一种声速剖面展开的正交基函数获取方法

为了评估经验正交函数(Empirical Orthogonal Functions)在声速剖面的声学反演应用中的可靠性和适用性,降低声速剖面基函数的获取对样本数据的依赖性,提出了一种声速剖面展开的正交基函数的获取方法.该方法通过分析引起声速剖面变化的海洋动力学过程,利用动力学方程求解得到的水动力简正波(Hydrodynamic Normal Modes)来给出声速剖面展开的基函数.HNMs方法获得的声速剖面正交基函数与EOFs方法的结果非常吻合,且对样本数据的依赖性小。HNMs方法物理意义清晰,能够给出决定声速剖面正交基函数的物理参数,使评估经验正交函数的准确性和适用性成为可能。      

Tracking-positioning of sound speed profiles and moving acoustic source in shallow water

An ensemble Kalman filter(EnKF) approach is proposed to perform sequential tracking of water column sound speed profile(SSP) using a moving acoustic source. First,the SSPs are discretized in depth and range, and are expressed by the empirical orthogonal functions(EOFs). Second, the acoustic source state information and the first three orders of EOF coefficients are expressed as the state variable, and the acoustic field information received by the vertical line array are the measured values. Successively, the state variables and measured values are used to establish the state-measure model. Last, the EnKF is utilized to track the state variables. The simulation results show that the root mean square error of SSP and the absolute error of source are all small, and thus the acoustic source tracking-positioning has high accuracy. Moreover, increasing the number of sample collection, the signal-to-noise ratio and the number of receiving elements can improve the tracking-positioning results. The method is verified using the experimental data of the East China Sea.     

南海北部海域声速剖面水平变化环境声学层析

为获取水平变化的海水声速分布,在等效平均海水声速反演基础上,提出了一种声速剖面水平变化环境声学层析方法。首先利用经验正交函数结合匹配场处理方法反演不同距离下的等效平均声速剖面,进而通过逐步迭代重构出随水平距离变化的声速场分布,并通过数值仿真及海上实验两方面验证了声速剖面水平变化环境声学层析方法的可行性及其准确性。结果表明:声速剖面水平变化环境声学层析结果与实验测量声速剖面均方根误差小于0.8 m/s,利用声传播信号基本能较为准确地重构出随距离水平变化的海水声速分布,为进一步层析中尺度三维结构及声呐水声环境保障应用奠定了基础。      

浅海时变声速环境下的自适应匹配场定位算法实现*

针对浅海环境下声速剖面失配引起的匹配场处理器失配问题,提出了一种自适应匹配场定位算法在声速剖面时变环境下的实现方式。将先验声速剖面集简化为经验正交函数表示,结合蒙特卡洛方法与环境扰动约束算法对当下时刻的目标声源进行匹配场定位。本文以某次试验获取的连续20小时的声速剖面数据为研究对象,通过仿真试验对该算法进行验证,结果表明：在先验声速剖面集的半小时之后,利用自适应算法的距离和深度定位成功率较常规匹配场算法有较大提升,其中,深度正确定位概率相对较低。     

浅海声速剖面与移动声源的跟踪定位

在水平非均匀分布的浅海环境中,针对移动声源跟踪时,声速剖面的变化会对声场产生影响,提出了一种利用集合卡尔曼滤波算法的声速剖面跟踪反演和移动声源跟踪定位的方法。首先,将声速剖面进行距离和深度的参数化表示,从而将对声速剖面的跟踪转化为对声速剖面前3阶经验正交函数系数的跟踪;其次,通过将声源状态信息和声速剖面信息表示为状态变量,而将垂直线列阵接收到的声场信息作为测量值建立状态-测量模型,然后利用集合卡尔曼滤波方法对模型状态变量进行跟踪。仿真结果得出:声速剖面跟踪反演的均方根误差和移动声源跟踪定位的绝对误差都非常小,对声源的跟踪定位精度很高。并且通过增加集合样本数、增加接收信号信噪比以及增加接收阵元数目都可以提高跟踪定位结果精度。最后,利用东海实验数据对本方法进行了验证。      

