A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is const...A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is constructed.And then,by using the theory of differential inequalities the uniformly validity of solution is proved.展开更多
A class of initial boundary value problems of differential-difference equations for reaction diffusion with a small time delay is considered. Under suitable conditions and by using the stretched variable method, a for...A class of initial boundary value problems of differential-difference equations for reaction diffusion with a small time delay is considered. Under suitable conditions and by using the stretched variable method, a formal asymptotic solution is constructed. Then, by use of the theory of differential inequalities, the uniform validity of the solution is proved.展开更多
The reaction diffusion Gray-Scott model with time delay is put forward with the assumption of Neumann boundary condition is satisfied. Based on the Turing bifurcation condition, the Turing curves on two parameter plan...The reaction diffusion Gray-Scott model with time delay is put forward with the assumption of Neumann boundary condition is satisfied. Based on the Turing bifurcation condition, the Turing curves on two parameter plane are discussed without time delay. The normal form is computed via applying Lyapunov-Schmidt reduction method in system of PDE, and the bifurcating direction of pitchfork bifurcation underlying codimension-1 singularity of Turing point is computed. The continuation of Pitchfork bifurcation is simulated with varying free parameter continuously near the turing point, which is in coincidence with the theoritical analysis results. The wave pattern formation in the case of turing instability is also simulated which discover Turing oscillation phenomena from periodicity to irregularity.展开更多
The bending behavior of double-row stabilizing plies is associated with the constructional time delay(CTD),which can be defined as the time interval between the installations of the front stabilizing pile and the rear...The bending behavior of double-row stabilizing plies is associated with the constructional time delay(CTD),which can be defined as the time interval between the installations of the front stabilizing pile and the rear stabilizing pile.This paper investigates the effect of CTD on the bending moments of double-row stabilizing piles and a method for determining the optimal CTD is proposed.The stabilizing pile is modeled as a cantilever pile embedded in the Winkler elastic foundation.A triangular distributed earth pressure is assumed on the pile segment in the sliding layer.The front stabilizing pile and the rear stabilizing pile are connected by a beam with pinned joints.The analytical solutions of bending moments on the front and the rear stabilizing piles are derived and the accuracy of bending moment solutions is validated by comparing the tensile strain measured from the Hongyan landslide project,Taizhou,Zhejiang,China.It is concluded that CTD has a significant influence on the bending moments of double-row stabilizing piles.An optimal CTD can be obtained when the maximum tensile stress in the front stabilizing pile is equal to that in the rear stabilizing pile,which is 1.4 months for the Hongyan landslide project.展开更多
An extended car-following model with multiple delays is constructed to describe driver's driving behavior.Through stability analysis,the stability condition of this uncontrolled model is given.To dampen the negati...An extended car-following model with multiple delays is constructed to describe driver's driving behavior.Through stability analysis,the stability condition of this uncontrolled model is given.To dampen the negative impact of the driver's multiple delays(i.e.,stability condition is not satisfied),a novel control strategy is proposed to assist the driver in adjusting vehicle operation.The control strategy consists of two parts:the design of control term as well as the design of the parameters in the term.Bifurcation analysis is performed to illustrate the necessity of the design of parameters in control terms.In the course of the design of parameters in the control term,we improve the definite integral stability method to reduce the iterations by incorporating the characteristics of bifurcation,which can determine the appropriate parameters in the control terms more quickly.Finally,in the case study,we validate the control strategy by utilizing measured data and configuring scenario,which is closer to the actual traffic.The results of validation show that the control strategy can effectively stabilize the unstable traffic flow caused by driver's delays.展开更多
