Using a direct perturbation method, we investigate the stability of a diatomic molecule modelled by a weakly laser-driven Morse oscillator. It is shown that stationary state solution of the system is stable in the sen...Using a direct perturbation method, we investigate the stability of a diatomic molecule modelled by a weakly laser-driven Morse oscillator. It is shown that stationary state solution of the system is stable in the sense of Lyapunov and the periodical one possesses conditional stability, namely its stability depends on the initial conditions and system parameters. The corresponding sufficient and necessary conditions are established that indicate the stable states associated with some discrete energies. The results reveal how a diatomic molecule can be stabilized or dissociated with a weak laser, and demonstrate that the mathematical conditional stability works in the considered physical system.展开更多
Dear Editor,H_(∞)This letter develops a new framework for the robust stability and performance conditions as well as the relevant controller synthesis with respect to uncertain robot manipulators.There often exist mo...Dear Editor,H_(∞)This letter develops a new framework for the robust stability and performance conditions as well as the relevant controller synthesis with respect to uncertain robot manipulators.There often exist model uncertainties between the nominal model and the real robot manipulator and disturbances. Hence, dealing with their effects plays a crucial role in leading to high tracking performances, as discussed in [1]–[5].展开更多
This paper introdnces some concepts of conditional stability of stochasticVolterra equations with anticipating kernel. Snfficient conditions of these types of sta-bility are established via Lyapunov funciton.
For reasonable assessment and safe exploitation of marine gas hydrate resource, it is important to determine the stability conditions of gas hydrates in marine sediment. In this paper, the seafloor water sample and se...For reasonable assessment and safe exploitation of marine gas hydrate resource, it is important to determine the stability conditions of gas hydrates in marine sediment. In this paper, the seafloor water sample and sediment sample （saturated with pore water） from Shenhu Area of South China Sea were used to synthesize methane hydrates, and the stability conditions of methane hydrates were investigated by multi-step heating dissociation method. Preliminary experimental results show that the dissociation temperature of methane hydrate both in seafloor water and marine sediment, under any given pressure, is depressed by approximately -1.4 K relative to the pure water system. This phenomenon indicates that hydrate stability in marine sediment is mainly affected by pore water ions.展开更多
Conventional finite-difference(FD)methods cannot model acoustic wave propagation beyond Courant-Friedrichs-Lewy(CFL)numbers 0.707 and 0.577 for two-dimensional(2D)and three-dimensional(3D)equal spacing cases,respectiv...Conventional finite-difference(FD)methods cannot model acoustic wave propagation beyond Courant-Friedrichs-Lewy(CFL)numbers 0.707 and 0.577 for two-dimensional(2D)and three-dimensional(3D)equal spacing cases,respectively,thereby limiting time step selection.Based on the definition of temporal and spatial FD operators,we propose a variable-length temporal and spatial operator strategy to model wave propagation beyond those CFL numbers while preserving accuracy.First,to simulate wave propagation beyond the conventional CFL stability limit,the lengths of the temporal operators are modified to exceed the lengths of the spatial operators for high-velocity zones.Second,to preserve the modeling accuracy,the velocity-dependent lengths of the temporal and spatial operators are adaptively varied.The maximum CFL numbers for the proposed method can reach 1.25 and 1.0 in high velocity contrast 2D and 3D simulation examples,respectively.We demonstrate the effectiveness of our method by modeling wave propagation in simple and complex media.展开更多
Considering the instability of data transferred existing in high speed network, a new method is proposed for improving the stability using control theory. Under this method, the mathematical model of such a network is...Considering the instability of data transferred existing in high speed network, a new method is proposed for improving the stability using control theory. Under this method, the mathematical model of such a network is established. Stability condition is derived from the mathematical model. Several simulation experiments are performed. The results show that the method can increase the stability of data transferred in terms of the congestion window, queue size, and sending rate of the source.展开更多
