Adhesive Contact of a Membrane with a Hemispherical Indenter: Theoretical Analysis and Model Liquid System

The axisymmetric Laplace equation is solved numerically to extract contact-angle data for a flat liquid/vapor interface contacting a submerged hemispherical solid. The liquid/vapor interface is treated as a membrane, with a membrane tension equal to the surface energy of the liquid. By measuring the vertical displacement of the membrane and the projected contact area the membrane makes with the hemisphere, the contact angle and correspondingly the driving force for motion of the contact line can be measured. We show that characteristic receding and advancing contact angles can be obtained by measuring the contact radii formed upon initial contact between the interface and hemisphere and final contact just prior to detachment of the interface, respectively. Use of the technique is illustrated with a model experiment involving the contact of an air/water interface with a poly(methyl methacrylate) surface.     

Non‐reflecting artificial boundaries for transient scalar wave propagation in a two‐dimensional infinite homogeneous layer

This paper presents an exact non‐reflecting boundary condition for dealing with transient scalar wave propagation problems in a two‐dimensional infinite homogeneous layer. In order to model the complicated geometry and material properties in the near field, two vertical artificial boundaries are considered in the infinite layer so as to truncate the infinite domain into a finite domain. This treatment requires the appropriate boundary conditions, which are often referred to as the artificial boundary conditions, to be applied on the truncated boundaries. Since the infinite extension direction is different for these two truncated vertical boundaries, namely one extends toward x →∞ and another extends toward x→‐ ∞, the non‐reflecting boundary condition needs to be derived on these two boundaries. Applying the variable separation method to the wave equation results in a reduction in spatial variables by one. The reduced wave equation, which is a time‐dependent partial differential equation with only one spatial variable, can be further changed into a linear first‐order ordinary differential equation by using both the operator splitting method and the modal radiation function concept simultaneously. As a result, the non‐reflecting artificial boundary condition can be obtained by solving the ordinary differential equation whose stability is ensured. Some numerical examples have demonstrated that the non‐reflecting boundary condition is of high accuracy in dealing with scalar wave propagation problems in infinite and semi‐infinite media. Copyright © 2003 John Wiley & Sons, Ltd.     

Analytical solution for the axisymmetric plane strain electroelastic dynamics of a special non-homogeneous piezoelectric hollow cylinder

By virtue of the introduction of a dependent variable and the separation of variables technique, the axisymmetric plane strain electroelastic dynamic problem of a special non-homogeneous piezoelectric hollow cylinder is transformed to a Volterra integral equation of the second kind about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solutions of displacements, stresses, electric displacements and electric potential are obtained. The present method is suitable for a piezoelectric hollow cylinder with an arbitrary thickness subjected to arbitrary mechanical and electrical loads. Numerical results are finally presented.     

Molecular Dynamics Simulation of Gas Diffusion in B2O3 and SiC

Molecular dynamics simulation using a universal force field has been employed to determine the diffusion coefficients of O2 and Na2SO4 vapor into B2O3 and SiC from 700 K to 1273 K, respectively. Einstein diffusion was observed in a 250～300 ps simulation.     

注蒸汽开发稠油油藏采收率计算公式探讨

从辽河油区的地质条件和开发特征出发．立足单因素分析，在着重研究渗进率、净总厚度比和单层厚度对原油采收率影响的基础上。利用《价值工程》中的“功能重要评价法”，优化出不同类型稠油油藏蒸汽吞吐和蒸汽驱开发阶段的采收率计算公式．经实际资料验证，该公式对油田开发前期确定采收率丰和可采储量，具有较好的适用性。     

Boussinesq方程的永形波的级数解

对于用层平均速度势(或速度)与波高给出的非线性等水深Boussinesq方程,与KdV方程一样,存在两类永形波—孤立波和周期波。不同的是,对于Boussinesq方程,孤立波和周期波一样,是以反函数的积分形式给出的,这在使用上是不方便的。本文对这两类波,分别给出了相应的级数形式的正函数解。对于孤立波,级数的收敛速度是十分快的,且文中还给出了一个具有高精度的十分简单的近似解,对于周期波,只要有关参数选得合适,解的收敛速度也是相当快的。这就有效地克服了反函数形式解在使用上的不方便。     