Through integrating advanced communication and data processing technologies into smart vehicles and roadside infrastructures,the Intelligent Transportation System(ITS)has evolved as a promising paradigm for improving ...Through integrating advanced communication and data processing technologies into smart vehicles and roadside infrastructures,the Intelligent Transportation System(ITS)has evolved as a promising paradigm for improving safety,efficiency of the transportation system.However,the strict delay requirement of the safety-related applications is still a great challenge for the ITS,especially in dense traffic environment.In this paper,we introduce the metric called Perception-Reaction Time(PRT),which reflects the time consumption of safety-related applications and is closely related to road efficiency and security.With the integration of the incorporating information-centric networking technology and the fog virtualization approach,we propose a novel fog resource scheduling mechanism to minimize the PRT.Furthermore,we adopt a deep reinforcement learning approach to design an on-line optimal resource allocation scheme.Numerical results demonstrate that our proposed schemes is able to reduce about 70%of the RPT compared with the traditional approach.展开更多
A simple algorithm is proposed for step-by-step time integration of stiff ODEs in Chemical Kinetics. No predictor-corrector technique is used within each step of the algorithm. It is assumed that species concentration...A simple algorithm is proposed for step-by-step time integration of stiff ODEs in Chemical Kinetics. No predictor-corrector technique is used within each step of the algorithm. It is assumed that species concentrations less than 10-6 mol·L-1 do not activate any chemical reaction. So, within each step, the time steplength Δt of the algorithm is determined from the fastest reaction rate maxR by the formula Δt = 10-6mol·L-1/max R. All the reversible elementary reactions occur simultaneously;however, by a simple book-keeping technique, the updating of species concentrations, within each step of the algorithm, is performed within each elementary reaction separately. The above proposed simple algorithm for Chemical Kinetics is applied to a simple model for hydrogen combustion with only five reversible elementary reactions (Initiation, Propagation, First and Second Branching, Termination by wall destruction) with six species (H2, O2, H, O, HO, H2O). These five reversible reactions are recommended in the literature as the most significant elementary reactions of hydrogen combustion [1] [2]. Based on the proposed here simple algorithm for Chemical Kinetics, applied to the global mechanism of proposed five reversible elementary reactions for hydrogen combustion, a simple and short computer program has been developed with only about 120 Fortran instructions. By this proposed program, the following are obtained: 1) The total species concentration of hydrogen combustion, starting from the sum of initial reactants concentrations [H2] + [O2], gradually diminishes, due to termination reaction by wall destruction, and tends to the final concentration of the product [H2O], that is to the 2/3 of its initial value, in accordance to the established overall stoichiometric reaction of hydrogen combustion 2H2 + O2 → 2H2O. 2) Time-histories for concentrations of main species H2, O2, H, H2O of hydrogen combustion, in explosion and equilibrium regions, obtained by the proposed program, are compared to corresponding ones obtained by accurate computational studies of [3]. 3) In the first step of the algorithm, the only nonzero species concentrations are those of reactants [H2], [O2]. So, the maximum reaction rate is that of the forward initiation reaction max R = Rif = kif[H2] [O2], where the rate constant kif is very slow. Thus, the first time steplength Δt1 = 10-6mol·L-1/max R results long in sec. After the first step, the sequences of all the following Δt’s are very short, in μsec. So, the first time steplength Δt1 can be considered as ignition delay time. 4) It is assumed that explosion corresponds to ignition delay time Δt1 t1 = 10 sec., can be considered as explosion limit curve. This curve is compared to the corresponding one obtained by the accurate computational studies of [2].展开更多
基金the National Natural Science Foundation of China (Nos.40676016 and 40876010)the National Basic Research Program (973) of China (Nos.2003CB415101-03 and 2004CB418304)+2 种基金the Knowledge Innovation Project of Chinese Academy of Sciences (No.KZCX2-YW-Q03-08)LASG State Key Laboratory Special FundE-Institutes of Shanghai Municipal Education Commission (No.E03004)
文摘A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is constructed.And then,by using the theory of differential inequalities the uniformly validity of solution is proved.
