水平变化波导中的简正波耦合与能量转移

针对海底地形水平变化对声场能量传播和声场干涉结构的影响,对简正波之间的耦合和能量转移进行了研究.建立了一种二维大步长格式的耦合简正波模型和三维楔形波导耦合简正波模型,以便快速有效地分析简正波之间的耦合和能量转移.基于耦合简正波模型,阐述了前向声场能量在水平变化波导中传播时的转移过程.并根据射线简正波理论,解释了海底地形变化对声场能量分布的影响机理.水平变化波导中声场的仿真计算表明,当本征值虚部发生剧烈变化时声场存在着较强的简正波耦合和能量转移,且海底地形变化将导致声场能量的水平传播方向偏转至海水深度增加的方向.在声场能量转移和传播方向变化中,声场的能量趋于保留在波导中而不向海底泄漏.同时,声场能量分布受到类似于压缩或稀疏的作用,从而形成椭圆状的干涉结构.     

一种水平变化可穿透波导中声传播问题的耦合简正波方法

通过利用标准简正波程序KRAKEN计算本地简正波解及耦合矩阵, 进一步发展了求解水平变化波导中声场的全局矩阵耦合简正波方法(Luo et al., "A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides," Sci. China-Phys. Mech. Astron. 55, 572 (2012)), 使得该方法可以处理具有可穿透海底及随深度变化声速剖面等实际问题, 并提供声场的完全双向解. 本文还给出了双层波导中耦合矩阵的解析表达式, 并利用其验证了本方法中耦合矩阵数值算法的精度. 最后, 利用改善后的全局矩阵耦合简正波模型(DGMCM)计算了美国声学学会(ASA)提出的可穿透楔形波导标准问题, 将所得数值解与参考解比较, 结果表明DGMCM方法可以精确处理水平变化波导中声传播实际问题. 关键词： 耦合简正波理论 全局矩阵方法 可穿透楔形波导     

水平变化双层波导声传播问题的耦合简正波解

为了验证现有模型的精度,导出了全反射下边界双层波导中简正波耦合矩阵的解析表达式,并将其应用到全局矩阵耦合简正波模型(Direct Global Matrix Coupled-Mode)中,使得该模型可以提供水平变化双层波导问题的标准解。文中首先利用COUPLE的简正波及耦合矩阵数值解验证了该简正波及耦合矩阵解析表达式的正确性;其次,采用改进的DGMCM模型求解了双层波导海山声传播损失,结果表明,改进后的DGMCM模型可以非常精确地求解水平变化双层波导问题,可作为求解此类问题的标准模型使用。     

水平变化波导中一种声场计算方法的数值实现

全局矩阵方法计算水平变化环境中的声场具有稳定性好、速度快、精度高等优点,在数值实现中如何快速、准确的求解大规模矩阵是该方法的一个关键问题。本文针对全局矩阵的特点,分别利用两种矩阵求解器,PARDISO和LAPACK,求解该问题。经过比较和讨论,得出结论:LAPACK对于全局矩阵的求解更有优势,求解速度快,而且可求解问题规模相对较大。使用不同的数值实现方法计算了楔形波导的传播损失(ASA标准问题),与解析解比较,证明全局矩阵方法计算精度很高。     

全局矩阵耦合简正波方法与现有模型的比较

水平变化波导中的全局矩阵耦合简正波方法具有数值稳定、计算精度高、计算效率高、适用范围广等优点。骆文于等人开发了全局矩阵耦合简正波模型DGMCM (Luo et al, \     

等声速环境中目标前向声散射简正波耦合的垂直阵空域响应特征

水下目标的前向声散射会引起声波传播过程中的简正波耦合效应,使得接收声场结构发生变化,研究目标前向散射引起的垂直阵列上空域响应变化特征,可实现对直达波强干扰背景下的前向散射检测。通过将垂直阵波束形成技术分别用于信道中目标散射场理论模型计算数据和湖上实验验证数据,分析了等声速环境中目标前向声散射简正波耦合的垂直阵空域响应特征。结果表明,目标靠近接收端时前向散射引起的声波垂直达到结构与无目标时相比差异显著,高阶简正波向低阶简正波转化导致信号到达时延宽度展宽,采用指向水平方向的窄波束可显著提取目标前向散射引起的接收声波变化特征。     

一种水平变化波导中声传播问题的耦合模态法

针对介质参数及海底边界水平变化波导中的声传播问题,本文基于多模态导纳法提出一种能量守恒且便于数值稳定求解的耦合模态方法.将声压表示为一组正交完备的本地本征函数之和,对声压满足的Helmholtz方程在本地本征函数上作投影,推导出关于声压模态系数的二阶耦合模态方程组.耦合矩阵直观描述水平变化因素对模态耦合的贡献.为避免直接求解二阶耦合模态方程组可能遇到的数值发散问题,将其重构为两个耦合的一阶演化方程组,引入导纳矩阵并使用Magnus数值积分方法获得稳定的声场解.利用该耦合模态方法数值计算水平变化波导中的声场,并与COMSOL参考解比较,结果表明该耦合模态理论能够精确求解水平变化波导中的点源及分布源传播问题.     

