Acoustical wave propagator for time-domain flexural waves in thin plates

In this paper, an explicit acoustical wave propagator technique is introduced to describe the time-domain evolution of acoustical waves in two-dimensional plates. A combined scheme with Chebyshev polynomial expansion and fast Fourier transformation is used to implement the operation of the acoustical wave propagator. Through this operation, the initial wave packet at t = 0 is mapped into the wave packet at any instant t > 0. By comparison of the results of the exact analytical solution and the Euler numerical method, we find that this new Chebyshev-Fourier scheme is highly accurate and computationally effective in predicting the acoustical wave propagation in thin plates. This method offers an opportunity for future study of dynamic stress concentration and time-domain energy flow in coupled structures.     

Dynamic stress concentration in a ribbed plate using the acoustical wave propagator technique

This paper presents an explicit acoustical wave propagator technique to investigate the flexural wave scattering and dynamic stress concentration in a ribbed plate based on Mindlin plate theory. A scheme combining Chebyshev polynomial expansion and fast Fourier transformation is introduced to implement the operation of the acoustical wave propagator. The exact analytical solutions are also presented to demonstrate the validity of the present technique. The wave propagation patterns are used to investigate the effect of rib on the flexural wave scattering and distribution of dynamic stress concentration. Dynamic stress concentration factors around the discontinuities are examined in detail.     

基于声传播算子的声源定位实验模拟方法研究

声传播算子是一种高效的时域声场计算方法,它能够很方便地计算出给定系统参数下任意时刻任意位置的声场变化情况,本文采用这种方法计算所得的二维房间声场信息进行传声器阵列的声源定位仿真实验。计算结果表明,用该方法获取的阵列数据能有效地应用于阵列信号处理算法中,准确地估计出初始高斯脉冲声源的方向。声传播算子声场计算方法能为传声器阵列声源定位的实验提供方便,使得传声器阵列声源定位算法在不同混响时间的鲁棒性实验研究变得更加简捷。     

Acoustical wave propagator for time-domain dynamic stress concentration in a plate with a sharp change of section

The acoustical wave propagator technique is applied to study the time-domain dynamic stress concentration in a two-dimensional flexible plate with a sharp change of section. As a wave packet approaches the plate discontinuity where the sharp change of thickness is introduced, the spatial interference patterns in the displacement of the plate and internal stresses vary with time. The constructive interference of stresses is referred to as time-domain stress concentration. The superposition of wave fronts of incident and reflected wave packets is used to explain the spatial distribution of the interference patterns. The increase of dynamic stress near the vicinity of the discontinuity boundary of the plate is studied as a function of time and the thickness ratio of the plates.     

一种基于波动方程的新高阶FDTD方法

 提出了一种基于二阶波动方程的（2M,4）高阶时域有限差分(FDTD)方法，通过使用辛积分传播子(SIP)在时域上获得4阶精度，使用离散奇异卷积(DSC)方法在空域上达到2M阶精度。与已有的(2M，4) 阶FDTD方法相比，虽然两者都采用SIP和DSC方法，但是此二者的不同点在于：第一，新方法基于二阶波动方程；第二，在离散计算空间时使用单一网格而不是传统的Yee网格；第三，单独计算某一场分量从而节约内存并减少计算量。数值计算结果表明，与传统高阶算法相比，基于波动方程的高阶FDTD方法耗费的机时只有它的50%,内存消耗下降10%, 而两者的计算结果之间相对误差小于5‰。     

Functional integral formulation of classical wave equations

It is shown in this paper that classical wave equations admit path integral formulations. For this, the evolution of the system is first set-up in terms of a fundamental solution or propagator. We choose this last name because it suggests a connection with functional integrals, which are exploited in this work. A functional integral in terms of non-singular functions is then proposed and shown to converge to the propagator in the appropriate limit for the case of scalar wave equations. One of the advantages of such formulation is that it provides an adequate framework for mesh-free numerical methods. This is demonstrated through a computational implementation that combines a simple second-degree polynomial local approximation of the continuous field and an approximate statement of the exact evolution equations. Numerical simulations of modal analysis and transient dynamics indicate the feasibility of the technique.     

