On the forced vibrations of an oscillator with a periodically time-varying mass

In this paper the forced vibrations of a linear, single degree of freedom oscillator (sdofo) with a time-varying mass will be studied. The forced vibrations are due to small masses which are periodically hitting and leaving the oscillator with different velocities. Since these small masses stay for some time on the oscillator surface the effective mass of the oscillator will periodically vary in time. Additionally, an external harmonic force will be applied to the oscillator with a time-varying mass. Not only solutions of the oscillator equation will be constructed, but also stability properties for the forced vibrations will be presented for various parameter values.     

On the stability properties of a damped oscillator with a periodically time-varying mass

In this paper the vibrations of a damped, linear, single degree of freedom oscillator (sdofo) with a time-varying mass will be considered. Both the free and forced vibrations of the oscillator will be studied. For the free vibrations the minimal damping rates will be computed, for which the oscillator is always stable. The forced vibrations are partly due to small masses, which are periodically hitting and leaving the oscillator with different velocities. Since these small masses stay for some time on the oscillator surface the effective mass of the oscillator will periodically vary in time. Additionally, an external harmonic force will be applied to the oscillator. Not only solutions of the oscillator equations will be constructed, but also stability properties for the free, and for the forced vibrations will be presented for various parameter values. For the external, harmonic forcing case an interesting resonance condition will be derived.     

Re-evaluation of some lithium dipole properties and dipole-dipole and dipole-quadrupole van der Waals constants

Our previous one-centre pseudo-state results for some ground-state Li atom dipole oscillator strength sums, the dipole-dipole dispersion energy constants for the Li-Li, Li-H and Li-He ground-state interactions and the dipole-quadrupole dispersion energy constant for the Li-Li interaction are re-evaluated in the light of a more reliable selection for the resonance dipole oscillator strength of the Li atom. These and some of our previous lithium pseudo-state results are compared with corresponding literature values.     

Independent oscillator model of a heat bath: Exact diagonalization of the Hamiltonian

The problem of a quantum oscillator coupled to an independent-oscillator model of a heat bath is discussed. The transformation to normal coordinates is explicitly constructed using the method of Ullersma. With this transformation an alternative derivation of an exact formula for the oscillator free energy is constructed. The various contributions to the oscillator energy are calculated, with the aim of further understanding this formula. Finally, the limitations of linear coupling models, such as that used by Ullersma, are discussed in the form of some critical remarks.     

Oscillator with random trichotomous mass

In addition to the case usually considered of a stochastic harmonic oscillator subject to an external random force (Brownian motion in a parabolic potential) or to a random frequency and random damping, we consider an oscillator with random mass subject to an external periodic force, where the molecules of a surrounding medium, which collide with a Brownian particle are able to adhere to the oscillator for a random time, changing thereby the oscillator mass. The fluctuations of mass are modelled as trichotomous noise. Using the Shapiro–Loginov procedure for splitting the correlators, we found the first two moments. It turns out that the second moment is a non-monotonic function of the characteristics of noise and periodic signal, and for some values of these parameters, the oscillator becomes unstable.     

天体中的高电离态硫原子跃迁振子强度的研究

简要地研究了高电离态硫原子的某能级跃迁振子强度f值,并对利用能级寿命确定出的振子强度结果做了简要讨论.     

Integral cross sections for electron impact excitations of argon and carbon dioxide

Electron-impact excitation integral cross sections play an important role in understanding the energy transfer processes in many applied physics. Practical applications require integral cross sections in a wide collision energy range from the excitation threshold to several keV. The recently developed BE-scaling method is able to meet the demands of integral cross sections for dipole-allowed transitions while the prerequisite relies on the accurate generalized oscillator strengths. Fast electron and x-ray scatterings are the conventional experimental techniques to approach the generalized oscillator strengths, and the joint study by both methods can provide credible cross-checks. The validated generalized oscillator strengths can then be used to extrapolate optical oscillator strengths by fitting the data with the Lassettre formula. The fitted curve also enables the integration of generalized oscillator strengths over the whole momentum transfer region to obtain the BE-scaled integral excitation cross sections. Here, experimental measurements by both fast electron and x-ray scattering of argon and carbon dioxide are reviewed. The integral cross sections for some low-lying states are derived from the cross-checked generalized oscillator strengths for the first time. The integral cross sections presented in this paper are openly available at https://doi.org/10.11922/sciencedb.01466.     

Stability Properties of a Damped Nonlinear Oscillator Including Persistent Perturbations

The equation of motion of a damped nonlinear multidimensional oscillator disturbed by some (stochastic) persistent force is investigated for Lyapunov stability. With the aid of stability statements on the stationary solutions of the undisturbed equation, estimations for the trajectories are found. Applications of this oscillator as useful model in physics are mentioned.     

Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrödinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for someparametric moving boundaries as well.     

Two coupled impact oscillators

A forced impact oscillator is coupled to a second freely moving oscillator with no amplitude constraint. The influence of the coupling strength and the external frequency is studied in detail. For intermediate coupling strength many of the long-period or chaotic motions are suppressed and replaced by short-period motions at least for not too high frequencies. Phase space trajectories are discussed for some characteristic examples.     

