一维光子晶体缺陷模的偏振特性研究

利用周期结构的布洛赫定理推导了一维无限光子晶体缺陷模方程,研究了缺陷模的偏振特性,以及在不同入射角和缺陷层厚度下缺陷模位置的变化.利用传输矩阵方法对有限周期数光子晶体也进行了研究,分别对应一维无限光子晶体和有限周期数光子晶体给出了数值计算结果.通过比较这两者的数值结果得出了缺陷模随入射角和缺陷层厚度变化的一般规律.     

引力波观测支持黑洞面积定理

黑洞面积定理表明黑洞顺时演化面积不会减小,这被证明与热力学第二定律相对应.注意到LIGO近来的4次引力波观测数据均来自双黑洞的融合过程,进而本文利用这些观测数据对面积定理进行验证.结果显示该4次观测结果均支持黑洞面积定理.此外,本文也从理论上给出了N个黑洞融合时面积定理的等价表述.     

基于波传播法的周期复合板振动带隙衰减特性研究

运用波传播法对有限和无限周期对边简支复合板的振动带隙衰减特性进行了研究.在建立相邻板结构边界连续方程的基础上, 分别运用传递矩阵和Bloch定理建立了有限和无限周期复合板的耦合运动方程, 并详细对比分析了有限和无限周期复合板带隙衰减特性的关联关系.研究表明: 周期板结构的振动带隙频率范围与激励方式和激励位置是相关的, 若周期复合板在宽度方向按某阶模态进行线激励, 则该激励下的振动带隙与无限周期复合板在该阶模态下的振动带隙是一致的; 若周期板在点激励作用, 则该点激励下的振动带隙是参与振动的各阶模态振动带隙的交集. 此外, 还进一步研究了结构阻尼对振动衰减带隙的影响. 关键词： 周期复合板 带隙衰减特性 波传播法 结构阻尼     

基于multisine激励与整周期采样的多频电阻抗成像系统设计

本文从周期信号的整周期采样无频谱泄露这一原理出发,提出基于multisine信号的整周期采样理论,从理论上推导出满足multisine整周期采样的采样率设置条件,构建了基于FPGA+数模转换器+模数转换器的整周期采样实现方法,研制了一种基于multisine激励和整周期采样的新型多频电阻抗成像(mfEIT)系统;设计了胡萝卜棒+黄瓜棒的双目标成像模型,并进行了多频时差成像和频差成像实验.实验表明,本mfEIT系统能够在一个基波周期(1 ms)内实现20个频率点(2—997 kHz)多目标组织边界的全频阻抗测量,成像结果可区分具有不同电特性生物组织的结构与位置.本文提出的基于multisine信号的整周期采样理论及其实现方法,只需一个multisine基波周期即可完成一次全频阻抗测量,为研制高速mfEIT系统奠定了理论和技术基础.     

两类单负材料组成的一维半无限光子晶体反射谱

运用传输矩阵方法和Bloch定理计算了两类单负材料组成的一维半无限光子晶体反射谱,与有限多层结构通带中振荡的反射谱相比,半无限结构的反射谱曲线是光滑的,是有限周期结构反射谱振幅取平均的结果,可用来估计通带中的反射率.研究半无限结构的反射谱,有利于分析带隙的位置和宽度,结果表明,由两类单负材料组成的光子晶体中,不仅存在零有效位相带隙,还存在角度带隙,尤其发现高频处的Bragg带隙也是一个全方位带隙.     

空气阻力与球体运动速度的函数关系

通过研究乒乓球在空气阻力和重力作用下的一维落体及多次反弹运动,探索轻质量球体在运动过程中所受到的空气阻力与运动速度的函数关系.设空气阻力f=kvα,k和α待定,选定多组(kl,αl)值分别求解球体运动的动力学方程,得到多组球体位移随时间演化的函数关系,分别计算出每个函数关系对应的球体多次落地时刻tln及反弹高度hln,与实验观测得到的球体落地时刻tsn及反弹高度hsn比较,从多组(kl,αl)对应的理论计算数据{(tln,hln)}中选出最接近实验数据的一组{(tsn,hsn)}值,它对应的(kn,αn)值,就决定了球体运动所受阻力随速度变化的规律f=knvan.     

