Boundary Control of Coupled Wave Systems with Spatially-Varying Coefficients

This paper considers the stabilization of the coupled wave systems with spatially-varying coefficients.The authors design a state feedback controller by backstepping method.In contrast to the previous work in the literature,the kernel equations become more complicated and the main difficulty lies in proving the existence and uniqueness of the solution to the kernel equations.Firstly,using the backstepping approach,the authors verify the kernel equations,which is a system of coupled hyperbolic equations with spatially-varying coefficients.Then,the existence and uniqueness of the kernel matrices is obtained.Finally,the authors use a Lyapunov function to get the exponential stabilization of the closed-loop system.A numerical example is presented to illustrate the effectiveness of the proposed controller.

Recovering of Damping Coefficients for a System of Coupled Wave Equations with Neumann Boundary Conditions:Uniqueness and Stability

The authors study the inverse problem of recovering damping coefficients for two coupled hyperbolic PDEs with Neumann boundary conditions by means of an additional measurement of Dirichlet boundary traces of the two solutions on a suitable, explicit subportion F1 of the boundary F, and over a computable time interval T 〉 0. Under sharp conditions on Г0= Г／Г1, T 〉 0, the uniqueness and stability of the damping coefficients are established. The proof uses critically the Carleman estimate due to Lasiecka et al. in 2000, together with a convenient tactical route ＂post-Carleman estimates＂ suggested by Isakov in 2006.

Verification of an operational ocean circulation-surface wave coupled forecasting system for the China＇s seas

An operational ocean circulation-surface wave coupled forecasting system for the seas off China and adjacent areas（OCFS-C） is developed based on parallelized circulation and wave models. It has been in operation since November 1, 2007. In this paper we comprehensively present the simulation and verification of the system, whose distinguishing feature is that the wave-induced mixing is coupled in the circulation model. In particular, with nested technique the resolution in the China＇s seas has been updated to（1/24）° from the global model with（1/2）°resolution. Besides, daily remote sensing sea surface temperature（SST） data have been assimilated into the model to generate a hot restart field for OCFS-C. Moreover, inter-comparisons between forecasting and independent observational data are performed to evaluate the effectiveness of OCFS-C in upper-ocean quantities predictions, including SST, mixed layer depth（MLD） and subsurface temperature. Except in conventional statistical metrics, non-dimensional skill scores（SS） is also used to evaluate forecast skill. Observations from buoys and Argo profiles are used for lead time and real time validations, which give a large SS value（more than 0.90）. Besides, prediction skill for the seasonal variation of SST is confirmed. Comparisons of subsurface temperatures with Argo profiles data indicate that OCFS-C has low skill in predicting subsurface temperatures between 100 m and 150 m. Nevertheless, inter-comparisons of MLD reveal that the MLD from model is shallower than that from Argo profiles by about 12 m, i.e., OCFS-C is successful and steady in MLD predictions. Validation of 1-d, 2-d and 3-d forecasting SST shows that our operational ocean circulation-surface wave coupled forecasting model has reasonable accuracy in the upper ocean.

Localized waves in three-component coupled nonlinear Schrdinger equation

We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.

Comparison of heating mechanisms of argon helicon plasma in different wave modes with and without blue core

In this work,we investigated the discharge characteristics and heating mechanisms of argon helicon plasma in different wave coupled modes with and without blue core.Spatially resolved spectroscopy and emission intensity of argon atom and ion lines were measured via local optical emission spectroscopy,and electron density was measured experimentally by an RFcompensated Langmuir probe.The relation between the emission intensity and the electron density was obtained and the wavenumbers of helicon and’Trivelpiece-Gould’(TG)waves were calculated by solving the dispersion relation in wave modes.The results show that at least two distinct wave coupled modes appear in argon helicon plasma at increasing RF power,i.e.blue core(or BC)mode with a significant bright core of blue lights and a normal wave(NW)mode without blue core.The emission intensity of atom line 750.5 nm(lArⅠ750.5nm)is related to the electron density and tends to be saturated in wave coupled modes due to the neutral depletion,while the intensity of ion line 480.6 nm(IArⅡ480.6nm)is a function of the electron density and temperature,and increases dramatically as the RF power is increased.Theoretical analysis shows that TG waves are strongly damped at the plasma edge in NW and/or BC modes,while helicon waves are the dominant mechanism of power deposition or central heating of electrons in both modes.The formation of BC column mainly depends on the enhanced central electron heating by helicon waves rather than TG waves since the excitation of TG waves would be suppressed in this special anti-resonance region.