To further investigate car-following behaviors in the cooperative adaptive cruise control（CACC） strategy,a comprehensive control system which can handle three traffic conditions to guarantee driving efficiency and s...To further investigate car-following behaviors in the cooperative adaptive cruise control（CACC） strategy,a comprehensive control system which can handle three traffic conditions to guarantee driving efficiency and safety is designed by using three CACC models.In this control system,some vital comprehensive information,such as multiple preceding cars’ speed differences and headway,variable safety distance（VSD） and time-delay effect on the traffic current and the jamming transition have been investigated via analytical or numerical methods.Local and string stability criterion for the velocity control（VC） model and gap control（GC） model are derived via linear stability theory.Numerical simulations are conducted to study the performance of the simulated traffic flow.The simulation results show that the VC model and GC model can improve driving efficiency and suppress traffic congestion.展开更多
As the core of the Energy-Minimization Multi-Scale(EMMS) approach,the so-called stability condi-tion has been proposed to reflect the compromise between different dominant mechanisms and believed to be in-dispensable ...As the core of the Energy-Minimization Multi-Scale(EMMS) approach,the so-called stability condi-tion has been proposed to reflect the compromise between different dominant mechanisms and believed to be in-dispensable for understanding the complex nature of gas-solid fluidization systems.This approach was recently ex-tended to the study of gas-liquid bubble columns.In this article,we try to analyze the intrinsic similarity between gas-solid and gas-liquid systems by using the EMMS approach.First,the model solution spaces for the two systems are depicted through a unified numerical solution strategy,so that we are able to find three structural hierarchies in the EMMS model for gas-solid systems.This may help to understand the roles of cluster diameter correlation and stability condition.Second,a common characteristic of gas-solid and gas-liquid systems can be found by comparing the model solutions for the two systems,albeit structural parameters and stability criteria are specific in each system:two local minima of the micro-scale energy dissipation emerges simultaneously in the solution space of structure parameters,reflecting the compromise of two different dominant mechanisms.They may share an equal value at a critical condition of operating conditions,and the global minimum may shift from one to the other when the oper-ating condition changes.As a result,structure parameters such as voidage or gas hold-up exhibit a jump change due to this shift,leading to dramatic structure variation and hence regime transition of these systems.This demonstrates that it is the stability condition that drives the structure variation and system evolution,which may be the intrinsic similarity of gas-solid and gas-liquid systems.展开更多
We study the space of stability conditions on K3 surfaces from the perspective of mirror symmetry. This is done in the attractor backgrounds(moduli). We find certain highly non-generic behaviors of marginal stability ...We study the space of stability conditions on K3 surfaces from the perspective of mirror symmetry. This is done in the attractor backgrounds(moduli). We find certain highly non-generic behaviors of marginal stability walls(a key notion in the study of wall crossings)in the space of stability conditions. These correspond via mirror symmetry to some nongeneric behaviors of special Lagrangians in an attractor background. The main results can be understood as a mirror correspondence in a synthesis of the homological mirror conjecture and SYZ mirror conjecture.展开更多
This paper proposes a new method to improve the stability condition of difference scheme of a parabolic equation. Necessary and sufficient conditions of the stability of this new method are given and proved. Some nume...This paper proposes a new method to improve the stability condition of difference scheme of a parabolic equation. Necessary and sufficient conditions of the stability of this new method are given and proved. Some numerical examples show that this method has some calculation advantages.展开更多
In this paper,we point out that for a static system the eigenvalue integral relation(iσ)~2I +iσΦ+Σ=0 derived from an eigenequation (?)Ψ=[(iσ)~2(?)_2+(iσ)(?)_1+(?)_0]Ψ(r)=0 only gives the suffi- ciency of condi...In this paper,we point out that for a static system the eigenvalue integral relation(iσ)~2I +iσΦ+Σ=0 derived from an eigenequation (?)Ψ=[(iσ)~2(?)_2+(iσ)(?)_1+(?)_0]Ψ(r)=0 only gives the suffi- ciency of condition Σ>0 for the stability of a certain mode,but it can not provide the necessity to the condition in general.Three theorems presented in this paper show that under some conditions, Σ>0 makes the mode stable,while Σ<0 makes the mode unstable.展开更多
To obtain analytically relativistic quintessence anisotropic spherical solutions in the f(T)paradigm is the primary objective of this paper.To do this,the pressure anisotropy condition is imposed,and we employ a metri...To obtain analytically relativistic quintessence anisotropic spherical solutions in the f(T)paradigm is the primary objective of this paper.To do this,the pressure anisotropy condition is imposed,and we employ a metric potential of the Tolman–Kuchowicz(TK)type.We also suppose that our current model incorporates a quintessence field characterized by a parameterωq,in addition to the anisotropic matter distribution.In the presence of the parameterα,the field equations are modified by the choice of the f(T)function.The f(T)gravity parameterαadds new components to the basic physical characteristics,such as density,pressure,subliminal sound velocity,surface redshift,etc,of the present model.By selecting the compact star Her X-1 and varyingαfrom 0.5 to 2.5,we examined all the physical characteristics of the model parameter of the configuration.The graphical process demonstrates that a more compact item is produced with greater values ofα.The hydrostatic equilibrium condition of the model is discussed,as well as the mass-radius relationship for our current model is obtained.展开更多
