In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarant...In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.展开更多
In this paper, authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order, They first give the well posedness of general discontinuous boundary...In this paper, authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order, They first give the well posedness of general discontinuous boundary value problems, reduce the discontinuous boundary value problems to a variation problem, and then find the numerical solutions of above problem by the finite element method. Finally authors give some error-estimates of the foregoing numerical solutions.展开更多
For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional...For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method are discussed.展开更多
A framework to obtain numerical solution of the fractional partial differential equation using Bernstein polynomials is presented. The main characteristic behind this approach is that a fractional order operational ma...A framework to obtain numerical solution of the fractional partial differential equation using Bernstein polynomials is presented. The main characteristic behind this approach is that a fractional order operational matrix of Bernstein polynomials is derived. With the operational matrix, the equation is transformed into the products of several dependent matrixes which can also be regarded as the system of linear equations after dispersing the variable. By solving the linear equations, the numerical solutions are acquired. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples are provided to show that the method is computationally efficient.展开更多
In this paper, the variable-coefficient diffusion-advection （DA） equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by deter...In this paper, the variable-coefficient diffusion-advection （DA） equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended （Gl/G）-expansion method is applied to the DA equation to construct some new non-traveling wave solutions.展开更多
Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximatin...Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformal mappings in the plane is discussed.展开更多
When plasma size scale is comparable with the wavelength of electromagnetic waves, W.K.B. solution isn't applicable. In this paper a new numerical solution technique to investigate interactions of microwave with p...When plasma size scale is comparable with the wavelength of electromagnetic waves, W.K.B. solution isn't applicable. In this paper a new numerical solution technique to investigate interactions of microwave with plasmas is presented by using Runge-Kutta method. The results of numerical solution coincide with that of analytical solution while the model is linear electron density profile in calculated accuracy.展开更多
This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)metho...This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.展开更多
An asymmetric actuated 3-PPPS parallel mechanism was analyzed in its application to an aircraft wing adjustment process.The posture alignment precision at the wing ends was enhanced with a kinematic calibration method...An asymmetric actuated 3-PPPS parallel mechanism was analyzed in its application to an aircraft wing adjustment process.The posture alignment precision at the wing ends was enhanced with a kinematic calibration method.A constraint equation was built based on a constraint condition that distances among spherical joints of the mechanism were constant,and further eight groups of analytic forward solutions of all poses of the mechanism were solved.An inverse equation of the posture alignment displacements of aircraft wing parts was built based on space vector chains,and a mapping equation of the pose and geometric errors of the posture alignment mechanism containing 39 error sources was derived by differentiating the kinematic equation of the mechanism.After kinematic calibration experiments,the maximum position error of the posture alignment platform dropped from 2.67 mm to 0.82 mm,the maximum angle error decreased from 0.481° to 0.167°,and the posture alignment precision of the aircraft wing end was improved.展开更多
This paper points out the limitation of Beck formula and gives a revised formula owing to the water content and 222Rn escape in soil for calculating γ radiation doserate through the experimental fitting from 576 sets...This paper points out the limitation of Beck formula and gives a revised formula owing to the water content and 222Rn escape in soil for calculating γ radiation doserate through the experimental fitting from 576 sets of measured values in ZhejiangProvince. When the revised formula is applied to Beijing Municipality, where there is a great difference in the meteorology and soil conditions, the calculated average in general is only 3.5% different from that measured; those of every position deviate only 2.1% averagely; and their dispersion is in the experimental errors. Therefore, the revised formula possesses a high reliability and a broad suitability, and is an effective method to estimate the ac radiation dose rate oil the land.展开更多
Backfill is increasingly used in underground mines to reduce the surface impact from the wastes produced by the mining operations. But the main objectives of backfilling are to improve ground stability and reduce ore ...Backfill is increasingly used in underground mines to reduce the surface impact from the wastes produced by the mining operations. But the main objectives of backfilling are to improve ground stability and reduce ore dilution. To this end, the backfill in a stope must possess a minimum strength to remain self-standing during mining of an adjacent stope. This required strength is often estimated using a solution proposed by Mitchell and co-workers, which was based on a limit equilibrium analysis of a wedge exposed by the open face. In this paper, three dimensional numerical simulations have been performed to assess the behavior of the wedge model. A new limit equilibrium solution is proposed, based on the backfill displacements obtained from the simulations. Comparisons are made between the proposed solution and experimental and numerical modeling results. Compared with the previous solution, a better agreement is obtained between the new solution and experimental results for the required cohesion and factor of safety. For large scale(field) conditions, the results also show that the required strength obtained from the proposed solution corresponds quite well to the simulated backfill response.展开更多
