A refinement of an analytical approximation of the surface potential in MOSFETs is proposed by introducing a high-order term. As compared to the conventional treatment with accuracy between 1nV and 0. 03mV in the case...A refinement of an analytical approximation of the surface potential in MOSFETs is proposed by introducing a high-order term. As compared to the conventional treatment with accuracy between 1nV and 0. 03mV in the cases with an oxide thickness tox = 1 ～ 10nm and substrate doping concentration Na = 1015 ～ 1018 cm-3 , this method yields an accuracy within about 1pV in all cases. This is comparable to numerical simulations, but does not require trading off much computation efficiency. More importantly, the spikes in the error curve associated with the traditional treatment are eliminated.展开更多
Until now, most researches into the rogue-wave-structure interaction have relied on experimental measurement and numerical simulation. Owing to the complexity of the physical mechanism of rogue waves, theoretical stud...Until now, most researches into the rogue-wave-structure interaction have relied on experimental measurement and numerical simulation. Owing to the complexity of the physical mechanism of rogue waves, theoretical study on the wave-structure issue still makes little progress. In this paper, the rogue wave flow around a vertical cylinder is analytically studied within the scope of the potential theory. The rogue wave is modeled by the Gauss envelope, which is one particular case of the well-known focusing theory. The formulae of the wave-induced horizontal force and bending moment are proposed. For the convenience of engineering application, the derived formulae are simplified appropriately, and verified against numerical results. In addition, the influence of wave parameters, such as the energy focusing degree and the wave focusing position, is thoroughly investigated.展开更多
An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution...An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.展开更多
In this paper,an in-band and out-of-band microwave wireless power-transmission characteristic analysis of a slot ring radome based on an approximate analytical method is proposed.The main contribution of this paper is...In this paper,an in-band and out-of-band microwave wireless power-transmission characteristic analysis of a slot ring radome based on an approximate analytical method is proposed.The main contribution of this paper is that,in the approximate analysis of the ring radome,a unified expression of the incident field on the radome surface is derived with E-plane and H-plane scanning,and the ring is approximated as 30 segments of straight strips.Solving the corresponding 60×60 linear equations yields the electric current distribution along the ring strip.The magnetic current along the complementary slot ring is obtained by duality.Thanks to the fully analytical format of the current distribution,the microwave wireless power-transmission characteristics are efficiently calculated using Munk’s scheme.An example of a slot ring biplanar symmetric hybrid radome is used to verify the accuracy and efficiency of the proposed scheme.The central processing unit(CPU)time is about 690 s using Ansys HFSS software versus 2.82 s for the proposed method.展开更多
Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric d...Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.展开更多
In the scenario that a solid-fuel launch vehicle maneuvers in outer space at high angles of attack and sideslip for energy management,Approximate Analytical Solutions(AAS)for the threedimensional(3D)ascent flight stat...In the scenario that a solid-fuel launch vehicle maneuvers in outer space at high angles of attack and sideslip for energy management,Approximate Analytical Solutions(AAS)for the threedimensional(3D)ascent flight states are derived,which are the only solutions capable of considering time-varying Mass Flow Rate(MFR)at present.The uneven MFR makes the thrust vary nonlinearly and thus increases the difficulty of the problem greatly.The AAS are derived based on a 3D Generalized Ascent Dynamics Model(GADM)with a normalized mass as the independent variable.To simplify some highly nonlinear terms in the GADM,several approximate functions are introduced carefully,while the errors of the approximations relative to the original terms are regarded as minor perturbations.Notably,a finite series with positive and negative exponents,called Exponent-Symmetry Series(ESS),is proposed for function approximation to decrease the highest exponent in the AAS so as to reduce computer round-off errors.To calculate the ESS coefficients,a method of seeking the Optimal Interpolation Points(OIP)is proposed using the leastsquares-approximation theory.Due to the artful design of the approximations,the GADM can be decomposed into two analytically solvable subsystems by a perturbation method,and thus the AAS are obtained successfully.Finally,to help implement the AAS,two indirect methods for measuring the remaining mass and predicting the burnout time in flight are put forward using information from accelerometers.Simulation results verify the superiority of the AAS under the condition of time-varying MFR.展开更多