Although the Chen-Ricles（CR）method and the Kolay-Ricles（KR）method have been applied to conduct pseudodynamic tests,they have both been found to have some adverse numerical properties,such as conditional stability ...Although the Chen-Ricles（CR）method and the Kolay-Ricles（KR）method have been applied to conduct pseudodynamic tests,they have both been found to have some adverse numerical properties,such as conditional stability for stiffness hardening systems and an unusual overshoot in the steady-state response of a high-frequency mode.An improved formulation for each method can be achieved by using a stability amplification factor to boost the unconditional stability range for stiffness hardening systems and a loading correction term to eliminate the unusual overshoot in the steady-state response of a high-frequency mode.The details for developing improved formulations for each method are shown in this work.展开更多
In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O（τ^2＋ h%4）, and the stability c...In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O（τ^2＋ h%4）, and the stability condition is given. Finally, the numerical examples and numerical results are presented to show the advantage of the schemes and the correctness of theoretical analysis.展开更多
The role of dispersions in the numerical solutions of hydrodynamic equation systems has been realized for long time.It is only during the last two decades that extensive studies on the dispersion-controlled dissipativ...The role of dispersions in the numerical solutions of hydrodynamic equation systems has been realized for long time.It is only during the last two decades that extensive studies on the dispersion-controlled dissipative(DCD)schemes were reported.The studies have demonstrated that this kind of the schemes is distinct from conventional dissipation-based schemes in which the dispersion term of the modified equation is not considered in scheme construction to avoid nonphysical oscillation occurring in shock wave simulations.The principle of the dispersion controlled aims at removing nonphysical oscillations by making use of dispersion characteristics instead of adding artificial viscosity to dissipate the oscillation as the conventional schemes do.Research progresses on the dispersion- controlled principles are reviewed in this paper,including the exploration of the role of dispersions in numerical simulations,the development of the dispersion-controlled principles,efforts devoted to high-order dispersion-controlled dissipative schemes,the extension to both the finite volume and the finite element methods,scheme verification and solution validation,and comments on several aspects of the schemes from author's viewpoint.展开更多
The parameter X of the Muskingum method is a physical parameter that reflects the flood peak attenuation and hydrograph shape flattening of a diffusion wave in motion. In this paper, the historic process that hydrolog...The parameter X of the Muskingum method is a physical parameter that reflects the flood peak attenuation and hydrograph shape flattening of a diffusion wave in motion. In this paper, the historic process that hydrologists have undergone to find a physical explanation of this parameter is briefly discussed. Based on the fact that the Muskingum method is the second-order accuracy difference solution to the diffusion wave equation, its numerical stability condition is analyzed, and a conclusion is drawn： X ≤ 0.5 is the uniform condition satisfying the demands for its physical meaning and numerical stability. It is also pointed out that the methods that regard the sum of squares of differences between the calculated and observed discharges or stages as the objective function and the routing coefficients C0, C1 and C2 of the Muskingum method as the optimization parameters cannot guarantee the physical meaning of X.展开更多
This article deals with the consensus problem of multi-agent systems by developing a fixed-time consensus control approach with a dynamic event-triggered rule. First, a new fixedtime stability condition is obtained wh...This article deals with the consensus problem of multi-agent systems by developing a fixed-time consensus control approach with a dynamic event-triggered rule. First, a new fixedtime stability condition is obtained where the less conservative settling time is given such that the theoretical settling time can well reflect the real consensus time. Second, a dynamic event-triggered rule is designed to decrease the use of chip and network resources where Zeno behaviors can be avoided after consensus is achieved, especially for finite/fixed-time consensus control approaches. Third, in terms of the developed dynamic event-triggered rule, a fixed-time consensus control approach by introducing a new item is proposed to coordinate the multi-agent system to reach consensus. The corresponding stability of the multi-agent system with the proposed control approach and dynamic eventtriggered rule is analyzed based on Lyapunov theory and the fixed-time stability theorem. At last, the effectiveness of the dynamic event-triggered fixed-time consensus control approach is verified by simulations and experiments for the problem of magnetic map construction based on multiple mobile robots.展开更多
