Perturbed Solving Method for Interdecadal Sea-air Oscillator Model

A coupled system of the interdecadal sea-air oscillator model is studied. The E1 Nifio-southem oscillation （ENSO） atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The oscillator model is involved with the variations of both the eastern and western Pacific anomaly pat- terns. This paper proposes an ENSO atmospheric physics model using a method of the perturbation theory. The aim is to create an asymptotic solving method for the ENSO model. Employing the perturbed method, the asymptotic solution of corresponding problem is obtained, and the asymptotic behaviour of the solution is studied. Thus we can obtain the prognoses of the sea surface temperature anomaly and related physical quantities.

The homotopic mapping method for sea-air oscillator model of interdecadal climate fluctuations

The E1 Nifio/La Nifia Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a coupled system of sea-air oscillator model is studied. The aim is to create an asymptotic solving method of nonlinear equation for the ENSO model. And based on a class of oscillators of ENSO model, employing the method of homotopic mapping, the approximate solution of corresponding problem is studied. It is proven from the results that the homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model.

Asymptotic solution for the El Nio time delay sea-air oscillator model

A sea-air oscillator model is studied using the time delay theory. The aim is to find an asymptotic solving method for the El Nino-southern oscillation （ENSO） model. Employing the perturbed method, an asymptotic solution of the corresponding problem is obtained. Thus we can obtain the prognoses of the sea surface temperature （SST） anomaly and the related physical quantities.

VARIATIONAL ITERATION SOLVING METHOD FOR SEA-AIR OSCILLATOR MODEL OF INTERDECADAL CLIMATE FLUCTUATIONS

Atmospheric physics is a very complicated natural phenomenon and needs to simplify its basic models for the sea-air oscillator. And it is solved by using the approximate method. The variational iteration method is a simple and valid method. In this paper the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is considered. Firstly, through introducing a set of functions, and computing the variations, the Lagrange multipliers are obtained. And then, the generalized expressions of variational iteration are constructed. Finally, through selecting appropriate initial iteration from the iteration expressions, the approximations of solution for the sea-air oscillator model are solved successively.

A Novel Wake Oscillator Model for Vortex-Induced Vibrations Prediction of A Cylinder Considering the Influence of Reynolds Number

It is well known that the Reynolds number has a significant effect on the vortex-induced vibrations(VIV) of cylinders. In this paper, a novel in-line(IL) and cross-flow(CF) coupling VIV prediction model for circular cylinders has been proposed, in which the influence of the Reynolds number was comprehensively considered. The Strouhal number linked with the vortex shedding frequency was calculated through a function of the Reynolds number. The coefficient of the mean drag force was fitted as a new piecewise function of the Reynolds number, and its amplification resulted from the CF VIV was also taken into account. The oscillating drag and lift forces were modelled with classical van der Pol wake oscillators and their empirical parameters were determined based on the lock-in boundaries and the peak-amplitude formulas. A new peak-amplitude formula for the IL VIV was developed under the resonance condition with respect to the mass-damping ratio and the Reynolds number. When compared with the results from the experiments and some other prediction models, the present model could give good estimations on the vibration amplitudes and frequencies of the VIV both for elastically-mounted rigid and long flexible cylinders. The present model considering the influence of the Reynolds number could generally provide better results than that neglecting the effect of the Reynolds number.

Asymptotic solution for a class of sea-air oscillator model for El Nio-southern oscillation

The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.

Perturbation method of studying the EI Nifio oscillation with two parameters by using the delay sea-air oscillator model

The EI Nino-southern oscillation （ENSO） is an interannual phenomenon involved in tropical Pacific ocean- atmosphere interactions. In this paper, we develop an asymptotic method of solving the nonlinear equation using the ENSO model. Based on a class of the oscillator of the ENSO model, a approximate solution of the corresponding problem is studied employing the perturbation method.

Asymptotic solving method for a sea air oscillator model of atmospheric physics

In this paper, a class of coupled system for the E1 Nifio/La Nifia southern oscillation （ENSO） atmospheric physics oscillation model is considered. We propose an ENSO atmospheric physics model using a method from the asymptotic theory. It is indicated from the results that the asymptotic method can be used for analyzing the sea surface temperature anomaly and the thermocline depth anomaly of the atmosphere-ocean oscillation for the ENSO model in the equatorial Pacific.

A NEW WAKE OSCILLATOR MODEL FOR PREDICTING VORTEX INDUCED VIBRATION OF A CIRCULAR CYLINDER

This article proposes a new wake oscillator model for vortex induced vibrations of an elastically supported rigid circular cylinder in a uniform current. The near wake dynamics related with the fluctuating nature of vortex shedding is modeled based on the classical van der Pol equation, combined with the equation for the oscillatory motion of the body. An appropriate approach is developed to estimate the empirical parameters in the wake oscillator model. The present predicted results are compared to the experimental data and previous wake oscillator model results. Good agreement with experimental results is found.