囚禁有限unitary费米气体的热力学性质

应用分数不相容统计,研究了三维简谐势阱中有限unitary费米气体在绝对零度和有限温度下的热力学性质,并与势阱中满足热力学极限条件的unitary费米气体进行了比较.结果表明:绝对零度时有限系统的费米能、粒子平均能量随粒子数的增加而增大,并以满足热力学极限系统的对应物理量为上限,有限系统的费米能、粒子平均能量随势阱边界变化存在极大值.有限温度条件下给定粒子数时,有限系统的粒子平均能量、粒子平均熵、粒子平均热容量分别存在对应的特征温度,当温度等于物理量对应的特征温度时,有限系统与满足热力学极限系统的同一物理量相等,低于(或高于)物理量对应的特征温度时,有限系统的物理量将大于(或小于)满足热力学极限系统的同一量.给定温度条件下,有限系统粒子平均能量、粒子平均熵、粒子平均热容量分别存在对应的特征粒子数,当粒子数等于物理量对应的特征粒子数时,有限系统与满足热力学极限系统的同一物理量相等,少于(或多于)物理量对应的特征粒子数时,有限系统的物理量将小于(或大于)满足热力学极限系统的同一量.     

粒子数密度对飞秒Gauss型脉冲传播及光谱特性的影响

利用预估校正-时域有限差分(PC-FDTD)法求解全波Maxwell-Bloch方程,研究介质粒子数密度(N)对飞秒Gauss型激光脉冲在Λ型三能级原子介质中传播及光谱特性的影响.结果表明:小面积2π脉冲在不同N介质中都不发生分裂,脉冲频谱基本没有新的高频成分产生,随N增大中心频率附近光谱强度明显减小.面积4π脉冲,在N较大的稀疏介质及稠密介质中都产生分裂,在稀疏介质中随N增大频谱展宽幅度及高频成分强度增大,但在稠密介质中频谱展宽变小且远小于N较大时的稀疏介质情况.大面积8π脉冲,脉冲分裂情况与4π脉冲情况相似,但随N增大频谱展宽幅度及高频成分强度单调增大,且在稠密介质中的频谱展宽幅度及高频成分强度远大于N较小的稀疏介质情况.     

量纲方法与Π定理之应用一例——低阻尼RLC电磁振荡周期的二级修正

将量纲理论中的Π定理结合示波器实验观测,应用于低阻尼度情形RLC电磁振荡的瞬态过程的周期公式相对于理想情形的修正的研究;精确地推导其一级修正系数,并预估其二级修正系数及其量级;所得谐振周期的修正公式,与RLC电磁振荡的微分方程的严格解的近似展开的结果正相吻合,最后阐明了应用量纲方法的一般技巧与原则.     

光谱分析采样数据重建原始信号

用光谱分析方法分析信号的采样与恢复。用三个改进的升余弦脉冲构造对称的限带频谱F(ω),经理论推导获得时域信号f(t)。采用梳状函数δ_T(t)对f(t)采样,调节T值,获得Shannon采样。应用快速傅里叶变换,计算采样的频谱F_d(ω),比较计算频谱F_d(ω)与限带频谱F(ω)的差别,讨论由采样频谱F_d(ω)重建f(t)的方法。结果发现：计算频谱F_d(ω)与限带频谱F(ω)非常相似,由采样数据可以在时域直接重建原始信号,而由频谱数据经快速逆傅里叶变换,同样能准确重建原始信号。因此,信号存储,既可以存储其采样信号,也可以存储采样信号的数字频谱。     

Phasing arbitrarily sampled multidimensional NMR data

The recent re-introduction of the two-dimensional Fourier transformation (2D-FT) has allows for the transformation of arbitrarily sampled time domain signals. In this respect, radial sampling, where two incremented time dimensions (t(1) and t(2)) are sampled such that t(1)=taucosalpha and t(2)=tausinalpha, is especially appealing because of the relatively small leakage artifacts that occur upon Fourier transformation. Unfortunately radially sampled time domain data results in a fundamental artifact in the frequency domain manifested as a ridge of intensity extending through the peak positions perpendicular to +/- the radial sampling angle. Successful removal of the ridge artifacts using existing algorithms requires absorptive line shapes. Here we present two procedures for retrospective phase correction of arbitrarily sampled data.     

