有限振幅脉冲波在管道中的传播

本文分析有限振幅声波在刚性管道中的传播.首先讨论忽略管壁阻尼影响时Burgers方程的解,以反对称N波解为基础,获得了非对称的N波解,能更好地适配实际产生的N波。然后把管壁阻尼的影响作为小量进行修正,获得了广义Burgers方程的近似解.文中对实验测试作了扼要介绍,表明理论预测与实验结果良好相符。     

三维周期结构弱无条件稳定时域有限差分算法

从麦克斯韦方程出发,导出了适用于周期结构的三维弱无条件稳定时域有限差分（FDTD）算法的迭代式,在理论上证明了其稳定性条件,其稳定性条件比普通FDTD的稳定性条件要宽松,并将周期边界条件应用到迭代式中,得到了可直接编程迭代的方程,给出了对其特有的一类非三对角阵的解决办法。最后通过算例将计算结果与常规FDTD及ADI-FDTD计算结果比较,验证了算法的精确性和有效性。     

有源弯曲波导反馈特性的三维时域有限差分法仿真

半导体光放大器的耦合光纤形成的外腔反馈通过引入弯曲损耗得以抑制.通过对半导体光放大器有源波导引入对前、后向光场非对称散射损耗,以前向光场部分损耗为代价,反馈光场能量被分布式地较强辐射.时域有限差分法仿真研究表明,通过优化弯曲有源波导的结构,相对于通常的有源直波导,在相同的材料增益和输入、输出条件下,反馈可以下降10 dB以上.由此可以简化高增益半导体光放大器的器件结构.     

大振幅简正波

本文将简正波理论推广到大振幅声场,计及声场内的非线性效应。这涉及非线性偏微分方程的固有振动解的问题。简正波具有驻波性质,基本已反映在一阶近似解中。高阶近似解只是非线性引致参量的局部变化或修正,并不影响分布。根据这个概念解决了过去的数学困难,求得了大振幅简正函数,为线性商正函数及其谐频项,此外还有常数项,代表辐射压,与经典辐射压值作了比较。     

圆形活塞声源的有限振幅反射波

本文研究了圆形活塞声源的有限振幅声波的反射。应用像源法计算已产生的谐波本身在边界上的反射,将它们看成是反射边界上振动的新声源所产生的辐射场,再应用弱冲击理论来计算这部分场自己产生的谐波场。在水池中作了二阶谐波的反射实验,反射界面是水池壁。结果表明,谐波声压随距离的平均衰减规律与理论符合得很好。实验还表明,反射谐波场沿纵向距离以及与它相垂直的横断面上有强烈的干涉现象,而纵向相干长度比横向相干长度大一个数量级。通过理论估计,认为这种现象是由于反射壁的有限厚度、它的两个平面之间有一个很小的角度以及发射波束有一定的宽度所造成的。这样估算出来的两个相干长度与实验符合。 关键词：     

三维时域有限差分法计算金纳米粒子尺寸与SERS活性的关联

通过合成一系列不同粒径(16～160 nm)的金纳米粒子.观察到120～135 nm的金纳米粒子在632.8nm波长激发下具有最高的SERS活性,这与前人报道的电磁场理论及实验的结果不同.利用三维时域有限差分法对金纳米粒子的SERS活性与其尺寸以及入射光波长的关系进行模拟计算.在632.8 nm激发线下,金纳米粒子二聚体体系在粒径为110 nm左右具有最佳增强效应,其光电场耦合最强的热点处的增强因子高达109考虑到体系的平均SERS增强因子通常会比最大值低约2个数量级,计算得到的107的增强因子与实验测量值相符.同时对目前实验上尚难以合成的大尺寸的金纳米粒子进行模拟,结果表明受多极矩和大尺寸效应的影响在粒径220 nm时又出现SERS增强另一峰值.在325 nm的紫外激发线下,计算得到的增强因子仅为102.     