Induced generalized exact boundary synchronizations for a coupled system of wave equations

Taking a coupled system of wave equations with Dirichlet boundary controls as an example,by splitting and merging some synchronization groups of the state variables cor-responding to a given generalized synchronization matrix,this paper introduces two kinds of induced generalized exact boundary synchronizations to better determine its generalized exactly synchronizable states.

An Efficient Three-Dimensional Coupled Normal Mode Model and Its Application to Internal Solitary Wave Problems

We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.

Sound Wave of Spin-Orbit Coupled Bose-Einstein Condensates in Optical Lattice

We study the phonon mode excitation of spin–orbit （SO） coupled Bose–Einstein condensates trapped in a one-dimensional optical lattice. The sound speed of the system is obtained analytically. Softening of the phonon mode, i.e., the vanishing of sound speed, in the optical lattice is revealed. When the lattice is absent, the softening of phonon mode occurs only at the phase transition point, which is not influenced by the atomic interaction and Raman coupling when the SO coupling is strong. However, when the lattice is present, the softening of phonon modes can take place in a regime near the phase transition point. Particularly, the regime is widened as lattice strength and SO coupling increase or atomic interaction decreases. The suppression of sound speed by the lattice strongly depends on atomic interaction, Raman coupling, and SO coupling. Furthermore, we find that the sound speed in plane wave phase regime and zero-momentum phase regime behaves with very different characteristics as Raman coupling and SO coupling change. In zero-momentum phase regime, sound speed monotonically increases/decreases with Raman coupling/SO coupling, while in plane wave phase regime, sound speed can either increase or decrease with Raman coupling and SO coupling, which depends on atomic interaction.

Formation of Nonlinear Solitary Vortical Structures by Coupled Electrostatic Drift and Ion-Acoustic Waves

Propagation of coupled electrostatic drift and ion-acoustic waves（DIAWs） is presented. It is shown that nonlinear solitary vortical structures can be formed by low-frequency coupled electrostatic DIAWs. Primary waves of distinct（small, intermediate and large） scales are considered. Appropriate set of 3 D equations consisting of the generalized Hasegawa-Mima equation for the electrostatic potential（involving both vector and scalar nonlinearities） and the equation of motion of ions parallel to magnetic field are obtained. According to experiments of laboratory plasma mainly focused to large scale DIAWs, the possibility of self-organization of DIAWs into the nonlinear solitary vortical structures is shown analytically. Peculiarities of scalar nonlinearities in the formation of solitary vortical structures are widely discussed.

Design of periodic metal-insulator-metal waveguide back structures for the enhancement of light absorption in thin-film solar cells

To increase the absorption in a thin layer of absorbing material （amorphous silicon, a-Si）, a light trapping design is presented. The designed structure incorporates periodic metal-insulator-metal waveguides to enhance the optical path length of light within the solar cells. The new design can result in broadband optical absorption enhancement not only for transverse magnetic （TM）-polarized light, but also for transverse electric （TE）-polarized light. No plasmonic modes can be excited in TE-polarization, but because of the coupling into the a-Si planar waveguide guiding modes and the diffraction of light by the bottom periodic structures into higher diffraction orders, the total absorption in the active region is also increased. The results from rigorous coupled wave analysis show that the overall optical absorption in the active layer can be greatly enhanced by up to 40%. The designed structures presented in this paper can be integrated with back contact technology to potentially produce high-efficiency thin-film solar cell devices.

Studies of TLP Dynamic Response Under Wind, Waves and Current

Investigated is the coupled response of a tension leg platform （TLP） for random waves. Inferred are the mass matrix, coupling stiffness matrix, damping matrix in the vibration differential equation and external load of TLP in moving coordinating system. Infinitesimal method is applied to divide columns and pontoons into small parts. Time domain motion equation is solved by Runge-Kutta integration scheme. Jonswap spectrum is simulated in the random wave, current is simulated by linear interpolation, and NPD spectrum is applied as wind spectrum. The Monte Carlo method is used to simulate random waves and fluctuated wind. Coupling dynamic response, change of tendon tension and riser tension in different sea conditions are analyzed by power spectral density （PSD）. The influence of approach angle on dynamic response of TLP and tendon tension is compared.