SEnD NMR: Sensitivity Enhanced n-Dimensional NMR

Sparse sampling offers tremendous potential for overcoming the time limitations imposed by traditional Cartesian sampling of indirectly detected dimensions of multidimensional NMR data. However, in many instances sensitivity rather than time remains of foremost importance when collecting data on protein samples. Here we explore how to optimize the collection of radial sampled multidimensional NMR data to achieve maximal signal-to-noise. A method is presented that exploits a rigorous definition of the minimal set of radial sampling angles required to resolve all peaks of interest in combination with a fundamental statistical property of radial sampled data. The approach appears general and can achieve a substantial sensitivity advantage over Cartesian sampling for the same total data acquisition time. Termed Sensitivity Enhanced n-Dimensional or SEnD NMR, the method involves three basic steps. First, data collection is optimized using routines to determine a minimal set of radial sampling angles required to resolve frequencies in the radially sampled chemical shift evolution dimensions. Second, appropriate combinations of experimental parameters (transients and increments) are defined by simple statistical considerations in order to optimize signal-to-noise in single angle frequency domain spectra. Finally, the data is processed with a direct multidimensional Fourier transform and a statistical artifact and noise removal step is employed.     

Two-dimensional Fourier transform of arbitrarily sampled NMR data sets

A new procedure for Fourier transform with respect to more than one time variable simultaneously is proposed for NMR data processing. In the case of two-dimensional transform the spectrum is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Therefore, it enables one to Fourier transform arbitrarily sampled time domain and thus allows for analysis of high dimensionality spectra acquired in a short time. The proposed method is not limited to radial sampling, it requires only to fulfill the Nyquist theorem considering two or more time domains at the same time. We show the application of new approach to the 3D HNCO spectrum acquired for protein sample with radial and spiral time domain sampling.     

窄带高光谱干涉成像的压缩采样复原方法

利用干涉成像光谱仪对目标进行窄带高光谱成像探测具有高光通量、高光谱分辨率和高目标分辨率等优点。按照尼奎斯特定理对窄带光谱干涉信息进行采样存在较大的数据冗余,增加了后期傅里叶变换的数据处理量,影响光谱的复原效率。在分析窄带光谱傅里叶变换特性的基础上,提出了基于滤光片光谱透射率函数的窄带光谱压缩采样方法。引入滤光片参数和混叠参数,可以复原不同精度的窄带光谱信息。配以符合要求的多带通窄带滤光片,可对目标进行压缩采样获取多个谱段的窄带光谱信息,从而避免了逐个谱段探测,提高了探测效率。对该方法进行了仿真分析和实验验证,得到了与目标光谱相吻合的复原窄带光谱。     

Reconstruction of band-limited signals from multichannel and periodic nonuniform samples in the linear canonical transform domain

Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. This paper addresses the problem of signal reconstruction from multichannel and periodic nonuniform samples in the LCT domain. Firstly, the multichannel sampling theorem (MST) for band-limited signals with the LCT is proposed based on multichannel system equations, which is the generalization of the well-known sampling theorem for the LCT. We consider the problem of reconstructing the signal from its samples which are acquired using a multichannel sampling scheme. For this purpose, we propose two alternatives. The first scheme is based on the conventional Fourier series and inverse LCT operation. The second is based on the conventional Fourier series and inverse Fourier transform (FT) operation. Moreover, the classical Papoulis MST in FT domain is shown to be special case of the achieved results. Since the periodic nonuniformly sampled signal in the LCT has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived MST and the specific space-shifting property of the LCT. Last, the potential applications of the MST are presented to show the advantage of the theory.     