A car-following model is presented, in which the effects of non-motor vehicles on adjacent lanes are taken into ac- count. A control signal including the velocity differences between the following vehicle and the targ...A car-following model is presented, in which the effects of non-motor vehicles on adjacent lanes are taken into ac- count. A control signal including the velocity differences between the following vehicle and the target vehicle is introduced according to the feedback control theory. The stability condition for the new model is derived. Numerical simulation is used to demonstrate the advantage of the new model including the control signal; the results are consistent with the analytical ones展开更多
This paper is concerned with the design of a memory state feedback controller for linear systems with interval time-varying delays.The time delay is assumed to be a time-varying continuous function belonging to a give...This paper is concerned with the design of a memory state feedback controller for linear systems with interval time-varying delays.The time delay is assumed to be a time-varying continuous function belonging to a given interval,which means that the lower and upper bounds of time-varying delay are available.First,a less conservative delay-range-dependent stability criteria is proposed by using a new interval fraction method.In the process of controller synthesis,the history information of system is considered in the controller design by introducing the lower delay state.Moreover,the usual memoryless state feedback controller for the underlying systems could be considered as a special case of the memory case.Finally,two numerical examples are given to show the effectiveness of the proposed method.展开更多
This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model ...This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 10275023）, and by the Science Foundation of the Laboratory of Magnetic Resonance and Atomic and Molecular Physics of China （Grant No T152504）.
文摘Using a direct perturbation method, we investigate the stability of a diatomic molecule modelled by a weakly laser-driven Morse oscillator. It is shown that stationary state solution of the system is stable in the sense of Lyapunov and the periodical one possesses conditional stability, namely its stability depends on the initial conditions and system parameters. The corresponding sufficient and necessary conditions are established that indicate the stable states associated with some discrete energies. The results reveal how a diatomic molecule can be stabilized or dissociated with a weak laser, and demonstrate that the mathematical conditional stability works in the considered physical system.
基金support by “R&D Program for Forest Science Technology(RS-2024-0040 3460)” provided by Korea Forest Service(Korea Forestry Promotion Institute)
文摘Dear Editor,H_(∞)This letter develops a new framework for the robust stability and performance conditions as well as the relevant controller synthesis with respect to uncertain robot manipulators.There often exist model uncertainties between the nominal model and the real robot manipulator and disturbances. Hence, dealing with their effects plays a crucial role in leading to high tracking performances, as discussed in [1]–[5].
基金Supported by Natural Science Foundation of Beijing (1022004)
文摘This paper introdnces some concepts of conditional stability of stochasticVolterra equations with anticipating kernel. Snfficient conditions of these types of sta-bility are established via Lyapunov funciton.
基金supported by the National Basic Research Program of China(No.2009CB219503)the Special Fund for Ministry of Land and Resources research of China in the Public Interest(201111026)the Natural Science Foundation of Shandong Province of China(No.ZR2009FQ017)
文摘For reasonable assessment and safe exploitation of marine gas hydrate resource, it is important to determine the stability conditions of gas hydrates in marine sediment. In this paper, the seafloor water sample and sediment sample （saturated with pore water） from Shenhu Area of South China Sea were used to synthesize methane hydrates, and the stability conditions of methane hydrates were investigated by multi-step heating dissociation method. Preliminary experimental results show that the dissociation temperature of methane hydrate both in seafloor water and marine sediment, under any given pressure, is depressed by approximately -1.4 K relative to the pure water system. This phenomenon indicates that hydrate stability in marine sediment is mainly affected by pore water ions.
