The heterogeneous variational nodal method(HVNM)has emerged as a potential approach for solving high-fidelity neutron transport problems.However,achieving accurate results with HVNM in large-scale problems using high-...The heterogeneous variational nodal method(HVNM)has emerged as a potential approach for solving high-fidelity neutron transport problems.However,achieving accurate results with HVNM in large-scale problems using high-fidelity models has been challenging due to the prohibitive computational costs.This paper presents an efficient parallel algorithm tailored for HVNM based on the Message Passing Interface standard.The algorithm evenly distributes the response matrix sets among processors during the matrix formation process,thus enabling independent construction without communication.Once the formation tasks are completed,a collective operation merges and shares the matrix sets among the processors.For the solution process,the problem domain is decomposed into subdomains assigned to specific processors,and the red-black Gauss-Seidel iteration is employed within each subdomain to solve the response matrix equation.Point-to-point communication is conducted between adjacent subdomains to exchange data along the boundaries.The accuracy and efficiency of the parallel algorithm are verified using the KAIST and JRR-3 test cases.Numerical results obtained with multiple processors agree well with those obtained from Monte Carlo calculations.The parallelization of HVNM results in eigenvalue errors of 31 pcm/-90 pcm and fission rate RMS errors of 1.22%/0.66%,respectively,for the 3D KAIST problem and the 3D JRR-3 problem.In addition,the parallel algorithm significantly reduces computation time,with an efficiency of 68.51% using 36 processors in the KAIST problem and 77.14% using 144 processors in the JRR-3 problem.展开更多
The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this ...The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.展开更多
By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is propose...By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.展开更多
A LES model is proposed to predict the dispersion of particles in the atmosphere in the context of Chemical,Biological,Radiological and Nuclear(CBRN)applications.The code relies on the Finite Element Method(FEM)for bo...A LES model is proposed to predict the dispersion of particles in the atmosphere in the context of Chemical,Biological,Radiological and Nuclear(CBRN)applications.The code relies on the Finite Element Method(FEM)for both the fluid and the dispersed solid phases.Starting from the Navier-Stokes equations and a general description of the FEM strategy,the Streamline Upwind Petrov-Galerkin(SUPG)method is formulated putting some emphasis on the related assembly matrix and stabilization coefficients.Then,the Variational Multiscale Method(VMS)is presented together with a detailed illustration of its algorithm and hierarchy of computational steps.It is demonstrated that the VMS can be considered as a more general version of the SUPG method.The final part of the work is used to assess the reliability of the implemented predictor/multicorrector solution strategy.展开更多
A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conce...A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. An E1 Niйo atmospheric physics model is proposed using a method for the variational iteration theory. Using the variational iteration method, the approximate expansions of the solution of corresponding problem are constructed. That is, firstly, introducing a set of functional and accounting their variationals, the Lagrange multiplicators are counted, and then the variational iteration is defined, finally, the approximate solution is obtained. From approximate expansions of the solution, the zonal sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillation for E1 Niйo atmospheric physics model can be analyzed. E1 Niйo is a very complicated natural phenomenon. Hence basic models need to be reduced for the sea-air oscillator and are solved. The variational iteration is a simple and valid approximate method.展开更多
A class of coupled system for the E1 Nifio-Southern Oscillation (ENSO) mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO mode...A class of coupled system for the E1 Nifio-Southern Oscillation (ENSO) mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.展开更多
The simplified linear model of Grad-Shafranov (GS) reconstruction can be reformulated into an inverse boundary value problem of Laplace's equation. Therefore, in this paper we focus on the method of solving the inv...The simplified linear model of Grad-Shafranov (GS) reconstruction can be reformulated into an inverse boundary value problem of Laplace's equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace's equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace's equation. Then, the 'L-Curve' principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.展开更多