基于类表面等离子体激元的矩形金属光栅色散特性的研究

等离子体激元(surface plasmon polaritons, SPP)因其独特的光学和物理特性, 使其具有诸如透射增强和局域共振等一系列新颖现象, 已成为当前国内外学者研究的热点. 本文对基于类表面等离子体激元(Spoof Surface Plasmons, SSP)的矩形金属光栅色散特性和模式分布进行了研究. 利用本征函数法并结合场匹配条件, 获得了矩形栅表面SSP的场表达式、色散关系和模式分布, 并通过电磁仿真进行了验证. 在此基础上分析了矩形栅各参数对SSP色散及模式分布的影响, 研究结果表明: 由本征函数法获得的SSP色散特性与仿真结果基本符合; 增大金属栅高度或减小排列周期能减小SSP的相速度; 而增大金属栅周期占空比能在一定程度上拓展SSP与电子束互作用的带宽; 改变金属盖板高度对慢波SSP色散模式基本没有影响; 减小金属栅侧面宽度能增大模式之间的间隔, 从而能有效避免模式竞争的发生. 本文对基于SSP的矩形金属光栅色散特性的研究将为进一步研究SSP与电子束的相互作用, 形成高效、宽带的新型太赫兹源奠定良好的理论基础.     

New reconstruction and forecasting algorithm for TEC data

To reconstruct the missing data of the total electron content(TEC) observations, a new method is proposed, which is based on the empirical orthogonal functions(EOF) decomposition and the value of eigenvalue itself. It is a self-adaptive EOF decomposition without any prior information needed, and the error of reconstructed data can be estimated. The interval quartering algorithm and cross-validation algorithm are used to compute the optimal number of EOFs for reconstruction.The interval quartering algorithm can reduce the computation time. The application of the data interpolating empirical orthogonal functions(DINEOF) method to the real data have demonstrated that the method can reconstruct the TEC map with high accuracy, which can be employed on the real-time system in the future work.     

An eigen-based high-order expansion basis for structured spectral elements

We present an eigen-based high-order expansion basis for the spectral element approach with structured elements. The new basis exhibits a numerical efficiency significantly superior, in terms of the conditioning of coefficient matrices and the number of iterations to convergence for the conjugate gradient solver, to the commonly-used Jacobi polynomial-based expansion basis. This basis results in extremely sparse mass matrices, and it is very amenable to the diagonal preconditioning. Ample numerical experiments demonstrate that with the new basis and a simple diagonal preconditioner the number of conjugate gradient iterations to convergence has essentially no dependence or only a very weak dependence on the element order. The expansion bases are constructed by a tensor product of a set of special one-dimensional (1D) basis functions. The 1D interior modes are constructed such that the interior mass and stiffness matrices are simultaneously diagonal and have identical condition numbers. The 1D vertex modes are constructed to be orthogonal to all the interior modes. The performance of the new basis has been investigated and compared with other expansion bases.     

Application of the RBF meshless method to the solution of the radiative transport equation

In this paper, we introduce a radial basis function collocation method for computing solutions to the time-dependent radiative transfer equation. For these computations, we use finite differences to discretize the time coordinate, a discrete ordinate method to discretize the directional variable, and an expansion in radial basis functions to approximate the spatial dependence of the solution. The main advantages of the RBF method are that it does not require any mesh or grid, achieves spectral accuracy in multi-dimensions for arbitrary node layouts, and it is extremely simple to implement.     

A three-dimensional frequency selective structure based on the modes coupling of spoof surface plasmon and waveguide transmission

A three-dimensional frequency selective structure (3D FSS) was proposed by applying the spoof surface plasmon (SSP) structures into periodic waveguides, which realizes an enhanced broadband transmission in low frequencies, below the cut-off frequency of periodic waveguides. The transmission characteristics of SSP structures and periodic waveguides as well as their coupling modes are investigated by simulation and experiment method. According to our analysis, the pass-band of this 3D FSS can be customized through changing the values of structure parameters and it also has a good angular stability. In addition, this paper also provides a simple assembly plan for sample preparation. This proposal may be useful for improving filtering performances and gives an effective approach for designing 3D FSSs.     

