A variational technique (VT) is applied to estimate surface sensible and latent heat fluxes based on observations of air temperature, wind speed, and humidity, respectively, at three heights (1 m, 4 m, and 10 m), and ...A variational technique (VT) is applied to estimate surface sensible and latent heat fluxes based on observations of air temperature, wind speed, and humidity, respectively, at three heights (1 m, 4 m, and 10 m), and the surface energy and radiation budgets by the surface energy and radiation system (SERBS). The method fully uses all information provided by the measurements of air temperature, wind, and humidity profiles, the surface energy budget, and the similarity profile formulae as well. Data collected at Feixi experiment station installed by the China Heavy Rain Experiment and Study (HeRES) Program are used to test the method. Results show that the proposed technique can overcome the well-known unstablility problem that occurs when the Bowen method becomes singular; in comparison with the profile method, it reduces both the sensitivities of latent heat fluxes to observational errors in humidity and those of sensible heat fluxes to observational errors in temperature, while the estimated heat fluxes approximately satisfy the surface energy budget. Therefore, the variational technique is more reliable and stable than the two conventional methods in estimating surface sensible and latent heat fluxes.展开更多
A P-vector method was optimized using variational data assimilation technique, with which the vertical structures and seasonal variations of zonal velocities and transports were investigated. The results showed that w...A P-vector method was optimized using variational data assimilation technique, with which the vertical structures and seasonal variations of zonal velocities and transports were investigated. The results showed that westward and eastward flowes occur in the Luzon Strait in the same period in a year. However the net volume transport is westward. In the upper level (0m -500m),the westward flow exits in the middle and south of the Luzon Strait, and the eastward flow exits in the north. There are two centers of westward flow and one center of eastward flow. In the middle of the Luzon Strait, westward and eastward flowes appear alternately in vertical direction. The westward flow strengthens in winter and weakens in summer. The net volume transport is strong in winter (5.53 Sv) but weak in summer (0.29 Sv). Except in summer, the volume transport in the upper level accounts for more than half of the total volume transport (0m bottom). In summer, the net volume transport in the upper level is eastward (1.01 Sv), but westward underneath.展开更多
In this paper, we introduce and study a new system of generalized vari- ational inclusions involving H-η-monotone operators in uniformly smooth Banach spaces. Using the resolvent operator technique associated with H-...In this paper, we introduce and study a new system of generalized vari- ational inclusions involving H-η-monotone operators in uniformly smooth Banach spaces. Using the resolvent operator technique associated with H-η-monotone opera- tors, we prove the approximation solvability of solutions using an iterative algorithm. The results in this paper extend and improve some known results from the literature.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
Many methods have been proposed in the literature for solving the split variational inequality problem.Most of these methods either require that this problem is transformed into an equivalent variational inequality pr...Many methods have been proposed in the literature for solving the split variational inequality problem.Most of these methods either require that this problem is transformed into an equivalent variational inequality problem in a product space,or that the underlying operators are co-coercive.However,it has been discovered that such product space transformation may cause some potential difficulties during implementation and its approach may not fully exploit the attractive splitting nature of the split variational inequality problem.On the other hand,the co-coercive assumption of the underlying operators would preclude the potential applications of these methods.To avoid these setbacks,we propose two new relaxed inertial methods for solving the split variational inequality problem without any product space transformation,and for which the underlying operators are freed from the restrictive co-coercive assumption.The methods proposed,involve projections onto half-spaces only,and originate from an explicit discretization of a dynamical system,which combines both the inertial and relaxation techniques in order to achieve high convergence speed.Moreover,the sequence generated by these methods is shown to converge strongly to a minimum-norm solution of the problem in real Hilbert spaces.Furthermore,numerical implementations and comparisons are given to support our theoretical findings.展开更多
The purpose of this paper is to introduce and study a new class of generalized strongly mixed implicit quasi-variational inequalities in Hilbert spaces, which includes the known class of generalized mixed implicit qua...The purpose of this paper is to introduce and study a new class of generalized strongly mixed implicit quasi-variational inequalities in Hilbert spaces, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case.By applying the auxiliary variational principle technique, the existence of solutions for this class of quasi-variational inequalities is proved. Moreover, a new iterative algorithm for computing approximate solutions is constructed and the convergence criteria for this iterative algorithm are also established.展开更多
Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorith...Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.展开更多
This paper compares the variational iteration method(VIM),the Adomian decomposition method(ADM)and the Picard iteration method(PIM)for solving a system of first o rder n onlinear o rdinary d ifferential e quations(ODE...This paper compares the variational iteration method(VIM),the Adomian decomposition method(ADM)and the Picard iteration method(PIM)for solving a system of first o rder n onlinear o rdinary d ifferential e quations(ODEs).A unification of the concepts underlying these three methods is attempted by considering a very general iterative algorithm for VIM.It is found that all the three methods can be regarded as special cases of using a very general matrix of Lagrange multipliers in the iterative algorithm of VIM.The global variational iteration method is briefly reviewed,and further recast into a Local VIM,which is much more convenient and capable of predicting long term complex dynamic responses of nonlinear systems even if they are chaotic.展开更多
A new system of generalized nonlinear variational-like inclusions involving A- maximal m-relaxed η-accretive （so-called, （A, η）-accretive in [36]） mappings in q-uniformly smooth Banach spaces is introduced, and ...A new system of generalized nonlinear variational-like inclusions involving A- maximal m-relaxed η-accretive （so-called, （A, η）-accretive in [36]） mappings in q-uniformly smooth Banach spaces is introduced, and then, by using the resolvent operator technique associated with A-maximal m-relaxed ~/-accretive mappings due to Lan et al., the exis- tence and uniqueness of a solution to the aforementioned system is established. Applying two nearly uniformly Lipschitzian mappings 81 and 82 and using the resolvent operator technique associated with A-maximal m-relaxed ~？-accretive mappings, we shall construct a new perturbed N-step iterative algorithm with mixed errors for finding an element of the set of the fixed points of the nearly uniformly Lipschitzian mapping Q = （S1, S2） which is the unique solution of the aforesaid system. We also prove the convergence and stability of the iterative sequence generated by the suggested perturbed iterative algorithm under some suitable conditions, The results presented in this paper extend and improve some known results in the literature.展开更多
基金This work was supported by the National Natural Science Foundation of China under Grant No.E-D0119-90202014the National Key Programme for Developing Basic Sciences of China under Great No.G1998040902.
文摘A variational technique (VT) is applied to estimate surface sensible and latent heat fluxes based on observations of air temperature, wind speed, and humidity, respectively, at three heights (1 m, 4 m, and 10 m), and the surface energy and radiation budgets by the surface energy and radiation system (SERBS). The method fully uses all information provided by the measurements of air temperature, wind, and humidity profiles, the surface energy budget, and the similarity profile formulae as well. Data collected at Feixi experiment station installed by the China Heavy Rain Experiment and Study (HeRES) Program are used to test the method. Results show that the proposed technique can overcome the well-known unstablility problem that occurs when the Bowen method becomes singular; in comparison with the profile method, it reduces both the sensitivities of latent heat fluxes to observational errors in humidity and those of sensible heat fluxes to observational errors in temperature, while the estimated heat fluxes approximately satisfy the surface energy budget. Therefore, the variational technique is more reliable and stable than the two conventional methods in estimating surface sensible and latent heat fluxes.
基金Supported by the Major State Basic Research Program (No. G1999043810) Open Laboratory for Tropical Marine Environmental Dynamics (LED)+2 种基金 South China Sea Institute of Oceanology Chinese Academy of Sciences and the NSFC (No. 40306004).
文摘A P-vector method was optimized using variational data assimilation technique, with which the vertical structures and seasonal variations of zonal velocities and transports were investigated. The results showed that westward and eastward flowes occur in the Luzon Strait in the same period in a year. However the net volume transport is westward. In the upper level (0m -500m),the westward flow exits in the middle and south of the Luzon Strait, and the eastward flow exits in the north. There are two centers of westward flow and one center of eastward flow. In the middle of the Luzon Strait, westward and eastward flowes appear alternately in vertical direction. The westward flow strengthens in winter and weakens in summer. The net volume transport is strong in winter (5.53 Sv) but weak in summer (0.29 Sv). Except in summer, the volume transport in the upper level accounts for more than half of the total volume transport (0m bottom). In summer, the net volume transport in the upper level is eastward (1.01 Sv), but westward underneath.
