In this paper classical linear elastic variational principles are systematically derivedfrom the reciprocal theorem and mixed variational principles of variations of boundaryconditions are given.
This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations The present method cuts down computing time enormously and greatly promote...This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations The present method cuts down computing time enormously and greatly promotes the efficiency of the elasto-plastic analvsis for large scale structures展开更多
Quantum power system state estimation(QPSSE)offers an inspiring direction for tackling the challenge of state estimation through quantum computing.Nevertheless,the current bottlenecks originate from the scarcity of pr...Quantum power system state estimation(QPSSE)offers an inspiring direction for tackling the challenge of state estimation through quantum computing.Nevertheless,the current bottlenecks originate from the scarcity of practical and scalable QPSSE methodologies in the noisy intermediate-scale quantum(NISQ)era.This paper devises a NISQ−QPSSE algorithm that facilitates state estimation on real NISQ devices.Our new contributions include:(1)A variational quantum circuit(VQC)-based QPSSE formulation that empowers QPSSE analysis utilizing shallow-depth quantum circuits;(2)A variational quantum linear solver(VQLS)-based QPSSE solver integrating QPSSE iterations with VQC optimization;(3)An advanced NISQ-compatible QPSSE methodology for tackling the measurement and coefficient matrix issues on real quantum computers;(4)A noise-resilient method to alleviate the detrimental effects of noise disturbances.The encouraging test results on the simulator and real-scale systems affirm the precision,universal-ity,and scalability of our QPSSE algorithm and demonstrate the vast potential of QPSSE in the thriving NISQ era.展开更多
The spectra of Rydberg hydrogen atom in magnetic fields have been calculated using linear variational method with B-splines basis functions [Acta Phys. Sin. 55 （2006） 3380]. Based on these calculations we have done...The spectra of Rydberg hydrogen atom in magnetic fields have been calculated using linear variational method with B-splines basis functions [Acta Phys. Sin. 55 （2006） 3380]. Based on these calculations we have done some statistics analysis about the high Rydberg energy levels. The nearest-neighbor energy spacing distribution and the 3-statistics have been shown about diamagnetic Rydberg hydrogen atom with the magnetic field being 0.6 T and 6 T. The phenomena of multiply crossing, multiply anti-crossing, and the mixed of crossing and anti-crossing of energy levels have appeared in this paper. For both cases, in range of lower energy, the energy 1evel statistics properties close to Poisson distribution. With the increasing of the energy, the energy level statistics properties are away to Poisson distribution and tend to Wigner distribution step by step.展开更多
The problem of correcting simultaneously mass and stiffness matrices of finite element model of undamped structural systems using vibration tests is considered in this paper.The desired matrix properties,including sat...The problem of correcting simultaneously mass and stiffness matrices of finite element model of undamped structural systems using vibration tests is considered in this paper.The desired matrix properties,including satisfaction of the characteristic equation,symmetry,positive semidefiniteness and sparsity,are imposed as side constraints to form the optimal matrix pencil approximation problem.Using partial Lagrangian multipliers,we transform the nonlinearly constrained optimization problem into an equivalent matrix linear variational inequality,develop a proximal point-like method for solving the matrix linear variational inequality,and analyze its global convergence.Numerical results are included to illustrate the performance and application of the proposed method.展开更多
The new version （version 8） TOMS （Total Ozone Mapping Spectrometer） ozone and noontime erythemal ultraviolet （UV） irradiance products are used to analyze their long-term changes in this paper. It is shown that t...The new version （version 8） TOMS （Total Ozone Mapping Spectrometer） ozone and noontime erythemal ultraviolet （UV） irradiance products are used to analyze their long-term changes in this paper. It is shown that the summer UV irradiance has increased significantly from Central China to the northern and western parts of China, especially in Central China near Chongqing, Shaanxi, and Hubei provinces; whereas the UV irradiance has decreased significantly in the southern part of China, especially in South China. In July, when UV irradiance is at its maximum and hence when the most serious potential damage may happen, the results indicate an increase in the UV irradiance in Central China and the Yangtze River- Huaihe River valley and a decrease in South China and the eastern part of North China. At the same time, the total ozone amount is lower over China in summer with the most serious depletion occurring in Northeast China and Northwest China. It is found that the thinning of the ozone layer is not the main reason for the UV irradiance trend in the eastern and southern parts of China, but that the rainfall and the related cloud variations may dominate the long-term changes of the UV irradiance there. In addition, the future UV irradiance trend in China is also estimated.展开更多
