Error estimates for the interpolating moving least-squares method in n-dimensional space

In this paper, the interpolating moving least-squares (IMLS) method is discussed in details. A simpler expression of the approximation function of the IMLS method is obtained. Compared with the moving least-squares (MLS) approximation, the shape function of the IMLS method satisfies the property of Kronecker δ function. Then the meshless method based on the IMLS method can overcome the difficulties of applying the essential boundary conditions. The error estimates of the approximation function and its first and second order derivatives of the IMLS method are presented in n-dimensional space. The theoretical results show that if the weight function is sufficiently smooth and the order of the polynomial basis functions is big enough, the approximation function and its partial derivatives are convergent to the exact values in terms of the maximum radius of the domains of influence of nodes. Then the interpolating element-free Galerkin (IEFG) method based on the IMLS method is presented for potential problems. The advantage of the IEFG method is that the essential boundary conditions can be applied directly and easily. For the purpose of demonstration, some selected numerical examples are given to prove the theories in this paper.     

Interactions of single-stranded DNA on microcantilevers

The microcantilever approach has attracted considerable attention in recent years as a means of label-free detection of a variety of biomolecular and chemical reactions. The underlying physics of the intermolecular interactions that result in mechanical motions is yet to be fully explored, but it seems both rich in science and of technological importance. This paper presents an overview of experiments and theories related to interactions of single-stranded DNA immobilized on microcantilevers. Experiments and theories show that, at high grafting density, hydration forces are the dominant factor determining cantilever deflections, not electrostatics or conformational entropy.     

Linear instability of ultra-thin liquid films flowing down cylindrical fibre

The stability characteristics of an ultra-thin layer of a viscous liquid flowing down a cylindrical fibre are investigated by a linear theory. The film with the thickness less than 100 nm is driven by an external force and under the influence of the van der Waals forces. The results show that, when the relative film thickness decreases, the curvature of the fibre depresses the development of the linear perturbations, whereas the van der Waals forces promote the instabilities. This competition results in a non-monotonous dependence of the growth rate on the relative film thickness. The critical curves are also obtained to describe the transition from the absolute instability to the convective instability, indicating that the van der Waals forces can enlarge the absolutely unstable region. Furthermore, the surface tension can cause the development of the absolute instability, whereas the external force has an opposite effect.     

Rotor wake capture improvement based on high-order spatially accurate schemes and chimera grids

A high-order upwind scheme has been developed to capture the vortex wake of a helicopter rotor in the hover based on chimera grids. In this paper, an improved fifth-order weighted essentially non-oscillatory (WENO) scheme is adopted to interpolate the higher-order left and right states across a cell interface with the Roe Riemann solver updating inviscid flux, and is compared with the monotone upwind scheme for scalar conservation laws (MUSCL). For profitably capturing the wake and enforcing the period boun...     

Numerical investigations on vortical structures of viscous film flows along periodic rectangular corrugations

Two-dimensional gravity-driven film flows along a substrate with rectangular corrugations are studied numerically by using Finite Volume Method. The volume of fluid (VOF) method is utilized to capture the evolution of free surfaces. The film flows down an inclined plate are simulated to validate the numerical implementation of the present study. Results obtained indicate that the phase shift between the surface wave and the wall corrugation increases as the Reynolds number. The parametric studies on the interesting resonant phenomenon indicate that the peak Reynolds numbers increase as the raise of the wall depth or the decline of the inclination angle. The dependence of the flow fields is analyzed on the Reynolds numbers and wall depth in details. It is found that the vortical structures in the steady flows, either produced by the interaction between capillary wrinkling and inertia, or by the rectangular geometry, are closely related to the remarkable deformation of the free surfaces. This conclusion is also confirmed by the transient flow development of two typical simulations, i.e., flows in capillary–inertial regime and in inertial regime.     

