Ionospheric delay is one of the major error sources in GNSS navigation and positioning.Nowadays,the dual-frequency technique is the most widely used in ionospheric refraction correction.However,dual-frequency measurem...Ionospheric delay is one of the major error sources in GNSS navigation and positioning.Nowadays,the dual-frequency technique is the most widely used in ionospheric refraction correction.However,dual-frequency measurements can only eliminate the first-order term of ionospheric delay,while the effect of the second-order term on GNSS observations may be several centimeters.In this paper,two models,the International Reference Ionosphere (IRI) 2007 and International Geomagnetic Reference Field (IGRF) 11 are used to estimate the second-order term through the integral calculation method.Besides,the simplified single layer ionosphere model in a dipole moment approximation for the earth magnetic field is used.Since the traditional integral calculation method requires large calculation load and takes much time,it is not convenient for practical use.Additionally,although the simplified single layer ionosphere model is simple to implement,it results in larger errors.In this study,second-order term ionospheric correction formula proposed by Hoque (2007) is improved for estimating the second-order term at a global scale.Thus,it is more practicable to estimate the second-order term.More importantly,its results have a higher precision of the sub-millimeter level for a global scale in normal conditions.Compared with Hoque's original regional correction model,which calculates coefficients through polynomial fitting of elevation and latitudes,this study proposes a piece-wise look-up table and interpolation technique to modify Hoque model.Through utilizing a table file,the modified Hoque model can be conveniently implemented in an engineering software package,like as PANDA in this study.Through applying the proposed scheme for the second-order ionospheric correction into GNSS precise positioning in both PPP daily and epoch solutions,the results have shown south-shift characteristics in daily solution at a global scale and periodic change with VTEC daily variation in epoch positioning solution.展开更多
Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple the...Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.展开更多
We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics,both in time and space,which include the relaxation schemes by Jin and Xin.These methods can use the...We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics,both in time and space,which include the relaxation schemes by Jin and Xin.These methods can use the CFL number larger or equal to unity on regular Cartesian meshes for the multi-dimensional case.These kinetic models depend on a small parameter that can be seen as a"Knudsen"number.The method is asymptotic preserving in this Knudsen number.Also,the computational costs of the method are of the same order of a fully explicit scheme.This work is the extension of Abgrall et al.(2022)[3]to multidimensional systems.We have assessed our method on several problems for two-dimensional scalar problems and Euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions.展开更多
A fractional-order memristor load Buck-Boost converter causes periodic system oscillation,electromagnetic noise,and other phenomena due to the frequent switching of the switch in actual operation,which is detrimental ...A fractional-order memristor load Buck-Boost converter causes periodic system oscillation,electromagnetic noise,and other phenomena due to the frequent switching of the switch in actual operation,which is detrimental to the stable operation of the power electronic converter.It is of great significance to the study of the modeling method and chaos control strategy to suppress the nonlinear behavior of the Buck-Boost converter and expand the safe and stable operation range of the power system.An estimation-correction modeling method based on a fractional active voltage-controlled memristor load peak current Buck-Boost converter is proposed.The discrete numerical solution of the state variables in the continuous mode of the inductor current is derived.The bursting oscillation phenomenon when the system introduces external excitation is analyzed.Using bifurcation,Lyapunov exponent,and phase diagrams,a large number of numerical simulations are performed.The results show that the Buck-Boost converter is chaotic for certain selected parameters,which is the prerequisite for the introduction of the controller.Based on the idea of parameter perturbation and state association,a three-dimensional hybrid control strategy for a fractional memristor Buck-Boost converter is designed.The effectiveness of the control strategy is verified by simulations,and it is confirmed that the system is controlled in a stable periodic state when the external tunable parameter s,which represents the coupling strength between the state variables in the system,gradually decreases in[-0.4,0].Compared with integer-order controlled systems,the stable operating range of fractional-order controlled systems is much larger.展开更多