Quantum power flow(QPF)offers an inspiring direction for overcoming the computation challenge of power flow through quantum computing.However,the practical implementation of existing QPF algorithms in today’s noisy-i...Quantum power flow(QPF)offers an inspiring direction for overcoming the computation challenge of power flow through quantum computing.However,the practical implementation of existing QPF algorithms in today’s noisy-intermediate-scale quantum(NISQ)era remains limited because of their sensitivity to noise.This paper establishes an NISQ-QPF algorithm that enables power flow computation on noisy quantum devices.The main contributions include:(1)a variational quantum circuit(VQC)-based alternating current(AC)power flow formulation,which enables QPF using short-depth quantum circuits;(2)NISQ-compatible QPF solvers based on the variational quantum linear solver(VQLS)and modified fast decoupled power flow;and(3)an error-resilient QPF scheme to relieve the QPF iteration deviations caused by noise;(3)a practical NISQ-QPF framework for implementable and reliable power flow analysis on noisy quantum machines.Extensive simulation tests validate the accuracy and generality of NISQ-QPF for solving practical power flow on IBM’s real,noisy quantum computers.展开更多
In this paper, we consider a nonlinear hybrid dynamic （NHD） system to describe fedbatch culture where there is no analytical solutions and no equilibrium points. Our goal is to prove the strong stability with respec...In this paper, we consider a nonlinear hybrid dynamic （NHD） system to describe fedbatch culture where there is no analytical solutions and no equilibrium points. Our goal is to prove the strong stability with respect to initial state for the NHD system. To this end, we construct corresponding linear variational system （LVS） for the solution of the NHD system, also prove the boundedness of fundamental matrix solutions for the LVS. On this basis, the strong stability is proved by such boundedness.展开更多
Most economic and industrial processes are governed by inherently nonlinear dynamic system in which mathematical analysis （with few exceptions） is unable to provide general solutions; even the conditions to the exis...Most economic and industrial processes are governed by inherently nonlinear dynamic system in which mathematical analysis （with few exceptions） is unable to provide general solutions; even the conditions to the existence of equilibrium point for the nonlinear dynamic system are simply not established in some special cases. In this paper, based on numerical solution of a nonlinear multi-stage automatic control dynamic （NMACD） in fed-batch culture of glycerol bioconversion to 1,3-propanediol （1,3-PD） induced by KlebsieUa pneumoniae （K. pneumoniae）, we consider an optimal design of the NMACD system. For convenience, the NMACD system is reconstructed together with the existence, uniqueness and continuity of solutions are discussed. Our goal is to prove the strong stability with respect to the perturbation of initial state for the solution to the NMACD system. To this end, we construct corresponding linear variational system for the solution to the NMACD system, and also prove the boundedness of fundamental matrix solutions to the linear variational system. On this basis, we prove the strong stability appearing above through the application of this boundedness.展开更多
This paper investigates various Weber problems including unconstrained Weber problems and constrained Weber problems under l1, l2 and l∞-norms. First with a transformation technique various Weber problems are turned ...This paper investigates various Weber problems including unconstrained Weber problems and constrained Weber problems under l1, l2 and l∞-norms. First with a transformation technique various Weber problems are turned into a class of monotone linear variational inequalities. By exploiting the favorable structure of these variational inequalities, we present a new projection-type method for them. Compared with some other projection-type methods which can solve monotone linear variational inequality, this new projection-type method is simple in numerical implementations and more efficient for solving this class of problems; Compared with some popular methods for solving unconstrained Weber problem and constrained Weber problem, a singularity would not happen in this new method and it is more reliable by using this new method to solve various Weber problems.展开更多
The accurate and efficient simulation of ocean circulation is a fundamental topic in marine science;however,it is also a well-known and dauntingly difficult problem that requires solving nonlinear partial differential...The accurate and efficient simulation of ocean circulation is a fundamental topic in marine science;however,it is also a well-known and dauntingly difficult problem that requires solving nonlinear partial differential equations with multiple variables.In this paper,we present for the first time an algorithm for simulating ocean circulation on a quantum computer to achieve a computational speedup.Our approach begins with using primitive equations describing the ocean dynamics and then discretizing these equations in time and space.It results in several linear system of equations(LSE)with sparse coefficient matrices.We solve these sparse LSE using the variational quantum linear solver that enables the present algorithm to run easily on near-term quantum computers.Additionally,we develop a scheme for manipulating the data flow in the algorithm based on the quantum random access memory and l∞norm tomography technique.The efficiency of our algorithm is verified using multiple platforms,including MATLAB,a quantum virtual simulator,and a real quantum computer.The impact of the number of shots and the noise of quantum gates on the solution accuracy is also discussed.Our findings demonstrate that error mitigation techniques can efficiently improve the solution accuracy.With the rapid advancements in quantum computing,this work represents an important first step toward solving the challenging problem of simulating ocean circulation using quantum computers.展开更多
文摘In this paper classical linear elastic variational principles are systematically derivedfrom the reciprocal theorem and mixed variational principles of variations of boundaryconditions are given.
