条状功能梯度材料中偏心裂纹对反平面简谐波的散射问题

利用Schmidt方法研究了条状功能梯度材料中偏心裂纹对反平面简谐波的散射问题,裂纹垂直于条状功能梯度材料的边界．通过Fourier变换,问题可以转换为对一对未知变量是裂纹表面位移差的对偶积分方程求解．为了求解对偶积分方程,把裂纹表面的位移差展开为Jacobi多项式级数形式,进而得到了功能梯度参数、裂纹位置以及入射波频率对应力强度因子影响的规律．     

羟丙基-β-环糊精与丹参酮IIA包合作用的研究

采用相溶解度法研究了丹参酮 IIA在不同pH和不同摩尔浓度的羟丙基-β-环糊精水溶液中的溶解度及二者的包合常数; 采用热力学方法研究了温度对包合反应的影响, 计算了包合过程的熵变、焓变及自由能变化; 用分子模拟方法进一步证实了该包合物的形成; 用红外光谱对固体包合物进行了表征.     

Boundary film shear elastic modulus effect in hydrodynamic contact. Part II: influence of operational parameters

The present paper is the subsequent research of the first part (Theor Comput Fluid Dyn, 2009). It investigates the boundary film shear elastic modulus effect in a hydrodynamic contact in different operating conditions. The hydrodynamic contact is one-dimensional, composed of two parallel plane surfaces, which are respectively rough rigid with rectangular micro projections in profile periodically distributed on the surface and ideally smooth rigid. The whole contact consists of cavitated area and hydrodynamic area. The hydrodynamic area consists of many micro Raleigh bearings which are discontinuously and periodically distributed in the contact. The hydrodynamic contact in a micro Raleigh bearing consists of boundary film area and fluid film area which, respectively, occur in the outlet and inlet zones. In boundary film area, the film slips at the upper contact surface due to the limited shear stress capacity of the film–contact interface, while the film does not slip at the lower contact surface due to the shear stress capacity of the film–contact interface large enough. In boundary film area, the viscosity, density, and shear elastic modulus of the film are varied across the film thickness due to the film–contact interactions, and their effective values are used in modeling which depends on the film thickness. In fluid film area, the film does not slip at either of the contact surfaces, and the shear elastic modulus of the film is neglected. It is found from the simulation results that the boundary film shear elastic modulus influences are normally negligible on the mass flow through the contact, the carried load of the contact and the overall film thickness of the contact, and the boundary film shear elastic modulus would normally influence the local film thickness in an elastic contact when the local film thickness is on the film molecule diameter scale. It is also found that the boundary film shear elastic modulus effect has the tendency of being increased with the reduction of the width of a micro contact. It is increased with the reduction of the boundary film–contact interfacial shear strength or with the increase of the critical boundary film thickness, while it is strongest at certain values of the contact surface roughness, the width ratio of fluid film area to boundary film area, and the lubricant film shear elastic modulus.

---

     

Homogenization of the Prager model in one-dimensional plasticity

We propose a new method for the homogenization of hysteresis models of plasticity. For the one-dimensional wave equation with an elasto-plastic stress-strain relation we derive averaged equations and perform the homogenization limit for stochastic material parameters. This generalizes results of the seminal paper by Franců and Krejčí. Our approach rests on energy methods for partial differential equations and provides short proofs without recurrence to hysteresis operator theory.      

Energy elastic effects and the concept of temperature in flowing polymeric liquids

The incorporation of energy elastic effects in the modeling of flowing polymeric liquids is discussed. Since conformational energetic effects are determined by structural features much smaller than the end-to-end vector of the polymer chains, commonly employed single conformation tensor models are insufficient to describe energy elastic effects. The need for a local structural variable is substantiated by studying a microscopic toy model with energetic effects in the setting of a generalized canonical ensemble. In order to examine the dynamics of flowing polymeric liquids with energy elastic effects, a thermodynamically admissible set of evolution equations is presented that accounts for the evolution of the microstructure in terms of a slow tensor, as well as a fast, local scalar variable. It is demonstrated that the temperature used in the definition of the heat flux is directly related to the Lagrange multiplier of the microscopic energy in the generalized canonical partition function. The temperature equation is discussed with respect to, first, the dependence of the heat capacity on the polymer conformation and, second, the possibility to measure experimentally the effects of the conformational energy.

On dynamics of elastic rod based on exact Cosserat model

The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov's stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.     

Stability of theoretical model for catastrophic weather prediction

Stability related to theoretical model for catastrophic weather prediction, which includes non-hydrostatic perfect elastic model and anelastic model, is discussed and analyzed in detail. It is proved that non-hydrostatic perfect elastic equations set is stable in the class of infinitely differentiable function. However, for the anelastic equations set, its continuity equation is changed in form because of the particular hypothesis for fluid, so "the matching consisting of both viscosity coefficient and incompressible assumption" appears, thereby the most important equations set of this class in practical prediction shows the same instability in topological property as Navier-Stokes equation, which should be avoided first in practical numerical prediction. In light of this, the referenced suggestions to amend the applied model are finally presented.     

Anchoring properties of substrate with a grating surface

The anchoring properties of substrate with a grating surface are investigated analytically. The alignment of nematic liquid crystal (NLC) in a grating surface originates from two mechanisms, thus the anchoring energy consists of two parts. One originates from the interaction potential between NLC molecules and the molecules on the substrate surface, and the other stems from the increased elastic strain energy. Based on the two mechanisms, the expression of anchoring energy per unit area of a projected plane of this grating surface is deduced and called the equivalent anchoring energy formula. Both the strength and the easy direction of equivalent anchoring energy are a function of the geometrical parameters (amplitude and pitch) of a grating surface. By using this formula, the grating surface can be replaced by its projected plane and its anchoring properties can be described by the equivalent anchoring energy formula.     

天然流体包裹体中甲烷水合物生成条件原位变温拉曼光谱研究

准确获取流体包裹体中气体水合物的生成条件一直是传统包裹体分析方法面临的一个难题。文章采用原位拉曼光谱技术分析了天然流体包裹体中甲烷水合物的生成条件。并由常温拉曼光谱分析表明,研究流体包裹体的流体组成为CH4-H2O体系。通过三种方法控制实验温度的变化,在第三种方法实验条件下获得了-170 ℃时甲烷水合物与冰的拉曼光谱,逐渐升温原位观测甲烷水合物的消失温度。原位拉曼光谱检测结果表明,研究包裹体中甲烷水合物的生成温度为7.5 ℃。结合CH4-H2O体系水合物形成条件相平衡计算,得到包裹体中甲烷水合物生成时的压力为5.587 3 MPa。研究结果表明,原位拉曼光谱技术是准确获取流体包裹体种气体水合物生成条件的一种有效方法。     

Experimental study of bubble generation during β‐BaB2O4 single crystal growth

The generation of bubble‐inclusions during BaB₂O₄ (BBO) crystal growth from high temperature solution has been optically observed by an in situ observation technique. It was found that bubbles are formed from the peripheries of some hexagonal defects in the (0001) plane of the growing crystal, which may be caused by the evaporation of the air‐opened interface at the high temperature. In addition, atomic force microscope (AFM) was used to investigate the distribution of bubbles. Results revealed that the bubble generation and distribution depend strongly on the microscopic structure of the interface: on a rough interface, bubbles are easily formed and grow rapidly; however, they are greatly suppressed by step trains on a vicinal interface. In the latter case, the height value of a bubble is close to that of the step, which is in the order of several tens of nanometers. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)