基金Project supported by the National Natural Science Foundation of China (No. 40876010)the Major Projects of Knowledge Innovation Program of Chinese Academy of Sciences (No. KZCX2-YW-Q03-08)+2 种基金the Research and Development Special Fund for Public Welfare Industry (No. GYHY200806010)the Special Fund of the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, the Foundation of Shanghai Municipal Education Commission(No. E03004)the Natural Science Foundation of Zhejiang Province (No. Y6090164)
文摘A class of initial boundary value problems of differential-difference equations for reaction diffusion with a small time delay is considered. Under suitable conditions and by using the stretched variable method, a formal asymptotic solution is constructed. Then, by use of the theory of differential inequalities, the uniform validity of the solution is proved.
文摘The reaction diffusion Gray-Scott model with time delay is put forward with the assumption of Neumann boundary condition is satisfied. Based on the Turing bifurcation condition, the Turing curves on two parameter plane are discussed without time delay. The normal form is computed via applying Lyapunov-Schmidt reduction method in system of PDE, and the bifurcating direction of pitchfork bifurcation underlying codimension-1 singularity of Turing point is computed. The continuation of Pitchfork bifurcation is simulated with varying free parameter continuously near the turing point, which is in coincidence with the theoritical analysis results. The wave pattern formation in the case of turing instability is also simulated which discover Turing oscillation phenomena from periodicity to irregularity.
基金Project supported by the National Natural Science Foundation of China (No. 40972187)the Key Innovation Team Support Project of Zhejiang Province (No. 2009R50050)
文摘The bending behavior of double-row stabilizing plies is associated with the constructional time delay(CTD),which can be defined as the time interval between the installations of the front stabilizing pile and the rear stabilizing pile.This paper investigates the effect of CTD on the bending moments of double-row stabilizing piles and a method for determining the optimal CTD is proposed.The stabilizing pile is modeled as a cantilever pile embedded in the Winkler elastic foundation.A triangular distributed earth pressure is assumed on the pile segment in the sliding layer.The front stabilizing pile and the rear stabilizing pile are connected by a beam with pinned joints.The analytical solutions of bending moments on the front and the rear stabilizing piles are derived and the accuracy of bending moment solutions is validated by comparing the tensile strain measured from the Hongyan landslide project,Taizhou,Zhejiang,China.It is concluded that CTD has a significant influence on the bending moments of double-row stabilizing piles.An optimal CTD can be obtained when the maximum tensile stress in the front stabilizing pile is equal to that in the rear stabilizing pile,which is 1.4 months for the Hongyan landslide project.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China(Grant No.LY20G010004)the Program of Humanities and Social Science of Education Ministry of China(Grant No.20YJA630008)+1 种基金the National Key Research and Development Program of China–Traffic Modeling,Surveillance and Control with Connected&Automated Vehicles(Grant No.2017YFE9134700)the K.C.Wong Magna Fund in Ningbo University,China。
文摘An extended car-following model with multiple delays is constructed to describe driver's driving behavior.Through stability analysis,the stability condition of this uncontrolled model is given.To dampen the negative impact of the driver's multiple delays(i.e.,stability condition is not satisfied),a novel control strategy is proposed to assist the driver in adjusting vehicle operation.The control strategy consists of two parts:the design of control term as well as the design of the parameters in the term.Bifurcation analysis is performed to illustrate the necessity of the design of parameters in control terms.In the course of the design of parameters in the control term,we improve the definite integral stability method to reduce the iterations by incorporating the characteristics of bifurcation,which can determine the appropriate parameters in the control terms more quickly.Finally,in the case study,we validate the control strategy by utilizing measured data and configuring scenario,which is closer to the actual traffic.The results of validation show that the control strategy can effectively stabilize the unstable traffic flow caused by driver's delays.