基金the National Natural Science Foundation of China(No.41874144)the Research Foundation of China University of PetroleumBeijing at Karamay(RCYJ2018A-01-001).
文摘Conventional finite-difference(FD)methods cannot model acoustic wave propagation beyond Courant-Friedrichs-Lewy(CFL)numbers 0.707 and 0.577 for two-dimensional(2D)and three-dimensional(3D)equal spacing cases,respectively,thereby limiting time step selection.Based on the definition of temporal and spatial FD operators,we propose a variable-length temporal and spatial operator strategy to model wave propagation beyond those CFL numbers while preserving accuracy.First,to simulate wave propagation beyond the conventional CFL stability limit,the lengths of the temporal operators are modified to exceed the lengths of the spatial operators for high-velocity zones.Second,to preserve the modeling accuracy,the velocity-dependent lengths of the temporal and spatial operators are adaptively varied.The maximum CFL numbers for the proposed method can reach 1.25 and 1.0 in high velocity contrast 2D and 3D simulation examples,respectively.We demonstrate the effectiveness of our method by modeling wave propagation in simple and complex media.
基金the National Natural Science Foundation of China (50579022 50539140).
文摘Considering the instability of data transferred existing in high speed network, a new method is proposed for improving the stability using control theory. Under this method, the mathematical model of such a network is established. Stability condition is derived from the mathematical model. Several simulation experiments are performed. The results show that the method can increase the stability of data transferred in terms of the congestion window, queue size, and sending rate of the source.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.71571107 and 11302110)The Scientific Research Fund of Zhejiang Province,China(Grant Nos.LY15A020007,LY15E080013,and LY16G010003)+2 种基金The Natural Science Foundation of Ningbo City(Grant Nos.2014A610030and 2015A610299)the Fund from the Government of the Hong Kong Administrative Region,China(Grant No.City U11209614)the K C Wong Magna Fund in Ningbo University,China
文摘To further investigate car-following behaviors in the cooperative adaptive cruise control（CACC） strategy,a comprehensive control system which can handle three traffic conditions to guarantee driving efficiency and safety is designed by using three CACC models.In this control system,some vital comprehensive information,such as multiple preceding cars’ speed differences and headway,variable safety distance（VSD） and time-delay effect on the traffic current and the jamming transition have been investigated via analytical or numerical methods.Local and string stability criterion for the velocity control（VC） model and gap control（GC） model are derived via linear stability theory.Numerical simulations are conducted to study the performance of the simulated traffic flow.The simulation results show that the VC model and GC model can improve driving efficiency and suppress traffic congestion.
基金Supported by the National Basic Research Program of China (2009CB219906)the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA07080304)the International Science and Technology Cooperation Program (2011DFA61360)
文摘As the core of the Energy-Minimization Multi-Scale(EMMS) approach,the so-called stability condi-tion has been proposed to reflect the compromise between different dominant mechanisms and believed to be in-dispensable for understanding the complex nature of gas-solid fluidization systems.This approach was recently ex-tended to the study of gas-liquid bubble columns.In this article,we try to analyze the intrinsic similarity between gas-solid and gas-liquid systems by using the EMMS approach.First,the model solution spaces for the two systems are depicted through a unified numerical solution strategy,so that we are able to find three structural hierarchies in the EMMS model for gas-solid systems.This may help to understand the roles of cluster diameter correlation and stability condition.Second,a common characteristic of gas-solid and gas-liquid systems can be found by comparing the model solutions for the two systems,albeit structural parameters and stability criteria are specific in each system:two local minima of the micro-scale energy dissipation emerges simultaneously in the solution space of structure parameters,reflecting the compromise of two different dominant mechanisms.They may share an equal value at a critical condition of operating conditions,and the global minimum may shift from one to the other when the oper-ating condition changes.As a result,structure parameters such as voidage or gas hold-up exhibit a jump change due to this shift,leading to dramatic structure variation and hence regime transition of these systems.This demonstrates that it is the stability condition that drives the structure variation and system evolution,which may be the intrinsic similarity of gas-solid and gas-liquid systems.