In this paper,a scheme of dual-Doppler radar wind analysis based on a three-dimensional variational method is proposed and performed in two steps.First,the horizontal wind field is simultaneously recovered through min...In this paper,a scheme of dual-Doppler radar wind analysis based on a three-dimensional variational method is proposed and performed in two steps.First,the horizontal wind field is simultaneously recovered through minimizing a cost function defined as a radial observation term with the standard conjugate gradient method,avoiding a weighting parameter specification step.Compared with conventional dual-Doppler wind synthesis approaches,this variational method minimizes errors caused by interpolation from radar observation to analysis grid in the iterative solution process,which is one of the main sources of errors.Then,through the accelerated Liebmann method,the vertical velocity is further reestimated as an extra step by solving the Poisson equation with impermeable conditions imposed at the ground and near the tropopause.The Poisson equation defined by the second derivative of the vertical velocity is derived from the mass continuity equation.Compared with the method proposed by O’Brien,this method is less sensitive to the uncertainty of the boundary conditions and has better stability and reliability.Furthermore,the method proposed in this paper is applied to Doppler radar observation of a squall line process.It is shown that the retrieved vertical wind profile agrees well with the vertical profile obtained with the velocity–azimuth display(VAD)method,and the retrieved radial velocity as well as the analyzed positive and negative velocity centers and horizontal wind shear of the squall line are in accord with radar observations.There is a good correspondence between the divergence field of the derived wind field and the vertical velocity.And,the horizontal and vertical circulations within and around the squall line,as well as strong updrafts,the associated downdrafts,and associated rear inflow of the bow echo,are analyzed well.It is worth mentioning that the variational method in this paper can be applied to simultaneously synthesize the three-dimensional wind field from multiple-Doppler radar observations.展开更多
In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png"...In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.展开更多
The variational principle of minimum free energy(MFEVP) has been widely used in research of soft matter statics.The MFEVP can be used not only to derive equilibrium equations(including both bulk equations and boundary...The variational principle of minimum free energy(MFEVP) has been widely used in research of soft matter statics.The MFEVP can be used not only to derive equilibrium equations(including both bulk equations and boundary conditions),but also to develop direct variational methods(such as Ritz method) to find approximate solutions to these equilibrium equations. We apply these variational methods to study long-range force transmission in nonlinear elastic biopolymer gels.It is shown that the slow decay of cell-induced displacements measured experimentally for fibroblast spheroids in threedimensional fibrin gels can be well explained by variational approximations based on the three-chain model of biopolymer gels.展开更多
In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structure...In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.展开更多
An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation o...An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of the ground state wave function. The key of the method is to introduce a variational parameter λ,which can be determined by minimizing the energy functional. Using this method, we calculate the physical observables with high accuracy in comparison with the numerical exact ones. Our method evidently improves over the widely used general rotating-wave approximation(GRWA) in both qualitative and quantitative aspects.展开更多
This paper applies the variational iteration method to obtain approximate analytic solutions of compressible Euler equations in gas dynamics. This method is based on the use of Lagrange multiplier for identification o...This paper applies the variational iteration method to obtain approximate analytic solutions of compressible Euler equations in gas dynamics. This method is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Using this method, a rapid convergent sequence is produced which converges to the exact solutions of the problem. Numerical results and comparison with other two numerical solutions verify that this method is very convenient and efficient.展开更多
The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models...The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models with fractional derivatives are investigated analytically, and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order.展开更多
This paper studies a delayed air-sea coupled oscillator describing the physical mechanism of El Nino Southern Oscillation. The approximate expansions of the delayed differential equation's solution are obtained succe...This paper studies a delayed air-sea coupled oscillator describing the physical mechanism of El Nino Southern Oscillation. The approximate expansions of the delayed differential equation's solution are obtained successfully by the modified variational iteration method. The numerical results illustrate the effectiveness and correctness of the method by comparing with the exact solution of the reduced model.展开更多