文摘This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations The present method cuts down computing time enormously and greatly promotes the efficiency of the elasto-plastic analvsis for large scale structures
基金supported in part by the National Science Foundation under Grant No.ITE-2134840.This work relates to Department of Navy award N00014-23-1-2124 issued by the Office of Naval Research.The United States Government has a royalty-free license throughout the world in all copyrightable material contained herein.
文摘Quantum power system state estimation(QPSSE)offers an inspiring direction for tackling the challenge of state estimation through quantum computing.Nevertheless,the current bottlenecks originate from the scarcity of practical and scalable QPSSE methodologies in the noisy intermediate-scale quantum(NISQ)era.This paper devises a NISQ−QPSSE algorithm that facilitates state estimation on real NISQ devices.Our new contributions include:(1)A variational quantum circuit(VQC)-based QPSSE formulation that empowers QPSSE analysis utilizing shallow-depth quantum circuits;(2)A variational quantum linear solver(VQLS)-based QPSSE solver integrating QPSSE iterations with VQC optimization;(3)An advanced NISQ-compatible QPSSE methodology for tackling the measurement and coefficient matrix issues on real quantum computers;(4)A noise-resilient method to alleviate the detrimental effects of noise disturbances.The encouraging test results on the simulator and real-scale systems affirm the precision,universal-ity,and scalability of our QPSSE algorithm and demonstrate the vast potential of QPSSE in the thriving NISQ era.
基金Supported by the National Natural Science Foundation of China under Grant No.10774042
文摘The spectra of Rydberg hydrogen atom in magnetic fields have been calculated using linear variational method with B-splines basis functions [Acta Phys. Sin. 55 （2006） 3380]. Based on these calculations we have done some statistics analysis about the high Rydberg energy levels. The nearest-neighbor energy spacing distribution and the 3-statistics have been shown about diamagnetic Rydberg hydrogen atom with the magnetic field being 0.6 T and 6 T. The phenomena of multiply crossing, multiply anti-crossing, and the mixed of crossing and anti-crossing of energy levels have appeared in this paper. For both cases, in range of lower energy, the energy 1evel statistics properties close to Poisson distribution. With the increasing of the energy, the energy level statistics properties are away to Poisson distribution and tend to Wigner distribution step by step.
基金The work was supported by the National Natural Science Foundation of China(No.11571171)。
文摘The problem of correcting simultaneously mass and stiffness matrices of finite element model of undamped structural systems using vibration tests is considered in this paper.The desired matrix properties,including satisfaction of the characteristic equation,symmetry,positive semidefiniteness and sparsity,are imposed as side constraints to form the optimal matrix pencil approximation problem.Using partial Lagrangian multipliers,we transform the nonlinearly constrained optimization problem into an equivalent matrix linear variational inequality,develop a proximal point-like method for solving the matrix linear variational inequality,and analyze its global convergence.Numerical results are included to illustrate the performance and application of the proposed method.
基金This work was supported by the Chinese Key Developing Program for Basic Sciences （Grant No. 2004CB418303） the National Natural Science Foundation of China （Grant Nos. 40375021 and 40575026）.
文摘The new version （version 8） TOMS （Total Ozone Mapping Spectrometer） ozone and noontime erythemal ultraviolet （UV） irradiance products are used to analyze their long-term changes in this paper. It is shown that the summer UV irradiance has increased significantly from Central China to the northern and western parts of China, especially in Central China near Chongqing, Shaanxi, and Hubei provinces; whereas the UV irradiance has decreased significantly in the southern part of China, especially in South China. In July, when UV irradiance is at its maximum and hence when the most serious potential damage may happen, the results indicate an increase in the UV irradiance in Central China and the Yangtze River- Huaihe River valley and a decrease in South China and the eastern part of North China. At the same time, the total ozone amount is lower over China in summer with the most serious depletion occurring in Northeast China and Northwest China. It is found that the thinning of the ozone layer is not the main reason for the UV irradiance trend in the eastern and southern parts of China, but that the rainfall and the related cloud variations may dominate the long-term changes of the UV irradiance there. In addition, the future UV irradiance trend in China is also estimated.
基金supported in part by the U.S.Department of Energy’s Office of Energy Efficiency and Renewable Energy(EERE)Solar Energy Technologies Office Award(No.38456)in part by the National Science Foundation(No.OIA-2134840).
文摘Quantum power flow(QPF)offers an inspiring direction for overcoming the computation challenge of power flow through quantum computing.However,the practical implementation of existing QPF algorithms in today’s noisy-intermediate-scale quantum(NISQ)era remains limited because of their sensitivity to noise.This paper establishes an NISQ-QPF algorithm that enables power flow computation on noisy quantum devices.The main contributions include:(1)a variational quantum circuit(VQC)-based alternating current(AC)power flow formulation,which enables QPF using short-depth quantum circuits;(2)NISQ-compatible QPF solvers based on the variational quantum linear solver(VQLS)and modified fast decoupled power flow;and(3)an error-resilient QPF scheme to relieve the QPF iteration deviations caused by noise;(3)a practical NISQ-QPF framework for implementable and reliable power flow analysis on noisy quantum machines.Extensive simulation tests validate the accuracy and generality of NISQ-QPF for solving practical power flow on IBM’s real,noisy quantum computers.
