Theoretical analysis and numerical simulation of acoustic waves in gas hydrate-bearing sediments

Based on Carcione-Leclaire model,the time-splitting high-order staggered-grid finite-difference algorithm is proposed and constructed for understanding wave propagation mechanisms in gas hydrate-bearing sediments.Three compressional waves and two shear waves,as well as their energy distributions are investigated in detail.In particular,the influences of the friction coefficient between solid grains and gas hydrate and the viscosity of pore fluid on wave propagation are analyzed.The results show that our proposed numerical simulation algorithm proposed in this paper can effectively solve the problem of stiffness in the velocity-stress equations and suppress the grid dispersion,resulting in higher accuracy compared with the result of the Fourier pseudospectral method used by Carcione.The excitation mechanisms of the five wave modes are clearly revealed by the results of simulations.Besides,it is pointed that,the wave diffusion of the second kind of compressional and shear waves is influenced by the friction coefficient between solid grains and gas hydrate,while the diffusion of the third compressional wave is controlled by the fluid viscosity.Finally,two fluid-solid(gas-hydrate formation)models are constructed to study the mode conversion of various waves.The results show that the reflection,transmission,and transformation of various waves occur on the interface,forming a very complicated wave field,and the energy distribution of various converted waves in different phases is different.It is demonstrated from our studies that,the unconventional waves,such as the second and third kinds of compressional waves may be converted into conventional waves on an interface.These propagation mechanisms provide a concrete wave attenuation explanation in inhomogeneous media.     

Theoretical and experimental investigations of flexural wave propagation in periodic grid structures designed with the idea of phononic crystals

The propagation characteristics of flexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined analysis yields phase constant surfaces, which predict the location and the extension of band gaps, as well as the directions and the regions of wave propagation at assigned frequencies. The predictions are validated by computation and experimental analysis of the harmonic responses of a finite structure with 11× 11 unit cells. The flexural wave is localized at the point of excitation in band gaps, while the directional behaviour occurs at particular frequencies in pass bands. These studies provide guidelines to designing periodic structures for vibration attenuation.     

Propagation and Interaction of Ion-Acoustic Solitary Waves in a Two-Dimensional Plasma Consisting of Isothermal Electrons and Hot Ions

We study the propagation and interaction of ion-acoustic solitary waves in a simple two-dimensional plasma by using the extended Poincare Lighthill-Kuo perturbation method. We consider the interaction between two ion-acoustic solitary waves with different propagation directions in such a system, and obtain two Korteweg-de Vries equations for small but finite amplitude solitary waves along both ξ and η trajectories. The effects of the ratio of ion temperature σ the ratio of heat capacity γ and the colliding angle a on the amplitude, the width of the new nonlinear wave created by the collision between two solitary waves are studied. The effects of these parameters on both the colliding solitary waves are examined as well. It is found that all the above-mentioned parameters have significant effects on the properties of these nonlinear waves.     

Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas

By one-dimensional particle-in-cell(PIC) simulations, the propagation and stability of relativistic electromagnetic(EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas.The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 10²³ m^-3 and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases(decreases) with the increase of the carrier wave frequency(vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude.This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.     

Scattering of light waves by electron electrostatic waves in laser produced plasmas

The propagation of light waves in an underdense plasma is studied using one-dimensional Vlasov-Maxwell numerical simulation.It is found that the light waves can be scattered by electron plasma waves as well as other heavily and weakly damping electron wave modes,corresponding to stimulated Raman and Brilluoin-like scatterings.The stimulated electron acoustic wave scattering is also observed as a high scattering level.High frequency plasma wave scattering is also observed.These electron electrostatic wave modes are due to a non-thermal electron distribution produced by the wave-particle interactions.The collision effects on stimulated electron acoustic wave and the laser intensity effects on the scattering spectra are also investigated.     

Singular Wave Solutions of Two Integrable Generalized KdV Equations

We present some singular wave solutions such as multi-peaked periodic waves, multi-peaked kink waves, multi-peaked peakons as well as kink-compactons, associated with singular curves of generalized KdV equation and modified KdV equation. When a trajectory intersects with the singular curve, it may be divided into segments. Different combinations of these segments may lead to different singular wave solutions, while at the intersection points, peaks on the waves can be observed.     