The variation principle is discussed and Rayleigh-Ritz method is proposed for construction of veloci ty field. A kinematically admissible velocity field based on polynomials was appIied to the determina tion of forgin...The variation principle is discussed and Rayleigh-Ritz method is proposed for construction of veloci ty field. A kinematically admissible velocity field based on polynomials was appIied to the determina tion of forging load and deformed buIge profile during upset forging of blocks. Simulation of upsetforging of rectangular blocks under various friction condjtions was performed. Comparison of the computed results with experiments and FEM shows good agreement. It is shown that this techniquecan be used for 3D simulation of metal forming process.展开更多
The generalized method of variational analysis (GMVA) suggested for 2-D wind observations by Huang et al. is extended to 3-D cases. Just as in 2-D cases, the regularization idea is applied. But due to the complexity...The generalized method of variational analysis (GMVA) suggested for 2-D wind observations by Huang et al. is extended to 3-D cases. Just as in 2-D cases, the regularization idea is applied. But due to the complexity of the 3-D cases, the vertical vorticity is taken as a stable functional. The results indicate that wind observations can be both variationally optimized and ?ltered. The e?ciency of GMVA is also checked in a numerical test. Finally, 3-D wind observations with random disturbances are manipulated by GMVA after being ?ltered.展开更多
In this study, we applied the variational iteration method to solve the Boussinesq time equation. Bossiness’s article from 1872 introduced the equations that are now known as the Boussinesq equations. Numerical metho...In this study, we applied the variational iteration method to solve the Boussinesq time equation. Bossiness’s article from 1872 introduced the equations that are now known as the Boussinesq equations. Numerical methods are commonly utilized to solve nonlinear equation systems. Several research papers have documented the values of the variational iteration method and its applications for various categories of differential equations. A comparison of the exact and numerical solutions was obtained using the variational iteration method. The variational iteration method shows that the proposed method is very effective and convenient. The results are shown for different specific cases of the problem. The variational iteration method is useful in numerical simulations and approximate analytical solutions, and it is used to resolve nonlinear differential equations in various situations using Maple. For example, the linear Boussinesq equation was resolved using the variational iteration method. By comparing the numerical results, we found that the variable repetition method produced accurate results and was close to the exact solution, allowing it to be widely applied to the Boussinesq equation. This proves the effectiveness of the method and the capability to quickly and effectively obtain the numerical number solution related to the exact solution using the Maple 18 program. Additionally, the outcomes are extremely precise.展开更多
A model for both stochastic jumps and volatility for equity returns in the area of option pricing is the stochastic volatility process with jumps (SVPJ). A major advantage of this model lies in the area of mean revers...A model for both stochastic jumps and volatility for equity returns in the area of option pricing is the stochastic volatility process with jumps (SVPJ). A major advantage of this model lies in the area of mean reversion and volatility clustering between returns and volatility with uphill movements in price asserts. Thus, in this article, we propose to solve the SVPJ model numerically through a discretized variational iteration method (DVIM) to obtain sample paths for the state variable and variance process at various timesteps and replications in order to estimate the expected jump times at various iterates resulting from executing the DVIM as n increases. These jumps help in estimating the degree of randomness in the financial market. It was observed that the average computed expected jump times for the state variable and variance process is moderated by the parameters (variance process through mean reversion), Θ (long-run mean of the variance process), σ (volatility variance process) and λ (constant intensity of the Poisson process) at each iterate. For instance, when = 0.0, Θ = 0.0, σ = 0.0 and λ = 1.0, the state variable cluttered maximally compared to the variance process with less volatility cluttering with an average computed expected jump times of 52.40607869 as n increases in the DVIM scheme. Similarly, when = 3.99, Θ = 0.014, σ = 0.27 and λ = 0.11, the stochastic jumps for the state variable are less cluttered compared to the variance process with maximum volatility cluttering as n increases in the DVIM scheme. In terms of option pricing, the value 52.40607869 suggest a better bargain compared to the value 20.40344029 due to the fact that it yields less volatility rate. MAPLE 18 software was used for all computations in this research.展开更多
In this paper,we are concerned with solutions to the fractional Schrodinger-Poisson system■ with prescribed mass ∫_(R^(3))|u|^(2)dx=a^(2),where a> 0 is a prescribed number,μ> 0 is a paremeter,s ∈(0,1),2 <...In this paper,we are concerned with solutions to the fractional Schrodinger-Poisson system■ with prescribed mass ∫_(R^(3))|u|^(2)dx=a^(2),where a> 0 is a prescribed number,μ> 0 is a paremeter,s ∈(0,1),2 <q <2_(s)^(*),and 2_(s)^(*)=6/(3-2s) is the fractional critical Sobolev exponent.In the L2-subcritical case,we show the existence of multiple normalized solutions by using the genus theory and the truncation technique;in the L^(2)-supercritical case,we obtain a couple of normalized solutions by developing a fiber map.Under both cases,to recover the loss of compactness of the energy functional caused by the doubly critical growth,we need to adopt the concentration-compactness principle.Our results complement and improve upon some existing studies on the fractional Schrodinger-Poisson system with a nonlocal critical term.展开更多
