MULTIFRACTAL FORMALISMS：BOXED VERSUS CENTERED INTERVALS

There are mainly two approaches to the multifractal analysis of measures. The first one, which is used in applications and in studying problems arising from dynamical systems, uses a hierarchy of boxes. The second one, which is more satisfactory from the viewpoint of geometric measure theory, uses more intrinsicconcepts. This article is an account of a work by J. Barral, F. Ben Nasr, and J. Peyriere [3] which pro-vides a bridge between these two theories.     

Structures of large transition metal clusters

The present review surveys the results of X-ray diffraction studies of large stoichiometric transition metal clusters containing from 20 to 145 atoms in metal cores surrounded by ligand shells (72 compounds). Structures of such clusters have fragments of close packings (face-centered cubic (f.c.c.), hexagonal close (h.c.p.), and body-centered cubic (b.c.c.) packings) characteristic of crystalline bulk metals as well as mixed packings (f.c.c./h.c.p.), local close packings with pentagonal symmetry, and strongly distorted amorphous packings. The observed packing types, their distortions, and the relationship between the atomic structures of metal cores and the atomic radial distribution functions (RDF) are discussed. The structural principles established for the large clusters are applied to analysis of the experimental RDF for metal nanoparticles determined by X-ray diffraction and EXAFS spectroscopy.     

圆截面弹性螺旋杆的稳定性与振动

基于Kirchhoff理论讨论圆截面弹性螺旋杆的动力学问题.以杆中心线的Frenet坐标系为参考系，建立用欧拉角描述的弹性杆动力学方程.讨论其在端部轴向力和扭矩作用下保持的无扭转螺旋线平衡状态.在静力学和动力学领域内讨论其平衡稳定性问题.还讨论了弹性杆平衡的Lyapunov稳定性和欧拉稳定性两种不同稳定性概念之间的区别和联系.在一次近似意义下证明了螺旋杆在空间域内的欧拉稳定性条件是时域内Lyapunov稳定性的必要条件.导出了解析形式螺旋杆三维弯曲振动的固有频率，为螺旋线倾角和受扰挠性线波数的函数. 关键词： 弹性螺旋杆 Kirchhoff动力学比拟 Lyapunov稳定性 欧拉稳定性     

微米BCN棒的制备及相关材料的物理性质

轻元素共价键硼碳氮（ＢＣＮ）化合物随组分和原子环境的变化，表现了由半金属到宽湿润地导体之间可调的物理性质，利用偏压辅助的热丝化学气相沉积方法，成功地制备了直径为２０μｍ、长度为１００μｍ的微米量级ＢＣＮ棒，并进一步研究了它的化学成分和原子键态。     

On hydraulic permeability of random packs of monodisperse spheres: Direct flow simulations versus correlations

Hydraulic permeability is studied in porous media consisting of randomly distributed monodisperse spheres by means of computational fluid dynamics (CFD) simulations. The packing of spheres is generated by inserting a certain number of nonoverlapping spherical particles inside a cubic box at both low and high packing fractions using proper algorithms. Fluid flow simulations are performed within the interparticulate porous space by solving Navier-Stokes equations in a low-Reynolds laminar flow regime. The hydraulic permeability is calculated from the Darcy equation once the mean values of velocity and pressure gradient are calculated across the particle packing. The simulation results for the pressure drop across the packing are verified by the Ergun equation for the lower range of porosities (<0.75), and the Stokes equation for higher porosities (∼1). Using the results of simulations, the effects of porosity and particle diameters on the hydraulic permeability are investigated. Simulations precisely specified the range of applicability of empirical or semi-empirical correlations for hydraulic permeability, namely the Carman-Kozeny, Rumpf-Gupte, and Howells-Hinch formulas. The number of spheres in the model is gradually decreased from 2000 to 20 to discover the finite-size effect of pores on the hydraulic permeability of spherical packing, which has not been clearly addressed in the literature. In addition, the scale dependence of hydraulic permeability is studied via simulations of the packing of spheres shrunk to lower scales. The results of this work not only reveal the validity range of the aforementioned correlations, but also show the finite-size effect of pores and the scale-independence of direct CFD simulations for hydraulic permeability.     

Existence results for dynamic adhesive contact of a rod

The existence and uniqueness of the weak solution to the model for the dynamics of a viscoelastic rod which is in adhesive contact with an obstacle is established. The model consists of a hyperbolic equation for the vibrations of the rod coupled with a nonlinear ordinary differential equation (ODE) for the evolution of the bonding function. The model allows for failure, i.e., complete debonding, in finite time. The existence of the weak solution is established by using an existence result for ODEs and the Schauder fixed-point theorem. The limit of an elastic rod when the viscosity vanishes is studied, too.     

Braided reinforced composite rods for the internal reinforcement of concrete

This paper reports on the development of braided reinforced composite rods as a substitute for the steel reinforcement in concrete. The research work aims at understanding the mechanical behaviour of core-reinforced braided fabrics and braided reinforced composite rods, namely concerning the influence of the braiding angle, the type of core reinforcement fibre, and preloading and postloading conditions. The core-reinforced braided fabrics were made from polyester fibres for producing braided structures, and E-glass, carbon, HT polyethylene, and sisal fibres were used for the core reinforcement. The braided reinforced composite rods were obtained by impregnating the core-reinforced braided fabric with a vinyl ester resin. The preloading of the core-reinforced braided fabrics and the postloading of the braided reinforced composite rods were performed in three and two stages, respectively. The results of tensile tests carried out on different samples of core-reinforced braided fabrics are presented and discussed. The tensile and bending properties of the braided reinforced composite rods have been evaluated, and the results obtained are presented, discussed, and compared with those of conventional materials, such as steel. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 327–338, May–June, 2008.     

光学相干层析系统的耦合效率分析

在高斯光束传输理论的基础上，利用矩阵光学原理和高斯光束耦合理论，得出光学相干层析系统中参考反射镜的空间位置对系统耦合效率影响的表达式，并用计算机模拟系统的耦合效率与参考反射镜和棒透镜间的距离及参考反射镜偏转角度的关系曲线。实验结果和理论分析相符合。     

概率空间上一类集合的分形维数

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Geometry of random sequential adsorption

By sequentially adding line segments to a line or disks to a surface at random positions without overlaps, we obtain configurations of the one- and two-dimensional random sequential adsorption (RSA) problem. We have simulated the one- and two-dimensional problem with periodic boundary condition. The one-dimensional simulations are compared with the exact analytical solutions to give an estimate of the accuracy of the simulation. In two dimensions the geometrical properties of the RSA configuration are discussed and in addition known results of the RSA process are reproduced. Various statistical distributions of the Voronoi-Dirichlet (VD) network corresponding to the RSA disk configuration are analyzed. In order to characterize pores in the RSA configuration, we introduce circular holes. There is a direct correspondence between vertices of the VD network and these holes, and also between direct/indirect geometrical neighbors and these holes. The hole size distribution is found to be a parabola. We also find general relations that connect the asymptotic behavior of the surface coverage, the correlation function, and the hole size distribution.