On two models in the three-dimensional theory of stability of composites

A comparative analysis is made of the infinite-fiber and finite-fiber models in the three-dimensional theory of stability of composites. The results analyzed have been obtained using the three-dimensional linearized theory of stability of deformable bodies. A historical sketch is given of the theory of stability for and approaches used in the mechanics of laminated and fibrous composite materials Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 3–31, August 2008.     

三维电阻抗成像的体积元方法的数值模拟和分析

电阻抗成像是一类椭圆方程反问题,本文在三维区域上对其进行数值模拟和分析.对于椭圆方程Neumann边值正问题,本文提出了四面体单元上的一类对称体积元格式,并证明了格式的半正定性及解的存在性;引入单元形状矩阵的概念,简化了系数矩阵的计算;提出了对电阻率进行拼接逼近的方法来降低反问题求解规模,使之与正问题的求解规模相匹配;导出了误差泛函的Jacobi矩阵的计算公式,利用体积元格式的对称性和特殊的电流基向量,将每次迭代中需要求解的正问题的个数降到最低.一系列数值实验的结果验证了数学模型的可靠性和算法的可行性.本文所提出的这些方法,已成功应用于三维电阻抗成像的实际数值模拟.     

Assessment of regularized delta functions and feedback forcing schemes for an immersed boundary method

We present an improved immersed boundary method for simulating incompressible viscous flow around an arbitrarily moving body on a fixed computational grid. To achieve a large Courant–Friedrichs–Lewy number and to transfer quantities between Eulerian and Lagrangian domains effectively, we combined the feedback forcing scheme of the virtual boundary method with Peskin's regularized delta function approach. Stability analysis of the proposed method was carried out for various types of regularized delta functions. The stability regime of the 4‐point regularized delta function was much wider than that of the 2‐point delta function. An optimum regime of the feedback forcing is suggested on the basis of the analysis of stability limits and feedback forcing gains. The proposed method was implemented in a finite‐difference and fractional‐step context. The proposed method was tested on several flow problems, including the flow past a stationary cylinder, inline oscillation of a cylinder in a quiescent fluid, and transverse oscillation of a circular cylinder in a free‐stream. The findings were in excellent agreement with previous numerical and experimental results. Copyright © 2008 John Wiley & Sons, Ltd.     

Thermogravimetric Analysis of Aromatic Polyamides with Benzimidazolyl Side Group

The TG studies are presented for isomers of benzimidazolyl-substituted polyamides (BIPA). The TG data are compared with those polyamides (PA) of identical backbones without substitution, in view of the mechanism of thermal degradation. The TG mass loss curves divided to three temperature ranges reflect the decomposition reactions in the respective temperature ranges: (1) cleavage of single bonds of nitrogen to aromatic ring, (2) random scission of single bonds, (3) condensation of the remained rings. Liberation of benzimidazole rings occurs in the temperature range (2). The final product, char, contains benzimidazole rings. Terephthaloyl-rich BIPA's retard liberation of benzimidazole from the decomposed polymer. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kinetic Studies of Bulk Ge22Se78−xBix (x=0, 4 and 8) Semiconducting Glasses

Results of phase transformations, enthalpy released and specific heat of Ge₂₂Se_78–xBi_x(x=0, 4 and 8) chalcogenide glasses, using differential scanning calorimetry (DSC), under non-isothermal condition have been reported and discussed. The glass transition temperature, T _g, is found to increase with an average coordination number and heating rates. Following Gibbs—Dimarzio equation, the calculated values of T _g (i.e. 462.7, 469.7 and 484.4 K) and the experimental values (i.e. 463.1, 467.3 and 484.5 K) increase with Bi concentration. Both values of T _g, at a heating rate of 5 K min^–1, are found to be in good agreement. The glass transition activation energy increases i.e. 102±2, 109±3 and 115±8 kJ mol^–1 with Bi concentration. The demand for thermal stability has been ensured through the temperature difference T _c–T _g and the enthalpy released during the crystallization process. Below T _g, specific heat has been observed to be temperature independent but highly compositional dependent. The growth kinetic has been investigated using the Kissinger, Ozawa, Matusita and modified JMA equations. Results indicate that the crystallization ability is enhanced, the activation energy of crystallization increases with increasing the Bi content and the crystal growth of these glasses occur in 3 dimensions.This revised version was published online in November 2005 with corrections to the Cover Date.     

On the Robustness of Gaussian Elimination with Partial Pivoting

It has been recently shown that large growth factors might occur in Gaussian Elimination with Partial Pivoting (GEPP) also when solving some plausibly natural systems. In this note we argue that this potential problem could be easily solved, with much smaller risk of failure, by very small (and low cost) modifications of the basic algorithm, thus confirming its inherent robustness. To this end, we first propose an informal model with the goal of providing further support to the comprehension of the stability properties of GEPP. We then report the results of numerical experiments that confirm the viewpoint embedded in the model. Basing on the previous observations, we finally propose a simple scheme that could be turned into (even more) accurate software for the solution of linear systems.     

L-拓扑空间中的相对强F紧性与相对超F紧性

In this paper,two concepts of relative compactness-the relative strong fuzzy compactness and the relative ultra-fuzzy compactness are defined in L-topological spaces for an arbitrary L-set.Properties of relative strong fuzzy sets and relative ultra-fuzzy compact sets are studied in detail and some characteristic theorems are given.Some examples are illustrated.     

Polyurethane vascular prostheses in pigs

Microporous, compliant vascular prostheses made from segmented polyurethanes of various molecular stability, have been implanted in the infrarenal aorta of young pigs. Prostheses prepared from a hydrolytically suble polyetherurethane showed a limited patency up to 1 month. Composite prostheses with the wall made from a hydrolytically stable polyurethane and the lumen side prepared from a degradable polyurethane, were patent up to one year. A degradable layer of this composite prosthesis induced the growth of a neo-artery. Prostheses prepared from a degradable polyurethane alone, were substituted within 4 months with a functional neo-artery.Presented in part at the 17th International Biomaterials Symposium, San Diego, California, April 1985.     

Global stability for a class of mass action systems allowing for latency in tuberculosis

A very general compartmental model of the spread of an infectious disease with mass action incidence is given. The global stability of this system is completely determined using Lyapunov functions. The general system exhibits the traditional threshold behaviour. The dimension of the system is arbitrary, allowing, in particular, for detailed modelling of the distribution of latency times for tuberculosis.     

Solubility of copper (I) bromide in aqueous solutions of potassium bromide

The solubilities of cuprous bromide were measured at 24.8°C in aqueous KBr and in aqueous KBr-KNO₃ mixtures. The results have been analyzed to give equilibrium constanns from formation of neutral and negatively charged complexes of CuBr, and sets of virial parameters suitable for calculation of activity coefficients for the complexes.