Governing Equations and Numerical Solutions of Tension Leg Platform with Finite Amplitude Motion

It is demonstrated that when tension leg platform (TLP) moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP. The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theoretical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.

Nonlinear Dynamic Response of Tension Leg Platform

Tension Leg Platform (TLP) is a typical compliant offshore structure for oil exploitation in deep water. Most of the existing mathematical models for analyzing the dynamic response of TLP are based on explicit or implicit assumptions that displacements (translations and rotations) are small magnitude. Herein a theoretical method for analyzing the nonlinear dynamic behavior of TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e. finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Using this theoretical model, we perform the numerical analysis of dynamic response of a representative TLP. The comparison between the degenerative linear solution of the proposed nonlinear model and the published one shows good agreements. Furthermore, numerical results are presented which illustrate that nonlinearities exert a distinct influence on the dynamic responses of the TLP.

Short-Term Nonlinear Response of Tension Leg Platform in Random Sea Waves

Most of the existing mathematical models for analyzing the dynamic response of TLP are based on explicit or implicit assumptions that motions (translations and rotations) are small magnitude. However, when TLP works in severe adverse conditions, the a priori assumption on small displacements may be inadequate. In such situation, the motions should be regarded as finite magnitude. This paper will study stochastic nonlinear dynamic responses of TLP with finite displacements in random waves. The nonlinearities considered are: large amplitude motions, coupling the six degrees-of-freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. The nonlinear dynamic responses are calculated by using numerical integration procedure in the time domain. After the time histories of the dynamic responses are obtained, we carry out cycle counting of the stress histories of the tethers with rain-flow counting method to get the stress range distribution.

Parametric studies of tension leg platform with large amplitude motions

Tension leg platform (TLP) is an important kind of working station for deep water exploration and development in ocean, whose dynamic responses deserve a serious thought. It is shown that for severe sea state, the effects of nonlinearities induced by large displacements of TLP may be noteworthy, and then employment of small displacements model should be restrained. In such situation, large amplitude motion model may be an appropriate alternative. The numerical experiments are performed to study the differences of dynamic responses between the two models. It is shown that for most cases, differences between results of the two models are significant. The variances of the differences vs. the wave period are the most remarkable, and that of the differences vs. wave heading angle are also apparent.

Nonlinear Dynamic Responses of Tension Leg Platform with Slack-Taut Tether

The slack-taut state of tether is a particular Averse circumstance, which may influence the normal operation stale of tension leg platform (TLP). The dynamic responses of TLP with slack-taut tether are studied with consideration of several nonlinear factors introduced by large amplitude motions. The time histories of stresses of tethers of a typical TLP in slack-taut state are given. In addition, the sensitivities of slack to stiffness and mass are investigated by varying file stiffness of tether and mass of TLP. It is found that slack is sensitive to the mass of TLP. The critical culled surfaces (over which indicates the slack) for the increase of mass are obtained.

Enhancement of ultrafast four-wave mixing in a polar molecule medium

We investigate the ultrafast four-wave mixing (FWM) with two-color few-cycle ultrashort pulses propagating in a two-level polar molecule medium. It is found that the enhancement of FWM can be achieved even for low intensity pulses due to the effects of permanent dipole moments (PDM) in polar molecules. Moreover, the conversion efficiency of FWM can be controlled by the carrier-envelope phases (CEP) of two ultrashort pulses. (c) 2006 Optical Society of America

Enhancement of four-wave mixing induced by interacting dark resonances

We analyse a four-wave mixing (FWM) scheme in a five-level atomic system in which double-dark resonances are present. It is found that the enhancement of FWM in both electromagnetically induced transparency (EIT) windows can be obtained even without the condition of multiphoton resonance. Moreover, the conversion efficiency of FWM in one EIT window can be much larger than that in the other due to the presence of interacting dark resonances.

Coherent population transfer with chirped few-cycle laser pulses in an excited-doublet four-level system

The behavior of population transfer in an excited-doublet four-level system driven by linear polarized few-cycle ultrashort laser pulses is investigated numerically. It is shown that almost complete population transfer can be achieved even when the adiabatic criterion is not fulfilled. Moreover, the robustness of this scheme in terms of the Rabi frequencies and chirp rates of the pulses is explored.

