横观各向同性层状场地对入射SH波的响应分析

本文采用横观各向同性层状弹性模型模拟半空间之上的层状了，推导了在ＳＨ波入射时这种场地土的动力刚度矩阵及基岩输入运动时场地呼应的计算公式，算例表明，横观各向同性层状场地与各向同性层状了频谱特性有明显的区别，应当引起重视。     

Generation of beams of three-dimensional periodic internal waves by sources of various types

The energy and force characteristics of periodic internal wave beams in a viscous exponentially stratified fluid are analyzed. The exact solutions of linearized problems of generation obtained by integral transformations describe not only three-dimensional internal waves but also the associated boundary layers of two types. The solutions not containing empirical parameters are brought to a form that allows a direct comparison with experimental data for generators of various types (friction, piston, and combined) of rectangular or elliptic shape. The stress tensor and force components acting on the generator are given in quadratures. In the limiting cases, the solutions are uniformly transformed to the corresponding expressions for the problems in a two-dimensional formulation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 12–23, May–June, 2006     

Interface crack between two shear deformable elastic layers

An improved method based on the first-order shear deformable plate theory is developed to calculate the energy release rate and stress intensity factor for a crack at the interface of a bi-layer structure. By modeling the uncracked region of the structure as two separate Reissner-Mindlin plates bonded perfectly along the interface, this method is able not only to take into account the shear deformation in the cracked region, but also to capture the shear deformation in the uncracked region of the structure. A closed form solution of energy release rate and mode decomposition at the interface crack is obtained for a general loading condition, and it indicates that the energy release rate and stress intensity factor are determined by two independent loading parameters. Compared to the approach based on the classical plate theory, the proposed method provides a more accurate prediction of energy release rate as well as mode decomposition. The computational procedures introduced are relatively straightforward, and the closed form solution can be used to predict crack growth along the layered structures.     

Turbulence Energy Distribution in the Stokes Layer

Using the method of matched asymptotic expansions, an analytical solution of the balance equation for turbulence energy is constructed for a shallow basin (sea) in which the fluid depth does not exceed the Stokes layer thickness. In this case, a gradient-viscous balance is established with the turbulent viscosity being balanced mainly by the pressure gradient. It is shown that nonlinear boundary layers attributable to turbulence energy diffusion are formed near the bottom and the free surface (or ice). In the neighborhood of the point of maximum flow velocity (if this maximum is attained inside the flow), a nonlinear internal boundary layer also develops. Outside these layers, the turbulence energy generation is in the first approximation balanced by the energy dissipation. Asymptotic solutions for the boundary layers are constructed.     

Interaction forces between adsorbed polymer layers

The interaction forces between adsorbed polymer layers were investigated. Two types of graft copolymers that were adsorbed on hydrophobic surfaces have been investigated: (i) a graft copolymer consisting of polymethylmethacrylate/polymethacrylic acid back bone (the B chain) on which several poly(ethylene oxide) chains are grafted (to be referred to as PMMA/PEO_n); and (ii) a graft copolymer consisting of inulin (linear polyfructose with degree of polymerization > 23) (the A chain) on which several C₁₂ chains are grafted (INUTEC SP1). In the first case adsorbed layers of the graft copolymer were obtained on mica sheets and the interaction forces were measured using the surface force apparatus. In the second case the interaction forces were measured using Atomic Force Microscopy (AFM). For this purpose a hydrophobically modified glass sphere was attached to the tip of the cantilever of the AFM and the glass plate was also made hydrophobic. Both the sphere and the glass plate contained an adsorbed layer of INUTEC SP1.In the surface forces apparatus one essentially measures the energy E(D)–distance D curves for the graft copolymer of PMMA/PEO_n between mica surfaces bearing the graft copolymer and this could be converted to interaction energy between flat surfaces. Using the de Gennes scaling theory, it is possible to calculate the interaction energy between the polymer layers. The same graft copolymer was used in latex dispersions and the high frequency modulus G′_∝ was measured as a function of the volume fraction ? of the dispersion. This high frequency modulus could be related to the potential of mean force. In this way one could compare the results obtained from rheology and those obtained from direct measurement of interaction forces.In the AFM method, the interaction forces are measured in the contact area between two surfaces, i.e. a spherical glass particle and a glass plate. Both glass spheres and plates were hydrophobized using dichlorodimethylsilane. Results were obtained for adsorbed layers of INUTEC SP1 in water and in the presence of various concentrations of Na₂SO₄ (0.3, 0.8, 1.0 and 1.5 mol dm^{− 3}). All results showed a rapid increase of force with a decrease of separation distance and the forces were still repulsive up to the highest Na₂SO₄ concentration. This explains the high stability of dispersions when using INUTEC SP1 as stabilizer.     