On the applicability of a spherical basis for spheroidal layered scatterers

The applicability of an analog of the extended boundary condition method, which is popular in light-scattering theory, is studied in combination with the standard spherical basis for the solution of an electrostatic problem appearing for spheroidal layered scatterers the sizes of which are small as compared to the incident radiation wavelength. In the case of two or more layers, polarizability and other optical characteristics of particles in the far zone are shown to be undeterminable if the condition under which the appearing systems of linear equations for expansion coefficients of unknown fields are Fredholm systems solvable by the reduction method is broken. For two-layer spheroids with confocal boundaries, this condition is transformed into a simple restriction on the ratio of particle semiaxes a/b< $\sqrt 2 $ + 1. In the case of homogeneous particles, the solvability condition is that the radius of convergence of the internal-field expansion must exceed that of the expansion of an analog of the scattering field. Since homogeneous spheroids (ellipsoids) are unique particles inside which the electrostatic field is homogeneous, it is shown that the solution can be always found in this case. The obtained results make it possible to match in principle the results of theoretical and numerical determinations of the domain of applicability for the extended boundary condition method with a spherical basis for spheroidal scatterers.     

The calculation of reactions of the type (a,ab) using the plane-wave expansion method: (I). General formalism for the direct one-step process

A formalism for the evaluation of the transition matrix element for reactions of the type (a, ab) in the direct distorted-wave approximation is presented. The plane-wave expansion method is used to represent the optical model wave function for the entrance and exit channels. Because of the use of the plane-wave expansion method the completely off-the-energy-shell behavior is easily demonstrated when distorted waves are used. The use of this expansion method also shows how difficult it is to extract the momentum dependence of the bound particle. We also apply the plane-wave expansion method to evaluate the transition matrix element for the effective f-operator DWTA approach. We also discuss an approximation to the complete transition matrix element which seems equivalent to the DWTA but yet makes use of completely off-the-energy-shell matrix elements.     

半空间球面波函数叠加法重构声源直接辐射声场

提出了基于半空间球面波函数叠加的声场重构方法,以重构含有限声阻抗边界半空间中声源直接辐射的声场。在半空间中多极子声源声压场的解析解的基础上,构造出以边界声阻抗为参量的半空间球面波函数的正交基;通过求逆获得半空间总声压解的基函数系数,同时也获得声源直接辐射声场即自由空间中的基函数系数,进而重构出声源直接辐射的声场。在边界声阻抗已知和边界声阻抗未知两种条件下,对该方法进行了仿真验证和参数分析,并在全消声室内进行了实验验证。结果表明,所提方法能重构出半空间中典型声源即球形声源和平面声源的直接辐射声场;该方法在边界声阻抗已知时的重构精度与稳定性高于在边界声阻抗未知时的情形。      

Testing the fidelity of Gaussian processes for cosmography

The dependence of implications from observations on cosmological models is an intractable problem not only in cosmology, but also in astrophysics. Gaussian processes(GPs), a powerful nonlinear interpolating tool without assuming a model or parametrization, have been widely used to directly reconstruct functions from observational data(e.g., expansion rate and distance measurements) for cosmography. However, the fidelity of this reconstructing method has never been checked. In this study, we test the fidelity of GPs for cosmography by mocking observational data sets comprising different number of events with various uncertainty levels. These factors are of great importance for the fidelity of reconstruction. That is, for the expansion rate measurements, GPs are valid for reconstructing the functions of the Hubble parameter versus redshift when the number of observed events is as many as 256 and the uncertainty of the data is ～3%. Moreover, the distance-redshift relation reconstructed from the observations of the upcoming Dark Energy Survey type la supernovae is credible.     

On the thermal stability of the cobalt nanostructure formed under severe plastic deformation

The results of the investigations of the temperature dependence of thermal expansion of nanostructured cobalt have been presented. It has been shown that deformation nanostructuring results in the nonlinear behavior of the cobalt thermal expansion curve, and the manifestation of a stepwise sample elongation in the phase transformation temperature range in this curve disappears. It has been found that the sample length at room temperature changes after cycles of heating to various temperatures. Based on the results obtained and X-ray diffraction data, it has been demonstrated that there is a correlation of these changes with recovery and recrystallization processes.     

