Space time fractional KdV Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged non- thermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold （hot） dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space-time fractional KdV-Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.

FAST SOLUTION OF TRANSIENT SCATTERING FROM ELECTRICALLY LARGE COMPLEX OBJECTS BASED ON TIME DOMAIN INTEGRAL EQUATION SOLVERS

A fast Time Domain Integral Equation(TDIE) solver is presented for analysis of transient scattering from electrically large conducting complex objects.The numerical process of Marching-On-in-Time(MOT) method based TDIE encounters high computational cost and exorbitant memory requirements.A group-style accelerated method-Plane Wave Time Domain(PWTD) algorithm,which permits rapid evaluation of transient wave field generated by temporally bandlimited sources,is employed to reduce the computational cost of MOT-based TDIE solvers.An efficient compressed storage technique for sparse matrix is adopted to decrease the enormous memory requirements of MOT.The scheme of the Multi-Level PWTD(MLPWTD)-enhanced MOT with compressed storage for sparse matrix is presented for analysis of transient scattering from electrically large complex objects in this paper.The numerical simulation results demonstrate the validity and efficiency of the presented scheme.

Implementation of Time-Scale Transformation Based on Continuous Wavelet Theory

The basic objective of time-scale transformation is to compress or expand the signal in time field while keeping the same spectral properties. This paper presents two methods to derive time-scale transformation formula based on continuous wavelet transform. For an arbitrary given square-integrable function f(t),g(t) = f(t/λ) is derived by continuous wavelet transform and its inverse transform. The result shows that time-scale transformation may be obtained through the modification of the time-scale of wavelet function filter using equivalent substitution. The paper demonstrates the result by theoretic derivations and experimental simulation.

Non-Split PML Boundary Condition for Finite Element Time-Domain Modeling of Ground Penetrating Radar

As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite Element Time Domain (FETD) simulation based on the second order electromagnetic wave equation. This paper developed a non-split perfectly matched layer (NPML) boundary condition for GPR FETD simulation based on the second order electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived according to the definition of complex extending coordinate transformation. Then it transformed into time domain by means of auxiliary differential equation method, and its FETD equation is derived based on Galerkin method. On this basis, a GPR FETD forward program based on NPML boundary condition is developed. The merits of NPML boundary condition are certified by compared with wave field snapshots, signal and reflection errors of homogeneous medium model with split and non-split PML boundary conditions. The comparison demonstrated that the NPML algorithm can reduce memory occupation and improve calculation efficiency. Furthermore, numerical simulation of a complex model verifies the good absorption effects of the NPML boundary condition in complex structures.

A Scalar Acoustic Equation for Gases, Liquids, and Solids, Including Viscoelastic Media

The work deals with a mathematical model for real-time acoustic monitoring of material parameters of media in multi-state viscoelastic engineering systems continuously operating in irregular external environments (e.g., wind turbines in cold climate areas, aircrafts, etc.). This monitoring is a high-reliability time-critical task. The work consistently derives a scalar wave PDE of the Stokes type for the non-equilibrium part (NEP) of the average normal stress in a medium. The explicit expression for the NEP of the corresponding pressure and the solution-adequateness condition are also obtained. The derived Stokes-type wave equation includes the stress relaxation time and is applicable to gases, liquids, and solids.

Propagation of Acoustic Waves Caused by the Accelerations of Vibrating Hand-Held Tools in Viscoelastic Soft Tissues of Human Hands and a Mechanobiological Picture for the Related Injuries