A study on dynamical features of air-sea coupling waves in the tropics

The dynamical features of air-sea coupling waves and their stabilities in a simple coupled air-sea model in the tropics have been studied with respect to interaction occurring among different types of the free waves in the o-cean and in the atmosphere. It is pointed out that there exist a stable and an unstable air-sea interaction modes in the tropical coupled system , respectively. The propagation of the unstable mode relies greatly on the zonal space scale, i. e. only for wave length ranging from 5 000 km to 10 000 km can the disturbance unstably move slowly eastward. The waves that slowly propagate unstably eastward agree well with the observational facts. Finally,it is also proposed that the interaction between Kelvin wave in one medium and Rossby wave in another medium is a necessary condition for the occurrence of destabilization of the coupled air-sea system in the tropics.

Coupling Response of Heave and Moonpool Water Motion of A Truss Spar Platform in Random Waves

This paper presents the heave responses and the moonpool water motions of a truss Spar platform with semi-closed moonpool in random waves. A 2-DOF（degree of freedom） coupling dynamical equations of the platform heave and vertical motions of the moonpool water are derived. The linear wave theory is used to simulate the random waves. The response statistical values and the power spectrums are calculated to analyze the mutual influences between the platform heave and the moonpool water motions for different opening ratios of the moonpool. The effect of coupling parameters on the platform heave and the moonpool water motions are analyzed. The results show that motions of the moonpool water significantly affected the platform heave when the characteristic wave period is far away from the natural period of the platform heave, and different moonpool opening ratios lead to different heave amplitudes of the platform. In the actual design, an optimized moonpool opening ratio can be designed to reduce heave motions of the platform.

Mechanistic Drifting Forecast Model for A Small Semi-Submersible Drifter Under Tide–Wind–Wave Conditions

Understanding the drifting motion of a small semi-submersible drifter is of vital importance regarding monitoring surface currents and the floating pollutants in coastal regions. This work addresses this issue by establishing a mechanistic drifting forecast model based on kinetic analysis. Taking tide–wind–wave into consideration, the forecast model is validated against in situ drifting experiment in the Radial Sand Ridges. Model results show good performance with respect to the measured drifting features, characterized by migrating back and forth twice a day with daily downwind displacements. Trajectory models are used to evaluate the influence of the individual hydrodynamic forcing. The tidal current is the fundamental dynamic condition in the Radial Sand Ridges and has the greatest impact on the drifting distance. However, it loses its leading position in the field of the daily displacement of the used drifter. The simulations reveal that different hydrodynamic forces dominate the daily displacement of the used drifter at different wind scales. The wave-induced mass transport has the greatest influence on the daily displacement at Beaufort wind scale 5–6; while wind drag contributes mostly at wind scale 2–4.

A nonlinear wave coupling algorithm and its programing and application in plasma turbulences

The fully developed turbulence can be regarded as a nonlinear system,with wave coupling inside,which causes the nonlinear energy to transfer,and drives the turbulence to develop further or be suppressed.Spectral analysis is one of the most effective methods to study turbulence system.In order to apply it to the study of the nonlinear wave coupling process of edge plasma turbulence,an efficient algorithm based on spectral analysis technology is proposed to solve the nonlinear wave coupling equation.The algorithm is based on a mandatory temporal static condition with the nonideal spectra separated from the ideal spectra.The realization idea and programing flow are given.According to the characteristics of plasma turbulence,the simulation data are constructed and used to verify the algorithm and its implementation program.The simulation results and experimental results show the accuracy of the algorithm and the corresponding program,which can play a great role in the studying the energy transfer in edge plasma turbulences.As an application,the energy cascade analysis of typical edge plasma turbulence is carried out by using the results of a case calculation.Consequently,a physical picture of the energy transfer in a kind of fully developed turbulence is constructed,which confirms that the energy transfer in this turbulent system develops from lower-frequency region to higher-frequency region and from linear growing wave to damping wave.