For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln（ψ） =∑k=0^n akψ（k） where the constant coefficients...For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln（ψ） =∑k=0^n akψ（k） where the constant coefficients ak C R may be adapted to f.展开更多
In this paper, the approximate analytical solutions of the fractional coupled mKdV equation are obtained by homotopy analysis method (HAM). The method includes an auxiliary parameter which provides a convenient way of...In this paper, the approximate analytical solutions of the fractional coupled mKdV equation are obtained by homotopy analysis method (HAM). The method includes an auxiliary parameter which provides a convenient way of adjusting and controlling the convergence region of the series solution. The suitable value of auxiliary parameter is determined and the obtained results are presented graphically.展开更多
The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded(FG)cylindrical shells under multi-physics fields is investigated.Grounded in the Kirchhoff-Love thin shell theory,the geometric nonl...The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded(FG)cylindrical shells under multi-physics fields is investigated.Grounded in the Kirchhoff-Love thin shell theory,the geometric nonlinearity is incorporated into the model,and the constitutive equations are derived.The physical parameters of functionally graded materials(FGMs),which exhibit continuous variation across the thickness gradient,are of particular interest.The nonlinear magneto-thermoelastic governing equations are derived in accord with Hamilton's principle.The nonlinear partial differential equations are discretized with the Galerkin method,and the analytical expression of traveling wave frequencies is derived with an approximate method.The accuracy of the proposed method is validated through the comparison with the results from the literature and numerical solutions.Finally,the visualization analyses are conducted to examine the effects of key parameters on the traveling wave frequencies.The results show that the factors including the power-law index,temperature,magnetic field intensity,and rotating speed have the coupling effects with respect to the nonlinear vibration behavior.展开更多
In this research article,we present convenient analytical-approximate solutions for fluid flow models known as multi-dimensional Navier-Stokes equations containing time-fractional order by using a relatively new analy...In this research article,we present convenient analytical-approximate solutions for fluid flow models known as multi-dimensional Navier-Stokes equations containing time-fractional order by using a relatively new analytical method called modified generalized Mittag-Leffler function method.The Caputo fractional derivative is used to describe fractional mathematical formalism.The approximate solutions for five problems are implemented to demonstrate the validity and accuracy of the proposed method.It is also demonstrated that the solutions obtained from our method when=1 coincide with the exact solutions,this is displayed by using some 2D and 3D plots for each problem.Moreover,the comparison between our outcomes with given exact solutions and results obtained by other methods in the literature besides absolute error is provided in some tables.Additionally,we offer some plots when has different values to present the effect of fractional order on the solution of each suggested problem.The numerical simulation presented in this work indicates that the proposed method is efficient,reliable,accurate and easy which has less computational ability to give analytical-approximate solution form.So,this method can be extended to implement on different related problems arising in various areas of innovation and research.展开更多
Analytical approximation of the maximal invariant ellipsoid for discrete-time linear systems with saturated optimal control is established,which is less conservative than existing computationally un-intensive results....Analytical approximation of the maximal invariant ellipsoid for discrete-time linear systems with saturated optimal control is established,which is less conservative than existing computationally un-intensive results.Simultaneously,necessary and sufficient conditions for such approximation being equal to the real maximal invariant ellipsoid is presented.All results are given analytically and can easily be implemented in practice.An illustrative example is given to show the effectiveness of the proposed approach.展开更多
The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.
In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.T...In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.展开更多
In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.
