The numerical analysis of the approximate inertial manifold in,weakly damped forced KdV equation is given. The results of numerical analysis under five models is the same as that of nonlinear spectral analysis.
区域综合能源系统(regional integrated energy system,RIES)的最优能流计算是求解RIES的设备配置、优化调度、故障分析等问题的基础。考虑供冷/热和供气管道传输能量的动态特性,建立RIES动态最优能流计算模型,其中基于特征线法获得了供...区域综合能源系统(regional integrated energy system,RIES)的最优能流计算是求解RIES的设备配置、优化调度、故障分析等问题的基础。考虑供冷/热和供气管道传输能量的动态特性,建立RIES动态最优能流计算模型,其中基于特征线法获得了供冷/热管道和供气管道动态偏微分方程的代数解析解。针对基于供冷/热系统质–量调节模式下管道能量传输时滞变量造成RIES的动态能流计算模型难以求解的问题,提出采用分段插值法获得供冷/热管道两端节点温度之间关系的近似表达式并加入动态最优能流计算模型中。此外,针对优化模型中供冷/热系统的流量与温度相乘的双线性项,提出一种能够缩紧松弛间隙的分段凸包络松弛方法将原混合整数非线性优化模型转化为混合整数二次约束规划模型,能够在保证计算精度的同时实现高效求解。最后以某个RIES算例进行分析,验证了所提方法的计算准确性和高效性,并与常用的质调节模式相比,表明在供冷/热系统质–量调节模式下能找到经济性更优的RIES运行点。展开更多
Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equati...Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.展开更多
A new theory on the construction of optimal truncated Low-Dimensional Dynamical Systems (LDDSs) with different physical meanings has been developed, The physical properties of the optimal bases are reflected in the us...A new theory on the construction of optimal truncated Low-Dimensional Dynamical Systems (LDDSs) with different physical meanings has been developed, The physical properties of the optimal bases are reflected in the user-defined optimal conditions, Through the analysis of linear and nonlinear examples, it is shown that the LDDSs constructed by using the Proper Orthogonal Decomposition (POD) method are not the optimum. After comparing the errors of LDDSs based on the new theory POD and Fourier methods, it is concluded that the LDDSs based on the new theory are optimally truncated and catch the desired physical properties of the systems.展开更多
A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriat...A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence.展开更多
We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our constru...We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.展开更多
When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The q...When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The quintic B-spline collocation method is used for solving such nonlinear partial differential equations. The developed plan uses the collocation approach and finite difference method to solve the problem under consideration. The given problem is discretized in both time and space directions. Forward difference formula is used for temporal discretization. Collocation method is used for spatial discretization. Additionally, by using Von Neumann stability analysis, it is demonstrated that the devised scheme is stable and convergent with regard to time. Examining two analytical approaches to show the effectiveness and performance of our approximate solution.展开更多
Noise reduction is one of the most exciting problems in electronic speckle pattern interferometry. We present a homomorphic partial differential equation filtering method for interferometry fringe patterns. The diffus...Noise reduction is one of the most exciting problems in electronic speckle pattern interferometry. We present a homomorphic partial differential equation filtering method for interferometry fringe patterns. The diffusion speed of the equation is determined based on the fringe density. We test the new method on the computer-simulated fringe pattern and experimentally obtain the fringe pattern, and evaluate its filtering performance. The qualitative and quantitative analysis shows that this technique can filter off the additive and multiplicative noise of the fringe patterns effectively, and avoid blurring high-density fringe. It is more capable of improving the quality of fringe patterns than the classical filtering methods.展开更多
We present quantum numerical methods for the typical initial boundary value problems(IBVPs)of convection-diffusion equations in fluid dynamics.The IBVP is discretized into a series of linear systems via finite differe...We present quantum numerical methods for the typical initial boundary value problems(IBVPs)of convection-diffusion equations in fluid dynamics.The IBVP is discretized into a series of linear systems via finite difference methods and explicit time marching schemes.To solve these discrete systems in quantum computers,we design a series of quantum circuits,including four stages of encoding,amplification,adding source terms,and incorporating boundary conditions.In the encoding stage,the initial condition is encoded in the amplitudes of quantum registers as a state vector to take advantage of quantum algorithms in space complexity.In the following three stages,the discrete differential operators in classical computing are converted into unitary evolutions to satisfy the postulate in quantum systems.The related arithmetic calculations in quantum amplitudes are also realized to sum up the increments from these stages.The proposed quantum algorithm is implemented within the open-source quantum computing framework Qiskit[2].By simulating one-dimensional transient problems,including the Helmholtz equation,the Burgers’equation,and Navier-Stokes equations,we demonstrate the capability of quantum computers in fluid dynamics.展开更多
文摘The numerical analysis of the approximate inertial manifold in,weakly damped forced KdV equation is given. The results of numerical analysis under five models is the same as that of nonlinear spectral analysis.
