Comparison of Linear Level I Green-Naghdi Theory with Linear Wave Theory for Prediction of Hydroelastic Responses of VLFS

Very Large Floating Structures (VLFS) have drawn considerable attention recently due to their potential significance in the exploitation of ocean resources and in the utilization of ocean space. Efficient and accurate estimation of their hydroelastic responses to waves is very important for the design. Recently, an efficient numerical algorithm was developed by Ertekin and Kim (1999). However, in their analysis, the linear Level I Green-Naghdi (GN) theory is employed to describe fluid dynamics instead of the conventional linear wave (LW) theory of finite water depth. They claimed that this linear level I GN theory provided better predictions of the hydroelastic responses of VLFS than the linear wave theory. In this paper, a detailed derivation is given in the conventional linear wave theory framework with the same quantity as used in the linear level I GN theory framework. This allows a critical comparison between the linear wave theory and the linear level I GN theory. It is found that the linear level I GN theory can be regarded as an approximation to the linear wave theory of finite water depth. The consequences of the differences between these two theories in the predicted hydroelastic responses are studied quantitatively. And it is found that the linear level I GN theory is not superior to the linear wave theory. Finally, various factors affecting the hydroelastic response of VLFS are studied with the implemented algorithm.

Unified Water Gravity Wave Theory and Improved Linear Wave

Based on Least Square Method, this paper presents variational principle for handling various water gravity wave theories and the unified water gravity wave theory was given. By using this variational principle of unified water wave theory, two kinds of improved linear waves were derived. The first one uses the same boundary conditions which were applied to derive 5-order Stokes wave. The second one uses the accurate boundary conditions (Eqs. 11 and 12). The two improved linear waves were compared with the existing linear wave.

Classical and nonclassical symmetry classifications of nonlinear wave equation with dissipation

A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such nonlinear wave equations admit richer classical and nonclassical symmetries, leading to the conservation laws and the reduction of the wave equations. Some exact solutions of the considered wave equations for particular cases are derived.

Dispersion Relation of Linear Waves in Quantum Magnetoplasmas

The quantum magnetohydrodynamic （QMHD） model is applied in investigating the propagation of linear waves in quantum magnetoplasmas. Using the QMHD model, the dispersion equation for quantum magnetoplasmas and the dispersion relations of linear waves are deduced. Results show that quantum effects affect the propagation of electron plasma waves and extraordinary waves （X waves）. When we select the plasma parameters of the laser-based plasma compression （LBPC） schemes for calculation, the quantum correction cannot be neglected. Meanwhile, the corrections produced by the Fermi degeneracy pressure and Bohm potential are compared under different plasma parameter conditions.

Linear superposition solutions to nonlinear wave equations

The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K（2,2,1）, the Oliver water wave equation, and the k（n, n） equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed.

Predicting Nonlinear Wave Trough Distributions Utilizing A Transformed Linear Simulation Method

This paper first proposes a new approach for predicting the nonlinear wave trough distributions by utilizing a transformed linear simulation method. The linear simulation method is transformed based on a Hermite transformation model where the transformation is chosen to be a monotonic cubic polynomial and calibrated such that the first four moments of the transformed model match the moments of the true process. The proposed new approach is applied for calculating the wave trough distributions of a nonlinear sea state with the surface elevation data measured at the coast of Yura in the Japan Sea, and its accuracy and efficiency are convincingly validated by comparisons with the results from two theoretical distribution models, from a linear simulation model and a secondorder nonlinear simulation model. Finally, it is further demonstrated in this paper that the new approach can be applied to all the situations characterized by similar nondimensional spectrum.

