用可变阶数的代数方法研究双原子体系的完全振动能谱和离解能

不同双原子分子电子态的势能(或振动能谱)的展开性质可能不同,文章将固定阶数的代数方法(AM)改进为可变阶数的代数方法,使得该方法可以研究各种不同性质(不同能量展开阶数)的双原子分子电子态,也可以解决光谱计算中可能出现的"蝴蝶效应"问题。利用阶数可变的AM方法研究了原来固定阶数的AM方法难以给出正确结果的N2-a′1Σu-,Li2+-2 2Σg+,4 He D+-X1Σ+和39 K85 Rb-(2)3Σ+等不同双核体系的完全振动能谱与离解能,不但得到了与实验数据精确相符的理论结果,还正确地预言了许多由于实验条件与技术原因而未能测得的物理数据。研究表明阶数可变的AM方法能够更广泛地用于研究各类双核电子态体系的完全振动能谱和体系离解能。     

用节点变分的代数方法研究双原子体系的完全振动能谱和离解能

对于使用实验数据作为原数据进行的数值计算, 由于实验误差的普遍存在, 在数值计算过程中可能存在对实验误差的放大效应, 使得微小的实验误差对数值计算的结果产生明显影响. 因此本文通过在AM (algebraic method) 方法中加入用以抵消实验误差的微小变分项δE, 从而将AM改进为节点变分的代数方法VAM (variational algebraic method). 该方法具有更广泛的适用范围, 尤其对处理那些实验数据较少、 误差较大、 已知的实验振动能级远离体系离解能的双原子体系效果明显. 本文利用VAM方法研究了AM方法难以处理的5¹Π_u⁷Li₂, (6d)¹Δ_g Na₂, (7d)¹Δ_gNa₂ 和5¹∑⁺ NaK 等不同碱金属双原子分子的完全振动能谱与离解能, 不但得到了与实验数据精确相符的理论结果, 还正确地预言了许多由于实验条件与技术原因而未能测得的物理数据. 充分表明了VAM 方法的可行性与正确性. 此处对数值误差的分析和物理思考对其他精确的数值计算 或数值模拟研究也有积极的参考意义.     

Ionization energies of bosonic Coulomb systems

We consider atomic and molecular systems with fixed nuclei where the electrons are assumed to be bosons. Then the ionization energies are rigorously computable in the limit of large particle numbers.     

Ionization energies and term energies of the ground states ls22s of lithium-like systems

We extend the Hamiltonian method of the full-core plus correlation （FCPC） by minimizing the expectation value to calculate the non-relativistic energies and the wave functions of ls22s states for the lithium-like systems from Z = 41 to 50. The mass-polarization and the relativistic corrections including the kinetic-energy correction, the Darwin term, the electron-electron contact term, and the orbit-orbit interaction are calculated perturbatively as first-order correction. The contribution from quantum electrodynamic （QED） is also explored by using the effective nuclear charge formula. The ionization potential and term energies of the ground states 1 s22s are derived and compared with other theoretical calculation results. It is shown that the FCPC methods are also effective for theoretical calculation of the ionic structure for high nuclear ion of lithium-like systems.     

Improved control of distributed parameter systems using wireless sensor and actuator networks:An observer-based method

In this paper,the control problem of distributed parameter systems is investigated by using wireless sensor and actuator networks with the observer-based method.Firstly,a centralized observer which makes use of the measurement information provided by the fixed sensors is designed to estimate the distributed parameter systems.The mobile agents,each of which is affixed with a controller and an actuator,can provide the observer-based control for the target systems.By using Lyapunov stability arguments,the stability for the estimation error system and distributed parameter control system is proved,meanwhile a guidance scheme for each mobile actuator is provided to improve the control performance.A numerical example is finally used to demonstrate the effectiveness and the advantages of the proposed approaches.     

Calculations of vacancy formation energies and divacancy binding energies for noble metals using pseudopotential formalism

Vacancy formation energies (E^f_1v) and divacancy binding energies (E^B_2v) for noble metals have been calculated using the Moriarty's pseudopotential. While the calculated E^f_1v are coincident with the experimental values except Cu, E^B_2v agree with them for all the metals tolerably.     

Equivalent higher order linear and non-linear systems

The object of this study is to put forth the concept of equivalence of classes of linear and non-linear systems of higher order. In particular, the equivalence of classes of non-linear (non-autonomous/autonomous) systems of order n described by partial/ordinary differential equations with corresponding classes of linear systems of order (n + 1) is established through a differential transformation of the dependent variable. In view of the fact that the resulting linear systems are amenable to existing state-space techniques, this approach can be expected to be of value in the study of many non-linear problems arising in a variety of disciplines. The possible applications of the technique are illustrated with an example.     

Monotonicity of ionization energies for three electron lithium-type systems

Although it is quite obvious that an increasing amount of energy is required to remove more and more electrons from an atom, the proof of this observation seems to be a remarkably difficult problem in mathematical physics. Here, by using well-known energy bounds, we show the monotonicity of ionization energies for the simplest nontrivial system, i.e., a nucleus (with infinite mass) and three electrons, which physically corresponds to ionization in the lithium isoelectronic series via the para-channel.PHYMAT, Dept. de math. Univ. de Toulon et du Var F-83130 La Garde, France.On leave from Stranski Institut, TEL 33 Tech. Univ. Berlin D-1000 Berlin 10, F.R.G.Laboratoire propre du Centre Nationale de la Recherche Scientifique.     