Using a proper approximation scheme to the centrifugal term, we study any l-wave continuum states of the Schrodinger equation for the modified Morse potential. The normalised analytical radial wave functions are prese...Using a proper approximation scheme to the centrifugal term, we study any l-wave continuum states of the Schrodinger equation for the modified Morse potential. The normalised analytical radial wave functions are presented, and a corresponding calculation formula of phase shifts is derived. It is shown that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. Some numerical results are calculated to show the accuracy of our results.展开更多
Systemreliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods.A fast conditional reduction ...Systemreliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods.A fast conditional reduction method based on conditional probability theory is proposed to solve the sensitivity analysis based on the approximate analytic method.The relevant concepts are introduced to characterize the correlation between failure modes by the reliability index and correlation coefficient,and conditional normal fractile the for the multi-dimensional conditional failure analysis is proposed based on the two-dimensional normal distribution function.Thus the calculation of system failure probability can be represented as a summation of conditional probability terms,which is convenient to be computed by iterative solving sequentially.Further the system sensitivity solution is transformed into the derivation process of the failure probability correlation coefficient of each failure mode.Numerical examples results show that it is feasible to apply the idea of failure mode relevancy to failure probability sensitivity analysis,and it can avoid multi-dimension integral calculation and reduce complexity and difficulty.Compared with the product of conditional marginalmethod,a wider value range of correlation coefficient for reliability analysis is confirmed and an acceptable accuracy can be obtained with less computational cost.展开更多
In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The pr...In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.展开更多
This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrodinger equation for the generalized Hulthen potential by taking an improved new approximate scheme for the centrifuga...This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrodinger equation for the generalized Hulthen potential by taking an improved new approximate scheme for the centrifugal term. The normalized analytical radial wave functions of the 1-wave SchrSdinger equation for the generalized Hulthen potential are presented and the corresponding calculation formula of phase shifts is derived. Some useful figures are plotted to show the improved accuracy of the obtained results and two special cases for the standard Hulthen potential and Woods-Saxon potential are also studied briefly.展开更多
Take the single degree of freedom nonlinear oscillator with clearance under harmonic excitation as an example,the 1/3 subharmonic resonance of piecewise-smooth nonlinear oscillator is investigated.The approximate anal...Take the single degree of freedom nonlinear oscillator with clearance under harmonic excitation as an example,the 1/3 subharmonic resonance of piecewise-smooth nonlinear oscillator is investigated.The approximate analytical solution of 1/3 subharmonic resonance of the single-degree-of-freedom piecewise-smooth nonlinear oscillator is presented.By changing the solving process of Krylov-Bogoliubov-Mitropolsky(KBM)asymptotic method for subharmonic resonance of smooth nonlinear system,the classical KBM method is extended to piecewise-smooth nonlinear system.The existence conditions of 1/3 subharmonic resonance steady-state solution are achieved,and the stability of the subharmonic resonance steady-statesolution is also analyzed.It is found that the clearance affects the amplitude-frequency response of subharmonic resonance in the form of equivalent negative stiffness.Through a demonstration example,the accuracy of approximate analytical solution is verified by numerical solution,and they have good consistency.Based on the approximate analytical solution,the infuences of clearance on the critical frequency and amplitude-frequency response of 1/3 subharmonic resonance are analyzed in detail.The analysis results show that the KBM method is an effective analytical method for solving the subharmonic resonance of piecewise-smooth nonlinear system.And it provides an effective reference for the study of subharmonicr esonance of other piecewise-smooth systems.展开更多
An approximate analytical solution of moving boundary problem for diffusion release of drug from a cylinder polymeric matrix was obtained by use of refined integral method. The release kinetics has been analyzed for n...An approximate analytical solution of moving boundary problem for diffusion release of drug from a cylinder polymeric matrix was obtained by use of refined integral method. The release kinetics has been analyzed for non-erodible matrices with perfect sink condition. The formulas of the moving boundary and the fractional drug release were given. The moving boundary and the fractional drug release have been calculated at various drug loading levels, mid the calculated results were in good agreement with those of experiments. The comparison of the moving boundary in spherical, cylinder, planar matrices has been completed. An approximate formula for estimating the available release time was presented. These results are useful for the clinic experiments. This investigation provides a new theoretical tool for studying the diffusion release of drug from a cylinder polymeric matrix and designing the controlled released drug.展开更多