An effective scheme within two displaced bosonic operators with equal positive and negative displacements is extended to study qubit-oscillator systems analytically in a unified way. Many previous analytical treatment...An effective scheme within two displaced bosonic operators with equal positive and negative displacements is extended to study qubit-oscillator systems analytically in a unified way. Many previous analytical treatments, such as generalized rotating-wave approximation （GRWA） [Phys. Rev. Lett. 99, 173601 （2007）] and an expansion in the qubit tunneling matrix element in the deep strong coupling regime [Phys. Rev. Lett. 105, 263603 （2010）] can be recovered straightforwardly within the present scheme. Moreover, further improving GRWA and the extension to the finite-bias case are implemented easily. The algebraic formulae for the eigensolutions are then derived explicitly and uniquely, which work well in a wide range of the coupling strengths, detunings, and static bias including the recent experimentally accessible parameters. The dynamics of the qubit for an oscillator in the ground state is also studied. At the experimentally accessible coupling regime, GRWA can always work well. When the coupling is enhanced to the intermediate regime, only the improving GRWA can give the correct description, while the result of GRWA shows strong deviations. The previous Van Vleck perturbation theory is not valid to describe the dynamics in the present-day experimentally accessible regime, except for the strongly biased cases.展开更多
Distributed acoustic sensing(DAS)is increasingly used in seismic exploration owing to its wide frequency range,dense sampling and real-time monitoring.DAS radiation patterns help to understand angle response of DAS re...Distributed acoustic sensing(DAS)is increasingly used in seismic exploration owing to its wide frequency range,dense sampling and real-time monitoring.DAS radiation patterns help to understand angle response of DAS records and improve the quality of inversion and imaging.In this paper,we solve the 3D vertical transverse isotropic(VTI)Christoffel equation and obtain the analytical,frst-order,and zero-order Taylor expansion solutions that represent P-,SV-,and SH-wave phase velocities and polarization vectors.These analytical and approximated solutions are used to build the P/S plane-wave expression identical to the far-feld term of seismic wave,from which the strain rate expressions are derived and DAS radiation patterns are thus extracted for anisotropic P/S waves.We observe that the gauge length and phase angle terms control the radiating intensity of DAS records.Additionally,the Bond transformation is adopted to derive the DAS radiation patterns in title transverse isotropic(TTI)media,which exhibits higher complexity than that of VTI media.Several synthetic examples demonstrate the feasibility and effectiveness of our theory.展开更多
基金Supported by Russian Fund of Fund amental Investigations(Pr.990101064)and Russian Minister of Educatin
文摘In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.
文摘In this paper, authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order, They first give the well posedness of general discontinuous boundary value problems, reduce the discontinuous boundary value problems to a variation problem, and then find the numerical solutions of above problem by the finite element method. Finally authors give some error-estimates of the foregoing numerical solutions.
基金the Natural Science Foundation of CQ CSTC under Grant No. 2007BB2161.
文摘For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method are discussed.
基金supported by the Natural Science Foundation of Hebei Province under Grant No.A2012203407
文摘A framework to obtain numerical solution of the fractional partial differential equation using Bernstein polynomials is presented. The main characteristic behind this approach is that a fractional order operational matrix of Bernstein polynomials is derived. With the operational matrix, the equation is transformed into the products of several dependent matrixes which can also be regarded as the system of linear equations after dispersing the variable. By solving the linear equations, the numerical solutions are acquired. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples are provided to show that the method is computationally efficient.
文摘In this paper, the variable-coefficient diffusion-advection （DA） equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended （Gl/G）-expansion method is applied to the DA equation to construct some new non-traveling wave solutions.
基金This project is supported in part by NSF of China(60575004, 10231040)NSF of GuangDong, Grants from the Ministry of Education of China(NCET-04-0791)Grants from Sun Yat-Sen University
文摘Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformal mappings in the plane is discussed.
文摘When plasma size scale is comparable with the wavelength of electromagnetic waves, W.K.B. solution isn't applicable. In this paper a new numerical solution technique to investigate interactions of microwave with plasmas is presented by using Runge-Kutta method. The results of numerical solution coincide with that of analytical solution while the model is linear electron density profile in calculated accuracy.
基金the National Natural Science Foundation of China(Grant Nos.71961022,11902163,12265020,and 12262024)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(Grant Nos.2019BS01011 and 2022MS01003)+5 种基金2022 Inner Mongolia Autonomous Region Grassland Talents Project-Young Innovative and Entrepreneurial Talents(Mingjing Du)2022 Talent Development Foundation of Inner Mongolia Autonomous Region of China(Ming-Jing Du)the Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region Program(Grant No.NJYT-20-B18)the Key Project of High-quality Economic Development Research Base of Yellow River Basin in 2022(Grant No.21HZD03)2022 Inner Mongolia Autonomous Region International Science and Technology Cooperation High-end Foreign Experts Introduction Project(Ge Kai)MOE(Ministry of Education in China)Humanities and Social Sciences Foundation(Grants No.20YJC860005).
文摘This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.