文摘We study the space of stability conditions on K3 surfaces from the perspective of mirror symmetry. This is done in the attractor backgrounds(moduli). We find certain highly non-generic behaviors of marginal stability walls(a key notion in the study of wall crossings)in the space of stability conditions. These correspond via mirror symmetry to some nongeneric behaviors of special Lagrangians in an attractor background. The main results can be understood as a mirror correspondence in a synthesis of the homological mirror conjecture and SYZ mirror conjecture.
文摘This paper proposes a new method to improve the stability condition of difference scheme of a parabolic equation. Necessary and sufficient conditions of the stability of this new method are given and proved. Some numerical examples show that this method has some calculation advantages.
基金The project supported by the National Natural Science Foundation of China.
文摘In this paper,we point out that for a static system the eigenvalue integral relation(iσ)~2I +iσΦ+Σ=0 derived from an eigenequation (?)Ψ=[(iσ)~2(?)_2+(iσ)(?)_1+(?)_0]Ψ(r)=0 only gives the suffi- ciency of condition Σ>0 for the stability of a certain mode,but it can not provide the necessity to the condition in general.Three theorems presented in this paper show that under some conditions, Σ>0 makes the mode stable,while Σ<0 makes the mode unstable.
基金National Research Foundation(NRF)of South Africa for the postdoctoral fellowship award。
文摘To obtain analytically relativistic quintessence anisotropic spherical solutions in the f(T)paradigm is the primary objective of this paper.To do this,the pressure anisotropy condition is imposed,and we employ a metric potential of the Tolman–Kuchowicz(TK)type.We also suppose that our current model incorporates a quintessence field characterized by a parameterωq,in addition to the anisotropic matter distribution.In the presence of the parameterα,the field equations are modified by the choice of the f(T)function.The f(T)gravity parameterαadds new components to the basic physical characteristics,such as density,pressure,subliminal sound velocity,surface redshift,etc,of the present model.By selecting the compact star Her X-1 and varyingαfrom 0.5 to 2.5,we examined all the physical characteristics of the model parameter of the configuration.The graphical process demonstrates that a more compact item is produced with greater values ofα.The hydrostatic equilibrium condition of the model is discussed,as well as the mass-radius relationship for our current model is obtained.
文摘Although the Chen-Ricles（CR）method and the Kolay-Ricles（KR）method have been applied to conduct pseudodynamic tests,they have both been found to have some adverse numerical properties,such as conditional stability for stiffness hardening systems and an unusual overshoot in the steady-state response of a high-frequency mode.An improved formulation for each method can be achieved by using a stability amplification factor to boost the unconditional stability range for stiffness hardening systems and a loading correction term to eliminate the unusual overshoot in the steady-state response of a high-frequency mode.The details for developing improved formulations for each method are shown in this work.
基金Supported by NSF of the Education Department of Henan Province(20031100010)
文摘In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O（τ^2＋ h%4）, and the stability condition is given. Finally, the numerical examples and numerical results are presented to show the advantage of the schemes and the correctness of theoretical analysis.
基金The project supported by the National Natural Science Foundation of China(90205027)
文摘The role of dispersions in the numerical solutions of hydrodynamic equation systems has been realized for long time.It is only during the last two decades that extensive studies on the dispersion-controlled dissipative(DCD)schemes were reported.The studies have demonstrated that this kind of the schemes is distinct from conventional dissipation-based schemes in which the dispersion term of the modified equation is not considered in scheme construction to avoid nonphysical oscillation occurring in shock wave simulations.The principle of the dispersion controlled aims at removing nonphysical oscillations by making use of dispersion characteristics instead of adding artificial viscosity to dissipate the oscillation as the conventional schemes do.Research progresses on the dispersion- controlled principles are reviewed in this paper,including the exploration of the role of dispersions in numerical simulations,the development of the dispersion-controlled principles,efforts devoted to high-order dispersion-controlled dissipative schemes,the extension to both the finite volume and the finite element methods,scheme verification and solution validation,and comments on several aspects of the schemes from author's viewpoint.