文摘A refinement of an analytical approximation of the surface potential in MOSFETs is proposed by introducing a high-order term. As compared to the conventional treatment with accuracy between 1nV and 0. 03mV in the cases with an oxide thickness tox = 1 ～ 10nm and substrate doping concentration Na = 1015 ～ 1018 cm-3 , this method yields an accuracy within about 1pV in all cases. This is comparable to numerical simulations, but does not require trading off much computation efficiency. More importantly, the spikes in the error curve associated with the traditional treatment are eliminated.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51579146,51490674,and51609101)the Shanghai Rising-Star Program(Grant No.16QA1402300)
文摘Until now, most researches into the rogue-wave-structure interaction have relied on experimental measurement and numerical simulation. Owing to the complexity of the physical mechanism of rogue waves, theoretical study on the wave-structure issue still makes little progress. In this paper, the rogue wave flow around a vertical cylinder is analytically studied within the scope of the potential theory. The rogue wave is modeled by the Gauss envelope, which is one particular case of the well-known focusing theory. The formulae of the wave-induced horizontal force and bending moment are proposed. For the convenience of engineering application, the derived formulae are simplified appropriately, and verified against numerical results. In addition, the influence of wave parameters, such as the energy focusing degree and the wave focusing position, is thoroughly investigated.
基金This work was financially supported by the National Natural Science Foundation of China (No.50476083).
文摘An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.
基金supported in part by the National Key Research and Development Program(2021YFF1500100)Key Basic Research of Basic Strengthening Program of the Science and Technology Commission(2020-JCJQ-ZD-068)。
文摘In this paper,an in-band and out-of-band microwave wireless power-transmission characteristic analysis of a slot ring radome based on an approximate analytical method is proposed.The main contribution of this paper is that,in the approximate analysis of the ring radome,a unified expression of the incident field on the radome surface is derived with E-plane and H-plane scanning,and the ring is approximated as 30 segments of straight strips.Solving the corresponding 60×60 linear equations yields the electric current distribution along the ring strip.The magnetic current along the complementary slot ring is obtained by duality.Thanks to the fully analytical format of the current distribution,the microwave wireless power-transmission characteristics are efficiently calculated using Munk’s scheme.An example of a slot ring biplanar symmetric hybrid radome is used to verify the accuracy and efficiency of the proposed scheme.The central processing unit(CPU)time is about 690 s using Ansys HFSS software versus 2.82 s for the proposed method.
基金＊Supported by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2010291, the Professor and Doctor Foundation of Yancheng Teachers University under Grant No. 07YSYJB0203
文摘Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.
基金Supported in part by National Natural Science Foundation of China(No.62003012)in part by the Young Tulents Support Program funded by Bcihang Univer-sity,China(No.YWF-23-L-702).
文摘In the scenario that a solid-fuel launch vehicle maneuvers in outer space at high angles of attack and sideslip for energy management,Approximate Analytical Solutions(AAS)for the threedimensional(3D)ascent flight states are derived,which are the only solutions capable of considering time-varying Mass Flow Rate(MFR)at present.The uneven MFR makes the thrust vary nonlinearly and thus increases the difficulty of the problem greatly.The AAS are derived based on a 3D Generalized Ascent Dynamics Model(GADM)with a normalized mass as the independent variable.To simplify some highly nonlinear terms in the GADM,several approximate functions are introduced carefully,while the errors of the approximations relative to the original terms are regarded as minor perturbations.Notably,a finite series with positive and negative exponents,called Exponent-Symmetry Series(ESS),is proposed for function approximation to decrease the highest exponent in the AAS so as to reduce computer round-off errors.To calculate the ESS coefficients,a method of seeking the Optimal Interpolation Points(OIP)is proposed using the leastsquares-approximation theory.Due to the artful design of the approximations,the GADM can be decomposed into two analytically solvable subsystems by a perturbation method,and thus the AAS are obtained successfully.Finally,to help implement the AAS,two indirect methods for measuring the remaining mass and predicting the burnout time in flight are put forward using information from accelerometers.Simulation results verify the superiority of the AAS under the condition of time-varying MFR.