Global Smooth Solution for the Quasi-linear Wave Equation

在这份报纸，我们为下列伪线性的波浪方程 utt-2kuxxt=(unx ) 学习 Cauchy 问题 x k0 并且是 2 是的实数，和 n 一个整数。我们证明为任何 T0， Cauchy 问题承认唯一的全球光滑的答案 u C ((0， T ] ；H (R)) C ([0， T ] ；H2 (R)) C1 ([0， T ] ；L2 (R)) 在起始的数据上的合适的假设下面。

ALMOST CONSERVATION LAWS AND GLOBAL ROUGH SOLUTIONS OF THE DEFOCUSING NONLINEAR WAVE EQUATION ON R^2

In this article, we investigate the initial value problem（IVP） associated with the defocusing nonlinear wave equation on R^2 as follows：{δttu-△u=-u^3 u（0,x）=u0（x）,δtu＊（0,x）=u1（x,）where the initial data （uo,ul）∈H^s-1（R^2）It is shown that the IVP is global well-posedness in H^s（R^2）×H^s-1×H^s-1（R^2）for any 1 〉 s 〉2/5.The proof relies upon the almost conserved quantity in using multilinear correction term. The main difficulty is to control the growth of the variation of the almost conserved quantity. Finally, we utilize linear-nonlinear decomposition benefited from the ideas of Roy [1].

Linear superposition method for （2＋1）-dimensional nonlinear wave equations

New forms of different-periodic travelling wave solutions for the （2＋1）-dimensional Zakharov-Kuznetsov （ZK） equation and the Davey-Stewartson （DS） equation are obtained by the linear superposition approach of Jacobi elliptic function. A sequence of cyclic identities plays an important role in these procedures.

Nonlinear Waves in Solid Continua with Finite Deformation

This work considers initiation of nonlinear waves, their propagation, reflection, and their interactions in thermoelastic solids and thermoviscoelastic solids with and without memory. The conservation and balance laws constituting the mathematical models as well as the constitutive theories are derived for finite deformation and finite strain using second Piola-Kirchoff stress tensor and Green’s strain tensor and their material derivatives [1]. Fourier heat conduction law with constant conductivity is used as the constitutive theory for heat vector. Numerical studies are performed using space-time variationally consistent finite element formulations derived using space-time residual functionals and the non-linear equations resulting from the first variation of the residual functional are solved using Newton’s Linear Method with line search. Space-time local approximations are considered in higher order scalar product spaces that permit desired order of global differentiability in space and time. Computed results for non-linear wave propagation, reflection, and interaction are compared with linear wave propagation to demonstrate significant differences between the two, the importance of the nonlinear wave propagation over linear wave propagation as well as to illustrate the meritorious features of the mathematical models and the space-time variationally consistent space-time finite element process with time marching in obtaining the numerical solutions of the evolutions.

QUADRATIC CORRECTION TO THE LINEAR WAVE SPECTRUM OF TWO-DIMENSIONAL RANDOM WAVES

A perturbation expansion method’s first three order solutions of two-dimensional random gravity waves in finite uniform depth were used as bases to derive the quadratic correction to the linear wave spectrum (ie., the quadratic spectrum ). For infinite water depth, the expression of the quadratic spectrum given in this paper is much simpler then that of Sclavounos (1992) and Olemz and Milgram (1995).

A FAST ALGORITHM FOR FULL NON-LINEAR TRANSIENT WAVES

The transient surface wave motion is studied by a method which transfers the computational re- gion into a unit circle. In place of the Green's formula of harmonic function the Taylor's series of an analyti- cal function is used. The coefficients of the series are determined by FFT. The numerical filtration is accomplished in the Fourier domain.

DEFORMATION AND BREAKINC OF NONLINEAR WAVE IN WATER OF GRADUALLY VARYING DEPTH

Based upon the perturbation method,this paper used the method of conformal mapping to solve the deformation and breaking of nonlinear waves in water of gradually varying depth.The wave characteristics,such as wave deformation,velocity field,breaker type and breaker height are discussed by the third order approximation.Results obtained are compared with experimental data.

