A Note on the Legendre Series Solution of the Biharmonic Equation for Cylindrical Problems

The solution of cylindrical problems is addressed. A series solution is considered of the biharmonic equation, in which the series terms of the stress function Φ are expressions based upon Legendre polynomials and logarithmically singular functions. An explicit form of a polynomial supplementing each logarithmically singular part of the series solution is obtained.     

An Incompressible Fluid in a Weakly Deformable Shell. Part I: Analysis of the Model

We consider the flow of a viscous incompressible fluid in a pipe when the boundary is a deformable shell of Naghdi type. We prove that the corresponding system of partial differential equations has a solution when the deformation of the shell is smooth and small enough. We propose an algorithm that uncouples the unknowns and prove its convergence.     

Existence of Surface Waves and Band Gaps in Periodic Heterogeneous Half-spaces

We find a sufficient condition for the existence of surface (Rayleigh) waves based on the Rayleigh-Ritz variational method. When specialized to a homogeneous half-space, the sufficient condition recovers the known criterion for the existence of subsonic surface waves. A simple existence criterion in terms of material properties is obtained for periodic half-spaces of general anisotropic materials. Further, we numerically compute the dispersion relation of the surface waves for a half-space of periodic laminates of two materials and demonstrate the existence of surface wave band gaps.     

Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.     

A comparison of master equation and Fokker-Planck equation in the thermodynamic limit

The master equation and the Fokker-Planck equation are compared thoroughly in both of the stationary and the time-dependent cases for a one-dimensional system. The comparison includes the master equation without detailed balance.     

小型13C NMR谱图数据库

本文着重介绍用当前微机系统上流行的DBASEⅡ建立谱图数据库以及用BASIC语言进行结构检索的方法。检索系统能方便地提供用户收集、修正、查询、显示和打印谱图数据和分子结构图的功能。这种系统对建立专用的小型谱图数据库有实用价值。     

予条件共轭梯度法的收敛性

本文对某些予条件共轭梯度法的收敛性进行了一些分析,如ICCG法,ILUCK(K)法、ILUCG(P)法及所谓的"TCG法",其中用了许多分裂作为对所要解的线性代数方程组的系数矩阵A进行予条件的工具,这里设A为对角优势矩阵,文中还给出了若干数值算例来说明我们分析的结果。     

基于4，8-二氢二呋咱[3，}4-b，e]吡嗪高能材料的设计与筛选

为了寻找高能量密度的材料,本文设计了一系列基于4,8-二氢二呋咱[3,4-b,e]吡嗪的含能材料. 利用密度泛函理论研究了它们结构与性质之间的关系. 结果表明,这些设计化合物的性质受到含能基团和杂环取代基的影响. -N₃含能基团是提高设计化合物生成热的最有效取代官能团,而四唑环/-C(NO₂)₃基团对炸药的爆轰性能有较大贡献. 键解离能分析表明,引入-NHNH₂,-NHNO₂,-CH(NO₂)₃和-C(NO₂)₃基团会显著降低键解离能. 由于化合物A8,B8,C8,D8,E8和F8具有良好的爆轰性能和热稳定性,最终被筛选为潜在的高能密度材料. 此外,还计算了这些筛选化合物的电子结构.