）the National Science Fund for Distinguished Young Scholars （10025208）+1 种基金 the National Natural Science Foundation of China （Key Program） （10532040） the Research Fund for 0versea Chinese （10228028）.
文摘This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.
文摘The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integration schemes derived by the singlepoint precise integration method given in this paper are proved unconditionally stable.Comparisons between the schemes derived by the finite difference method and theschemes by the method employed in the present paper are made for diffusion andconvective-diffusion equations. Nunierical examples show the superiority of the singlepoint integration method.
文摘This paper explores pole placement techniques for the 4th order C1 DC-to-DC Buck converter focusing on optimizing various performance metrics. Refinements were made to existing ITAE (Integral of Time-weighted Absolute Error) polynomials. Additionally, metrics such as IAE (Integral Absolute Error), ISE (Integral of Square Error), ITSE (Integral of Time Squared Error), a MaxMin metric as well as LQR (Linear Quadratic Regulator) were evaluated. PSO (Particle Swarm Optimization) was employed for metric optimization. Time domain response to a step disturbance input was evaluated. The design which optimized the ISE metric proved to be the best performing, followed by IAE and MaxMin (with equivalent results) and then LQR.
基金supported by the National Natural Science Foun-dation of China (11172334)
文摘This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.
基金supported by the National Natural Science Foundation of China[grant numbers 41375110,11471244]
文摘The computational uncertainty principle states that the numerical computation of nonlinear ordinary differential equations（ODEs） should use appropriately sized time steps to obtain reliable solutions.However,the interval of effective step size（IES） has not been thoroughly explored theoretically.In this paper,by using a general estimation for the total error of the numerical solutions of ODEs,a method is proposed for determining an approximate IES by translating the functions for truncation and rounding errors.It also illustrates this process with an example.Moreover,the relationship between the IES and its approximation is found,and the relative error of the approximation with respect to the IES is given.In addition,variation in the IES with increasing integration time is studied,which can provide an explanation for the observed numerical results.The findings contribute to computational step-size choice for reliable numerical solutions.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11872090 and 12172023).
文摘In this article,the mode superposition method is combined with a time integration method like the trapezoidal rule to improve solution accuracy for linear dynamic systems.In this combination strategy,the essential thing is to decompose a dynamic system into two sub-systems,a small-scale low-frequency system and a high-frequency system.The former can be analytically and efficiently solved with the mode superposition method,and the latter is dealt with through a time integration method such as the Newmark method.The summation of the responses of these two sub-systems is the responses of the original dynamic system.It is concluded that,with little sacrifice of efficiency,the combination method based on the strategy is more accurate than the combined time integration method,but it has the same accuracy order as that of the combined method.Numerical experiments validate the effectiveness of the proposed strategy.