基金The NSF(60804065)of Chinathe Foundation(11A028)of China West Normal University
文摘In this paper, we introduce and study a new system of generalized vari- ational inclusions involving H-η-monotone operators in uniformly smooth Banach spaces. Using the resolvent operator technique associated with H-η-monotone opera- tors, we prove the approximation solvability of solutions using an iterative algorithm. The results in this paper extend and improve some known results from the literature.
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.
基金supported by the University of KwaZulu-Natal(UKZN)Doctoral Scholarshipsupported by the National Research Foundation(NRF)South Africa(S&F-DSI/NRF Free Standing Postdoctoral Fellowship(120784)supported by the National Research Foundation(NRF)South Africa Incentive Funding for Rated Researchers(119903).
文摘Many methods have been proposed in the literature for solving the split variational inequality problem.Most of these methods either require that this problem is transformed into an equivalent variational inequality problem in a product space,or that the underlying operators are co-coercive.However,it has been discovered that such product space transformation may cause some potential difficulties during implementation and its approach may not fully exploit the attractive splitting nature of the split variational inequality problem.On the other hand,the co-coercive assumption of the underlying operators would preclude the potential applications of these methods.To avoid these setbacks,we propose two new relaxed inertial methods for solving the split variational inequality problem without any product space transformation,and for which the underlying operators are freed from the restrictive co-coercive assumption.The methods proposed,involve projections onto half-spaces only,and originate from an explicit discretization of a dynamical system,which combines both the inertial and relaxation techniques in order to achieve high convergence speed.Moreover,the sequence generated by these methods is shown to converge strongly to a minimum-norm solution of the problem in real Hilbert spaces.Furthermore,numerical implementations and comparisons are given to support our theoretical findings.
基金This research is supported both by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education of MOE, P. R. C., and by the National Natural Science Foundation (19801023) of China.
文摘The purpose of this paper is to introduce and study a new class of generalized strongly mixed implicit quasi-variational inequalities in Hilbert spaces, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case.By applying the auxiliary variational principle technique, the existence of solutions for this class of quasi-variational inequalities is proved. Moreover, a new iterative algorithm for computing approximate solutions is constructed and the convergence criteria for this iterative algorithm are also established.
文摘Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.
文摘This paper compares the variational iteration method(VIM),the Adomian decomposition method(ADM)and the Picard iteration method(PIM)for solving a system of first o rder n onlinear o rdinary d ifferential e quations(ODEs).A unification of the concepts underlying these three methods is attempted by considering a very general iterative algorithm for VIM.It is found that all the three methods can be regarded as special cases of using a very general matrix of Lagrange multipliers in the iterative algorithm of VIM.The global variational iteration method is briefly reviewed,and further recast into a Local VIM,which is much more convenient and capable of predicting long term complex dynamic responses of nonlinear systems even if they are chaotic.
文摘A new system of generalized nonlinear variational-like inclusions involving A- maximal m-relaxed η-accretive （so-called, （A, η）-accretive in [36]） mappings in q-uniformly smooth Banach spaces is introduced, and then, by using the resolvent operator technique associated with A-maximal m-relaxed ~/-accretive mappings due to Lan et al., the exis- tence and uniqueness of a solution to the aforementioned system is established. Applying two nearly uniformly Lipschitzian mappings 81 and 82 and using the resolvent operator technique associated with A-maximal m-relaxed ~？-accretive mappings, we shall construct a new perturbed N-step iterative algorithm with mixed errors for finding an element of the set of the fixed points of the nearly uniformly Lipschitzian mapping Q = （S1, S2） which is the unique solution of the aforesaid system. We also prove the convergence and stability of the iterative sequence generated by the suggested perturbed iterative algorithm under some suitable conditions, The results presented in this paper extend and improve some known results in the literature.