The existing level set segmentation methods have drawbacks such as poor convergence,poor noise resistance,and long iteration times.In this paper,a fractional order distance regularized level set segmentation method wi...The existing level set segmentation methods have drawbacks such as poor convergence,poor noise resistance,and long iteration times.In this paper,a fractional order distance regularized level set segmentation method with bias correction is proposed.This method firstly introduces fractional order distance regularized term to punish the deviation between the level set function(LSF)and the signed distance function.Secondly a series of covering template is constructed to calculate fractional derivative and its conjugate of image pixel.Thirdly introducing the offset correction term and fully using the local clustering property of image intensity,the local clustering criterion of image intensity is defined and integrated with the neighborhood center to obtain the global criterion of image segmentation.Finally,the fractional distance regularization,offset correction,and external energy constraints are combined,and the energy optimization segmentation method for noisy image is established by level set.Experimental results show that the proposed method can accurately segment the image,and effectively improve the efficiency and robustness of exiting state of the art level set related algorithms.展开更多
This paper formulates and analyzes a line search method for general nonlinear equalityconstrained optimization based on filter methods for step acceptance and secant methods for searchdirection.The feature of the new ...This paper formulates and analyzes a line search method for general nonlinear equalityconstrained optimization based on filter methods for step acceptance and secant methods for searchdirection.The feature of the new algorithm is that the secant algorithm is used to produce a searchdirection,a backtracking line search procedure is used to generate step size,some filtered rules areused to determine step acceptance,second order correction technique is used to reduce infeasibility andovercome the Maratos effect.Global convergence properties of this method are analyzed:under mildassumptions it is showed that every limit point of the sequence of iterates generated by the algorithmis feasible,and that there exists at least one limit point that is a stationary point for the problem.Moreover,it is also established that the Maratos effect can be overcome in our new approach by addingsecond order correction steps so that fast local superlinear convergence to a second order sufficient localsolution is achieved.Finally,the results of numerical experiments are reported to show the effectivenessof the line search filter secant method.展开更多
Complete relativistic corrections of an effective Hamiltonian for a single-particle system in an external electromagnetic field and their unitary equivalent form up to the order of mα^(8) are obtained.The derivation ...Complete relativistic corrections of an effective Hamiltonian for a single-particle system in an external electromagnetic field and their unitary equivalent form up to the order of mα^(8) are obtained.The derivation is based on two approaches applying Foldy-Wouthuysen(FW)transformation to the Dirac Hamiltonian for a particle in an external electromagnetic field.The results are consistent with the previous work at the mα^(6) and mα^(8) order correction[Phys.Rev.A 71012503(2005);Phys.Rev.A 100012513(2019)].We also further consider the effect of anomalous magnetic moments,namely,the Dirac-Pauli equation,and obtain FW-Hamiltonians at the same order.The results obtained can be used for the subsequent calculation of relativistic and radiation effects in simple atomic and molecular systems.展开更多
基金supported by the National Basic Research Project of China (Grant No.2009CB72400205)the National Natural Science Foundation of China (Grant No.40804005)the National High Technology Research and Development Program of China (Grant No.2009AA121401)
文摘Ionospheric delay is one of the major error sources in GNSS navigation and positioning.Nowadays,the dual-frequency technique is the most widely used in ionospheric refraction correction.However,dual-frequency measurements can only eliminate the first-order term of ionospheric delay,while the effect of the second-order term on GNSS observations may be several centimeters.In this paper,two models,the International Reference Ionosphere (IRI) 2007 and International Geomagnetic Reference Field (IGRF) 11 are used to estimate the second-order term through the integral calculation method.Besides,the simplified single layer ionosphere model in a dipole moment approximation for the earth magnetic field is used.Since the traditional integral calculation method requires large calculation load and takes much time,it is not convenient for practical use.Additionally,although the simplified single layer ionosphere model is simple to implement,it results in larger errors.In this study,second-order term ionospheric correction formula proposed by Hoque (2007) is improved for estimating the second-order term at a global scale.Thus,it is more practicable to estimate the second-order term.More importantly,its results have a higher precision of the sub-millimeter level for a global scale in normal conditions.Compared with Hoque's original regional correction model,which calculates coefficients through polynomial fitting of elevation and latitudes,this study proposes a piece-wise look-up table and interpolation technique to modify Hoque model.Through utilizing a table file,the modified Hoque model can be conveniently implemented in an engineering software package,like as PANDA in this study.Through applying the proposed scheme for the second-order ionospheric correction into GNSS precise positioning in both PPP daily and epoch solutions,the results have shown south-shift characteristics in daily solution at a global scale and periodic change with VTEC daily variation in epoch positioning solution.
基金supported by the NSFC Grant no.12271492the Natural Science Foundation of Henan Province of China Grant no.222300420550+1 种基金supported by the NSFC Grant no.12271498the National Key R&D Program of China Grant no.2022YFA1005202/2022YFA1005200.
文摘Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.
基金funded by the SNF project 200020_204917 entitled"Structure preserving and fast methods for hyperbolic systems of conservation laws".