集总负载平行板有界波电磁脉冲模拟器的并行时域有限差分模拟

介绍了用于集总负载平行板有界波电磁脉冲模拟器模拟的并行时域有限差分方法,分析了模拟器的几个尺寸参数对工作空间的场的影响。研究表明:当下金属板宽度大于或等于工作空间平板宽度的1.5倍时,前过渡段附近的测试点电场的上升沿受前过渡段投影长度的影响较小,而工作空间中心附近的测试点电场的上升沿则随着投影长度的增大而减小,但减小趋于平缓;所有测试点电场的上升沿均随下金属板宽度的增大而减小,但减小趋于平缓;对于前过渡段投影长度固定的模拟器,其高度并不是越小(大)越好,而是存在一个最佳高度值。     

旋转体时域有限差分法的另一推导方法和单向波方程吸收边界条件

提出了旋转体时域有限差分法的另一推导方法.基于这一方法,推导了旋转体电磁波的波动方程,进一步得出了旋转体时域有限差分法的单向波方程吸收边界条件.数值实验证实了该吸收边界条件的正确性.     

集总负载平行板有界波电磁脉冲模拟器的并行时域有限差分模拟

介绍了用于集总负载平行板有界波电磁脉冲模拟器模拟的并行时域有限差分方法,分析了模拟器的几个尺寸参数对工作空间的场的影响。研究表明：当下金属板宽度大于或等于工作空间平板宽度的1.5倍时,前过渡段附近的测试点电场的上升沿受前过渡段投影长度的影响较小,而工作空间中心附近的测试点电场的上升沿则随着投影长度的增大而减小,但减小趋于平缓;所有测试点电场的上升沿均随下金属板宽度的增大而减小,但减小趋于平缓;对于前过渡段投影长度固定的模拟器,其高度并不是越小(大)越好,而是存在一个最佳高度值。     

四波混频用于振幅编码

本文讨论了瞬态四波混频用于光振幅编码的可行性,给出了一种较好的求解耦合方程的数值方法。结果表明,四波混频系统可以构成一种高速编码变换器,为超短脉冲的高速编码提供了一种新手段。     

Time-domain modeling of finite-amplitude sound beams in three-dimensional Cartesian coordinate system

A three-dimensional time-domain algorithm,which is based on the augmented KZK (Khokhlov-Zabolotskaya-Kuznetsov) equation,is proposed to simulate the nonlinear field of the parametric array.First,KZK equation is transformed into TBE(Transformed beam equation). Then,the effects of diffraction(in parabolic approximation),thermoviscous absorption,relaxation, and nonlinearity are solved with finite difference methods.The numerical results of this code agree well with the theoretical and experimental results presented in previous studies, which demonstrates the validity of the three-dimensional algorithm.Using this code to calculate the nonlinear field of the parametric array in air,it is found that the small time interval is important to the accuracy of the simulation results of the difference frequency wave in the case of high sound pressure level,and the errors caused by taking relaxation absorption for thermoviscous absorption are influenced by the characteristic frequency.     

Time-domain modeling of nonlinear distortion of pulsed finite amplitude sound beams

This work aims to validate a time domain numerical model for the nonlinear propagation of a short pulse of finite amplitude sound beam propagation in a tissue-mimicking liquid. The complete evolution equation is simply derived by a superposition of elementary operators corresponding to the 'one effect equation'. Diffraction LD, absorption and dispersion LAD, and nonlinear distortion LNL effects are treated independently using a first order operator-splitting algorithm. Using the method of fractional steps, the normal particle velocity and the acoustical pressure are calculated plane by plane, at each point of a two-dimensional spatial grid, from the surface of the plane circular transducer to a specified distance. The LA operator is a time convolution between the particle velocity and the causal attenuation filter built after the Kramers-Kroning relations. The LNL operator is a time-based transformation obtained by following an implicit Poisson analytic solution. The LD operator is the usual Rayleigh integral. We present a comparison between theoretical and experimental temporal pressure waveform and axial pressure curves for fundamental (2.25 MHz), second, third and fourth harmonics, obtained after spectral analysis.     

Model equation for strongly focused finite-amplitude sound beams

A model equation that describes the propagation of sound beams in a fluid is developed using the oblate spheroidal coordinate system. This spheroidal beam equation (SBE) is a parabolic equation and has a specific application to a theoretical prediction on focused, high-frequency beams from a circular aperture. The aperture angle does not have to be small. The theoretical background is basically along the same analytical lines as the composite method (CM) reported previously [B. Ystad and J. Berntsen, Acustica 82, 698-706 (1996)]. Numerical examples are displayed for the amplitudes of sound pressure along and across the beam axis when sinusoidal waves are radiated from the source with uniform amplitude distribution. The primitive approach to linear field analysis is readily extended to the case where harmonic generation in finite-amplitude sound beams becomes significant due to the inherent nonlinearity of the medium. The theory provides the propagation and beam pattern profiles that differ from the CM solution for each harmonic component.     