As is well known, hand-arm vibration syndrome (HAVS), or vibration-induced white finger (VWF), which is a secondary form of Raynaud’s syndrome, is an industrial injury triggered by regular use of vibrating hand-held tools. According to the related biopsy tests, the main vibration-caused lesion is an increase in the thickness of the artery walls of the small arteries and arterioles resulted from enlarged vascular smooth muscle cells (VSMCs) in the wall layer known as tunica media. The present work develops a mechanobiological picture for the cell enlargement. The work deals with acoustic variables in solid materials, i.e., the non-equilibrium components of mechanical variables in the materials in the case where these components are weakly non-equilibrium. The work derives an explicit expression for the infinite-time cell-volume relative enlargement. This enlargement is directly affected by the acoustic pressure in the soft living tissue (SLT). In order to reduce the enlargement, one can reduce either the ratio of the acoustic pressure in the SLT to the cell bulk modulus or the relaxation time induced by the cell osmosis, or both the characteristics. Also, a mechanoprotective role of the above relaxation time in the cell-volume maintenance is noted. The above mechanobiological picture focuses attention on the pressure in an SLT and, thus, modeling of propagation of acoustic waves caused by the acceleration of a vibrating hand-held tool. The present work analyzes the propagation along the thickness of an infinite planar layer of an SLT. The work considers acoustic modeling. As a general viscoelastic acoustic model, the work suggests linear non-stationary partial integro-differential equation (PIDE) for the weakly non-equilibrium component of the average normal stress (ANS) or, briefly, the acoustic ANS. The PIDE is, in the exponential approximation for the normalized stress-relaxation function (NSRF) reduced to the third-order linear non-stationary partial differential equation (PDE), which is of the Zener type. The unique advantage of the PIDE is that it presents a compact model for the acoustic ANS in an SLT, which explicitly includes the NSRF, thereby enabling a consistent description of the lossy-propagation effects inherent in SLTs. The one-spatial-coordinate version of this PDE in the planar SLT layer with the corresponding boundary conditions is considered. The relevance of these settings is motivated by a conclusion of other authors, which is based on the results of the frequency-domain simulation in three spatial coordinates. The boundary-value problem at arbitrary value of the stress-relaxation time (SRT) and arbitrary but sufficiently regular shape of the external acceleration is analytically solved by means of the Fourier method. The obtained solution is the steady-state acoustic ANS and allows calculation of the corresponding steady-state acoustic pressure as well. The derived analytical representations are computationally implemented. Propagation of the pressure waves in the SLT layer at zero and different nonzero values of the SRT, and the single-pulse external acceleration is presented. They complement the zero-SRT and zero-SRT-asymptote results with the results for various values of the SRT. The obtained pressure values are, at all of the space-time points under consideration, meeting the condition for the adequateness of the linear model. In the case where the SRT is zero, the results well agree with the ones obtained by using the simulation software package LS-DYNA. The dependence of the damping of acoustic variables in an SLT on the SRT in the present third-order case significantly generalizes the one in the second-order linear systems. The related resonance effect in the waves of the acoustic pressure propagating in an SLT is also discussed. The effects of the NSRF-originated memory function provided by the present third-order PDE model are necessary for proper simulation of the pressure, which is of special importance in the aforementioned mechanoboiological picture. The results obtained in the work present a viscoelastic acoustic framework for SLTs. These results open a way to quantitatively specific evaluation of technological strategies for reduction of the vibration-caused injuries or, loosely speaking, achieving “zero’’ injury.

An imaging condition for reverse time migration based on wavefield decomposition

Reverse Time Migration(RTM) is a high precision imaging method of seismic wavefield at present,but low-frequency noises severely affect its imaging results.Thus one of most important aspect of RTM is to select the proper noise suppression method.The wavefield characteristics of the Poynting vector are analyzed and the upgoing,downgoing,leftgoing and rightgoing waves are decomposed using the Poynting vector of the acoustic wave equation.The normalized wavefield decomposition cross-correlation imaging condition is used to suppress low-frequency noises in RTM and improve the imaging precision.Numerical experiments using the Mamousi velocity model are performed and the results demonstrate that the upgoing,downgoing,leftgoing and rightgoing waves are well decomposed using the Poynting vector.Compared with the normalized cross-correlation imaging and Laplacian filtering method,the results indicate that the low-frequency noises are well suppressed by using the normalized wavefield decomposition cross-correlation imaging condition.

An Oscillating Wave Energy Converter with Nonlinear Snap-Through Power-Take-Off Systems in Regular Waves

Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off（PTO） system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.

应用保辛Stereo-modeling方法的振幅补偿逆时偏移成像

地震波数值模拟的精度很大程度上决定了逆时偏移结果的分辨率,文中采用保辛近似解析离散化方法,在Birkhoffian系统下求解黏滞声波方程,并进行振幅补偿的逆时偏移(RTM)。首先,将黏滞声波方程构造成一个Birkhoffian系统,对于该系统采用二阶保辛Runge-Kutta法进行时间推进,分别采用Stereo-modeling法(STEM)和传统有限差分法进行空间算子离散,相应得到SSM(Symplectic Stereo-modeling Method)和CSM(Conventional Symplectic Method)两种方法。之后,对SSM和CSM进行一系列数值性质分析,包括数值频散分析、与解析解比较、效率对比、稳定性测试等。结果显示,SSM的最大数值频散误差约为9%,而CSM约为26%;SSM的计算效率高且长时计算稳定,计算效率约为CSM的两倍。最后,应用三个模型进行了正演数值模拟和逆时偏移试验。对于衰减数据,与声波RTM相比,黏滞声波RTM成像振幅更高,能获得与无衰减数据声波RTM相近的成像振幅。对于油气藏模型,SSM比CSM的成像精度更高、数值频散更小。