PROGRESS IN THE MODELLING OF AIR FLOW PATTERNS IN TIMBER KILNS

Progress in modelling air flow patterns in timber kilns using Computational Fluid Dynamics is reviewed in this work. These simulations are intended to predict the distribution of the flow in the fillet spaces between boards in a hydraulic model of a timber kiln. Here, the flow regime between the boards is transitional between laminar and turbulent flow, with Reynolds numbers of the order of 5000. Running the simulation as a transient calculation has shown few problems with convergence issues, reaching a mass residual of 0.2% of the total inflow after 40-100 iterations per time step for time steps of 0.01 s. Grid sensitivity studies have shown that non-uniform grids are necessary because of the sudden changes in flow cross section, and the flow simulations are insensitive to grid refinement for non-uniform grids with more than 300,000 cells. The best agreement between the experimentally-measured flow distributions between fillet spaces and those predicted by the simulation have been achieved for (effective) bulk viscosities between the laminar viscosity for water and ten times that value. This change in viscosity is not very large (less than an order of magnitude), given that effective turbulent viscosities are typically several orders of magnitude greater than laminar ones. This result is consistent with the transitional flows here.     

The initial behaviour of freshly etched copper in moderately acid, aerated chloride solutions

When freshly etched samples of various types of copper were exposed in moderately acid, aerated chloride solutions, two phenomena were observed. First the corrosion potential and the pH of the solution decreased over a shorter time, then the potential increased over a long period (600-1500 min), following an s-shaped pattern. Increase in pH during the second stage was avoided using a pH-stat. The corrosion rate increased little or not at all over the entire period. A tentative interpretation of the short-term behaviour is presented with some reservation. The long-term development of the potential suggests phase formation or transformation following the Avrami pattern. By suitable derivations it was possible to fit the development of potentials to the Avrami equation. Subsequent examinations by Auger spectroscopy proved the presence of thin layers of Cu₂O on the copper surfaces, increasing in thickness with exposure time. The dissolution kinetics can be described in terms of two parallel electrochemical reactions and a simultaneous non-electrochemical dissolution reaction.     

Efficient model reduction in non-linear dynamics using the Karhunen-Loève expansion and dual-weighted-residual methods

 We look at the task of computing the time-evolution of a non-linear system for a long time, in our case under random external influences. Our specific example is the fatigue evaluation of a wind turbine. To facilitate such a computation, we look at a reduction of the computational effort by projecting everything on a low-dimensional basis. In this case we take the Karhunen-Loève basis generated from running the model a little while under the random loading. It is important that the error which is caused by this reduction process can be controlled. We estimate the error by dual or adjoint methods. This in turn allows the process of model reduction to be performed adaptively. Dedicated to the memory of Prof. Mike Crisfield, for his cheerfulness and cooperation as a colleague and friend over many years.     

Accurate higher-order analytical approximate solutions to nonconservative nonlinear oscillators and application to van der Pol damped oscillators

In general, this paper deals with general nonlinear oscillations of a nonconservative and single degree-of-freedom system with odd nonlinearity and, in particular, it presents accurate higher-order analytical approximate solutions to van der Pol damped nonlinear oscillators having odd nonlinearity and the Rayleigh equation. By combining the linearization of the governing equation with harmonic balancing and the method of averaging, we establish accurate analytical approximate solutions for the general weakly damped nonlinear systems. Unlike the classical harmonic balance method, simple linear algebraic equations instead of nonlinear algebraic equations are obtained upon linearization prior to harmonic balancing. The combination of these two methods results in very accurate transient response of the periodic solution. In addition and for the first time, this paper also presents a method for deducing fourth-, fifth- and higher-order linearized governing equations from the lower-order equations without the requirement of formulating the problem from the first principle. Three examples including the van der Pol damped nonlinear oscillator are presented to illustrate the excellent agreement with approximate solution using the exact frequency.