ANALYTICAL SOLUTIONS FOR THE LAYERED GEO-MATERIALS SUBJECTED TO AN ARBITRARY POINT LOAD IN THE CARTESIAN COORDINATE

This paper presents analytical solutions for the stress and displacement field in elastic layered geo-materials induced by an arbitrary point load in the Cartesian coordinate system. The point load solutions can be obtained by referring to the integral transform and the transfer matrix technique. However, former solutions usually exist in the cylindrical coordinate system subjected to axisymmetric loading. Based on the proposed solutions in the Cartesian coordinate, it is very easy to solve asymmetric problems and consider the condition with internal loads in multi-layered geo-materials. Moreover, point load solutions can be used to construct solutions for analytical examination of elastic problems and incorporated into numerical schemes such as boundary element methods. The results discussed in this paper indicate that there is no problem in the evaluation of the point load solutions with high accuracy and efficiency, and that the material non-homogeneity has a significant effect on the elastic field due to adjacent loading.     

轴向变速粘弹性Rayleigh梁参数共振稳定性

运用近似解析方法和数值方法研究轴向变速运动黏弹性Rayleigh梁的次谐波共振和组合共振的稳定性区域。基于变分原理,考虑梁断面旋转惯性的影响,推导轴向速度有周期波动的微变形梁横向振动的数学模型;采用多尺度方法建立前两阶次谐波共振和组合共振范围内的参数振动的可解性条件;进而确定梁两端简支边界条件下,因共振而产生的失稳区域;通过微分求积方法求解表征细长Rayleigh梁横向振动的运动微分方程。数值算例分析了黏弹性系数和扭转系数对梁振动失稳区域的影响,将数值仿真结果与近似解析方法的结论进行比较。算例表明:近似解析解的精度较高,第一、第二阶主共振的最大误差分别为3.206%、4.213%。     

精确Cosserat弹性杆动力学的分析力学方法

以脱氧核糖核酸和工程中的细长结构为背景, 大变形大范围运动的弹性杆动力学受到关注. 将分析力学方法运用到精确Cosserat弹性杆动力学, 旨在为前者拓展新的应用领域, 为后者提供新的研究方法. 基于平面截面假定, 在弯扭基础上再计及拉压和剪切变形形成精确Cosserat弹性杆模型. 用刚体运动的概念描述弹性杆的变形, 导出弹性杆变形和运动的几何关系; 在定义截面虚位移及其变分法则的基础上, 建立用矢量表达的d’Alembert-Lagrange原理, 在线性本构关系下化作分析力学形式, 并导出Lagrange方程和Nielsen方程, 定义正则变量后化作Hamilton正则方程; 对于只在端部受力的弹性杆静力学, 导出了将守恒量预先嵌入的Lagrange方程, 并讨论了其首次积分. 从弹性杆的d’Alembert-Lagrange原理导出积分变分原理, 在线性本构关系下化作Hamilton原理. 形成的分析力学方法使弹性杆的全部动力学方程具有统一的形式, 为弹性杆动力学的对称性和守恒量的研究及其数值计算铺平道路. 关键词： 精确Cosserat弹性杆 分析动力学方法 变分原理 Lagrange方程     

智能交通系统的元胞自动机交通流模型

在Nagel-Schreckenberg(NS)模型的基础上，提出一种可应用智能交通系统（ITS）信息的新的交通流元胞自动机模型. 其中考虑了有效间距及刹车灯的作用，并引入了可变安全间距的新概念. 数值模拟表明：对于这种改进的ITS元胞自动机模型，道路交通量有了显著提高，体现了智能交通的优越性——有效地扩大交通流量，减少阻塞生成. 当考虑快车和慢车的混合交通流时，发现即使少量的慢车也会导致交通流量大幅度下降，说明了严格实施快慢道行驶的必要性. 关键词： 交通流 智能交通系统（ITS） 元胞自动机模型 刹车灯 可变安全间距     

Hartmann共振管及超音速雾化喷嘴

采用基于Roe解法的有限体积法，对Hartmann共振管中的气体流场进行了数值模拟，研究了当喷嘴轴线处存在针型激励器的情况下流场的振动情况，数值计算的结果与理论和相关的实验结果符合得较好．计算结果表明移除或引入激励器，将会使Hartmann共振管的共振模式发生转换．通过对超音速雾化喷嘴流场的数值模拟，研究了其中Hartmann共振腔和二级共振腔共同作用下的振动现象以及各物理参数对振动的影响，并对喷嘴中气流从亚音速向超音速的转变机理进行了研究．