Elastic Full Waveform Inversion Based on the Trust Region Strategy

In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. Usually, the line search method is used to update the model parameters iteratively. The line search method generates a search direction first and then finds a suitable step length along the direction. In the trust region method, it defines a trial step length within a certain neighborhood of the current iterate point and then solves a trust region subproblem. The theoretical methods for the trust region FWI with the Newton type method are described. The algorithms for the truncated Newton method with the line search strategy and for the Gauss-Newton method with the trust region strategy are presented. Numerical computations of FWI for the Marmousi model by the L-BFGS method, the Gauss-Newton method and the truncated Newton method are completed. The comparisons between the line search strategy and the trust region strategy are given and show that the trust region method is more efficient than the line search method and both the Gauss-Newton and truncated Newton methods are more accurate than the L-BFGS method.

Finite difference time domain analysis of two-dimensional surface acoustic wave piezoelectric phononic crystals at radio frequency

The finite-difference time-domain （FDTD） method is proposed for analyzing the surface acoustic wave （SAW） propagation in two-dimensional （2D） piezoelectric phononic crystals （PCs） at radio frequency （RF）, and also experiments are established to demonstrate its analysis result of the PCs＇ band gaps. The FDTD method takes the piezoelectric effect of PCs into account, in which periodic boundary conditions are used to decrease memory/time consumption and the perfectly matched layer boundary conditions are adopted as the SAW absorbers to attenuate artificial reflections. Two SAW delay lines are established with/without piezoelectric PCs located between interdigital transducers. By removing several echoes with window gating function in time domain, delay lines transmission function is achieved. The PCs＇ transmission functions and band gaps are obtained by comparing them in these two delay lines. When Aluminum/128°YX-LiNbO3 is adopted as scatter and substrate material, the PCs＇ band gap is calculated by this FDTD method and COMSOL respectively. Results show that computational results of FDTD agree well with experimental results and are better than that of COMSOL.

Hydroelastic Behaviour and Analysis of Marine Structures

Hydroelasticity of marine structures with and without forward speed is studied directly using time dependent Boundary Integral Equation Method with Neumann-Kelvin linearisation where the potential is considered as the impulsive velocity potential.The exciting and radiation hydrodynamic parameters are predicted in time with transient wave Green function whilst the structural analysis is solved with Euler-Bernoulli beam method at which modeshapes are defined analytically.The modal analysis is used to approximate the hydroelastic behaviour of the floating systems through fully coupling of the structural and hydrodynamic analyses.As it is expected,it is found with numerical experience that the effects of the rigid body modes are greater than elastic modes in the case of stiff structures.The predicted numerical results of the present in-house computational tool ITU-WAVE are compared with experimental results for validation purposes and show the acceptable agreements.

TIME DOMAIN BOUNDARY ELEMENT METHODS FOR THE NEUMANN PROBLEM： ERROR ESTIMATES AND ACOUSTIC PROBLEMS

We investigate time domain boundary element methods for the wave equation in R3, with a view towards sound emission problems in computational acoustics. The Neumann problem is reduced to a time dependent integral equation for the hypersingular operator, and we present a priori and a posteriori error estimates for conforming Galerkin approxima- tions in the more general case of a screen. Numerical experiments validate the convergence of our boundary element scheme and compare it with the numerical approximations ob- tained from an integral equation of the second kind. Computations in a half-space illustrate the influence of the reflection properties of a flat street.

Applying a Step Approach Method in Solving the Multi-Frequency Radiation From a Complex Obstacle

In this paper,a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies.The computing scheme is based on the Boundary Integral Equation and derived in the time domain;thus,the time-harmonic Neumann boundary condition can be imposed.By the present method,the values of the initial conditions are set to zero,and the approach process is carried forward in a loop from the first time step to the last.At each time step,the radiated pressure on each element is updated.After several loops,the correct radiated pressures can be obtained.A sphere pulsating with a monopole frequency in an infinite acoustic domain is calculated first.This result is compared with the analytical solution,and both of them are in good agreement.Then,a complex-shaped radiator is taken as the studied case.The pulsating frequency of this case is multiple,and the waves propagate in half space.It is shown that the present method can treat multiple-frequency pulsation well,even when the radiator is a complex shape,and a robust convergence can be attained quickly.