基于Rayleigh-Bloch模式的单层结构弯曲声波导

基于一维声栅中的Rayleigh-Bloch(RB)模式基本特点,设计了一种单层结构弯曲声波导.利用有限元方法从时域和频域两方面验证了弯曲声波导的有效性,RB模式波可以沿着波导的弯曲界面传播.研究发现,由于采用了环形结构基本单元,在该波导中存在两种传播模式,分别对应能量局域在单元间(模式-1)和单元内部(模式-2)两种情况.其中,模式-2声传输效果更佳,几乎可实现无损传输.时域研究中分别采用了调制脉冲和高斯脉冲两种信号形式,分析了它们在弯曲声波导中的传输过程.由于波导中只允许RB模式波传播,因此对于宽频信号来说,可起到滤波的效果.并且,不同模式(频率)的信号会出现在声波导的不同位置,所得结果对于声波定向传输、声探测与识别等研究具有理论与应用价值.     

Space–time transformation for the propagator in de Broglie–Bohm theory

A linear space–time transformation proposed to calculate the propagator in the de Broglie–Bohm theory, viewed as an expansion of the guiding wave function over the velocity space. It is shown that the quantum evolution is preserved in its semiclassical scheme through this change. The case of variable-frequency harmonic oscillator is presented as an example.     

An improved acoustical wave propagator method and its application to a duct structure

The pseudospectral time-domain method has long been used to describe the acoustical wave propagation. However, due to the limitation and difficulties of the fast Fourier transform (FFT) in dealing with nonperiodic problems, the dispersion error is inevitable and the numerical accuracy greatly decreases after the waves arrive at the boundary. To resolve this problem, the Lagrange-Chebyshev interpolation polynomials were used to replace the previous FFT, which, however, brings in an additional restriction on the time step. In this paper, a mapped Chebyshev method is introduced, providing the dual benefit of preserving the spectral accuracy and overcoming the time step restriction at the same time. Three main issues are addressed to assess the proposed technique: (a) Spatial derivatives in the system operator and the boundary treatment; (b) parameter selections; and (c) the maximum time step in the temporal operator. Furthermore, a numerical example involving the time-domain evolution of wave propagation in a duct structure is carried out, with comparisons to those obtained by Euler method, the fourth-order Runge-Kutta method, and the exact analytical solution, to demonstrate the numerical performance of the proposed technique.     

含时阻尼谐振子的传播子与严格波函数

通过正则化变换技巧,寻找到一种对阻尼系数随时间变化的阻尼谐振子直接量子化方案,进而采用高斯型传播子和费曼路径积分方法求出了含时阻尼谐振子的严格波函数,并对波函数的普遍意义,坐标和动量的零点涨落以及两者的不确定关系作了讨论 关键词： 含时阻尼 传播子 费曼路径积分     

Semiclassical wave packet tunneling in real-time

Quantum mechanical real-time tunneling through general scattering potentials is studied in the semiclassical limit. It is shown that the exact path integral of the real-time propagator is dominated in the long time sector by quasi-stationary fluctuations associated with caustics. This leads to an extended semiclassical propagation scheme for wave packet dynamics which accurately describes deep tunneling through static and, for the first time, driven barrier potentials.     

Design of sparse matrix representations for the propagator used in the BPM and directional wave field decomposition

Directional wave field decomposition can be accomplished with the aid of pseudo-differential operators. A fast numerical scheme requires sparse matrix representations of these operators. This paper focuses on designing sparse matrices for the propagator while keeping the accuracy high at the cost of ignoring critical-angle phenomena. The matrix representation follows from a rational approximation for the square root operator and the derivatives. The parameterization thus introduced lends itself to an overall optimization procedure that minimizes the errors for a chosen discretization rate. As such, the approach leads to an accurate propagator up to the (local) critical angle on a coarse numerical grid. This revised version was published online in November 2006 with corrections to the Cover Date.     

The quark propagator from the Dyson-Schwinger equations: (I). The chiral solution

Within the framework of the Dyson-Schwinger equations in the axial gauge, and using a truncation procedure which respects the Ward-Takahashi identities, we study the effect that nonperturbative glue has on the quark propagator. We show that within this truncation scheme, the requirement of matching perturbative QCD at high momentum transfer leads to a multiplicatively renormalisable equation. Technically, the matching with perturbation theory is accomplished by the introduction of a transverse part to the quark-gluon vertex. In the case of an analytic gluon propagator, this truncation scheme can lead to chiral symmetry breaking only after the introduction of such a transverse vertex: massless solutions do not exist beyond a critical value of as. Using the gluon propagator that we previously obtained, we obtain small corrections to the quark propagator, which keeps a pole at the origin in the chiral phase.     

