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Generalized Supersymmetric perturbation Theory

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Chinese Physics Letters 2004年第12期21卷 2330-2333页

作者： B.Goenül DepartmentofEngineeringPhysics UniversityofGaziantep27310GaziantepTurkey

Using the basic ingredient of supersymmetry, a simple alternative approach is developed to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wavefunctions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.

关键词： perturbation techniques

FOURTH ORDER EVOLUTION EQUATIONS WITH SLOWLY VARYING DEPTH AND CURRENT AND STABILITY OF STOKES WAVES

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Journal of Hydrodynamics 1991年第4期3卷 21-42页

作者： Chin-pu, Zhou Yan-sheng, Chen Zhongshan Univ Guangzhou China

Fourth order evolution equations with slowly varying depth and current have been derived for two-dimensional modulation Stokes waves in arbitrary water depth. In the absence of current and variation of topography the equations reduce to those of Brinch-Nielsen & Jonsson, and the third order terms agree with those of Turpin & Benmoussa & Mei. Stokes wave in the slowly varying depth and current is specified, and its instability to small sidebands is studied in detail. A general criterion of instability with growth rate 0(Ε2) is given, and the maximum growth rate has also been obtained. An interesting result is that in the fourth-order theory the existence of current and varying depth leads the Stokes wave to be always unstable to small sidebands disturbance.

关键词： Mathematical techniques Applications Mathematical techniques perturbation techniques Water Waves Mathematical Models

A Two-Flux Radiation Model for Helical Instability of Arcs

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Chinese Physics Letters 2005年第5期22卷 1187-1190页

作者：宫野郑殊徐翔邹秀刘金远刘悦王晓钢 StateKeyLaboratoryforMaterialsModificationbyLaser IonandElectronBeamsDalianUniversityofTechnologyDalian116024

A two-flux radiation model of the helical instability of arcs in axial magnetic field is presented. The temperature (and electrical conductivity) is approximated in a more realistic way (parabolic instead of flat profile) and a simplified term of radiation losses is included in the energy equation. The magnetohydrodynamic equations in an electrostatic approximation serve as the starting point of the theory. Using a linear time-dependent perturbation theory, the corresponding equations and an explicit analytic expression that corresponds to the term of radiation losses are derived in the presence of the radiation transfer energy, from which the marginal Maecker number and the growth rate of the helical instability can be given. It is found that, in comparison with the results without radiation, the arc stable area is reduced.

关键词： perturbation techniques

Robust H_∞ Stabilization of Uncertain Linear Time-Delay System with Delayed/Undelayed State Feedback Controllers

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Journal of Systems Engineering and Electronics 2001年第4期12卷 71-76页

作者：陈万义 College of Mathematics Nankai University Tianjin 300071 P. R. China

This paper focuses on the H∞ controller design for linear systems with time-varying delays and norm-bounded parameter perturbations in the system state and control/disturbance. On the existence of delayed/undelayed full state feedback controllers, we present a sufficient condition and give a design method in the form of Riccati equation. The controller can not only stabilize the time-delay system, but also make the H∞ norm of the closed-loop system be less than a given bound. This result practically generalizes the related results in current literature.

关键词： Closed loop control systems Feedback control Linear control systems perturbation techniques Riccati equations Robustness (control systems) State feedback System stability Time varying control systems Uncertain systems

perturbationAL FINITE DIFFERENCE SCHEME OF CONVECTION-DIFFUSION EQUATION

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Journal of Hydrodynamics 2002年第2期14卷 51-57页

作者： Gao, Zhi Hu, Li-Min Lab. of High Temp. Gas Dynamics Inst. of Mech. Chinese Acad. of Sci. Beijing 100080 China

The perturbational Finite Difference (PFD) method is a kind of high-order-accurate compact difference method, but its idea is different from the normal compact method and the multi-nodes method. This method can get a perturbational Exact Numerical Solution P(PENS) scheme for locally linearized Convection-Diffusion (CD) equation. The PENS scheme is similar to the Finite Analytical (FA) scheme and Exact Difference Solution (EDS) scheme, which are all exponential schemes, but PENS scheme is simpler and uses only 3,5 and 7 nodes for 1-, 2- and 3-dimensional problems, respectively. The various approximate schemes of PENs scheme are also called perturbational-High-order-accurate Difference (PHD) scheme. The PHD schemes can be got by expanding the exponential terms in the PENS scheme into power series of grid Reynolds number, and they are all upwind schemes and remain the concise structure form of first-order upwind scheme. For 1-dimensional (1-D) CD equation and 2-D incompressible Navier-Stokes equation, their PENS and PHD schemes were constituted in this paper, they all gave highly accurate results for the numerical examples of three 1-D CD equations and an incompressible 2-D flow in a square cavity.