Adequate representation of the dipole moment function for diatomic molecules and the matrices of vibration-rotation transition moments

An exponential representation of perturbations is used as a basis of the perturbed Morse oscillator approach which is applied, in a matrix form, for calculating the radial matrix elements for diatomic molecules. An analytic procedure is developed to deduce an exponential-power series expansion for the dipole moment function M(r) from experimental spectral intensities. It is shown that for real anharmonic molecules, the series expansion in powers of e^ar (α being the Morse parameter) is an adequate form for representing transition operators, just as the usual series expansion in powers of internuclear distance r is adequate for the case of a harmonic oscillator, and it is equivalent to a series expansion in vibrational wavefunctions. An exponential-power series expansion is derived as well for a model dipole moment function which has a correct long-range dependence and limit. To exemplify the accuracy and efficiency of the technique proposed, the (40 × 40) matrices of vibration-rotation transition moments 〈vJ|M(r)|v′J′〉(v, v′ = 0, 1, …, 39) have been calculated for the ground state of CO. Typical results of these computations are presented (up to v = 35, J = 100, and v′ ? v = 1–4) to illustrate the dependence of vibration-rotation interaction functions on the vibrational and rotational quantum numbers.     

A Haar-like Construction for the Ornstein Uhlenbeck Process

The classical Haar construction of Brownian motion uses a binary tree of triangular wedge-shaped functions. This basis has compactness properties which make it especially suited for certain classes of numerical algorithms. We present a similar basis for the Ornstein-Uhlenbeck process, in which the basis elements approach asymptotically the Haar functions as the index increases, and preserve the following properties of the Haar basis: all basis elements have compact support on an open interval with dyadic rational endpoints; these intervals are nested and become smaller for larger indices of the basis element, and for any dyadic rational, only a finite number of basis elements is nonzero at that number. Thus the expansion in our basis, when evaluated at a dyadic rational, terminates in a finite number of steps. We prove the covariance formulae for our expansion and discuss its statistical interpretation. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Determination of orientation distribution function of anisotropic paramagnetic species by analysis of ESR spectra angular dependence

A method has been developed to determine orientation distribution function (ODF) of anisotropic paramagnetic species by analysis of the angular dependence of the ESR spectra. The method is based on computational spectra simulation. The ODF is represented as an expansion in terms of orthonormal functions. The expansion coefficients are determined through minimization of discrepancies between simulated spectra and experimental ones. By means of the suggested method we have determined the orientation distribution functions for radical probe 2,2,6,6-tetramethyl-4-ol-piperidinooxyl in 4-n-amyl-4'-cyanobiphenyl aligned by magnetic field and 2-septadecyl-2,3,4,5,5-pentamethylimidazolidine in polyethylene stretched films. In each case, thermal evolution of the ODF has been investigated.     

采用振速测量的改进统计最优近场声全息方法

针对常规统计最优近场声全息在空间多源声场重建过程中所需波函数项数多、重建精度不理想的问题,本文提出了一种基于振速测量的改进统计最优近场声全息算法。与常规算法不同,改进算法主要根据声源特点选取合适的波函数组合来计算声场传递矩阵。通过数值仿真初步验证了该方法的准确性和有效性,并与常规算法进行了详细的对比分析。仿真结果表明,改进算法重建精度高,随频率的变化相对误差波动较小,且随着频率的增大相对误差有逐渐减小的趋势;此外,不同的波函数组合,重建效果差异很大,当选取的波函数与声源共形且数量一致时重建效果最好。     

基于基函数展开方法处理具有陡峭界面的Abel反演问题

在激光聚变研究中,存在大量具有陡峭不连续界面特性的靶丸等离子体诊断问题,需要借助Abel反演方法对结果进行分析。 提出了一种基于基函数展开处理不连续径向分布的Abel反演方法,采用带约束的Landweber迭代法求得优化结果。利用该算法可以对不连续阶跃分布进行比较准确的反演,获得阶跃结构特征。在理想情况下,针对不连续阶跃分布的反演方差好于10-4,即使在存在一定噪声的情况下也仍然可以获得较好的结果。该方法可用于对激光聚变研究中压缩过程中球壳的背光照相、自发光成像、光谱测量等诊断结果的数据分析。