Optimized angle selection for radial sampled NMR experiments

Sparse sampling offers tremendous potential for overcoming the time limitations imposed by traditional Cartesian sampling of indirectly detected dimensions of multidimensional NMR data. Unfortunately, several otherwise appealing implementations are accompanied by spectral artifacts that have the potential to contaminate the spectrum with false peak intensity. In radial sampling of linked time evolution periods, the artifacts are easily identified and removed from the spectrum if a sufficient set of radial sampling angles is employed. Robust implementation of the radial sampling approach therefore requires optimization of the set of radial sampling angles collected. Here we describe several methods for such optimization. The approaches described take advantage of various aspects of the general simultaneous multidimensional Fourier transform in the analysis of multidimensional NMR data. Radially sampled data are primarily contaminated by ridges extending from authentic peaks. Numerical methods are described that definitively identify artifactual intensity and the optimal set of sampling angles necessary to eliminate it under a variety of scenarios. The algorithms are tested with both simulated and experimentally obtained triple resonance data.     

Prony's method applied to estimate noise source locations and their sound powers

An application of Prony's method for evaluating the acoustic power and location of sound sources from spatially sampled data is described. A sound source considered as a point source has an intensity proportional to the inverse square of the distance between source and observation point. The Fourier transform of this intensity function is an exponential function with a real exponent. The shift property of the Fourier transform results in a spectral change in the phase angle, which is expressed in the transform domain by a multiplicative exponential function of pure imaginary exponent. In this paper the usual time axis of the Fourier pair of time and frequency is treated as a variable denoting the location of the sound source. Accordingly, each spectral component of spatially sampled sound intensity generated by n point sources can be expressed as a linear combination of n complex exponentials. By applying Prony's method to the spectral data, these unknown exponents can be calculated numerically. This paper deals with an estimation procedure to find the location and power of a noise source. The estimation is done by minimizing the sum of the squares of the errors between the model and measured data. The proposed method has general applicability to problems where the so-called inverse square law for intensity can be assumed to be valid.     

Compressed sensing with linear-in-wavenumber sampling in spectral-domain optical coherence tomography

We propose a novel method called compressed sensing with linear-in-wavenumber sampling (k-linear CS) to retrieve an image for spectral-domain optical coherence tomography (SD-OCT). An array of points that is evenly spaced in wavenumber domain is sampled from an original interferogram by a preset k-linear mask. Then the compressed sensing based on l1 norm minimization is applied on these points to reconstruct an A-scan data. To get an OCT image, this method uses less than 20% of the total data as required in the typical process and gets rid of the spectral calibration with numerical interpolation in traditional CS-OCT. Therefore k-linear CS is favorable for high speed imaging. It is demonstrated that the k-linear CS has the same axial resolution performance with ～30 dB higher signal-to-noise ratio (SNR) as compared with the numerical interpolation. Imaging of bio-tissue by SD-OCT with k-linear CS is also demonstrated.     

Comparing the geomagnetic thresholds of cosmic rays for two empirical models of the magnetosphere during the period of an extreme geomagnetic storm in November 2003

The accuracy of determining the geomagnetic cutoff rigidity (the geomagnetic threshold) is closely related to that of describing the magnetic field of the magnetosphere with the model used for calculations. Geomagnetic thresholds are calculated for two empirical models of the magnetosphere, Ts0l and Ts04, constructed on the basis of the same initial experimental data. The Ts01 model describes the average magnetosphere for certain conditions in the solar wind and interplanetary field. The Ts01 model focuses on describing the large-scale evolution of magnetospheric currents during a storm. A comparison of the geomagnetic thresholds for Ts0l and Ts04 with experimental thresholds calculated by the Spectrographic Global Survey from data of the CR global network stations shows that the Ts01 model describes the magnetic field of the magnetosphere more realistically. Our study was conducted for the period of a strong geomagnetic storm in November 2003.