关键词： Diffusion Finite difference method Incompressible flow Navier Stokes equations perturbation techniques Reynolds number Two dimensional

Ionization Balance in Non-Local-Thermodynamic-Equilibrium Plasmas

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Chinese Physics Letters 2004年第5期21卷 877-880页

作者：吴泽清逄锦桥韩国兴颜君 LaboratoryofComputationalPhysics InstituteofAppliedPhysicsandComputationalMathematicsPOBox8009-57Beijing100088

A collisional–radiative model is developed for population calculations of plasmas in non-local thermodynamic equilibrium. The rate equations in detailed configuration accounting are solved to obtain ion populations. The configuration averaged rate coefficients are used in the rate equations. The cross sections are calculated based on the first perturbation theory. Wavefunctions required in cross section calculations are obtained by the Hartree–Fock–Slater self-consistent-field model. This kinetic model is applied to low- and medium-Z as well as high-Z plasmas. The results are compared with those of other theoretical models and experiments. The comparisons show that the present results of the mean charge state for low- and medium-Z elements agree well with other theoretical ones, while for high-Z elements, the present mean ionization stages are about two stages lower than the experimental ones.

关键词： perturbation techniques

DOUBLE-PARAMETER perturbation SOLUTION TO 3-D NONLINEAR PROBLEM OF OBLIQUE WATER EXIT

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Journal of Hydrodynamics 1991年第4期3卷 96-103页

作者： Qu-yuan, Ye You-sheng, He Shanghai Jiao Tong Univ Shanghai China

With a new time-derivative operator, the nonlinear kinematic and dynamic free boundary conditions were modified to a convenient form for numerical computation. The original 3-D nonlinear problem of oblique water exit of an axisymmetric body at a large water exit-angle and a small angle of attack is reduced to a number of 2-D problems by means of the double-parameter-series expansion method and the Fourier-cosine-expansion method. Numerical results are presented of the free surface shapes and the forces exerted during the oblique water exit of a sphere at different Froude numbers.

关键词： Flow of Water Mathematical Models Mathematical techniques Nonlinear Equations Mathematical techniques perturbation techniques

Observer-based Adaptive Optimal Control for Unknown Singularly Perturbed Nonlinear Systems With Input Constraints

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IEEE/CAA Journal of Automatica Sinica 2017年第1期4卷 48-57页

作者： Zhijun Fu Wenfang Xie Subhash Rakheja Jing Na College of Mechanical Engineering Zhejiang University of Technology Department of Mechanical & Industrial Engineering Concordia University Faculty of Mechanical & Electrical Engineering Kunming University of Science & Technology

This paper introduces an observer-based adaptive optimal control method for unknown singularly perturbed nonlinear systems with input constraints. First, a multi-Time scales dynamic neural network MTSDNN observer with a novel updating law derived from a properly designed Lyapunov function is proposed to estimate the system states. Then, an adaptive learning rule driven by the critic NN weight error is presented for the critic NN, which is used to approximate the optimal cost function. Finally, the optimal control action is calculated by online solving the Hamilton-Jacobi-Bellman HJB equation associated with the MTSDNN observer and critic NN. The stability of the overall closed-loop system consisting of the MTSDNN observer, the critic NN and the optimal control action is proved. The proposed observer-based optimal control approach has an essential advantage that the system dynamics are not needed for implementation, and only the measured input U+002F output data is needed. Moreover, the proposed optimal control design takes the input constraints into consideration and thus can overcome the restriction of actuator saturation. Simulation results are presented to confirm the validity of the investigated approach. © 2014 Chinese Association of Automation.

关键词： Closed loop systems Cost functions Lyapunov functions Neural networks Nonlinear systems Optimal control systems perturbation techniques

Analysis of Instabilities in Non-Equilibrium Plasmas

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Chinese Physics Letters 2004年第10期21卷 1993-1996页

作者：林烈张澎王永庆 InstituteofMechanics ChineseAcademyofSciencesBeijing100080 ShenyangAircraftResearchInstitute Shenyang110035

Plasma instabilities with charged particle production processes in non-equilibrium plasma are analysed. A criterion on plasma instabilities is deduced by first-order perturbation theory. The relationship between plasma instabilities and certain factors (degree of non-equilibrium in plasma, the electron attachment rate coefficient and electron temperature) are described.

关键词： perturbation techniques