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.

Nonexistence of looping trajectories in hydromagnetic waves of finite amplitude. Breaking of waves in a cold collision-free plasma in a magnetic field. On stabilities of periodic waves in a cold collision-free plasma in a magnetic field.

This dissertation consists of three parts. In Part I, it is shown that looping trajectories cannot exist in finite amplitude stationary hydromagnetic waves propagating across a magnetic field in a quasi-neutral cold collision-free plasma. In Part II, time-dependent solutions in series expansion are presented for the magnetic piston problem, which describes waves propagating into a quasi-neutral cold collision-free plasma, ensuing from magnetic disturbances on the boundary of the plasma. The expansion is equivalent to Picard's successive approximations. It is then shown that orbit crossings of plasma particles occur on the boundary for strong disturbances and inside the plasma for weak disturbances. In Part III, the existence of periodic waves propagating at an arbitrary angle to the magnetic field in a plasma is demonstrated by Stokes expansions in amplitude. Then stability analysis is made for such periodic waves with respect to side-band frequency disturbances. It is shown that waves of slow mode are unstable whereas waves of fast mode are stable if the frequency is below the cutoff frequency. The cutoff frequency depends on the propagation angle. For longitudinal propagation the cutoff frequency is equal to one-fourth of the electron's gyrofrequency. For transverse propagation the cutoff frequency is so high that waves of all frequencies are stable.

A mathematical study of finite-amplitude rock-folding

The problem of the finite-amplitude folding of an isolated, linearly viscous layer under compression and imbedded in a medium of lower viscosity is treated theoretically by using a variational method to derive finite difference equations which are solved on a digital computer. The problem depends on a single physical parameter, the ratio of the fold wavelength, L, to the "dominant wavelength" of the infinitesimal-amplitude treatment, L_d. Therefore, the natural range of physical parameters is covered by the computation of three folds, with L/L_d = 0, 1, and 4.6, up to a maximum dip of 90°.

Significant differences in fold shape are found among the three folds; folds with higher L/L_d have sharper crests. Folds with L/L_d = 0 and L/L_d = 1 become fan folds at high amplitude. A description of the shape in terms of a harmonic analysis of inclination as a function of arc length shows this systematic variation with L/L_d and is relatively insensitive to the initial shape of the layer. This method of shape description is proposed as a convenient way of measuring the shape of natural folds.

The infinitesimal-amplitude treatment does not predict fold-shape development satisfactorily beyond a limb-dip of 5°. A proposed extension of the treatment continues the wavelength-selection mechanism of the infinitesimal treatment up to a limb-dip of 15°; after this stage the wavelength-selection mechanism no longer operates and fold shape is mainly determined by L/L_d and limb-dip.

Strain-rates and finite strains in the medium are calculated f or all stages of the L/L_d = 1 and L/L_d = 4.6 folds. At limb-dips greater than 45° the planes of maximum flattening and maximum flattening rat e show the characteristic orientation and fanning of axial-plane cleavage.

Optical bistability via amplitude and phase control of a microwave field

We investigate the steady-state optical bistability behavior in a three-level A-type atomic system closed by a microwave field under the condition that the applied fields are in resonance with corresponding atomic transitions. It is shown that the bistable hysteresis cycles can be controlled by both the amplitude and the phase of the microwave field. (c) 2006 Elsevier B.V. All rights reserved.

Comparison between complex amplitude envelope representation and complex analytic signal representation in studying pulsed Gaussian beam

Analytic propagation expressions of pulsed Gaussian beam are deduced by using complex amplitude envelope representation and complex analytic signal representation. Numerical calculations are given to illustrate the differences between them. The results show that the major difference between them is that there exists singularity in the beam obtained by using complex amplitude envelope representation. It is also found that singularity presents near propagation axis in the case of broadband and locates far from propagation axis in the case of narrowband. The critical condition to determine what representation should be adopted in studying pulsed Gaussian beam is also given. (C) 2004 Elsevier B.V. All rights reserved.

Comparison of uniform amplitude beam and intercepted Gaussian beam superresolution theories

The general superresolution theories for uniform amplitude beams and intercepted Gaussian beams are investigated. For these two types of incident beam, both two-zone amplitude and pure-phase filters are adopted to provide specific numerical descriptions of their differences in superresolution performances. Simulated results of comparisons between their performances indicate that, with the same spot size ratio, the intercepted Gaussian beam achieves a higher central image brightness ratio and significantly lower side-lobe effect irrespective of the filter used. (c) 2008 Elsevier Ltd. All rights reserved.