地球与月球关系的研究

基于鹦鹉螺外壳生长线条数的变化是月亮绕地球运动周期随年代变化反映的假设, 采用外推 法得出两个结论: (1) 月球最初被地球俘获绕地球运动时距地球的距离为目前月地距离的0.2 倍左右; (2) 月球最初被地球俘获绕地球运动时的时间距今为7亿年左右. 这 为进一步研究地球与月球的关系提供了有益的启示.     

犯罪信息网络分析与建模

基于2012年美国数学建模C题的数据,利用83人共15个种类的600条信息进行了犯罪信息网络分析,建立了概率网络模型和最短路径模型,设计了相应的求解算法,对所有人的可疑度进行了评价和排序,找出通信网络中的可疑嫌犯,并对两个模型进行了对比。然后基于中心性理论建立了识别嫌犯领导人的模型,得到犯罪集团中最可能的领导人。最后讨论了文本分析、语义网络分析方法在犯罪信息网络分析中的应用,并对模型在其他领域推广应用的可行性进行了探讨。     

SOME PROBLEMS WITH THE METHOD OF FUNDAMENTAL SOLUTION USING RADIAL BASIS FUNCTIONS

The present work describes the application of the method of fundamental solutions (MFS) along with the analog equation method (AEM) and radial basis function (RBF) approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson's equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition (SVD) technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric (MQ) are fully analyzed to provide useful reference.     

GUIDED CIRCUMFERENTIAL WAVES IN DOUBLE-WALLED CARBON NANOTUBES

A model of guided circumferential waves propagating in double-walled carbon nan- otubes is built by the theory of wave propagation in continuum mechanics,while the van der Waals force between the inner and outer nanotube has been taken into account in the model.The dispersion curves of the guided circumferential wave propagation are studied,and some dispersion characteristics are illustrated by comparing with those of single-walled carbon nanotubes.It is found that in double-walled carbon nanotubes,the guided circumferential waves will propagate in more dispersive ways.More interactions between neighboring wave modes may take place.In particular,it has been found that a couple of wave modes may disappear at a certain frequency and that,while a couple of wave modes disappear,another new couple of wave modes are excited at the same wave number.     

Generating of Conditionally Exactly Soluble Potentials by Method of Supersymmetric Quantum Mechanics

This paper suggests a systematic method based on supersymmetric quantum mechanics for generating conditionally exactly soluble potentials,and uses the variational supersymnetric WKB method to obtain the approximate wlues of the energy spectrum of the whole class.     

Low-Resistant Band-Passing Noise and Its Dynamical Effects

We propose an n-order noise, which is realized by driving an n-order linear differential equation with a Gaussian white noise. The time-derivative noise is a low-resistant band-passing noise. If the derivative noise is regarded as a thermal one, the system has a vanishing effective friction and it should induce ballistic diffusion of a free particle at long times. The simulation method for the generalized Langevin equation driven by the n-order noise is discussed systematically. The features of three-order derivative noises are presented when they are applied to a ratchet system.     

Analytical and Numerical Studies for Chaotic Dynamics of a Duffing Oscillator with a Parametric Force

The chaotic dynamics of a Duffing oscillator with a parametric force is investigated. By using the direct perturbation technique, we analytically obtain the general solution of the 1st-order equation. Through the boundedness condition of the general solution we get the famous Melnikov function predicting the onset of chaos. When the parametric and external forces are strong, numerical simulations show that increasing the amplitude of the parametric or external force can lead the system into chaos via period doubling.     

A Novel Method for Preparing Polyurethane Based Conductive Composites with Low Percolation Threshold

A novel method for preparing conductive carbon black filled polymer composites with low percolation threshold from polyurethane emulsion are reported in this paper. The experimental results indicate that with a rise in carbon black concentration the insulator-conductor transition in the emulsion blended composites occurs at 0.8-1.4vol%. In contrast, the solution blended composites exhibit drastic increase in conductivity at conducting filler fraction as high as 12.3-13.3vol%. It is demonstrated that the composites microstructure rather than chemical structure of the matrix polymer predominantly determines the electrical conduction performance of the composites.