Simulation on effect of poloidal power spectrum on lower hybrid wave propagation

The coupling of lower hybrid wave to the plasma is a crucial issue for efficient current drive in tokamaks. This paper establishes a new coupling model which assumes the antenna to be a curved face and the plasma to be a cylinder. Power spectrum considering the coupling between wave-guides in both poloidal and toroidal direction is simply estimated and discussed. The effect of the poloidal wave vector on wave propagation, power deposition and driven current is also investigated with the help of lower hybrid current drive code. Results show that the poloidal wave vector affects the ray tracing, and also has effect on power deposition and driven current. The effect of the poloidal wave vector on power deposition and driven current profile depends on plasma parameters. Preliminary studies suggest that it seems possible to control the current profile by adjusting the poloidal phase difference between the waveguide in poloidal direction.

A novel type of transverse surface wave propagating in a layered structure consisting of a piezoelectric layer attached to an elastic half-space

The existence and propagation of transverse surface waves in piezoelectric coupled solids is investigated, in which perfect bonding between a metal/dielectric substrate and a piezoelectric layer of finite-thickness is assumed. Dis- persion equations relating phase velocity to material con- stants for the existence of various modes are obtained in a simple mathematical form for a piezoelectric material of class 6mm. It is discovered and proved by numerical examples in this paper that a novel Bleustein-Gulyaev （B-G） type of transverse surface wave can exist in such piezoelectric cou- pled solid media when the bulk-shear-wave velocity in the substrate is less than that in the piezoelectric layer but greater than the corresponding B-G wave velocity in the same pie- zoelectric material with an electroded surface. Such a wave does not exist in such layered structures in the absence of pie- zoelectricity. The mode shapes for displacement and electric potential in the piezoelectric layer are obtained and discussed theoretically. The study extends the regime of transverse sur- face waves and may lead to potential applications to surface acoustic wave devices.

Sediment mathematical model for sand ridges and sand waves

A new theoretical model is formulated to describe internal movement mechanisms of the sand ridges and sand waves based on the momentum equation of a solid-liquid two-phase flow under a shear flow. Coupling this equation with two-dimensional shallow water equations and wave reflection-diffraction equation of mild slope, a two-dimensional coupling model is established and a validation is carried out by observed hydrogeology, tides,waves and sediment. The numerical results are compared with available observations. Satisfactory agreements are achieved. This coupling model is then applied to the Dongfang 1-1 Gas Field area to quantitatively predict the movement and evolution of submarine sand ridges and sand waves. As a result, it is found that the sand ridges and sand waves movement distance increases year by year, but the development trend is stable.

An Improved Coupling of Numerical and Physical Models for Simulating Wave Propagation

An improved coupling of numerical and physical models for simulating 2D wave propagation is developed in this paper. In the proposed model, an unstructured finite element model （FEM） based Boussinesq equations is applied for the numerical wave simulation, and a 2D piston-type wavemaker is used for the physical wave generation. An innovative scheme combining fourth-order Lagrange interpolation and Runge-Kutta scheme is described for solving the coupling equation. A Transfer function modulation method is presented to minimize the errors induced from the hydrodynamic invalidity of the coupling model and/or the mechanical capability of the wavemaker in area where nonlinearities or dispersion predominate. The overall performance and applicability of the coupling model has been experimentally validated by accounting for both regular and irregular waves and varying bathymetry. Experimental results show that the proposed numerical scheme and transfer function modulation method are efficient for the data transfer from the numerical model to the physical model up to a deterministic level.

Experimental Investigation of Lower Hybrid Wave Coupling in HT-7

Experiments on lower hybrid wave （LHW） coupling were investigated in the HT- 7 tokamak. Good coupling of LHW plasma has been demonstrated at different conditions in the HT-7 tokamak. Relevant results have proved that LHW-plasma coupling is affected by the phase difference between adjacent waveguides. Furthermore, the edge density around the grill and relevant coupling can be adjusted by changing the plasma line average density or the gap value between the LH grill and the last closed flux surfaces （LCFS）. It is found that the coupling of LHWs becomes poor when the edge density around the LH grill is large enough in the HT-7 tokamak, and that coupling remains good with a proper edge density. With increasing LHW power, it is also found that the reflection coefficients （RCs） increase due to non-linear effects under conditions of low edge recycling, but can decrease under high edge recycling. The edge density depends mainly on the competition between the ponderomotive force （PMF） and the edge recycling intensity in the HT-7 tokamak.