Propagation and interaction of ion-acoustic solitary waves in a quantum electron-positron-ion plasma

This paper discusses the existence of ion-acoustic solitary waves and their interaction in a dense quantum electron-positron-ion plasma by using the quantum hydrodynamic equations.The extended Poincar’e-Lighthill-Kuo perturbation method is used to derive the Korteweg-de Vries equations for quantum ion-acoustic solitary waves in this plasma.The effects of the ratio of positrons to ions unperturbation number density p and the quantum diffraction parameter H e (H p) on the newly formed wave during interaction,and the phase shift of the colliding solitary waves are studied.It is found that the interaction between two solitary waves fits linear superposition principle and these plasma parameters have significantly influence on the newly formed wave and phase shift of the colliding solitary waves.The investigations should be useful for understanding the propagation and interaction of ion-acoustic solitary waves in dense astrophysical plasmas (such as white dwarfs) as well as in intense laser-solid matter interaction experiments.     

Two-Mode Wave Solutions to the Degasperis--Procesi Equation

By introducing a new type of solutions, called the multiple-mode wave solutions which can be expressed in nonlinear superposition of single-mode waves with different speeds, we investigate the two-mode wave solutions in Degasperis-Procesi equation and two cases are derived. The explicit expressions for the two-mode waves as well as the existence conditions are presented. It is shown that the two-mode waves may be the nonlinear combinations of many types of single-mode waves, such as periodic waves, solJtons, compactons, etc., and more complicated multiple-mode waves can be obtained if higher order or more single-mode waves are taken into consideration. It is pointed out that the two-mode wave solutions can be employed to display the typical mechanism of the interactions between different single-mode waves.     

A Model for Periodic Nonlinear Electric Field Structures in Space Plasmas

In this study, we present a physical model to explain the generation mechanism of nonlinear periodic waves with a large amplitude electric field structures propagating obliquely and exactly parallel to the magnetic field. The ＂Sagdeev potential＂ from the MHD equations is derived and the nonlinear electric field waveforms are obtained when the Mach number, direction of propagation, and the initial electric field satisfy certain plasma conditions. For the parallel propagation, the amplitude of the electric field waves with ion-acoustic mode increases with the increase of initial electric field and Mach number but its frequency decreases with the increase of Mach number. The amplitude and frequency of the electric field waves with ion-cyclotron mode decrease with the increase of Mach number and become less spiky, and its amplitude increases with the increase of initial electric field. For the oblique propagation, only periodic electric field wave with an ion-cyclotron mode obtained, its amplitude and frequency increase with the increase of Mach number and become spiky. From our model the electric field structures show periodic, spiky, and saw-tooth behaviours corresponding to different plasma conditions.     

Nonlinear continuous bi-inductance electrical line with dissipative elements:Dynamics of the low frequency modulated waves

The dynamics of modulated waves in a nonlinear bi-inductance transmission line with dissipative elements are examined.We show the existence of two frequency modes and carry out intensive investigations on the low frequency mode.Thanks to the multiple scales method,the behavior of these waves is investigated and the dissipative effects are analyzed.It appears that the dissipation coefficient increases with the carrier wave frequency.In the continuous approximation,we derive that the propagation of these waves is governed by the complex Ginzburg-Landau equation instead of the Korteweg-de-Vries equation as previously established.Asymptotic studies of the dynamics of plane waves in the line reveal the existence of three additional regions in the dispersion curve where the modulational phenomenon is observed.In the low frequency mode,we demonstrate that the network allows the propagation of dark and bright solitons.Numerical findings are in perfect agreement with the analytical predictions.     

Propagation of Cylindrical Waves in Media of Time-Dependent Permittivity

We present the propagation of cylindrical waves in the media whose permittivity varies with time abruptly or continuously. By the method of variable separation, we derive the general expression of electric field of TM-polarized waves in two-dimensional space with excitation of any point at any time. With this expression,the solution for a spatially and temporally distributed source can be obtained theoretically. The focusing of reflected waves in the cross section is shown when the media undergoes a sudden or continuous change. The wave propagation in time-invariant media can be considered as a special case of the media under exponential variance.     

