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.     

PPT光纤波片耦合模方程的解析解

理论分析了PPT光纤波片耦合模方程，得出了一定条件下的解析解，将该解析解和渐进近似结果进行了比较，它们在实际应用的PPT光纤波片中具有很好的一致性。     

Ce3+离子对掺Er3+碲酸盐玻璃光谱性质的影响

研究了Ce3 + 对掺Er碲酸盐玻璃荧光光谱性质的影响 ,比较了不同的Ce3 + 掺杂浓度下Er3 + 离子荧光发光强度的变化 ,分析了Ce3 + 离子对Er3 + 离子作用的原理 ,应用经典方程计算了Er3 + 离子 4I1 1 / 2 能级的荧光寿命及其变化     

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。     

Beyond Wiener–Askey Expansions: Handling Arbitrary PDFs

In this paper we present a Multi-Element generalized Polynomial Chaos (ME-gPC) method to deal with stochastic inputs with arbitrary probability measures. Based on the decomposition of the random space of the stochastic inputs, we construct numerically a set of orthogonal polynomials with respect to a conditional probability density function (PDF) in each element and subsequently implement generalized Polynomial Chaos (gPC) locally. Numerical examples show that ME-gPC exhibits both p- and h-convergence for arbitrary probability measures     

Bounded Error Schemes for the Wave Equation on Complex Domains

This paper considers the application of the method of boundary penalty terms (SAT) to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell’s equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g., the staggered Yee scheme)—we achieve a decrease of two orders of magnitude in the level of the L₂-error.     

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.     

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.