层状介质时域有限差分方法斜入射平面波引入新方式

应用二维时域有限差分方法分析层状介质中的目标散射时,在总场-散射场边界斜入射平面波源用常规方法难以引入,因为在总场-散射场边界处设置的入射波实际上包含了入射脉冲以及各分层界面的反射和多次反射.为解决这个问题,提出了斜入射平面波的混合引入方式,即对总场-散射场的四个边界面采取不同的处理方式.对于总场-散射场的纵向侧边界,用含有斜入射角度的修正一维时域有限差分方法,只要在自由空间位置加入入射脉冲就会自行产生由各分层界面形成的反射波,包括多次反射.同时,把纵向总场-散射场侧边界向下延伸,使得总场-散射场下边界位于完全匹配层内,这样透射波和散射波均为外向行波而被吸收.对于总场-散射场的上边界,由于完全位于自由空间中,边界上各点的入射波将是总场-散射场纵向边界角点处入射波的带有时间延迟的复制.数值模拟结果表明了本文所提出方法的正确性和有效性. 关键词： 时域有限差分 层状介质 斜入射平面波 修正一维麦克斯韦方程     

一种新的基于最小平方逼近的广角光束传播方法

用最小平方逼近展开传播算子，实现了一种新的半矢量显式高阶有限差分光束传播方法-这种方法中不需要选择参考折射率，并在整个传播常数（包括辐射模的传播常数）分布区域进行逼近，解决了在泰勒展开和庞德逼近中存在的参考折射率选择和远离展开点误差增大等问题-用这种方法对几种典型波导结构进行了数值模拟，模拟结果验证了算法的正确性和可靠性- 关键词： 光束传播方法 有限差分 集成光学 数值方法     

爆震波传播速度同阻力和热损失的一般关系

本文采用－维稳态ＺＮＤ模型，从理论分析和数值计算上详细研究了爆震波的结构和非绝热粗糙管中摩擦阻力和热损失对爆震波传播的影响．推导了爆震波的传播方程，揭示了多种爆震机制和爆震极限的存在及其机理。对低速爆震的发生给出了理论解释．     

边界净流条件下的超声速热波

 物质中的辐射热波的行为一直是人们非常关注的问题。但是由于辐射热传导方程具有很强的非线性，其精确的解析解很难求出。利用微扰论推导出了任意边界净流条件下的边界温度的变化行为和热波传播轨迹的理论公式，并与辐射流体力学程序计算的数值结果进行了对比，结果显示理论计算的热波轨迹与数值模拟的结果符合得非常好。     

修正KP方程及其孤波解的稳定性

采用约化摄动法, 得到描述无磁场等离子体中离子声波传播的modified Kadomtsev- Petviashvili(mKP) 方程, 构造有限差分格式对mKP方程的一类特殊孤立波解的稳定性进行数值研究. 数值结果表明: 在两种特殊情形的初始扰动下, 该孤立波均不稳定.     

多尺度有限差分法模拟复杂介质波传问题

利用有限差分和紧支集正交小波变换对波动方程的时间、空间进行联合近似求解,提出一种适合于一般边界非均匀耗散介质中波传问题数值模拟的快速自适应混合算法——多尺度有限差分(multiresolution finite difference缩写为MRFD)方法.将波传问题的求解转换到小波域中进行,利用小波基的自适应性与消失矩特性,使偏微分算子矩阵稀疏化,有效改善了计算量等.地球物理勘探中的数值实例显示了算法具有良好效率 关键词： MRFD 小波变换 多尺度 波传问题     

斜入射非线性电离层Langmuir扰动的电磁波传播特性

基于广义Zakharov模型,结合斜入射等离子体的时域有限差分(FDTD)方法与双流体力学方程,通过由二维麦克斯韦方程等价转换的一维麦克斯韦方程,与等离子体流体力学方程建立了一个电磁波以不同角度入射电离层传播的数值模型.分析推导出TE_z波在斜入射非线性电离层等离子体的支配方程,然后推导了适用于计算电离层电磁波传播特性的FDTD算法.通过仿真来证明该方法在较小倾角下,电磁波对电离层加热形成Langmuir扰动及其传播特性的准确性和有效性.结果表明,在小角度入射下,大功率高频电磁波在电离层等离子体中的O波反射点附近激发出了Langmuir波,同时波粒相互作用导致O波转换为Z波并向电离层更高区域传播.本文进一步研究了基于电离层等离子体的电磁波传播特性,为全面深入分析电离层Langmuir扰动对电离层电波传播特性影响奠定数值算法的基础.     

