The homotopic method of travelling wave solution for El Nino tropic sea-air coupled oscillator

The EI Nimo and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. In this paper, an asymptotic method of solving nonlinear equations for the ENSO model is proposed. And based on a class of oscillator of the ENSO model and by employing the method of homotopic mapping, the approximate solution of equations for the corresponding ENSO model is studied. It is proved from the results that homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for the ENSO model.     

一类厄尔尼诺-南方涛动耦合振子动力学模型的震荡近似解

研究了一类厄尔尼诺和南方涛动(ENSO)耦合振子动力学模型. 利用奇摄动理论的参数变值法和平均法, 得到了对应ENSO耦合振子模型方程的震荡近似解. 关键词： ENSO振子 奇摄动 近似解     

Noise-Induced Transition in a Voltage-Controlled Oscillator Neuron Model

In the presence of Gaussian white noise, we study the properties of voltage-controlled oscillator neuron model and discuss the effects of the additive and multiplicative noise. It is found that the additive noise can accelerate and counterwork the firing of neuron, which depends on the value of central frequency of neuron itself, while multiplicative noise can induce the continuous change or mutation of membrane potential.     

Strategies for h-Adaptive Refinement for a Finite Element Treatment of Harmonic Oscillator Schrodinger Eigenproblem

A Schrodinger eigenvalue problem is solved for the 219 quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, （i） an application of the Kelly error estimator, and （ii） a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver.     

Classification and Approximate Solutions to Perturbed Nonlinear Diffusion-Convection Equations

This paper studies the perturbed nonlinear diffusion-convection equation with source term via the approximate generalized conditional symmetry （A GCS）. Complete classification of those perturbed equations which admit certain types of AGCSs is derived. Some approximate invariant solutions to the resulting equations can also be obtained.     

Undetermination of the synchronizability and relation between network betweenness centrality

Betweenness centrality is taken as a sensible indicator of the synchronizability of complex networks. To test whether betweenness centrality is a proper measure of the synchronizability in specific realizations of random networks, this paper adds edges to the networks and then evaluates the changes of betweenness centrality and network synchronizability. It finds that the two quantities vary independently.     

Classification and Approximate Solutions to a Class of Perturbed Nonlinear Wave Equations

A complete approximate symmetry classification of a class of perturbed nonlinear wave equations is performed using the method originated from Fushchich and Shtelen. Moreover, large classes of approximate invariant solutions of the equations based on the Lie group method are constructed.     

Notes on Application of WKB Method

The notes here presented are of the modifications introduced in the application of WKB method. The problems of two- and three-dimensional harmonic oscillator potential are revisited by WKB and the new formulation of quantization rule respectively. It is found that the energy spectrum of the radial harmonic oscillator, which is reproduced exactly by the standard WKB method with the Langer modification, is also reproduced exactly without the Langer modification via the new quantization rule approach. An alternative way to obtain the non-integral Maslov index for three-dimensional harmonic oscillator is proposed.     

Normally-Ordered Time Evolution Operator for Mass-Varying Harmonic Oscillator and Wigner Function of Squeezed Number State

For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integration operator in coherent state representation and then perform this integral by virtue of the technique of integration within an ordered product of operators. The normally ordered time evolution operator is thus obtained. We then derive the Wigner function of u（t）｜n,〉, where ｜n〉 is a Fock state, which exhibits a generalized squeezing, the squeezing effect is related to the varying mass with time.     

Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a reaJ polyatomic molecular species.     

HEM11 mode magnetically insulated transmission line oscillator： Simulation and experiment

A novel magnetically insulated transmission line oscillator （MILO） in which a modified HEM11 mode is taken as its main interaction mode （HEM11 mode MILO） is simulated and experimented in this paper. The excitation of the oscillation mode is made possible by carefully adjusting the arrangement of each resonant cavity in a two-dimensional slow wave structure. The special feature of such a device is that in the slow-wave-structure region, the interaction mode is HEM11 mode which is a TM-like one that could interact with electron beams effectively; and in the coaxial output region, the microwave mode is TE11 mode which has a favourable field density pattern to be directly radiated. Employing an electron beam of about 441 kV and 39.7 kA, the HEM11 mode MILO generates a high power microwave output of about 1.47 GW at 1.45 GHz in particle-in-cell simulation. The power conversion efficiency is about 8.4 % and the generated microwave is in a TEll-like circular polarization mode. In a preliminary experiment investigation, high power microwave is detected from the device with a frequency of 1.46 GHz, an output energy of 43 J 47 J, and a pulse duration of 44 ns-49 ns when the input voltage is 430 kV450 kV, and the diode current is 37 kA-39 kA.     