基金supported by National Key R&D Program of China(No.2018YFE010267)the Science and Technology Program of Sichuan Province,China(No.2019YFH0007)+2 种基金the National Natural Science Foundation of China(No.61601083)the Xi’an Key Laboratory of Mobile Edge Computing and Security(No.201805052-ZD-3CG36)the EU H2020 Project COSAFE(MSCA-RISE-2018-824019)
文摘Through integrating advanced communication and data processing technologies into smart vehicles and roadside infrastructures,the Intelligent Transportation System(ITS)has evolved as a promising paradigm for improving safety,efficiency of the transportation system.However,the strict delay requirement of the safety-related applications is still a great challenge for the ITS,especially in dense traffic environment.In this paper,we introduce the metric called Perception-Reaction Time(PRT),which reflects the time consumption of safety-related applications and is closely related to road efficiency and security.With the integration of the incorporating information-centric networking technology and the fog virtualization approach,we propose a novel fog resource scheduling mechanism to minimize the PRT.Furthermore,we adopt a deep reinforcement learning approach to design an on-line optimal resource allocation scheme.Numerical results demonstrate that our proposed schemes is able to reduce about 70%of the RPT compared with the traditional approach.
文摘A simple algorithm is proposed for step-by-step time integration of stiff ODEs in Chemical Kinetics. No predictor-corrector technique is used within each step of the algorithm. It is assumed that species concentrations less than 10-6 mol·L-1 do not activate any chemical reaction. So, within each step, the time steplength Δt of the algorithm is determined from the fastest reaction rate maxR by the formula Δt = 10-6mol·L-1/max R. All the reversible elementary reactions occur simultaneously;however, by a simple book-keeping technique, the updating of species concentrations, within each step of the algorithm, is performed within each elementary reaction separately. The above proposed simple algorithm for Chemical Kinetics is applied to a simple model for hydrogen combustion with only five reversible elementary reactions (Initiation, Propagation, First and Second Branching, Termination by wall destruction) with six species (H2, O2, H, O, HO, H2O). These five reversible reactions are recommended in the literature as the most significant elementary reactions of hydrogen combustion [1] [2]. Based on the proposed here simple algorithm for Chemical Kinetics, applied to the global mechanism of proposed five reversible elementary reactions for hydrogen combustion, a simple and short computer program has been developed with only about 120 Fortran instructions. By this proposed program, the following are obtained: 1) The total species concentration of hydrogen combustion, starting from the sum of initial reactants concentrations [H2] + [O2], gradually diminishes, due to termination reaction by wall destruction, and tends to the final concentration of the product [H2O], that is to the 2/3 of its initial value, in accordance to the established overall stoichiometric reaction of hydrogen combustion 2H2 + O2 → 2H2O. 2) Time-histories for concentrations of main species H2, O2, H, H2O of hydrogen combustion, in explosion and equilibrium regions, obtained by the proposed program, are compared to corresponding ones obtained by accurate computational studies of [3]. 3) In the first step of the algorithm, the only nonzero species concentrations are those of reactants [H2], [O2]. So, the maximum reaction rate is that of the forward initiation reaction max R = Rif = kif[H2] [O2], where the rate constant kif is very slow. Thus, the first time steplength Δt1 = 10-6mol·L-1/max R results long in sec. After the first step, the sequences of all the following Δt’s are very short, in μsec. So, the first time steplength Δt1 can be considered as ignition delay time. 4) It is assumed that explosion corresponds to ignition delay time Δt1 t1 = 10 sec., can be considered as explosion limit curve. This curve is compared to the corresponding one obtained by the accurate computational studies of [2].
基金the National Basic Research Development Program of China(No.2002CB312102)the NationalNatural Science Foundation of China(No.60475034+3 种基金6064300760675047)the National High Technology Research and DevelopmentProgram of China(No.2006AA04Z246)the Fund of Excellent Thesis of Doctor's Degree from Southeast University
基金This work was supported by the National Key Research and Development Program of China(No.2018YFB1004901)the Natural Science Foundation(No.LY20F020019+3 种基金LQ19F020012LQ20F020001)Basic Public Welfare Research Project(No.LGF19E050005)Major Scientific Research Project of Zhejiang Lab(No.2019MC0AD01)of Zhejiang Province,China。