粒子模拟中波导激励源的设计与实现

 讨论了粒子模拟中用时域有限差分(FDTD)法设计波导激励源的常见问题，并根据波的传播特性，提出一种模拟波导激励源的新方法，给出通用的计算公式，讨论了几种特殊情况下的算法修正。给出了2维柱坐标系下磁绝缘线振荡器(MILO)计算实例，结果表明：该方法能模拟较为复杂的波导激励源，并有效消除了激励源边界处的虚假反射，与传统波导激励源模拟方法比较，验证了该方法的正确性与优越性。     

用MEI方法研究脉冲线源辐射问题

 脉冲线电流源的辐射问题是研究高功率微波辐射、传播和散射问题的基础。用时域有限差分方法结合时域MEI吸收边界条件来对该问题进行求解，通过与不同种类边界条件配合得出的数值解的比较可以证明，利用时域MEI方法的一阶吸收边界条件对线源辐射问题进行处理时，可以使截断边界离源更近，从而减少了计算量，并达到提高计算精度的目的。     

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。      

New method of spatial superposition of attenuated waves for ultrasound field modelling

The objective of this work is the contrary issues of ultrasonic diagnostics in medicine when modern requirements for resolution are in conflict with strict safety issues. There is only one way to make progress by starting to take into account the attenuation in biological tissues and the wave diffraction phenomena. The aim of this work is to develop the flexible ultrasound field model implemented in routine algorithms of digital signal processing. The method consists of the calculation of plane wave propagation and the calculation of an ultrasound signal field. On the basis of the spatial impulse response of an aperture for calculation of space-spread ultrasound signals and the spectrum decomposition method for modelling plane wave propagation in lossy media, the modified method of spatial superposition of attenuated waves was developed. Using the method of equidistant line calculation the time and frequency features of the ultrasound signal field caused by the geometry and dynamics of the aperture, the attenuation and velocity dispersion in the medium are determined. The method was successfully applied to the investigation of the system for intracranial media monitoring, where a new measurement channel based on the changes of attenuation and dispersion in intracranial medium has been implemented.     

On open boundary conditions for long wave equation in the hodograph plane

We discuss implications of the seaward boundary conditions used in initial-boundary value problem formulation of nonlinear shallow-water wave propagation over a linear slope. We first demonstrate the reflection of wave velocity in the case of Dirichlet condition and that of water elevation in the case of Neumann condition. We then show that linear superposition of the two boundary conditions results in much less reflection at the artificial boundary. We also propose a new boundary condition of mixed type and compare its results with that of the aforementioned conditions.     

Investigation of linear and nonlinear frequency modulated excitation effects on tissue harmonic imaging

The generation of tissue harmonics is due to nonlinear nature of ultrasound wave propagation in biological tissues.The tissue harmonics for imaging i.e.tissue harmonic imaging (THI)uses higher frequency components for imaging in which the resolution improves significantly but signal-to-noise ratio(SNR)and penetration depth remains low as compared to both fundamental and second harmonic imaging.The coded excitations have potential to improve the SNR which ultimately leads to improved penetration depth.In the present work,the linear frequency modulated(chirp/LFM)and nonlinear frequency modulated(NLFM)signals have been used to investigate the nonlinear ultrasound wave propagation and harmonic generation in biological tissues.The SNR has been found to be substantially improved for coded tissue harmonic imaging(CTHI)as well as for coded superharmonic imaging(CSHI).     

Diffraction of a plane electromagnetic wave at a schwarzschild black hole

Using the technique of Debye potentials a rigorous solution of the diffraction problem is given as a superposition of an incident wave, strongly connected with the Coulomb scattering wave function, and a scattered wave, which is purely outgoing for large distances. The solution fulfils the boundary conditions to be the light of a very distant star and to be purely ingoing at the Schwarzschild horizon. The phase shifts of the partial waves are evaluated in the WBK approximation.     

Theoretical Analysis of the Biological Thermal Effect of Millimeter Waves in Layered-Dielectric-Slabs

The theory is presented for one method of determining the biological thermal effect of millimeter waves in microwave radiometry. It has been studied theoretically that millimeter waves propagation and absorption in a human body. The model is a plane straticulate homogeneous slab of tissues under the irradiance of normal incidence plane wave. It has been discussed by obtaining the electromagnetic field, absorbent power, specific absorption rate, temperature field and their distributions in the human trunk model. Also, the principle of thermal therapeutics of millimeter waves to cancer has been discussed preliminarily.     