基金supported by the National Natural Science Foundation of China (No.51275234)the Aeronautical Science Foundation of China(No.20131652027)
文摘An asymmetric actuated 3-PPPS parallel mechanism was analyzed in its application to an aircraft wing adjustment process.The posture alignment precision at the wing ends was enhanced with a kinematic calibration method.A constraint equation was built based on a constraint condition that distances among spherical joints of the mechanism were constant,and further eight groups of analytic forward solutions of all poses of the mechanism were solved.An inverse equation of the posture alignment displacements of aircraft wing parts was built based on space vector chains,and a mapping equation of the pose and geometric errors of the posture alignment mechanism containing 39 error sources was derived by differentiating the kinematic equation of the mechanism.After kinematic calibration experiments,the maximum position error of the posture alignment platform dropped from 2.67 mm to 0.82 mm,the maximum angle error decreased from 0.481° to 0.167°,and the posture alignment precision of the aircraft wing end was improved.
文摘This paper points out the limitation of Beck formula and gives a revised formula owing to the water content and 222Rn escape in soil for calculating γ radiation doserate through the experimental fitting from 576 sets of measured values in ZhejiangProvince. When the revised formula is applied to Beijing Municipality, where there is a great difference in the meteorology and soil conditions, the calculated average in general is only 3.5% different from that measured; those of every position deviate only 2.1% averagely; and their dispersion is in the experimental errors. Therefore, the revised formula possesses a high reliability and a broad suitability, and is an effective method to estimate the ac radiation dose rate oil the land.
基金financial support of the Natural Sciences and Engineering Research Council (NSERC) of Canada and the partners of Research Institute on Mines and the Environment (RIME UQAT-Polytechnique http://rime-irme.ca)
文摘Backfill is increasingly used in underground mines to reduce the surface impact from the wastes produced by the mining operations. But the main objectives of backfilling are to improve ground stability and reduce ore dilution. To this end, the backfill in a stope must possess a minimum strength to remain self-standing during mining of an adjacent stope. This required strength is often estimated using a solution proposed by Mitchell and co-workers, which was based on a limit equilibrium analysis of a wedge exposed by the open face. In this paper, three dimensional numerical simulations have been performed to assess the behavior of the wedge model. A new limit equilibrium solution is proposed, based on the backfill displacements obtained from the simulations. Comparisons are made between the proposed solution and experimental and numerical modeling results. Compared with the previous solution, a better agreement is obtained between the new solution and experimental results for the required cohesion and factor of safety. For large scale(field) conditions, the results also show that the required strength obtained from the proposed solution corresponds quite well to the simulated backfill response.
基金supported by the National Natural Science Foundation of China (Grants Nos. 11174254 and 11104363)the National Basic Research Program of China (Grant Nos. 2011CBA00103 and 2009CB929104)the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110191120046)
文摘An effective scheme within two displaced bosonic operators with equal positive and negative displacements is extended to study qubit-oscillator systems analytically in a unified way. Many previous analytical treatments, such as generalized rotating-wave approximation （GRWA） [Phys. Rev. Lett. 99, 173601 （2007）] and an expansion in the qubit tunneling matrix element in the deep strong coupling regime [Phys. Rev. Lett. 105, 263603 （2010）] can be recovered straightforwardly within the present scheme. Moreover, further improving GRWA and the extension to the finite-bias case are implemented easily. The algebraic formulae for the eigensolutions are then derived explicitly and uniquely, which work well in a wide range of the coupling strengths, detunings, and static bias including the recent experimentally accessible parameters. The dynamics of the qubit for an oscillator in the ground state is also studied. At the experimentally accessible coupling regime, GRWA can always work well. When the coupling is enhanced to the intermediate regime, only the improving GRWA can give the correct description, while the result of GRWA shows strong deviations. The previous Van Vleck perturbation theory is not valid to describe the dynamics in the present-day experimentally accessible regime, except for the strongly biased cases.
基金supported by the National Key R&D Program of China under grant No.2021YFA0716800。
文摘Distributed acoustic sensing(DAS)is increasingly used in seismic exploration owing to its wide frequency range,dense sampling and real-time monitoring.DAS radiation patterns help to understand angle response of DAS records and improve the quality of inversion and imaging.In this paper,we solve the 3D vertical transverse isotropic(VTI)Christoffel equation and obtain the analytical,frst-order,and zero-order Taylor expansion solutions that represent P-,SV-,and SH-wave phase velocities and polarization vectors.These analytical and approximated solutions are used to build the P/S plane-wave expression identical to the far-feld term of seismic wave,from which the strain rate expressions are derived and DAS radiation patterns are thus extracted for anisotropic P/S waves.We observe that the gauge length and phase angle terms control the radiating intensity of DAS records.Additionally,the Bond transformation is adopted to derive the DAS radiation patterns in title transverse isotropic(TTI)media,which exhibits higher complexity than that of VTI media.Several synthetic examples demonstrate the feasibility and effectiveness of our theory.