PERTURBED METHOD FOR SEA-AIR OSCILLATOR MODEL OF INTERDECADAL CLIMATE FLUCTUATIONS

A coupled system of sea-air oscillator model is studied. Using the perturbed theory, the approximations of the solution for the sea-air oscillator model are obtained.

Anharmonic oscillator model of overtone spectra for D_(3h) symmetry molecules

The bond stretching vibrations of XF_5 molecules with D_(3h)symmetry are treated computa- tionally on the Morse oscillator model in which the bond oscillators are coupled harmonically.Each calculation involves four parameters for two types of Morse potential and three parameters for the kinetic-energy,potontial coupling terms.The eigenvalue formula for overtone and combination states up to three are presented and can be used to predict all the vibrational energylevels from local mode molecules through normal mode molecules.For PF_5,AsF_5 and VF_5,the coupled Morse oscillator model gives a prediction in good agreement with the experimental data.

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 neuronmodel and discuss the effects of the additive and multiplicative noise.It is found that the additive noise can accelerate andcounterwork the firing of neuron,which depends on the value of central frequency of neuron itself,while multiplicativenoise can induce the continuous change or mutation of membrane potential.

Multiquark cluster form factors in the relativistic harmonic oscillator model

A QCD multiquark cluster system is studied in the relativistic harmonic oscillator potential model （RHOPM）, and the electromagnetic form factors of the pion, proton and deuteron in the RHOPM are predicted. The calculated theoretical results are then compared with existing experimental data, finding very good agreement between the theoretical predictions and experimental data for these three target particles. We claim that this model can be applied to study QCD hadronic properties, particularly neutron properties, and to find six-quark cluster and/or nine-quark cluster probabilities in light nuclei such as helium 3He and tritium 3H. This is a problem of particular importance and interest in quark nuclear physics.

The homotopic method of travelling wave solution for El Nio 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.

Asymptotic solution of a sea-air oscillator for ENSO mechanism

The EI Nino/La Nina-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a class of coupled system of the ENSO mechanism is considered. Based on a class of oscillator of ENSO model, the asymptotic solution of a corresponding problem is studied by employing the approximate method. It is proved from the results that the perturbation method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for the ENSO model.

Dissipative Travelling Wave Solution for El Nio Tropic Sea-air Coupled Oscillator

El Nifio and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. An asymptotic method of solving equations for the ENSO model is proposed. Based on a class of oscillator of ENSO model and by employing a simple and valid method of the variational iteration, the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is studied. Firstly, by introducing a set of functionals and computing the variationals, the Lagrange multipliers are obtained. And then, the generalized variational iteration expressions are constructed. Finally, by selecting appropriate initial iteration, and from the iterations expressions, the approximations of solution for the sea-air oscillator ENSO model are solved successively. The approximate dissipative travelling wave solution of equations for corresponding ENSO model is studied. It is proved from the results that the method of the variational iteration can be used for analyzing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for ENSO model.

Homotopic method of solving a class of EI Nino/La Nina-Southern Oscillation sea-air oscillator

The EI Nino/La Nina-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Ocean-atmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is created. And based on a class of oscillator of the ENSO model, the approximate solution of a corresponding problem is studied by employing the method of homotopic mapping. It is proved from the results that the homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for the ENSO model.

PERTURBED SOLUTION OF SEA-AIR OSCILLATOR FOR THE EL NI O/LA NI O-SOUTHERN OSCILLATION MECHANISM

A class of coupled system to oscillate of the E1 Nino/La Nino-Southern Oscillation （ENSO） mechanism is studied. Using the perturbed theory, the asymptotic expansions and asymptotic behavior of the solution for an ENSO model are obtained.

Perturbed solution of sea-air oscillator for the El Nino/ La Nina-Southern Oscillation mechanism

A class of coupled system of the E1 Nino/La Nina-Southern Oscillation （ENSO） mechanism is studied. Using the perturbed theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behavior of solution for corresponding problem is considered.

Analytical and computational modelling for wave energy systems：the example of oscillating wave surge converters

The development of new wave energy converters has shed light on a number of unanswered questions in fluid mechanics, but has also identified a number of new issues of importance for their future deployment. The main concerns relevant to the practical use of wave energy converters are sustainability, survivability, and maintainability. Of course,it is also necessary to maximize the capture per unit area of the structure as well as to minimize the cost. In this review, we consider some of the questions related to the topics of sustainability, survivability, and maintenance access, with respect to sea conditions, for generic wave energy converters with an emphasis on the oscillating wave surge converter. New analytical models that have been developed are a topic of particular discussion. It is also shown how existing numerical models have been pushed to their limits to provide answers to open questions relating to the operation and characteristics of wave energy converters.