Comparison of linear and nonlinear extreme wave statistics

An extremely large（＂freak＂） wave is a typical though rare phenomenon observed in the sea. Special theories（for example, the modulation instability theory） were developed to explain mechanics and appearance of freak waves as a result of nonlinear wave-wave interactions. In this paper, it is demonstrated that the freak wave appearance can be also explained by superposition of linear modes with the realistic spectrum. The integral probability of trough-to-crest waves is calculated by two methods： the first one is based on the results of the numerical simulation of a wave field evolution performed with one-dimensional and two-dimensional nonlinear models.The second method is based on calculation of the same probability over the ensembles of wave fields constructed as a superposition of linear waves with random phases and the spectrum similar to that used in the nonlinear simulations. It is shown that the integral probabilities for nonlinear and linear cases are of the same order of values

COMPARISON OF LINEAR AND NONLINEAR WAVES ASSOCIATED WITH STEADY-STATE FORCING SOURCES

Low-frequency phenomena in the atmosphere are intimately related to stationary waves and, in a sense, the former may even be viewed as the time-varying part of the quasi-stationary waves themselves, Much attention has been focused on nonlinear interactions in the conceptual study on stationary waves. Linear and nonlinear primitive-equation baroclinic spectral models are adopted to investigate the response of stationary waves to large- scale mechanical forcing and steady-state thermal forcing, both idealized and realistic, followed by calculations of the EP fluxes and three-dimensional wave activity fluxes (Plumb, 1985) for both the linear and nonlinear solu- tions. Results show that when the forcing source grows intense enough to be comparable to the real one, non- linear interaction becomes very important, especially for the maintenance of tropical and polar stationary waves. Care should be taken, however, in using the EP flux and Plumb's 3-D flux for diagnostic analysis of observational data as they are highly sensitive to nonlinear interaction.

Calculation of Electronic Structure of Anatase TiO_2 Doped with Transition Metal V,Cr,Fe and Cu Atoms by the Linearized Augmented Plane Wave Method

The electronic density of states and band structures of doped and un-doped anatase TiO2 were studied by the Linearized Augmented Plane Wave method based on the density functional theory. The calculation shows that the band structures of TiO2 crystals doped with transition metal atoms become narrower. Interesting, an excursion towards high energy level with increasing atomic number in the same element period could be observed after doping with transition metal atoms.

LINEAR THEORY OF GRAVITY WAVES ON A VOIGT VISCOELASTIC MEDIUM

Linear surface gravity waves on a semi-infinite incompressible Voigt medium are studied in this paper.Three dimensionless parameters,the dimensionless viscoelastic parameter (?),the dimensionless wave number and the dimensionless sur- face tension are introduced.A dimensionless characteristic equation describing the waves is derived.This is a sixth order complex algebraic equation which is solved to give the complex dispersion relation.Based on the numerical solution, two critical values of (?),(?)_A=0.607 and (?)_R=2.380,which represent the appearance of the cutoff region and the disappearance of the strong dispersion region,are found.The effects of (?) on the characteristic equation and the properties of the waves are discussed.

mKdV Equation for Solitary Rossby Waves with Linear Topography Effect in Barotropic Fluids

The modify Korteweg-de Vries(mKdV) equations,governing the evolution of the amplitude of solitary Rossby waves,are derived from quasi-geostrophic vorticity equation by using the perturbation method.The result manifests that the linear topography effect with the change of latitude can induce solitary Rossby wave.

Contact Analysis and Modeling of Standing Wave Linear Ultrasonic Motor

A contact model for describing the contact mechanics between the stator and slider of the standing wave linear ultrasonic motor was presented. The proposed model starts from the assumption that the vibration characteristics of the stator is not affected by the contact process. A modified friction models was used to analyze the contact problems. Firstly, the dynamic normal contact force, interface friction force, and steady-state characteristics were analyzed. Secondly, the influences of the contact layer material, the dynamic characteristics of the stator, and the pre-load on motor performance were simulated. Finally, to validate the contact model, a linear ultrasonic motor based on in-plane modes was used as an example. The corresponding results show that a set of simulation of motor performances based on the proposed contact mechanism is in good agreement with experimental results. This model is helpful to understanding the operation principle of the standing wave linear motor and thus contributes to the design of these types of motor.

Interaction of Conormal Waves With Strong and Weak Singularities For Semi－Linear Equations

We first define a kind of new function space, called the space of twice conormal distributions. With some estimates on these function spaces, we can prove that if there exist two characteristic hypersurfaces bearing strong and weak singularities respectively intersect transversally, then some new singularities will take place anti their strength will be no more than the original weak one.