振子强度密度理论研究——类锂离子3s态到p通道跃迁振子强度密度

以类锂离子3s态到p通道光跃迁为例,在单通道理论框架下统一处理从一个初态(3s)到一个通道(p通道)中无数个激发态(包括束缚态np和连续态εp)的光跃迁过程。具体地根据相对论性和非相对论性原子自洽场理论,分别计算了类锂离子3s态到p通道跃迁的有关振子强度密度,阐明了其相对论效应以及振子强度密度随原子序数变化的标度规律。根据本文所计算的振子强度密度,可方便地获得3s跃迁至所有np束缚激发态的振子强度。 关键词：     

Nonlinear parametric oscillations in certain stochastic systems: A random van der Pol oscillator

Astochastic model for some class ofnonlinear oscillators, which includes a van der Pol-type oscillator with random parameters, is analyzed in thediffusion limit. That is, small random fluctuations and long time are considered, while the nonlinearity is also assumed to be small. We show that there existstationary distributions, independent of the phase of the oscillator, a result proved earlier by R. L. Stratonovich assuming the random perturbations of the frequency to be delta correlated. The time behavior of the moments of the displacement of the oscillator from its rest position is also investigated and the results are compared with the corresponding ones for the linear random oscillator. A numerical study is also performed for the first two moments and plots are given.on leave from the University of Padua, Italy.     

Optical properties of ytterbium-doped tandem-pumped fiber oscillator

With the rapid development of ytterbium-doped fiber lasers, some obtrusive limitations on power scaling appeared. In order to avoid these problems, a scheme called tandem pumping is introduced into the fiber laser field. In this paper, the optical properties of an ytterbium-doped tandem-pumped fiber oscillator are presented. According to the oscillator profile, the proper gain fiber type and pump wavelength range are picked out, under the comprehensive consideration of laser conversion efficiency and beam quality. In addition, the photodarkening performances of tandem pumping lasers and conventional ones are compared based on practical application, with all possible impact parameters taken into account. Moreover, an all-fibered tandem-pumped oscillator centered at 1079.5 nm is built, in the way of clad pumping by a 1030-nm fiber laser. The laser power of the oscillator reaches 7 W, with an opto-optic efficiency of 82.4%.     

New Type of Brownian Motion

We consider an oscillator with a random mass for which the particles of the surrounding medium adhere to the oscillator for some random time after the collision (Brownian motion with adhesion for a harmonically bound particle). This is another form of a stochastic oscillator, different from oscillator usually studied that is subject to a random force or having random frequency or random damping. Calculation of the first two stationary moments shows that for white multiplicative noise of week strength the second moment coincides with that of usual Brownian motion, but for symmetric dichotomous noise, the second moment may appear the same type of the “energetic” instability, which exists for white noise random frequency or damping coefficient.     

The hydrogen atom confined in both Debye screening potential and impenetrable spherical box

The ground state energy, some low-lying excited state energies and oscillator strengths for a hydrogen atom confined in both a Debye screening potential and finite impenetrable spherical box have been calculated. These have been calculated using a linear variational method based on B-spline basis functions. The results have been compared with those of other authors. The evaluated energies and oscillator strengths with respect to different plasma screening parameters with a certain confinement radii are discussed.     

Two-Dimensional Linear Dependencies on the Coordinate Time-Dependent Interaction in Relativistic Non-Commutative Phase Space

In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate time-dependent potential, the Dirac equation is written in terms of Non-Commutative phase space parameters and solved in a general form by using Lewis-Riesenfield invariant method and the time-dependent invariant of Dirac equation with two-dimensional linear dependency on the coordinate time-dependent potential in Non-Commutative phase space has been constructed, then such latter operations are done for time-dependent Dirac oscillator. In order to solve the differential equation of wave function time evolution for Dirac equation and time-dependent Dirac oscillator which are partial differential equation some appropriate ordinary physical problems have been studied and at the end the interesting result has been achieved.     

EXACT SOLUTIONS TO THE N-BODY SCHRÖDINGER EQUATION FOR THE HARMONIC OSCILLATOR

The exact solutions to the N-body Schrödinger equation for the harmonic oscillator are presented analytically. The permutational symmetry of the solutions for the identical three-body system of the harmonic oscillator are discussed in some detail.     

忆阻混沌振荡器的动力学分析

忆阻器(memristor)是一种有记忆功能的非线性电阻器,它是除电阻器、电容器和电感器之外的第四种基本电路元件.采用一个具有光滑磁控特性曲线的忆阻器和一个负电导替换蔡氏振荡器中的蔡氏二极管,导出了一个基于忆阻器的振荡器电路.采用常规的动力学分析手段研究了电路参数和初始条件变化时该光滑忆阻振荡器的动力学特性.研究结果表明,光滑忆阻振荡器与一般的混沌系统完全不同,它的动力学行为除了与电路参数有关外,还极端依赖于电路的初始条件,存在瞬态混沌和状态转移等奇异的非线性物理现象.     

Infinitely many coexisting attractors of a dual memristive Shinriki oscillator and its FPGA digital implementation

In this paper, a novel chaotic oscillator is proposed, which is derived from the classical Shinriki oscillator by substituting the series-parallel diode loop with a flux-controlled memristor and connecting an active charge-controlled memristor in series with an inductor. The mathematical model of the circuit is established, and the stability distribution maps of three non-zero eigenvalues in the equilibrium plane are obtained. The basic dynamical behaviors depending on the variation of the circuit parameters and memristor initial conditions are investigated by standard nonlinear analysis tools, such as bifurcation diagrams, Lyapunov exponents and phase portraits. Particularly, some striking phenomena, including the routes to double-scroll chaotic attractors, coexisting periodic-chaotic bubbles and asymmetric coexisting behaviors are observed. Furthermore, extreme multistability of the new oscillator is revealed by attraction basins under the initial condition of different dynamic elements. Finally, the Shinriki oscillator with two memristors is realized through Field-Programmable Gate Array (i.e., FPGA) to verify the effectiveness of the numerical simulations.