Compact and tunable mid-infrared source based on a 2 μm dual-wavelength KTiOPO4 intracavity optical parametric oscillator

Using a double resonant KTiOPO 4 (KTP) intracavity optical parametric oscillator operating at degenerated point of 2 μm,we demonstrate a unique mid-infrared source based on difference frequency generation in GaSe crystal.The output tuning range is 8.42-19.52 μm,and a peak power of 834 W for type-I phase matching scheme and 730 W for type-II phase matching scheme are achieved.Experimental results show that this oscillator is a good alternative to the generator of a compact and tabletop mid-infrared radiation with a widely tunable range.     

Barut-Girardello and Gilmore-Perelomov coherent states for pseudoharmonic oscillators and their nonclassical properties： Factorization method

In this paper we try to introduce the ladder operators associated with the pseudoharmonic oscillator, after solving the corresponding Schro¨dinger equation by using the factorization method. The obtained generalized raising and lowering operators naturally lead us to the Dirac representation space of the system which is much easier to work with, in comparison to the functional Hilbert space. The SU(1, 1) dynamical symmetry group associated with the considered system is exactly established through investigating the fact that the deduced operators satisfy appropriate commutation relations. This result enables us to construct two important and distinct classes of Barut-Girardello and Gilmore-Perelomov coherent states associated with the system. Finally, their identities as the most important task are exactly resolved and some of their nonclassical properties are illustrated, numerically.     

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 Schrodinger 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 eases 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 some parametric moving boundaries as well.     

The nonlinear optical properties of a magneto-exciton in a strained Ga0.2In0.sAs/GaAs quantum dot

The magnetic field-dependent heavy hole excitonic states in a strained Gao.2Ino.sAs/GaAs quantum dot are investi- gated by taking into account the anisotropy, non-parabolicity of the conduction band, and the geometrical confinement. The strained quantum dot is considered as a parabolic dot of InAs embedded in a GaAs barrier material. The dependence of the effective excitonic g-factor as a function of dot radius and the magnetic field strength is numerically measured. The interband optical transition energy as a function of geometrical confinement is computed in the presence of a mag- netic field. The magnetic field-dependent oscillator strength of interband transition under the geometrical confinement is studied. The exchange enhancements as a function of dot radius are observed for various magnetic field strengths in a strained Gao.2Ino.sAs/GaAs quantum dot. Heavy hole excitonic absorption spectra, the changes in refractive index, and the third-order susceptibility of third-order harmonic generation are investigated in the Gao.2Ino.8As/GaAs quantum dot. The result shows that the effect of magnetic field strength is more strongly dependent on the nonlinear optical property in a low-dimensional semiconductor system.     

Approximate solution for the Klein-Gordon-SchrSdinger equation by the homotopy analysis method

The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution.     

A New Quasi-Exactly Solvable Problem and Its Connection with an Anharmonic Oscillator

The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods. Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KS transformation.     

Solutions of the Schrodinger Equation with Quantum Mechanical Gravitational Potential Plus Harmonic Oscillator Potential

The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained.     

Fiber optical parametric oscillator based on photonic crystal fiber pumped with all-normal-dispersion mode-locked Yb:fiber laser

We demonstrate a cost effective, linearly tunable fiber optical parametric oscillator based on a home-made photonic crystal fiber pumped with a mode-locked ytterbium-doped fiber laser, providing linely tuning ranges from 1018 nm to 1038 nm for the idler wavelength and from 1097 nm to 1117 nm for the signal wavelength by tuning the pump wavelength and the cavity length. In order to obtain the desired fiber with a zero dispersion wavelength around 1060 rim, eight sam- ples of photonic crystal fibers with gradually changed structural parameters are fabricated for the reason that it is difficult to accurately customize the structural dimensions during fabrication. We verify the usability of the fabricated fiber experimen- tally via optical parametric generation and conclude a successful procedure of design, fabirication, and verification. A seed source of home-made all-normal-dispersion mode-locked ytterbium-doped fiber laser with 38.57 ps pulsewidth around the 1064 nm wavelength is used to pump the fiber optical parametric oscillator. The wide picosecond pulse pump laser enables a larger walk-off tolerance between the pump light and the oscillating light as well as a longer photonic crystal fiber of 20 m superior to the femtosecond pulse lasers, resulting in a larger parametric amplification and a lower threshold pump power of 15.8 dBm of the fiber optical parametric oscillator.     

Generalized Harmonic Oscillator and the SchrSdinger Equation with Position-Dependent Mass

We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties corresponding effective potentials for several mass functions, for the system with PDM are also discussed. We give the the systems with such potentials are isospectral to the usual harmonic oscillator.