Spectral approximations of the Stokes problem by divergence-free functions

The method of Moser, Moin, and Leonard (1983) for the approximation of the three-dimensional Navier-Stokes equations using divergence-free subspaces is revisited and analyzed. It is shown that the computed velocity field converges to the physical one with spectral accuracy. Moreover, a method for recovering the pressure field is proposed. This method is stable and provides a pressure that converges to the physical one with spectral accuracy.     

光纤光栅最佳切趾函数的研究

采用耦合模理论，给出了用传输矩阵法计算光纤Bragg光栅（FBG）特性的方法，进而得到了在不同切趾函数形式下的FBG反射谱的数值解。通过理论分析，给出了最佳切趾函数反射谱和群时延特性曲线。     

一种实用的内插FFT信号处理方法

基于信号样本可以重建信号频谱包络,本文提出一种简单、实用的内插方法,将此方法的有效性和FFT的优越性结合起来应用于细化频率分辨率,以适应需要获取信号较多频谱信息的应用场合。     

套管井自然伽马能谱测井资料的应用分析

自然伽马能谱测井是一种新的测井方法。该文主要针对胜利油田的多个油区的套管井自然伽马能谱测井资料的应用实例进行了分析，指出它在开发过程中对研究管外窜槽、注水层的吸水量、判断水淹层和划分水淹级别、划分储集层和判断储集层性质、划分油层中的泥岩夹层、确定泥质含量及粘土类型等方面的重要作用。在综合其它测井方法后，能对研究储层变化、寻找剩余油分布等提供重要的手段。     

环形孔径对部分相干光光谱的影响

本文推导了部分相干光在经过环形孔径之后,远场轴上点的光谱S(ω)与环形孔径处光的光谱S~(0)(ω)之间的关系。数值计算结果表明,S(ω)不仅依赖于S~(0)(ω),而且还与环形孔径处光的相干性以及环形孔径的参数有关。     

最佳相位设计的MBE声码器语音合成

提出了一种基于最佳相位设计的语音合成技术,能够有效降低MBE声码器合成语音信号由于波形失衡而导致的饱和失真的概率.此外,为了保证合成滤波器的稳定性,对线谱频率(LSF)系数提取进行了优化.实验结果显示,合成语音信号波形近似平衡地分布在零幅度值的上下,语音听起来没有不舒服的感觉.实验结果表明,基于最佳相位设计的语音合成技术能够有效改善合成语音质量.     

波谱匹配支持的遥感专题地物自适应提取

为贴合地物表现的多样性和复杂性,提出一种波谱匹配支持下的遥感影像专题地物自适应提取方法,经过专题地物端元选取、波谱匹配、影像自动分割、"整体-局部"的空间转换,以及局部针对性、精细化地迭代逼近等一系列相互衔接的算法,全面、准确地提取遥感影像上的专题地物。通过在ETM+影像上水体和裸地的提取实验,并与最大似然法和SVM分类结果比较,证明了该方法对多样性专题地物提取的有效性和普适性。     

Energy and spectral dynamics in decaying compressible turbulence

The statistical properties of decaying compressible turbulence are investigated by direct numerical simulations of flow in a periodic cube. Starting with fully developed turbulence for various microscale Reynolds numbersR , rms Mach numbersM, and small- and large-scale compressive ratiosr _CS andr _CL , we find that the kinetic energy exhibits an exponential decay in time. Interactions between the compressive and rotational components of kinetic energy are weaker than self-interactions of the respective components. The energy spectrum of rotational component obeys the same Kolmogorov similarity law as for incompressible turbulence and forced compressible turbulence. The form of the energy spectrum of the compressive component, on the other hand, depends strongly onM. As the turbulence decays freely,R andM decrease in time butr _CS andr _CL tend to some universal values.     

近邻自适应局部尺度的谱聚类算法

提出一种在LUV空间中基于多层次化结构Nystrm方法的自适应谱聚类算法。首先引入LUV色彩空间,避免了RGB色彩空间中色彩辨别阈对分割的影响,在纹理、边缘区域取得了更好的分割效果;其次将谱聚类算法中基于多层次化结构的方法和基于Nystrm采样的方法结合起来,有效减少了运算时间、解决了数据量较大时计算过程中内存溢出的问题;最后在K均值聚类中通过对特征间隙(eigengap)的分析,自适应地选择K值的大小,解决了自动确定聚类数目的问题。将提出的方法在LUV色彩空间中和RGB色彩空间中分别进行图像分割实验,结果表明在LUV色彩空间中取得效果更加理想。同时也将提出的算法与基于Nystrm方法的谱聚类算法(spectral clustering-Nystrm,SC-N)进行比较。实验结果表明,该算法在数据运算量、运行时间和分割结果上都优于SC-N方法。     

An analytical and numerical study of the two-dimensional Bratu equation

Bratu's problem, which is the nonlinear eigenvalue equationu+ exp(u)=0 withu=0 on the walls of the unit square and as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance ofsymmetry: because of invariance under the C₄ rotation group and parity in bothx andy, one can slash the size of the basis set by a factor of eight and reduce the CPU time by three orders of magnitude. Second, the pseudospectral method is ananalytical as well as a numerical tool: the simple approximation3.2A exp(–0.64A), whereA is the maximum value ofu(x, y), is derived via collocation with but a single interpolation point, but is quantitatively accurate for small and moderateA. Third, the Newton-Kantorovich/Chebyshev pseudospectral algorithm is so efficient that it is possible to compute good numerical solutions—five decimal places—on amicrocomputer inbasic. Fourth, asymptotic estimates of the Chebyshev coefficients can be very misleading: the coefficients for moderately or strongly nonlinear solutions to Bratu's equations fall off exponentially rather than algebraically withv untilv is so large that one has already obtained several decimal places of accuracy. The corner singularities, which dominate the behavior of the Chebyshev coefficients in thelimit v, are so weak as to be irrelevant, and replacing Bratu's problem by a more complicated and realistic equation would merely exaggerate the unimportance of the corner branch points even more.