文摘区域综合能源系统(regional integrated energy system,RIES)的最优能流计算是求解RIES的设备配置、优化调度、故障分析等问题的基础。考虑供冷/热和供气管道传输能量的动态特性,建立RIES动态最优能流计算模型,其中基于特征线法获得了供冷/热管道和供气管道动态偏微分方程的代数解析解。针对基于供冷/热系统质–量调节模式下管道能量传输时滞变量造成RIES的动态能流计算模型难以求解的问题,提出采用分段插值法获得供冷/热管道两端节点温度之间关系的近似表达式并加入动态最优能流计算模型中。此外,针对优化模型中供冷/热系统的流量与温度相乘的双线性项,提出一种能够缩紧松弛间隙的分段凸包络松弛方法将原混合整数非线性优化模型转化为混合整数二次约束规划模型,能够在保证计算精度的同时实现高效求解。最后以某个RIES算例进行分析,验证了所提方法的计算准确性和高效性,并与常用的质调节模式相比,表明在供冷/热系统质–量调节模式下能找到经济性更优的RIES运行点。
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10375039, 10775100 and 90503008)the Doctoral Program Foundation of the Ministry of Education of China,the Center of Nuclear Physics of HIRFL of China
文摘Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
基金The project supported by the National Natural Science Foundation of ChinaLNM,Institute of Mechanics,CAS
文摘A new theory on the construction of optimal truncated Low-Dimensional Dynamical Systems (LDDSs) with different physical meanings has been developed, The physical properties of the optimal bases are reflected in the user-defined optimal conditions, Through the analysis of linear and nonlinear examples, it is shown that the LDDSs constructed by using the Proper Orthogonal Decomposition (POD) method are not the optimum. After comparing the errors of LDDSs based on the new theory POD and Fourier methods, it is concluded that the LDDSs based on the new theory are optimally truncated and catch the desired physical properties of the systems.
基金supported by NSF of China (10901065, 10971225, and11028102)the NSF Grants 1025422 and 0731201the Cheung Kong Scholars Program, and an open research grant from the State Key Laboratory for Nonlinear Mechanics at the Chinese Academy of Sciences
文摘A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence.
基金supported by the Scientific Research Fund of Education Department of Heilongjiang Province of China (Grant No. 11551020)
文摘We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.
文摘When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The quintic B-spline collocation method is used for solving such nonlinear partial differential equations. The developed plan uses the collocation approach and finite difference method to solve the problem under consideration. The given problem is discretized in both time and space directions. Forward difference formula is used for temporal discretization. Collocation method is used for spatial discretization. Additionally, by using Von Neumann stability analysis, it is demonstrated that the devised scheme is stable and convergent with regard to time. Examining two analytical approaches to show the effectiveness and performance of our approximate solution.
文摘Noise reduction is one of the most exciting problems in electronic speckle pattern interferometry. We present a homomorphic partial differential equation filtering method for interferometry fringe patterns. The diffusion speed of the equation is determined based on the fringe density. We test the new method on the computer-simulated fringe pattern and experimentally obtain the fringe pattern, and evaluate its filtering performance. The qualitative and quantitative analysis shows that this technique can filter off the additive and multiplicative noise of the fringe patterns effectively, and avoid blurring high-density fringe. It is more capable of improving the quality of fringe patterns than the classical filtering methods.
基金NSFC Basic Science Center Program for”Multiscale Problems in Nonlinear Mechanics”(Grant No.11988102)National Natural Science Foundation of China(Grant No.12202454).
文摘We present quantum numerical methods for the typical initial boundary value problems(IBVPs)of convection-diffusion equations in fluid dynamics.The IBVP is discretized into a series of linear systems via finite difference methods and explicit time marching schemes.To solve these discrete systems in quantum computers,we design a series of quantum circuits,including four stages of encoding,amplification,adding source terms,and incorporating boundary conditions.In the encoding stage,the initial condition is encoded in the amplitudes of quantum registers as a state vector to take advantage of quantum algorithms in space complexity.In the following three stages,the discrete differential operators in classical computing are converted into unitary evolutions to satisfy the postulate in quantum systems.The related arithmetic calculations in quantum amplitudes are also realized to sum up the increments from these stages.The proposed quantum algorithm is implemented within the open-source quantum computing framework Qiskit[2].By simulating one-dimensional transient problems,including the Helmholtz equation,the Burgers’equation,and Navier-Stokes equations,we demonstrate the capability of quantum computers in fluid dynamics.