High efficiency four-wave mixing induced by double-dark resonances in a five-level tripod system

A five-level tripod scheme is proposed for obtaining a high efficiency four-wave-mixing (FWM) process. The existence of double-dark resonances leads to a strong modification of the absorption and dispersion properties against a pump wave at two transparency windows. We show that both of them can be used to open the four-wave mixing channel and produce efficient mixing waves. In particular, higher FWM efficiency is always produced at the transparent window corresponding to the relatively weak-coupling field. By manipulating the intensity of the two coupling fields, the conversion efficiency of FWM can be controlled.

Lasing without or with inversion in an open four-level system with a phase-fluctuation driving field

The effect of exit rate and the ratio of atomic injection rate on gain behaviour has been investigated, and the effects of phase fluctuation on absorption, dispersion and population difference in an open four-level system have been analysed by using numerical simulation from the steady linear, analytical solution. The variation of the linewidth, Rabi frequency of the driving field, the exit rate or the ratio of atomic injection rate can change the lasing properties in the open system. The presence of finite linewidth due to driving-field phase fluctuation prevents the open four-level atomic system from obtaining a high refractive index along with zero absorption.

Creation of arbitrary coherent superposition states in four-level systems

Using the technique of stimulated Raman adiabatic passage, we propose schemes for creating arbi- trary coherent superposition states of atoms in four-level systems: a A-type system with twofold final states and a four-level ladder system. With the use of a control field, arbitrary coherent superposition states are created without the condition of multiphoton resonance. Suitable manipulation of detunings and the control field can create either a single state or any superposition states desired. (c) 2005 Pleiades Publishing, Inc.

The effect of the incident relative phase on the four-wave mixing field and the electromagnetically induced transparency

In a A-type system employing a two-photon pump field, a four-wave mixing field can be generated simultaneously and, hence, a closed-loop system forms. We study theoretically the effect of the relative phase between the two incident fields on the generated four-wave mixing field and the electromagnetically induced transparency. It is found that the phase of the generated four-wave mixing field is the sum of the incident relative phase and a fixed phase that is irrelative to the incident relative phase. Hence, the total phase of the closed-loop system is independent of the incident relative phase. As a result, the incident relative phase has no effect on the electromagnetically induced transparency, which is different from the case of a A-type loop system closed by a third incident field. (c) 2005 Pleiades Publishing, Inc.

Negative refractive index in a four-level atomic system

We propose a scheme for realizing negative refractive index in a four-level atomic system. It is shown that such a system can simultaneously exhibit negative permittivity and negative permeability in an optical frequency range. Furthermore, by analysing the dispersion property of the left-handed material, we find that the probe beam can be controlled from superluminal to subluminal or vice versa via choosing appropriate parameters.

Phase control of switching from positive to negative index material in a four-level atomic system

Electric and magnetic responses of the medium to the probe field are analysed in a four-level loop atomic system by taking into account the relative phase of the applied fields. An interesting phenomenon is found: under suitable conditions, a change of the refractive index from positive to negative can occur by modulating the relative phase of the applied fields. Then the medium can be switched from a positive index material to a negative index material in our scheme. In addition, a negative index material can be realized in different frequency regions by adjusting the relative phase. It may give us a convenient way to obtain the desired material with positive or negative index.

Atom localization in a four-level alkaline earth atomic system

We propose an atom localization scheme for a four-level alkaline earth atom via a classical standing-wave field, and give the analytical expressions of the localization peak positions as well as the widths versus the parameters of the optical fields. We show that the probability of finding the atom at a particular position can be increased from 1/4 to 1/3 or 1/2 by adjusting the detuning of the probe field and the Rabi frequencies of the optical fields. Furthermore, the localization precision can be dramatically enhanced by increasing the intensity of the standing-wave field or decreasing the detuning of the probe field. The analytical results are quite accordant to the numerical solutions.