Modeling of pulsed finite-amplitude focused sound beams in time domain.

A time-domain numerical model is presented for simulating the finite-amplitude focused acoustic pulse propagation in a dissipative and nonlinear medium with a symmetrical source geometry. In this method, the main effects responsible in finite-amplitude wave propagation, i.e., diffraction, nonlinearity, and absorption, are taken into account. These effects are treated independently using the method of fractional steps with a second-order operator-splitting algorithm. In this method, the acoustic beam propagates, plane-by-plane, from the surface of a highly focused radiator up to its focus. The results of calculations in an ideal (linear and nondissipative) medium show the validity of the model for simulating the effect of diffraction in highly focused pulse propagation. For real media, very good agreement was obtained in the shape of the theoretical and experimental pressure-time waveforms. A discrepancy in the amplitudes was observed with a maximum of around 20%, which can be explained by existing sources of error in our measurements and on the assumptions inherent in our theoretical model. The model has certain advantages over other time-domain methods previously reported in that it: (1) allows for arbitrary absorption and dispersion, and (2) makes use of full diffraction formulation. The latter point is particularly important for studying intense sources with high focusing gains.     

柱坐标系中截断光束的广义M2因子

推导出截断圆对称光束二阶矩的传输方程,它们与无截断光束的二阶矩满足相似的传输定律.因此,基于广义截断二阶矩方法,将直角坐标系中截断二维光束的二阶矩特征参数推广到柱坐标系中的截断圆对称光束,类似方法定义的广义M2因子(M2G因子)是一个传输不变量.对理论的自洽性作了物理解释.推导出柱坐标系中截断超高斯光束的二阶矩参数和M2G因子.对一些有意义的特殊情况作了讨论,并以数值计算例作了说明.     

Propagation of Cartesian beams in nonlocal nonlinear media

We introduce a very general self-trapped beam solution of the Snyder-Mitchell linear model in Cartesian coordinates. We name such a field a self-trapped Cartesian beam (CB) which is characterized by two parameters. The complex amplitude of the self-trapped CBs is described by the product of the parabolic cylinder functions and the Gaussian function. The self-trapped standard, elegant, and generalized Hermite-Gaussian beams can be obtained by treating them as the special cases of the self-trapped CBs.     

Time-domain simulation of sound production of the sho

A physical model based on the sound production mechanism of the sho is proposed with intention of applying it to sound synthesis. Time-domain simulation was done using this model, and effects of the tube length and blowing pressure on the sounding frequency and sounds spectra were investigated. The reed vibration, pressure variation inside the tube, and threshold blowing pressure for oscillation were measured by artificially blowing air into the sho. The experimental results are in acceptable agreement with simulation results in terms of the relationships between tube length and threshold pressure and between tube length and the sounding frequency. In addition, recorded sound waveforms and simulated ones have a common feature in the sense that high-frequency components of their spectra increase with increasing blowing pressure. Further, it is concluded that a sho reed acts as an "outward-striking valve."     

Time-domain simulations of sound propagation through screen-induced turbulence

A flow model in combination with a statistical-dynamical turbulence generator and a linearised Euler time-domain model for sound waves were used to simulate the effect of screen-induced turbulence on the noise level in the acoustical shadow of a screen in wind. Instead of simulating a great number of different frozen turbulence realisations, the concept of transient turbulence was successfully tested and applied. This concept is adequate to the time-domain model and reduces the computational demands. Several two-dimensional simulations allowed to isolate the individual effects of wind and screen on the propagation of 500 Hz sound waves over a 4-m high noise barrier. At a distance of 250 m from the source (240 m behind the screen) the sheltering effect of the screen and the refraction effect of the wind are in the order of 6 and 4 dB, respectively. The screen-induced turbulence leads to fluctuations in the noise level with a standard deviation of 1.2 dB and a maximum amplitude of 3 dB. However, the time averaged effect turned out to be in the order of merely 0.2 dB. The effect of the screen-induced turbulence on the average noise level behind the screen is therefore negligible.