文摘For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln（ψ） =∑k=0^n akψ（k） where the constant coefficients ak C R may be adapted to f.
文摘In this paper, the approximate analytical solutions of the fractional coupled mKdV equation are obtained by homotopy analysis method (HAM). The method includes an auxiliary parameter which provides a convenient way of adjusting and controlling the convergence region of the series solution. The suitable value of auxiliary parameter is determined and the obtained results are presented graphically.
基金supported by the National Natural Science Foundation of China(No.12172321)。
文摘The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded(FG)cylindrical shells under multi-physics fields is investigated.Grounded in the Kirchhoff-Love thin shell theory,the geometric nonlinearity is incorporated into the model,and the constitutive equations are derived.The physical parameters of functionally graded materials(FGMs),which exhibit continuous variation across the thickness gradient,are of particular interest.The nonlinear magneto-thermoelastic governing equations are derived in accord with Hamilton's principle.The nonlinear partial differential equations are discretized with the Galerkin method,and the analytical expression of traveling wave frequencies is derived with an approximate method.The accuracy of the proposed method is validated through the comparison with the results from the literature and numerical solutions.Finally,the visualization analyses are conducted to examine the effects of key parameters on the traveling wave frequencies.The results show that the factors including the power-law index,temperature,magnetic field intensity,and rotating speed have the coupling effects with respect to the nonlinear vibration behavior.
文摘In this research article,we present convenient analytical-approximate solutions for fluid flow models known as multi-dimensional Navier-Stokes equations containing time-fractional order by using a relatively new analytical method called modified generalized Mittag-Leffler function method.The Caputo fractional derivative is used to describe fractional mathematical formalism.The approximate solutions for five problems are implemented to demonstrate the validity and accuracy of the proposed method.It is also demonstrated that the solutions obtained from our method when=1 coincide with the exact solutions,this is displayed by using some 2D and 3D plots for each problem.Moreover,the comparison between our outcomes with given exact solutions and results obtained by other methods in the literature besides absolute error is provided in some tables.Additionally,we offer some plots when has different values to present the effect of fractional order on the solution of each suggested problem.The numerical simulation presented in this work indicates that the proposed method is efficient,reliable,accurate and easy which has less computational ability to give analytical-approximate solution form.So,this method can be extended to implement on different related problems arising in various areas of innovation and research.
基金the Major Program of National Natural Science Foundation of China(No.60710002)Program for Changjiang Scholars and Innovative Research Team in University.
文摘Analytical approximation of the maximal invariant ellipsoid for discrete-time linear systems with saturated optimal control is established,which is less conservative than existing computationally un-intensive results.Simultaneously,necessary and sufficient conditions for such approximation being equal to the real maximal invariant ellipsoid is presented.All results are given analytically and can easily be implemented in practice.An illustrative example is given to show the effectiveness of the proposed approach.
基金＊Supported by the National Natural Science Foundation of China under Grant No. 40876010, the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No. KZCX2-YW-Q03-08, the R ＆： D Special Fund for Public Welfare Industry （Meteorology） under Grant No. GYHY200806010, the LASG State Key Laboratory Special Fund and the Foundation of E-Institutes of Shanghai Municipal Education Commission （E03004）
文摘The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.
文摘In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.
基金Supported by the National Natural Science Foundation of China under Grant No.40876010the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No.KZCX2-YW-Q03-08+2 种基金the LASG State Key Laboratory Special Fundthe Foundation of Shanghai Municipal Education Commission under Grant No.E03004the Natural Science Foundation of Zhejiang Province under Grant No.Y6090164
文摘In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.
基金supported by Xi’an University of Arts and Science,China (Grant No.KYC200801)
文摘Using a proper approximation scheme to the centrifugal term, we study any l-wave continuum states of the Schrodinger equation for the modified Morse potential. The normalised analytical radial wave functions are presented, and a corresponding calculation formula of phase shifts is derived. It is shown that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. Some numerical results are calculated to show the accuracy of our results.