基金supported by the Scientific and Technological Basic Research Grant of the Ministry of Science and Technology of China (Grant No. 2007FY140900)the Public Welfare Industry Special Fund Project of the Ministry of Water Resources of China (Grant No. 200801033)
文摘The parameter X of the Muskingum method is a physical parameter that reflects the flood peak attenuation and hydrograph shape flattening of a diffusion wave in motion. In this paper, the historic process that hydrologists have undergone to find a physical explanation of this parameter is briefly discussed. Based on the fact that the Muskingum method is the second-order accuracy difference solution to the diffusion wave equation, its numerical stability condition is analyzed, and a conclusion is drawn： X ≤ 0.5 is the uniform condition satisfying the demands for its physical meaning and numerical stability. It is also pointed out that the methods that regard the sum of squares of differences between the calculated and observed discharges or stages as the objective function and the routing coefficients C0, C1 and C2 of the Muskingum method as the optimization parameters cannot guarantee the physical meaning of X.
基金supported in part by the National Natural Science Foundation of China (62073108)the Zhejiang Provincial Natural Science Foundation(LZ23F030004)+1 种基金the Key Research and Development Project of Zhejiang Province (2019C04018)the Fundamental Research Funds for the Provincial Universities of Zhejiang (GK229909299001-004)。
文摘This article deals with the consensus problem of multi-agent systems by developing a fixed-time consensus control approach with a dynamic event-triggered rule. First, a new fixedtime stability condition is obtained where the less conservative settling time is given such that the theoretical settling time can well reflect the real consensus time. Second, a dynamic event-triggered rule is designed to decrease the use of chip and network resources where Zeno behaviors can be avoided after consensus is achieved, especially for finite/fixed-time consensus control approaches. Third, in terms of the developed dynamic event-triggered rule, a fixed-time consensus control approach by introducing a new item is proposed to coordinate the multi-agent system to reach consensus. The corresponding stability of the multi-agent system with the proposed control approach and dynamic eventtriggered rule is analyzed based on Lyapunov theory and the fixed-time stability theorem. At last, the effectiveness of the dynamic event-triggered fixed-time consensus control approach is verified by simulations and experiments for the problem of magnetic map construction based on multiple mobile robots.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.11072117 and 61074142)the Scientific Research Fund of the Educational Department of Zhejiang Province,China (Grant No.Z201119278)+2 种基金the Natural Science Foundation of Ningbo,China (Grant Nos.2012A610152 and 2012A610038)the Disciplinary Project of Ningbo,China (Grant No.SZXL1067)the K.C.Wong Magna Fund in Ningbo University,China
文摘A car-following model is presented, in which the effects of non-motor vehicles on adjacent lanes are taken into ac- count. A control signal including the velocity differences between the following vehicle and the target vehicle is introduced according to the feedback control theory. The stability condition for the new model is derived. Numerical simulation is used to demonstrate the advantage of the new model including the control signal; the results are consistent with the analytical ones
基金supported by the 111 Project(No.B08015)the National Natural Science Foundation of China(No.60534010,60572070,60774048,60728307)the Program for Changjiang Scholars and Innovative Research Groups of China(No.60521003)
文摘This paper is concerned with the design of a memory state feedback controller for linear systems with interval time-varying delays.The time delay is assumed to be a time-varying continuous function belonging to a given interval,which means that the lower and upper bounds of time-varying delay are available.First,a less conservative delay-range-dependent stability criteria is proposed by using a new interval fraction method.In the process of controller synthesis,the history information of system is considered in the controller design by introducing the lower delay state.Moreover,the usual memoryless state feedback controller for the underlying systems could be considered as a special case of the memory case.Finally,two numerical examples are given to show the effectiveness of the proposed method.
基金Supported by National Natural Science Foundation of China(50977008,60904017,60774048,60728307),the Funds for Creative Research Groups of China(60521003),the Program for Cheung Kong Scholars and Innovative Research Team in University(IRT0421),and the 111 Project(B08015),National High Technology Research and Development Program of China(863 Program)(2006AA04Z183)
文摘This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.
