四色问题反例研究与民航空域频率覆盖

用Tait方法证明了Heawood反例是四色的;用Kempe链方法证明了Tutte反例也是四色的。讨论了民航空域覆盖的四色模型。

Kempe链的研究与民航空域频率覆盖重构

本文给出了构建Kempe链的算法,用Kempe链方法证明了Heawood反例是四色的,探讨了基于Kempe链模型的民航空域频率覆盖重构的可能性。

空域频谱分析及在齿轮传动系统诊断中的应用

根据空域转矩数据采集的特点，提出了以空间位移坐标代替时间坐标对传动系统的空域转矩进行频谱分析的方法，包括频谱分析及其相关频率计算公式、空域频谱的后处理、特征向量及其与传动系统结构参数的对应关系、应用方法等。

基于空域转矩的齿轮传动系统分析方法

根据空域转矩采集的特点，提出了以空间位移坐标代替时间坐标对齿轮传动系统空域转矩进行频谱分析的方法，即频谱分析及其相关频率计算公式、空域频谱的后处理、特征向量及其与传动系统结构参数的对应关系、应用方法等。该分析方法特别适合于旋转类机械系统如齿轮传动系统的智能诊断或性能分析的计算机自动实现。

3D anisotropic modeling and identification for airborne EM systems based on the spectral-element method

The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element （SE） method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell＇s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.

机载柱形共形阵低空风切变风速估计方法

针对机载柱形共形阵气象雷达在探测低空风切变时,有用信号会受到强地杂波影响的问题,提出了一种机载柱形共形阵体制下的低空风切变风速估计方法。该方法首先从柱形共形阵特殊阵列流型引起杂波抑制困难的本质原因出发,利用空域角频率补偿法对各个距离单元的回波数据进行补偿,获得多个独立同分布(Independent and Identically Distributed,IID)的样本后估计杂波协方差矩阵,然后构造适用于低空风切变目标的空时自适应(Space-Time Adaptive Processing,STAP)处理器,在自适应抑制地杂波的同时积累风切变信号,最终实现风场速度的精确估计。仿真结果表明,该方法可有效实现地杂波的抑制并精确地估计风速。

2.5D forward modeling and inversion of frequency-domain airborne electromagnetic data

Frequency-domain airborne electromagnetics is a proven geophysical exploration method.Presently,the interpretation is mainly based on resistivity-depth imaging and onedimensional layered inversion;nevertheless,it is difficult to obtain satisfactory results for two- or three-dimensional complex earth structures using 1D methods.3D forward modeling and inversion can be used but are hampered by computational limitations because of the large number of data.Thus,we developed a 2.5D frequency-domain airborne electromagnetic forward modeling and inversion algorithm.To eliminate the source singularities in the numerical simulations,we split the fields into primary and secondary fields.The primary fields are calculated using homogeneous or layered models with analytical solutions,and the secondary（scattered） fields are solved by the finite-element method.The linear system of equations is solved by using the large-scale sparse matrix parallel direct solver,which greatly improves the computational efficiency.The inversion algorithm was based on damping leastsquares and singular value decomposition and combined the pseudo forward modeling and reciprocity principle to compute the Jacobian matrix.Synthetic and field data were used to test the effectiveness of the proposed method.

2-D elastic wave modeling with frequency-space 25-point finite-difference operators

Numerical simulation in the frequency-space domain has inherent advantages, such as： it is possible to simulate wave propagation from multiple sources simultaneously; there are no cumulative errors; only the interesting frequencies can be selected; and it is more suitable for wave propagation in viscoelastic media. The only obstacle to using the method is the requirement of huge computer storage. We extend the compressed format for storing the coefficient matrix. It can reduce the required computer storage dramatically. We get the optimal coefficients by least-squares method to suppress the numerical dispersion and adopt the perfectly matched layer （PML） boundary conditions to eliminate the artificial boundary reflections. Using larger grid intervals decreases computer storage requirements and provides high computational efficiency. Numerical experiments demonstrate that these means are economic and effective, providing a good basis for elastic wave imaging and inversion.

Non-spreading Bessel spatiotemporal optical vortices

Non-spreading nature of Bessel spatiotemporal wavepackets is theoretically and experimentally investigated and orders of magnitude improvement in the spatiotemporal spreading has been demonstrated.The spatiotemporal confinement provided by the Bessel spatiotemporal wavepacket is further exploited to transport transverse orbital angular momentum through embedding spatiotemporal optical vortex into the Bessel spatiotemporal wavepacket, constructing a new type of wavepacket: Bessel spatiotemporal optical vortex. Both numerical and experimental results demonstrate that spatiotemporal vortex structure can be well maintained and confined through much longer propagation. High order spatiotemporal optical vortices can also be better confined in the spatiotemporal domain and prevented from further breaking up, overcoming a potential major obstacle for future applications of spatiotemporal vortex.

Area spectra of BTZ black holes via periodicity

Motivated by the recent work that the periodicity of a black hole is responsible for the area spectrum,we exclusively utilize the period of motion of an outgoing wave,which is shown to be related to the vibrational frequency of the perturbed black hole,to study area spectra of a non-rotating BTZ black hole and a rotating BTZ black hole.It is found that the area spectra and entropy spectra for both space times are equally spaced.In addition,we find that though the entropy spectra of the 3-dimensional BTZ black holes take the same form as those of the 4-dimensional black holes,the area spectra depend on the dimension of space times.Our result confirms that the entropy spectrum of a black hole is more fundamental than the area spectrum.