Lepton scattering off few-nucleon systems at medium and high energies

The interpretation of recent JLab experimental data on the exclusive process A(e,e′p)B off few-nucleon systems is analyzed in terms of realistic nuclear wave functions and the Glauber multiple scattering theory, both in its original form and within a generalized eikonal approximation. The relevance of the exclusive process ⁴He(e,e′p)³H for possible investigations of QCD effects is illustrated.     

Free vibrations of laminated composite shells with uniformly distributed attached mass using higher order shell theory including stiffness effect

In this paper, free vibrations of a cross-ply composite shell with or without a uniformly distributed attached mass are analyzed using higher order shell theory. The results of free vibrations without distributed attached mass are validated by previous literatures. The stiffness effect of this distributed attached mass are also considered and compared with those well-known published results in which this effect is ignored. Various results for composite shells under a variety of conditions such as variations in the thickness of the shell, variation in the thickness of the distributed attached mass, variation in the radii of curvatures and various elasticity moduli are presented in this paper. In some cases, to verify the novel results, first-order shear deformation theory (FSDT) is also used. In this paper, parameters which influence the natural frequencies of the shells with attached mass including the stiffness of the mass are investigated. Parameters which are investigated in this paper are thickness of the shell, thickness of the distributed attached mass, elasticity moduli of the distributed attached mass and radius of curvatures of shells. Increasing the thickness or elasticity moduli of the distributed attached mass will increase the fundamental natural frequency of the shell. The effect of the stiffness of the distributed attached mass is decreased by decreasing the radii of curvatures or increasing the thickness of the shells.     

Erratum to: Synthesis of exotic nuclei in heavy-ion collisions at higher energies

The charge equilibration upper energy-limit formula is proposed. It shows not only the basic mechanism of charge equilibration but also does imply the possibility of controlling the exotic nuclear synthesis. To understand the mechanism of charge equilibration, charge and mass distributions of final fragments of the heavy-ion collisions are studied based on three-dimensional time-dependent Hartree-Fock calculations with a Skyrme interaction.     

Real-time anti-node visualization of vibrating distributed systems in noisy environments using defocused laser speckle contrast analysis

A simple optical technique is described that allows for the direct whole-field visualization of anti-nodal patterns in noisy environments. The technique involves the combination of defocused laser speckle imaging with the laser speckle contrast analysis (LASCA) algorithm to relate local contrast reduction of a laser speckle pattern to the magnitude of the gradient vectors that arise due to the tilt deflection of a vibrating surface. The method requires no reference beam and is tolerant of environmental noise. The sensitivity of the technique is a direct function of the degree of defocus of the speckle pattern and thus can be readily adjusted. By ratioing the instantaneous contrast to the reference image contrast, a simple method for thresholding the noise floor (noise at reference state) is attained, thus increasing the method's tolerance to ambient disturbances. Results from forced vibration via acoustic excitation of a square and rectangular membrane—with and without simultaneous white noise excitation—are shown. Results are compared to theoretical predictions for an ideal membrane, with good agreement.     

Ionization energies and term energies of the ground states 1s22s of lithium-like systems

We extend the Hamiltonian method of the full-core plus correlation(FCPC) by minimizing the expectation value to calculate the non-relativistic energies and the wave functions of 1s22s states for the lithium-like systems from Z = 41 to 50. The mass-polarization and the relativistic corrections including the kinetic-energy correction, the Darwin term, the electron–electron contact term, and the orbit–orbit interaction are calculated perturbatively as first-order correction. The contribution from quantum electrodynamic(QED) is also explored by using the effective nuclear charge formula. The ionization potential and term energies of the ground states 1s22s are derived and compared with other theoretical calculation results. It is shown that the FCPC methods are also effective for theoretical calculation of the ionic structure for high nuclear ion of lithium-like systems.     

Deposition-evaporation stochastic systems in two and higher dimensions

We study the stochastic dynamics of deposition-evaporation cooperative processes of dimers, trimers, etc., in two- and higher-dimensional lattices. The dimer system in bipartite lattices allows for an exact solution of dynamic correlations and scaling functions by means of a quantum spin equivalence. Autocorrelations exhibit a diffusive asymptotic kinetics and crossovers of different dynamic regimes in highly anisotropic lattices. Monte Carlo simulations combined with finite-size scaling arguments support the validity of the diffusive picture in more general situations. Steady-state coverages and diffusion constants are obtained using mean-field approaches, spin wave calculations, and random walk analyses in nearly jammed configurations.     

Contact melting zone in two- and three-component systems

The composition of the contact melting zone was studied in the systems tin-cadmium and tin-cadmium-lead. It was found that in the contact melting zone of a binary alloy with pure metal a redistribution is observed of the alloying element between the solid and liquid phases.Translated from Izvestiya Vysshikh Zavedenii, Fizika, No. 10, pp. 112–116, October, 1973.