基金This work was supported by the National Science Foundation for the Youth of China （Grant Nos. 11501574, 11401073 and 11701063）, the National Natural Science Foundation of China （Grant Nos. 11771008, 61673083 and 61773086）, the National Science Foundation for the Tianyuan of China （Grant No. 11626053）, the Natural Science Foundation of Shandong Province in China （Grant No.： ZR2015FM014, ZR2015AL010 and ZR2017MA005）, the Fundamental Research Funds for the Cen- tral Universities in China （Grant No. DUT16LK07） and the Project funded by China Postdoctoral Science Foundation （Grant No. 2016M601296）.
文摘In this paper, we consider a nonlinear hybrid dynamic （NHD） system to describe fedbatch culture where there is no analytical solutions and no equilibrium points. Our goal is to prove the strong stability with respect to initial state for the NHD system. To this end, we construct corresponding linear variational system （LVS） for the solution of the NHD system, also prove the boundedness of fundamental matrix solutions for the LVS. On this basis, the strong stability is proved by such boundedness.
基金This work was supported by the National （Grant Nos. 11171050 and 11371164）, the Natural Science Foundation of China National Science Foundation for the Youth of China （Grant Nos. 11301051, 11301081, 11401073 and 11501574）, the Provincial Natural Science Foundation of Fujian （Grant No. 2014J05001）, the Fundamental Research Funds for Central Universities in China （Grant No. DUT15LK25）, Natural Science Foundation of Shandong Province in China （Grant No. ZR2015AL010） and the China Scholarship Council （CSC, Grant No. 201506060121）.
文摘Most economic and industrial processes are governed by inherently nonlinear dynamic system in which mathematical analysis （with few exceptions） is unable to provide general solutions; even the conditions to the existence of equilibrium point for the nonlinear dynamic system are simply not established in some special cases. In this paper, based on numerical solution of a nonlinear multi-stage automatic control dynamic （NMACD） in fed-batch culture of glycerol bioconversion to 1,3-propanediol （1,3-PD） induced by KlebsieUa pneumoniae （K. pneumoniae）, we consider an optimal design of the NMACD system. For convenience, the NMACD system is reconstructed together with the existence, uniqueness and continuity of solutions are discussed. Our goal is to prove the strong stability with respect to the perturbation of initial state for the solution to the NMACD system. To this end, we construct corresponding linear variational system for the solution to the NMACD system, and also prove the boundedness of fundamental matrix solutions to the linear variational system. On this basis, we prove the strong stability appearing above through the application of this boundedness.
文摘This paper investigates various Weber problems including unconstrained Weber problems and constrained Weber problems under l1, l2 and l∞-norms. First with a transformation technique various Weber problems are turned into a class of monotone linear variational inequalities. By exploiting the favorable structure of these variational inequalities, we present a new projection-type method for them. Compared with some other projection-type methods which can solve monotone linear variational inequality, this new projection-type method is simple in numerical implementations and more efficient for solving this class of problems; Compared with some popular methods for solving unconstrained Weber problem and constrained Weber problem, a singularity would not happen in this new method and it is more reliable by using this new method to solve various Weber problems.
基金supported by the National Natural Science Foundation of China(Grant No.12005212)the Natural Science Foundation of Shandong Province of China(Grant No.ZR2021ZD19)。
文摘The accurate and efficient simulation of ocean circulation is a fundamental topic in marine science;however,it is also a well-known and dauntingly difficult problem that requires solving nonlinear partial differential equations with multiple variables.In this paper,we present for the first time an algorithm for simulating ocean circulation on a quantum computer to achieve a computational speedup.Our approach begins with using primitive equations describing the ocean dynamics and then discretizing these equations in time and space.It results in several linear system of equations(LSE)with sparse coefficient matrices.We solve these sparse LSE using the variational quantum linear solver that enables the present algorithm to run easily on near-term quantum computers.Additionally,we develop a scheme for manipulating the data flow in the algorithm based on the quantum random access memory and l∞norm tomography technique.The efficiency of our algorithm is verified using multiple platforms,including MATLAB,a quantum virtual simulator,and a real quantum computer.The impact of the number of shots and the noise of quantum gates on the solution accuracy is also discussed.Our findings demonstrate that error mitigation techniques can efficiently improve the solution accuracy.With the rapid advancements in quantum computing,this work represents an important first step toward solving the challenging problem of simulating ocean circulation using quantum computers.