Heat and mass transport in the photoacoustic effect on liquids

The temperature oscillation accompanying the photoacoustic effect generates a periodic variation of the vapor pressure of a liquid. The propagation of the oscillating concentration of the vapor in the inert cell gas (air) is described by a mass diffusion wave on which a convective motion of the gas is superposed. The diffusion wave characterized by the diffusion coefficient of the cell gas alone can be measured by the Mirage effect, whereas a microphone detects the total mass flux including the convective flux, which increases with temperature. On approaching the boiling temperature, the convective flow will govern the oscillating transport of mass. The photoacoustic signal is determined directly from the flux of heat and mass at the boundary between liquid and gas using the Gauss' divergence theorem. We have found that the temperature behaviour of the amplitude and phase angle of the photoacoustic signal depends on the length of the gas column in the cell. The contribution of thermal expansion to the photoacoustic signal is considered using the composite piston model. The results of the calculations agree fairly well with the experimental data.     

Negative refraction of ultra-short electromagnetic pulses

We study pulse propagation across a boundary that separates an ordinary medium from a medium with simultaneously negative dielectric permittivity and magnetic permeability. Solving Maxwell’s equations with two spatial coordinates (one longitudinal, one transverse) and time we find negative refraction as the wave packet undergoes significant and unusual shape distortions. The pulse acquires and maintains a chirp as it traverses the interface, as expected, but with a sign that is opposite to the chirp attained upon traversal into a positive-index material. Both a direct calculation of the spatial derivative of the instantaneous, local phase of the pulse and a Fourier analysis of the signal reveal the same inescapable fact: that inside a negative-index material, a transmitted, forward-moving wave packet is indeed a superposition of purely negative wave vectors. The central findings of this paper are a confirmation that causality is not violated in the short-pulse regime, and that energy and group velocities never exceed the speed of light in vacuum.     

Performance improvement of magneto-acousto-electrical tomography for biological tissues with sinusoid-Barker coded excitation

By combining magnetics, acoustics and electrics, the magneto-acoustic-electrical tomography(MAET) proves to possess the capability of differentiating electrical impedance variation and thus improving the spatial resolution. However,the signal-to-noise ratio(SNR) of the collected MAET signal is still unsatisfactory for biological tissues with low-level electrical conductivity. In this study, the formula of MAET measurement with sinusoid-Barker coded excitation is derived and simplified for a planar piston transducer. Numerical simulations are conducted for a four-layered gel phantom with the 13-bit sinusoid-Barker coded excitation, and the performances of wave packet recovery with side-lobe suppression are improved by using the mismatched compression filter, which is also demonstrated by experimentally measuring a three-layered gel phantom. It is demonstrated that comparing with the single-cycle sinusoidal excitation, the amplitude of the driving signal can be reduced greatly with an SNR enhancement of 10 dB using the 13-bit sinusoid-Barker coded excitation. The amplitude and polarity of the wave packet filtered from the collected MAET signal can be used to achieve the conductivity derivative at the tissue boundary. In this study, we apply the sinusoid-Barker coded modulation method and the mismatched suppression scheme to MAET measurement to ensure the safety for biological tissues with improved SNR and spatial resolution, and suggest the potential applications in biomedical imaging.     

二元复合波片延迟相位方位效应探讨

在多级波片方位效应的基础上，探讨了复合波片的方位效应问题。通过对多级波片的设计与测量，论证了入射光方位是影响波片延迟量的关键因素。     

管间界面特性对周向超声导波传播特性的影响

采用界面弹簧模型对圆管结构的管间界面特性进行描述, 推导出含弱界面的圆管结构中声波沿周向传播时的位移场及应力场的数学表达式. 在此基础上采用导波的模式展开分析方法, 给出了与管间界面特性及激励源密切相关的周向超声导波模式展开系数的解析表达式. 数值分析了管间界面特性的变化对周向超声导波的频散和声场产生的影响. 理论与数值分析结果表明, 通过选择适当的驱动频率及周向导波模式, 可使周向超声导波的相速度及圆管外表面的位移场随管间界面特性的变化表现出非常敏感且单调的性质. 这一结果有助于采用周向超声导波方法准确定征圆管结构的管间界面特性.