基金supported by the National Key Research and Development Program of China(No.2020YFB1901900)the National Natural Science Foundation of China(Nos.U20B2011,12175138)the Shanghai Rising-Star Program。
文摘The heterogeneous variational nodal method(HVNM)has emerged as a potential approach for solving high-fidelity neutron transport problems.However,achieving accurate results with HVNM in large-scale problems using high-fidelity models has been challenging due to the prohibitive computational costs.This paper presents an efficient parallel algorithm tailored for HVNM based on the Message Passing Interface standard.The algorithm evenly distributes the response matrix sets among processors during the matrix formation process,thus enabling independent construction without communication.Once the formation tasks are completed,a collective operation merges and shares the matrix sets among the processors.For the solution process,the problem domain is decomposed into subdomains assigned to specific processors,and the red-black Gauss-Seidel iteration is employed within each subdomain to solve the response matrix equation.Point-to-point communication is conducted between adjacent subdomains to exchange data along the boundaries.The accuracy and efficiency of the parallel algorithm are verified using the KAIST and JRR-3 test cases.Numerical results obtained with multiple processors agree well with those obtained from Monte Carlo calculations.The parallelization of HVNM results in eigenvalue errors of 31 pcm/-90 pcm and fission rate RMS errors of 1.22%/0.66%,respectively,for the 3D KAIST problem and the 3D JRR-3 problem.In addition,the parallel algorithm significantly reduces computation time,with an efficiency of 68.51% using 36 processors in the KAIST problem and 77.14% using 144 processors in the JRR-3 problem.
文摘The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.
基金supported by the Natural Science Foundation of Zhejiang Province,China(Grant Nos.LY20A010021,LY19A010002,LY20G030025)the Natural Science Founda-tion of Ningbo City,China(Grant Nos.2021J147,2021J235).
文摘By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.
基金The authors received the funding of the Royal Higher Institute for Defence(MSP16-06).
文摘A LES model is proposed to predict the dispersion of particles in the atmosphere in the context of Chemical,Biological,Radiological and Nuclear(CBRN)applications.The code relies on the Finite Element Method(FEM)for both the fluid and the dispersed solid phases.Starting from the Navier-Stokes equations and a general description of the FEM strategy,the Streamline Upwind Petrov-Galerkin(SUPG)method is formulated putting some emphasis on the related assembly matrix and stabilization coefficients.Then,the Variational Multiscale Method(VMS)is presented together with a detailed illustration of its algorithm and hierarchy of computational steps.It is demonstrated that the VMS can be considered as a more general version of the SUPG method.The final part of the work is used to assess the reliability of the implemented predictor/multicorrector solution strategy.
文摘A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. An E1 Niйo atmospheric physics model is proposed using a method for the variational iteration theory. Using the variational iteration method, the approximate expansions of the solution of corresponding problem are constructed. That is, firstly, introducing a set of functional and accounting their variationals, the Lagrange multiplicators are counted, and then the variational iteration is defined, finally, the approximate solution is obtained. From approximate expansions of the solution, the zonal sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillation for E1 Niйo atmospheric physics model can be analyzed. E1 Niйo is a very complicated natural phenomenon. Hence basic models need to be reduced for the sea-air oscillator and are solved. The variational iteration is a simple and valid approximate method.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 90111011 and 10471039), the National Key Basic Research Special Foundation of China (Grant Nos 2003CB415101-03 and 2004CB418304), the Key Basic Research Foundation of the Chinese Academy of Sciences (Grant No KZCX3-SW-221) and in part by E-Institutes of Shanghai Municipal Education Commission (Grant No N.E03004).
文摘A class of coupled system for the E1 Nifio-Southern Oscillation (ENSO) mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.
基金Project supported by the National Natural Science Foundation of China(Grant No.41175025)
文摘The simplified linear model of Grad-Shafranov (GS) reconstruction can be reformulated into an inverse boundary value problem of Laplace's equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace's equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace's equation. Then, the 'L-Curve' principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.