Analysis of Electromagnetic Environment Effect Using TDIE-FDTD-MNA Hybrid Algorithm

It is important but difficult to analyze the electromagnetic environment effect(E3) in the designing of modern airborne,sea,space,and ground systems.Thus a hybrid algorithm of time domain integral equation,finite difference time domain and modified nodal analysis(TDIE-FDTD-MNA) is developed to analyze the E3 of complex systems with cables and nonlinear circuit structures.The plane wave time domain(PWTD) enhanced TDIE method is adopted to solve field problems.The higher order FDTD(2,4) is adopted to solve cable problems.The MNA is adopted to obtain the response of complex circuits(with nonlinear structures).Numerical examples demonstrate the effectiveness of the proposed algorithm.

声波移动障碍反散射问题研究

研究一种具有Dirichlet边界条件的时域声波移动障碍反散射问题。首先对时域波动方程进行求解,在有限观测时间内对移动障碍物采集动态声波近场数据;其次建立一个时域声波移动障碍反散射问题的神经网络模型,该模型将时域近场数据作为输入序列,已知形状的移动障碍物位置参数作为输出序列,求解该反散射问题;最后对于不同移动速度的情况,有效地反演出移动障碍物的位置和轨迹。数值实验表明了该方法的有效性。

基于三相Biot速度应力波动方程的水合物储层波场数值模拟

天然气水合物储层可以看作由骨架、水合物和孔隙水构成的三相孔隙介质。以三相Biot一阶速度应力波动方程作为声波在水合物储层传播的控制方程,用有限差分法(FDTD)进行数值模拟。波场快照可以清楚展现3个纵波和两个横波,与Biot理论相符。根据实测速度优化控制方程参数,使数值速度与实测速度相符。结果表明:孔隙度对水合物剪应力分量影响最显著,对水合物、孔隙水和骨架速度分量的影响次之,所以储层中孔隙度最适合用水合物剪应力分量来分析。骨架速度分量和应力分量受饱和度的影响较小,水合物剪应力分量受饱和度的影响最大,所以分析储层中水合物饱和度的最佳选择是水合物剪应力分量。

基于弹性反射波正演表达的转换波逆时偏移与反偏移

针对线性化弹性反射波方程无法直接用于弹性转换波反偏移模拟的问题,本文提出基于高频近似的一次反射波模拟新方法.该方法基于地震波传播的散射理论,先对地下速度扰动的空间变化进行高频近似,再基于散射波传播方程推导得到线性化一次反射波传播方程.基于弹性反射地震数据表达,本文采用线性算子的伴随估计反射系数,实现反射波逆时偏移.根据该线性表达,联合背景速度和成像值来模拟一次反射横波传播,实现了弹性波角度域反偏移,并进一步导出成像值关于波速的梯度.数值实验表明,基于弹性反射地震数据表达的偏移成像方法,既克服了极性反转效应,又使成像结果包含了更为丰富的反射角信息;一次反射波模拟方法获得的弹性地震数据具有较高的精度和稳定性,得到的弹性波场的振幅和相位信息与理论解析解吻合较好,有效保证了成像域层析速度反演梯度的稳定求解.

基于广义坐标变换的起伏地表频率域波动方程正演模拟与逆时偏移

高效精确的波动方程正演模拟是地震偏移成像和参数反演的核心,频率域的有限差分方法在正演模拟具备一定优势,包括能够在多震源模拟中计算效率更高,在选择网格间距时更具有灵活性等.然而,这种方法在处理起伏地表问题上较为困难.为了解决起伏地表情况下的频率域波动方程正演模拟与逆时偏移问题,我们提出通过建立广义坐标系,利用传统笛卡尔坐标系到起伏地表坐标系的映射关系,在起伏地表条件下高精度地模拟地震波传播波场.在此基础上,进一步讨论了实现频率域逆时偏移的可行性.并使用均匀模型和Foothills模型的数值测试来验证本文方法基本流程的有效性和计算效率.结果表明,在进行复杂地表场景的频率域地震成像和反演时,本文方法具有作为正演建模求解器的潜力.

天然气水合物饱和度与声学参数响应关系的实验研究

天然气水合物饱和度是评估天然气水合物资源量的重要参数,而用来估算饱和度的速度模型则是有限的几个,它们有的为经验公式,有的是以实验数据或野外资料为基础建立起来的,需要进行实验验证和参数分析以确定其使用的适用性.本文首次利用超声和时域反射联合探测技术,研究了沉积物中水合物饱和度与声学特性的关系.并对时间平均方程、伍德及其修正方程、李权重方程和BGTL(Biot-Gassmann Theory by Lee)理论等常用的水合物饱和度估算模型进行了验证.实验结果表明,超声和时域反射联合探测技术能有效地实时获得水合物饱和度和纵、横波速的实验数据,李权重方程和BGTL理论的速度预测值与实验值比较吻合,有广泛的适用性.