基金This research is supported by National Key Research and Development Project(Grant Number 2019YFD0901002)Also Natural Science Foundation of Liaoning Province(Grant Number 20170540105)Liaoning Province Education Foundation(Grant Number JL201913)are gratefully acknowledged.
文摘Systemreliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods.A fast conditional reduction method based on conditional probability theory is proposed to solve the sensitivity analysis based on the approximate analytic method.The relevant concepts are introduced to characterize the correlation between failure modes by the reliability index and correlation coefficient,and conditional normal fractile the for the multi-dimensional conditional failure analysis is proposed based on the two-dimensional normal distribution function.Thus the calculation of system failure probability can be represented as a summation of conditional probability terms,which is convenient to be computed by iterative solving sequentially.Further the system sensitivity solution is transformed into the derivation process of the failure probability correlation coefficient of each failure mode.Numerical examples results show that it is feasible to apply the idea of failure mode relevancy to failure probability sensitivity analysis,and it can avoid multi-dimension integral calculation and reduce complexity and difficulty.Compared with the product of conditional marginalmethod,a wider value range of correlation coefficient for reliability analysis is confirmed and an acceptable accuracy can be obtained with less computational cost.
基金Project supported by the Natural Science Foundation of Inner Mongolia of China (Grant No. 20080404MS0104)the Young Scientists Fund of Inner Mongolia University of China (Grant No. ND0811)
文摘In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.
文摘This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrodinger equation for the generalized Hulthen potential by taking an improved new approximate scheme for the centrifugal term. The normalized analytical radial wave functions of the 1-wave SchrSdinger equation for the generalized Hulthen potential are presented and the corresponding calculation formula of phase shifts is derived. Some useful figures are plotted to show the improved accuracy of the obtained results and two special cases for the standard Hulthen potential and Woods-Saxon potential are also studied briefly.
基金the National Natural Science Foundation of China(Grants 11872254,U1934201 and 11790282).
文摘Take the single degree of freedom nonlinear oscillator with clearance under harmonic excitation as an example,the 1/3 subharmonic resonance of piecewise-smooth nonlinear oscillator is investigated.The approximate analytical solution of 1/3 subharmonic resonance of the single-degree-of-freedom piecewise-smooth nonlinear oscillator is presented.By changing the solving process of Krylov-Bogoliubov-Mitropolsky(KBM)asymptotic method for subharmonic resonance of smooth nonlinear system,the classical KBM method is extended to piecewise-smooth nonlinear system.The existence conditions of 1/3 subharmonic resonance steady-state solution are achieved,and the stability of the subharmonic resonance steady-statesolution is also analyzed.It is found that the clearance affects the amplitude-frequency response of subharmonic resonance in the form of equivalent negative stiffness.Through a demonstration example,the accuracy of approximate analytical solution is verified by numerical solution,and they have good consistency.Based on the approximate analytical solution,the infuences of clearance on the critical frequency and amplitude-frequency response of 1/3 subharmonic resonance are analyzed in detail.The analysis results show that the KBM method is an effective analytical method for solving the subharmonic resonance of piecewise-smooth nonlinear system.And it provides an effective reference for the study of subharmonicr esonance of other piecewise-smooth systems.
文摘An approximate analytical solution of moving boundary problem for diffusion release of drug from a cylinder polymeric matrix was obtained by use of refined integral method. The release kinetics has been analyzed for non-erodible matrices with perfect sink condition. The formulas of the moving boundary and the fractional drug release were given. The moving boundary and the fractional drug release have been calculated at various drug loading levels, mid the calculated results were in good agreement with those of experiments. The comparison of the moving boundary in spherical, cylinder, planar matrices has been completed. An approximate formula for estimating the available release time was presented. These results are useful for the clinic experiments. This investigation provides a new theoretical tool for studying the diffusion release of drug from a cylinder polymeric matrix and designing the controlled released drug.