基金supported by the National Key Research and Development Program of China(Grant No.2019YFC1510400)the National Natural Science Foundation of China(Grant Nos.41975054 and 41930967)the Special Fund for Forecasters of China Meteorological Administration(Grant No.CMAYBY2018-040)。
文摘In this paper,a scheme of dual-Doppler radar wind analysis based on a three-dimensional variational method is proposed and performed in two steps.First,the horizontal wind field is simultaneously recovered through minimizing a cost function defined as a radial observation term with the standard conjugate gradient method,avoiding a weighting parameter specification step.Compared with conventional dual-Doppler wind synthesis approaches,this variational method minimizes errors caused by interpolation from radar observation to analysis grid in the iterative solution process,which is one of the main sources of errors.Then,through the accelerated Liebmann method,the vertical velocity is further reestimated as an extra step by solving the Poisson equation with impermeable conditions imposed at the ground and near the tropopause.The Poisson equation defined by the second derivative of the vertical velocity is derived from the mass continuity equation.Compared with the method proposed by O’Brien,this method is less sensitive to the uncertainty of the boundary conditions and has better stability and reliability.Furthermore,the method proposed in this paper is applied to Doppler radar observation of a squall line process.It is shown that the retrieved vertical wind profile agrees well with the vertical profile obtained with the velocity–azimuth display(VAD)method,and the retrieved radial velocity as well as the analyzed positive and negative velocity centers and horizontal wind shear of the squall line are in accord with radar observations.There is a good correspondence between the divergence field of the derived wind field and the vertical velocity.And,the horizontal and vertical circulations within and around the squall line,as well as strong updrafts,the associated downdrafts,and associated rear inflow of the bow echo,are analyzed well.It is worth mentioning that the variational method in this paper can be applied to simultaneously synthesize the three-dimensional wind field from multiple-Doppler radar observations.
文摘In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.
基金supported by the National Science Foundation for Young Scientists of China (Grant No. 12004082)Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2019), 2020 Li Ka Shing Foundation Cross-Disciplinary Research (Grant No. 2020LKSFG08A)+3 种基金Provincial Science Foundation of Guangdong (Grant No. 2019A1515110809)Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020B1515310005)Featured Innovative Projects (Grant No. 2018KTSCX282)Youth Talent Innovative Platforms (Grant No. 2018KQNCX318) in Universities in Guangdong Province。
文摘The variational principle of minimum free energy(MFEVP) has been widely used in research of soft matter statics.The MFEVP can be used not only to derive equilibrium equations(including both bulk equations and boundary conditions),but also to develop direct variational methods(such as Ritz method) to find approximate solutions to these equilibrium equations. We apply these variational methods to study long-range force transmission in nonlinear elastic biopolymer gels.It is shown that the slow decay of cell-induced displacements measured experimentally for fibroblast spheroids in threedimensional fibrin gels can be well explained by variational approximations based on the three-chain model of biopolymer gels.
基金supported by the National Natural Science Foundation of China(Grant Nos.11301350,11172120,and 11202090)the Liaoning University Prereporting Fund Natural Projects(Grant No.2013LDGY02)
文摘In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674139,11604009,and 11704025)the Program for Changjiang Scholars and Innovative Research Team in University,China(Grant No.IRT-16R35)+1 种基金the Fundamental Research Funds for the Central Universities,Chinathe financial support of the Future and Emerging Technologies(FET)programme within the Seventh Framework Programme for Research of the European Commission,under FET-Open Grant No.618083(CNTQC)
文摘An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of the ground state wave function. The key of the method is to introduce a variational parameter λ,which can be determined by minimizing the energy functional. Using this method, we calculate the physical observables with high accuracy in comparison with the numerical exact ones. Our method evidently improves over the widely used general rotating-wave approximation(GRWA) in both qualitative and quantitative aspects.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10771019 and 10826107)
文摘This paper applies the variational iteration method to obtain approximate analytic solutions of compressible Euler equations in gas dynamics. This method is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Using this method, a rapid convergent sequence is produced which converges to the exact solutions of the problem. Numerical results and comparison with other two numerical solutions verify that this method is very convenient and efficient.
基金Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 51134018).
文摘The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models with fractional derivatives are investigated analytically, and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order.
基金supported by the National Natural Science Foundation of China (Grant Nos.41105063 and 61070041)
文摘This paper studies a delayed air-sea coupled oscillator describing the physical mechanism of El Nino Southern Oscillation. The approximate expansions of the delayed differential equation's solution are obtained successfully by the modified variational iteration method. The numerical results illustrate the effectiveness and correctness of the method by comparing with the exact solution of the reduced model.