文摘We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics,both in time and space,which include the relaxation schemes by Jin and Xin.These methods can use the CFL number larger or equal to unity on regular Cartesian meshes for the multi-dimensional case.These kinetic models depend on a small parameter that can be seen as a"Knudsen"number.The method is asymptotic preserving in this Knudsen number.Also,the computational costs of the method are of the same order of a fully explicit scheme.This work is the extension of Abgrall et al.(2022)[3]to multidimensional systems.We have assessed our method on several problems for two-dimensional scalar problems and Euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region(Nos.2022D01C367 and 2022D01E33)National Natural Science Foundation of China(Nos.52065064 and 52267010).
文摘A fractional-order memristor load Buck-Boost converter causes periodic system oscillation,electromagnetic noise,and other phenomena due to the frequent switching of the switch in actual operation,which is detrimental to the stable operation of the power electronic converter.It is of great significance to the study of the modeling method and chaos control strategy to suppress the nonlinear behavior of the Buck-Boost converter and expand the safe and stable operation range of the power system.An estimation-correction modeling method based on a fractional active voltage-controlled memristor load peak current Buck-Boost converter is proposed.The discrete numerical solution of the state variables in the continuous mode of the inductor current is derived.The bursting oscillation phenomenon when the system introduces external excitation is analyzed.Using bifurcation,Lyapunov exponent,and phase diagrams,a large number of numerical simulations are performed.The results show that the Buck-Boost converter is chaotic for certain selected parameters,which is the prerequisite for the introduction of the controller.Based on the idea of parameter perturbation and state association,a three-dimensional hybrid control strategy for a fractional memristor Buck-Boost converter is designed.The effectiveness of the control strategy is verified by simulations,and it is confirmed that the system is controlled in a stable periodic state when the external tunable parameter s,which represents the coupling strength between the state variables in the system,gradually decreases in[-0.4,0].Compared with integer-order controlled systems,the stable operating range of fractional-order controlled systems is much larger.
基金This work was supported by the National Natural Science Foundation of China(62071378).
文摘The existing level set segmentation methods have drawbacks such as poor convergence,poor noise resistance,and long iteration times.In this paper,a fractional order distance regularized level set segmentation method with bias correction is proposed.This method firstly introduces fractional order distance regularized term to punish the deviation between the level set function(LSF)and the signed distance function.Secondly a series of covering template is constructed to calculate fractional derivative and its conjugate of image pixel.Thirdly introducing the offset correction term and fully using the local clustering property of image intensity,the local clustering criterion of image intensity is defined and integrated with the neighborhood center to obtain the global criterion of image segmentation.Finally,the fractional distance regularization,offset correction,and external energy constraints are combined,and the energy optimization segmentation method for noisy image is established by level set.Experimental results show that the proposed method can accurately segment the image,and effectively improve the efficiency and robustness of exiting state of the art level set related algorithms.
基金supported by the National Science Foundation under Grant No.10871130, the Ph.D. Foundation of Chinese Education Ministry under Grant No.20093127110005the Shanghai Leading Academic Discipline Project under Grant No.T0401
文摘This paper formulates and analyzes a line search method for general nonlinear equalityconstrained optimization based on filter methods for step acceptance and secant methods for searchdirection.The feature of the new algorithm is that the secant algorithm is used to produce a searchdirection,a backtracking line search procedure is used to generate step size,some filtered rules areused to determine step acceptance,second order correction technique is used to reduce infeasibility andovercome the Maratos effect.Global convergence properties of this method are analyzed:under mildassumptions it is showed that every limit point of the sequence of iterates generated by the algorithmis feasible,and that there exists at least one limit point that is a stationary point for the problem.Moreover,it is also established that the Maratos effect can be overcome in our new approach by addingsecond order correction steps so that fast local superlinear convergence to a second order sufficient localsolution is achieved.Finally,the results of numerical experiments are reported to show the effectivenessof the line search filter secant method.
基金supported by the National Natural Science Foundation of China(Grant Nos.12074295 and 12104420)。
文摘Complete relativistic corrections of an effective Hamiltonian for a single-particle system in an external electromagnetic field and their unitary equivalent form up to the order of mα^(8) are obtained.The derivation is based on two approaches applying Foldy-Wouthuysen(FW)transformation to the Dirac Hamiltonian for a particle in an external electromagnetic field.The results are consistent with the previous work at the mα^(6) and mα^(8) order correction[Phys.Rev.A 71012503(2005);Phys.Rev.A 100012513(2019)].We also further consider the effect of anomalous magnetic moments,namely,the Dirac-Pauli equation,and obtain FW-Hamiltonians at the same order.The results obtained can be used for the subsequent calculation of relativistic and radiation effects in simple atomic and molecular systems.