一种水平变化波导中匹配场定位的虚拟时反实现方法

在水平变化波导中,匹配场被动定位的计算量非常大,严重阻碍了其工程应用.本文提出了一种水平变化波导中匹配场定位的虚拟时反实现方法,其抛物方程模型计算网格总数远小于匹配场处理,从而大大减小计算代价.与匹配场处理不同,虚拟时反实现方法是一个利用介质互易性和叠加性的后向传输过程.通过在各水听器位置放置虚拟声源,并在搜索区域产生相应的模糊平面,对各个模糊平面进行相应加权求和,获得的定位模糊平面.利用地中海浅海实验数据验证了虚拟时反实现方法的快速性能.     

A two-way marching coupled-mode method for range-dependent propagation

##正##An efficient,accurate,and numerically stable coupled-mode solution is presented for acoustic propagation in a range-dependent waveguide.This method is numerically stable due to the appropriately normalized range solutions introduced in the formulation.In addition,by combining a forward marching and a backward marching,this method provides accurate solutions for range-dependent propagation problems,especially those characterized by large bottom slope angle and/or high impedance contrast between water and the bottom.Furthermore,this two-way solution also provides high efficiency,which is achieved by applying the single-scatter approximation.Numerical examples are also provided to demonstrate the efficiency,accuracy, and stability of this method.     

Analysis and comparison between two coupled-mode methods for acoustic propagation in range-dependent waveguides

Two coupled-mode methods,namely DGMCM(Direct-Global-Matrix CoupledMode Method)and CCMM(Consistent Coupled-Mode Method),are analyzed and compared.First,both of these two methods provide two-way solutions,and hence they are accurate models.Second、the series of local vertical modes in DGMCM converges as fast as that in CCMM,whereas DGMCM has a more tolerable requirement of the number of segments than CCMM.Third,these two models obtain the field solution by solving the coupled-mode system with different coefficient matrices,in which the computational etfort for the required parameters is almost the same.Finally,DGMCM can handle some problems which are difficult for CCMM,such as in a waveguide with a rough bottom,a line source located right on top of a sloping bottom,or in the presence of multiple sources.In DGMCM,closed-form expressions for coupling matrices in a two-layer waveguide are given.In addition.the formulation for the line-source problem in plane geometry is derived to update CCMM.     

Analysis and engineering of coupled cavity waveguides based on coupled-mode theory

The analytical expression for the transmission spectra of coupled cavity waveguides （CCWs） in photonic crystals （PCs） is derived based on the coupled-mode theory （CMT）. Parameters in the analytical expression can be extracted by simple numerical simulations. We reveal that it is the phase shift between the two adjacent PC defects that uniquely determines the flatness of the impurity bands of CCWs. In addition, it is found that the phase shift also greatly affects the bandwidth of CCWs. Thus, the engineering of the impurity bands of CCWs can be realized through the adjustment of the phase shift. Based on the theoretical results, an interesting phenomenon in which a CCW acts as a single PC defect and its impurity band possesses a Lorentz lineshape is predicted. Very good agreement between the analytical results and the numerical simulations based on transfer matrix method has been achieved.     

Application of small-roughness perturbation theory to reverberation in range-dependent waveguides

A rough-interface reverberation model is developed for range-dependent environments. First-order perturbation theory is employed, and the unperturbed background medium can be layered and heterogeneous with arbitrary range dependence. To calculate the reverberation field, two-way forward scatter due to the slowly changing unperturbed environment is handled by fast numerical methods. Backscatter due to small roughness superimposed on any of the slowly varying interfaces is handled efficiently using a Monte Carlo approach. Numerical examples are presented to demonstrate the application of the model. The primary purpose of the model is to incorporate relevant physics while improving computational speed.     

A new approach to a global fit of the CKM matrix

We report on a new approach to a global CKM matrix analysis taking into account most recent experimental and theoretical results. The statistical framework (Rfit) developed in this paper advocates frequentist statistics. Other approaches, such as Bayesian statistics or the 95% CL scan method are also discussed. We emphasize the distinction of a model testing and a model dependent, metrological phase in which the various parameters of the theory are estimated. Measurements and theoretical parameters entering the global fit are thoroughly discussed, in particular with respect to their theoretical uncertainties. Graphical results for confidence levels are drawn in various one and two-dimensional parameter spaces. Numerical results are provided for all relevant CKM parameterizations, the CKM elements and theoretical input parameters. Predictions for branching ratios of rare K and B meson decays are obtained. A simple, predictive SUSY extension of the Standard Model is discussed. Received: 18 April 2001 / Published online: 10 August 2001     

Simple global reduction technique based on decomposition approach

Large and complex (nonlinear) models of chemical kinetics are one of the major obstacles in simulations of reacting flows. In the present work a new approach for an automatic reduction of chemical kinetics models, the so-called Global Quasi-Linearization (GQL) method is presented. The method is similar to the ILDM and CSP approaches in the sense that it is based on a decomposition into fast/slow motions and on slow invariant manifolds, but has a global character which allows us to overcome difficulties with the application of slow invariant manifolds and significantly simplifies the construction procedure for approximation of the slow invariant system manifold. The method is implemented within the standard ILDM method and applied to a number of model examples and to a meaningful combustion chemistry model.