Effects of dust size distribution in ultracold quantum dusty plasmas

The effect of dust size distribution in ultracold quantum dusty plasmas are investigated in this paper. How the dispersion relation and the propagation velocity for the quantum dusty plasma vary with the system parameters and the different dust distribution are studied. It is found that as the Fermi temperature of the dust grains increases the frequency of the wave increases for large wave number dust acoustic wave. The quantum parameter of H_d also increases the frequency of the large wave number dust acoustic wave. It is also found that the frequency ω₀ and the propagation velocity v₀ of quantum dust acoustic waves all increase as the total number density increases. They are greater for unusual dusty plasmas than those of the usual dusty plasma.     

Propagation of Fast Magnetoacoustic Waves in Stratified Solar Atmosphere

The characteristics of magnetohydrodynamic fast wave propagation in the solar stratified atmosphere are studied by the ray tracing method. The propagation behaviour of the wavefronts is described in detail. A magnetic field incorporating the characteristics field spreading expected in flux tubes is used, which represents the main feature of an active region. Partly ionization is considered beside the stratified solar atmosphere consisting chromosphere, transition region and corona. The study may explain the characteristics in observations of Moreton and extraultraviolet image telescope （EIT） waves. The wavefront incurred by the disturbance initialized at the base of the transition region propagates fast initially due to strong magnetic field, and it slows down when arriving beyond the region of flux-tube. Meanwhile, the wave propagates in the corona with a more consistent speed, as seen in the observation of EIT waves. The speeds and propagated characteristics in chromosphere and corona of the wavefronts are in agreement with those observed in H~ Moreton and EIT waves, respectively.     

Application of higher-order KdV——mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere

Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV--mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.     

Low frequency Whistler waves excited in fast magnetic reconnection processes

Whistler waves generated in fast magnetic reconnection processes of collisionless high beta plasmas are reviewed in experiments and satellite observations, as well as in theory and simulation, and further studied in the two-fluid theory. It is found that low frequency whistler waves can be excited in tile ion inertial range of the reconnection region. The wave is found right-handed polarized with a quadrupolar out-of-plane magnetic perturbation, in accord with satellite observations in the geomagnetosphere.     

Borehole guided waves in a non-Newtonian (Maxwell) fluid-saturated porous medium

<正>The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian (Maxwell) fluid-saturated porous formation with a permeable wall is investigated.The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves,pseudo-Rayleigh waves,flexural waves,and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot-Tsiklauri model by calculating their velocity dispersion and attenuation coefficients.The corresponding acoustic waveforms illustrate their properties in time domain.The results are also compared with those based on generalized Biot's theory.The results show that the influence of non-Newtonian effect on acoustic guided wave,especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.     

REFLECTION AND REFRACTION OF PLANE SOUND WAVES IN MOVING STRATIFIED MEDIA

This paper deals with the fundamental problems concerning the propagation of plane soundwaves in moving stratified media.Starting from the wave equation in moving media,we haveaccomplished a systematic study of reflection and refraction of the waves at the interface between twomoving homogeneous media under the assumption that the Mach numbers of the motion are smallcompared with unity.The coefficients of reflection and transmission as well as the equation for thetotal reflection cone are obtained. Similar treatment is extended to a slowly varying stratified moving medium,and the W.K.B.solu-tion and the successive modifications to the sound field are worked out.Following the approachdeveloped by Gans,we have investigated the field within the total reflection zone where the geometricalacoustics is no longer valid,and obtained an appropriate solution which can be connected with thegeometrical acoustics solution at the boundaries of that zone.     

Propagation of flexural modal waves in a fluid-filled borehole

The propagation of multipole modal waves along the well-axisin a fluid-filled borehole surrounded by elastic and nonelastic,infinite andfinite formation is analysed by using the wave equations.The phase velocitydispersion and the excitation curves are numerically calculated.Thewaveforms excited by attenuating bursts are also calculated.Themeasurements with long-spaced dipole transducers made of PZT thin disksvibrating in bending mode are carried out in a concrete model well and theexperimental results are compared with the theoretical results.     

Various Kinds Waves and Solitons Interaction Solutions of Boussinesq Equation Describing Ultrashort Pulse in Quadratic Nonlinear Medium

The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.     

Evolutions of Wave Patterns in Whitham-Broer-Kaup Equation

Upon investigation of the parameter influence on the structure of WBK equation, transition boundaries are derived. All possible bounded waves as well as the existence conditions are obtained. The evolution of waves with variation of the parameters is discussed in detail, which reveals the bifurcation mechanism between different wave patterns.