Transonic viscous-inviscid interaction by a finite element method

A method is outlined for solving two-dimensional transonic viscous flow problems, in which the velocity vector is split into the gradient of a potential and a rotational component. The approach takes advantage of the fact that for high-Reynolds-number flows the viscous terms of the Navier-Stokes equations are important only in a thin shear layer and therefore solution of the full equations may not be needed everywhere. Most of the flow can be considered inviscid and, neglecting the entropy and vorticity effects, a potential model is a good approximation in the flow core. The rotational part of the flow can then be calculated by solution of the potential, streamfunction and vorticity transport equations. Implementation of the no-slip and no-penetration boundary conditions at the walls provides a simple mechanism for the interaction between the viscous and inviscid solutions and no extra coupling procedures are needed. Results are presented for turbulent transonic internal choked flows.     

Buckling instabilities in coupled nano-layers

We study the dynamic buckling of a pair of dissimilar Euler-Bernoulli beams subject to compressive edge loading whose transverse displacements are coupled through non-linear interactions, a problem motivated by the mechanics of graphene layers. The transverse coupling models van der Waals interaction and is derived from a Lennard-Jones 12-6 potential. The beams are assumed to be a fixed distance apart at their ends, although this distance is not necessarily equal to the equilibrium distance as identified from the Lennard-Jones potential. Therefore, the equilibrium configuration is not necessarily straight. Via a Galerkin method, the governing equations are reduced to a system that can be used to calculate equilibrium configurations as well as the stability of these configurations. We show that the buckling instability in this model is significantly affected by the presence of the interaction force as well as the separation of the graphene layers at the boundaries.     

Cubic spline method for a class of nonlinear singularly-perturbed boundary-value problems

In this paper, we present a numerical method for solving a class of nonlinear, singularly perturbed two-point boundary-value problems with a boundary layer on the left end of the underlying interval. The original second-order problem is reduced to an asymptotically equivalent first-order problem and is solved by a numerical method using a fourth-order cubic spline in the inner region. The method has been analyzed for convergence and is shown to yield anO(h ⁴) approximation to the solution. Some test examples have been solved to demonstrate the efficiency of the method.The authors thank the referee for his helpful comments.     

Structure of BaGd2（MoO4）4 Crystal

The title compound belongs to monoclinic,space group C2/c with a=5.2694(1),b=12.6659(4),c=19.4108(2) ,β=91.504(2)°,V=1295.06(5) 3,Z=4 and Dc=5.599 g/cm3. The structure of BaGd2(MoO4)4 contains a MoO4 tetrahedron,a distorted GdO8 polyhedron,and Ba2+ ions in a tenfold coordination. The GdO8 polyhedra are linked together through edge-sharing to give a two-dimensional Gd layer. The MoO4 tetrahedra connected to the Gd atoms are capped up and down the Gd layer through common oxygen apices,thus forming a new Gd-Mo layer. Finally,the Gd-Mo layers are held together through bridging BaO10 polyhedra to form a three-dimensional framework. Since the Ba-μ3-O bond has a large average distance of 2.888 ,this structural characteristic will result in a cleavage along the (001) plane.     

High‐order numerical methods for one‐dimensional parabolic singularly perturbed problems with regular layers

In this work we construct and analyze some finite difference schemes used to solve a class of time‐dependent one‐dimensional convection‐diffusion problems, which present only regular layers in their solution. We use the implicit Euler or the Crank‐Nicolson method to discretize the time variable and a HODIE finite difference scheme, defined on a piecewise uniform Shishkin mesh, to discretize the spatial variable. In both cases we prove that the numerical method is uniformly convergent with respect to the diffusion parameter, having order near two in space and order one or 3/2, depending on the method used, in time. We show some numerical examples which illustrate the theoretical results, in the case of using the Euler implicit method, and give better numerical behaviour than that predicted theoretically, showing order two in time and order N^?2log²N in space, if the Crank‐Nicolson scheme is used to discretize the time variable. Finally, we construct a numerical algorithm by combining a third order A‐stable SDIRK with two stages and a third‐order HODIE difference scheme, showing its uniformly convergent behavior, reaching order three, up to a logarithmic factor. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005