Spectral approximations of the Stokes problem by divergence-free functions

The method of Moser, Moin, and Leonard (1983) for the approximation of the three-dimensional Navier-Stokes equations using divergence-free subspaces is revisited and analyzed. It is shown that the computed velocity field converges to the physical one with spectral accuracy. Moreover, a method for recovering the pressure field is proposed. This method is stable and provides a pressure that converges to the physical one with spectral accuracy.     

An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations

The tanh-function method for finding explicit travelling solitary wave solutions to non-linear evolution equations is described. The method is usually extremely tedious to use by hand. We present a Mathematica package ATFM that deals with the tedious algebra and outputs directly the required solutions. The use of the package is illustrated by applying it to a variety of equations; not only are previously known solutions recovered but in some cases more general forms of solution are obtained.     

Solving applied general equilibrium models represented as a mixture of linearized and levels equations

General equilibrium moels are usually represented as a system of levels equations (e.g., in North America) or a system of linearized equations (e.g., in Australia). Either representation can be used to obtain accurate solutions. General-purpose software is available in both cases-GAMS or MPS/GE is typically used by levels modellers and GEMPACK by linearizers. Some equations (notably accounting identities) are naturally expressed in the levels while others (especially behavioural equations) are naturally expressed in a linearized form. This paper describes the new GEMPACK facility for solving models represented as a mixture of levels and linearized equations and discusses the advantages to modellers of using such a representation.     

An Operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow

In this paper we present a simple, general methodology for the generation of high-order operator decomposition (splitting) techniques for the solution of time-dependent problems arising in ordinary and partial differential equations. The new approach exploits operator integration factors to reduce multiple-operator equations to an associated series of single-operator initial-value subproblems. Two illustrations of the procedure are presented: the first, a second-order method in time applied to velocity-pressure decoupling in the incompressible Stokes problem; the second, a third-order method in time applied to convection-Stokes decoupling in the incompressible Navier-Stokes equations. Critical open questions are briefly described.     

Bilateral polynomial matrix equations in two indeterminates

Two special cases of the bilateral 2-D polynomial matrix equationDU +VN=C whenC=I andC=I with being a -stable 2-D polynomial, which are related respectively to deadbeat and asymptotic control problems of 2-D systems, are first considered. By generalizing the concepts of factor coprimeness, zero coprimeness and zero skew primeness in the 2-D polynomial ring to the ring of causal -stable 2-D rational functions, a constructive solution of these two problems mentioned is proposed. Based on these results, we derive a solvability condition for the bilateral equiation whereC is a general 2-D polynomial matrix. The general solutions are investigated as well.     

Discretized LKF method for stability of coupled differential‐difference equations with multiple discrete and distributed delays

Time‐delay systems described by coupled differential‐functional equations include as special cases many types of time‐delay systems and coupled differential‐difference systems with time delays. This article discusses the discretized Lyapunov–Krasovskii functional (LKF) method for the stability problem of coupled differential‐difference equations with multiple discrete and distributed delays. Through independently dividing every delay region that the plane regions consists in two delays to discretize LKF, the exponential stability conditions for coupled systems with multiple discrete and distributed delays are established based on a linear matrix inequality (LMI). The numerical examples show that the analysis limit of delay bound in which the systems are stable may be approached by our result. Copyright © 2011 John Wiley & Sons, Ltd.     

Stability of Impulsive Stochastic Neutral Partial Differential Equations With Infinite Delays

In this paper, we study the existence and asymptotic stability in the pth moment of the mild solutions to impulsive stochastic neutral partial differential equations with infinite delays. Sufficient conditions ensuring the stability of the impulsive stochastic system are established. The results are obtained via the Banach fixed point theorem.     

Alternative Method of Solution of the Regulator Equation: L2‐Space Approach

An alternative method for the proof of solvability of the differential equation that is a part of the regulator equation which arises from the solution of the output regulation problem. The proof uses the L²‐space based theory of solutions of partial differential equations for the case of the linear output regulation problem. In the nonlinear case, a sequence of linear equations is defined so that their solutions converge to the solution of the nonlinear problem. This is proved using the Banach Contraction Theorem. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

水平阻尼作为干扰的平台式惯导统一控制方程

研究惯导系统统一控制的优化设计。传统的统一控制采用一体化设计方案,通用性不强。为简捷高效地实现惯导计算机的程序编排,提出了将水平阻尼作为干扰项的平台式惯导统一控制。通过改变系统框图结构,将无阻尼惯导系统和阻尼网络人为分离,水平阻尼网络的输出可视为干扰项。系统控制方程始终采用无阻尼条件下的表达式,惯导系统控制和阻尼网络可以实现模块化设计,使控制的实现形式和推导过程大为简化。给出了惯导计算机的运算流程,并分别在静、动基座条件下,对无阻尼、内水平阻尼和外水平阻尼状态的惯导系统做了仿真。结果表明新的统一控制模型有效体现了惯导系统的参数变化,且设计简便,具有更好的实用性。     

排桩式波浪能发电装置附近流场特性研究

基于雷诺时均Navier-Stokes方程和k?ω湍流模型,研究单排桩式振荡水柱式波浪能发电装置在规则波作用下的桩基附近流场特性. 通过物理模型实验验证所建数值波浪水槽的准确性. 模拟规则波作用下装置附近的流场特性,分析装置附近的涡特征以及其对装置附近泥沙冲刷情况的潜在影响. 结果表明,测试工况下,在桩式振荡水柱装置桩柱体的桩基附近观察到马蹄涡和尾涡现象,马蹄涡强度随着Keulegan–Carpenter（KC）数的增大而减小,尾涡强度随着KC数的增大而增大. 马蹄涡因强度过小,在模拟的KC数范围内不是装置桩基泥沙冲刷的主要因素,高强度的尾涡很可能成为装置桩基附近泥沙起动、输运和冲刷的重要影响因素.