Study of the gluon propagator in the axial gauge

It is shown that a non-linear integral equation for the gluon propagator in the axial gauge (Baker et al.) can be simplified considerably. A comparison is made with an approximate equation for the gluon propagator in the Landau gauge (Mandelstam). Both equations have polynomial kernels where the argument is the divisor of the internal and external momenta. A solution which behaves as a double pole for low momenta remains consistent.     

Fractional-harmonic components in an acoustical wave in a liquid

The amplitudes and frequencies of the components of the acoustical spectrum of an acoustical wave, generated in a non-viscous liquid filling a cavity, are calculated by solving a boundary value problem. Apart from forced oscillations, the frequencies of the acoustical spectrum are equal to the frequency of the fundamsntal oscillation of the liquid in the cavity and its higher harmonics. If the frequency of the driving acoustical wave coincides with one of these (proper) frequencies, thefractional harmonic components appear. The amplitudes of the component oscillations decrease monotonically as the absolute value of the difference between the frequency of the driving acoustical wave and the frequency of the respective oscillation is increased. The derived relations are compared with the results of some published measurements.     

Relativistic Hartree-Fock schemes and effect of self-consistency

A new effect of self-consistency in the relativistic Hartree-Fock (HF) approximation is studied by a simple model and a renormalized calculation. A comparison is made between two different HF schemes: one requiring self-consistency in the HF potential (scheme P) and the other in the baryon propagator (scheme BP). Our results show that scheme P is a good aproximation to scheme BP for the calculation of the baryon propagator and the self-consistency requirements make the results obtained by the two schemes closer to each other, because the self-consistency in scheme BP diminishes the continuum part of the spectral representation for the baryon propagator, while the self-consistency in scheme P yields a baryon propagator which approximates closely to the HF result contributed by the converged single particle part of the above spectral representation alone. Received: 12 March 1999 / Revised version: 6 September 1999     

次声波在平流层波导中传播的数值模拟

对次声波在大气中传播进行了建模。通过结合保色散关系空间差分格式和Runge-Kutta时间格式的数值方法,建立了次声波传播模型。应用该次声波模型,研究了在耗散的重力分层大气中次声波的平流层导行传播。数值模拟结果表明,当次声波波包在平流层高度上被反射时,反射区域存在焦散现象,在声波的声压下降的同时,声波的能量得到聚焦。通过数值模拟结果与射线计算结果的对比表明,大气中声波传播的轨迹的精确描述需要应用全波解。      

一种处理Cole-Cole色散媒质的FDTD改进方案

对柯尔-柯尔(Cole-Cole)色散媒质的时域有限差分(FDTD)方案尝试给出改进:(1)保留了Cole-Cole经验公式中的静态电导率项;(2)扩展到三维情形;(3)人体乳房组织的模型参数源于实验测量.数值算例结果初步证实改进方案的可行性和有效性.改进方案适用于模拟更一般柯尔-柯尔色散媒质中的电波传播.     

Finite element formulations for acoustical radiation

Finite and infinite element techniques are applied to linear acoustical problems involving infinite anechoic boundaries. Theory is presented for a simple one dimensional model based on Webster's horn equation. Results are then presented both for the one dimensional model and for two axisymmetric test cases. Comparisons with exact solutions indicate that both the infinite element and wave envelope schemes are effective in correctly predicting the near field. The wave envelope scheme is also shown to be capable of resolving the far field radiation pattern.     

Vibrations of a rectangular membrane with an eccentric inner circular boundary: A comparison of approximate methods

Three different approaches are used in order to obtain, independently, fundamental eigenvalues of the mechanical system under study: the Ritz method, the finite element algorithm and a Fourier expansion-collocation scheme. The agreement can be considered as very reasonable, especially in view of the relatively simple formulation of the Ritz approach in which two polynomial co-ordinate functions are employed. The results may also be of interest to acousticians and microwave specialists since they are applicable to soft-walled acoustical waveguides and TM modes in electromagnetic waveguides.