文摘The variation principle is discussed and Rayleigh-Ritz method is proposed for construction of veloci ty field. A kinematically admissible velocity field based on polynomials was appIied to the determina tion of forging load and deformed buIge profile during upset forging of blocks. Simulation of upsetforging of rectangular blocks under various friction condjtions was performed. Comparison of the computed results with experiments and FEM shows good agreement. It is shown that this techniquecan be used for 3D simulation of metal forming process.
基金the National Natural Science Foundation of China(No.40075014,40175014)Shanghai Science and Technology Association(No.02DJ14032).
文摘The generalized method of variational analysis (GMVA) suggested for 2-D wind observations by Huang et al. is extended to 3-D cases. Just as in 2-D cases, the regularization idea is applied. But due to the complexity of the 3-D cases, the vertical vorticity is taken as a stable functional. The results indicate that wind observations can be both variationally optimized and ?ltered. The e?ciency of GMVA is also checked in a numerical test. Finally, 3-D wind observations with random disturbances are manipulated by GMVA after being ?ltered.
文摘In this study, we applied the variational iteration method to solve the Boussinesq time equation. Bossiness’s article from 1872 introduced the equations that are now known as the Boussinesq equations. Numerical methods are commonly utilized to solve nonlinear equation systems. Several research papers have documented the values of the variational iteration method and its applications for various categories of differential equations. A comparison of the exact and numerical solutions was obtained using the variational iteration method. The variational iteration method shows that the proposed method is very effective and convenient. The results are shown for different specific cases of the problem. The variational iteration method is useful in numerical simulations and approximate analytical solutions, and it is used to resolve nonlinear differential equations in various situations using Maple. For example, the linear Boussinesq equation was resolved using the variational iteration method. By comparing the numerical results, we found that the variable repetition method produced accurate results and was close to the exact solution, allowing it to be widely applied to the Boussinesq equation. This proves the effectiveness of the method and the capability to quickly and effectively obtain the numerical number solution related to the exact solution using the Maple 18 program. Additionally, the outcomes are extremely precise.
文摘A model for both stochastic jumps and volatility for equity returns in the area of option pricing is the stochastic volatility process with jumps (SVPJ). A major advantage of this model lies in the area of mean reversion and volatility clustering between returns and volatility with uphill movements in price asserts. Thus, in this article, we propose to solve the SVPJ model numerically through a discretized variational iteration method (DVIM) to obtain sample paths for the state variable and variance process at various timesteps and replications in order to estimate the expected jump times at various iterates resulting from executing the DVIM as n increases. These jumps help in estimating the degree of randomness in the financial market. It was observed that the average computed expected jump times for the state variable and variance process is moderated by the parameters (variance process through mean reversion), Θ (long-run mean of the variance process), σ (volatility variance process) and λ (constant intensity of the Poisson process) at each iterate. For instance, when = 0.0, Θ = 0.0, σ = 0.0 and λ = 1.0, the state variable cluttered maximally compared to the variance process with less volatility cluttering with an average computed expected jump times of 52.40607869 as n increases in the DVIM scheme. Similarly, when = 3.99, Θ = 0.014, σ = 0.27 and λ = 0.11, the stochastic jumps for the state variable are less cluttered compared to the variance process with maximum volatility cluttering as n increases in the DVIM scheme. In terms of option pricing, the value 52.40607869 suggest a better bargain compared to the value 20.40344029 due to the fact that it yields less volatility rate. MAPLE 18 software was used for all computations in this research.
基金supported by the BIT Research and Innovation Promoting Project(2023YCXY046)the NSFC(11771468,11971027,11971061,12171497 and 12271028)+1 种基金the BNSF(1222017)the Fundamental Research Funds for the Central Universities。
文摘In this paper,we are concerned with solutions to the fractional Schrodinger-Poisson system■ with prescribed mass ∫_(R^(3))|u|^(2)dx=a^(2),where a> 0 is a prescribed number,μ> 0 is a paremeter,s ∈(0,1),2 <q <2_(s)^(*),and 2_(s)^(*)=6/(3-2s) is the fractional critical Sobolev exponent.In the L2-subcritical case,we show the existence of multiple normalized solutions by using the genus theory and the truncation technique;in the L^(2)-supercritical case,we obtain a couple of normalized solutions by developing a fiber map.Under both cases,to recover the loss of compactness of the energy functional caused by the doubly critical growth,we need to adopt the concentration-compactness principle.Our results complement and improve upon some existing studies on the fractional Schrodinger-Poisson system with a nonlocal critical term.