Thin-walled Beams: A Derivation of Vlassov Theory via Γ-Convergence

This paper deals with the asymptotic analysis of the three-dimensional problem for a linearly elastic cantilever having an open cross-section which is the union of rectangles with sides of order ε and ε ², as ε goes to zero. Under suitable assumptions on the given loads and for homogeneous and isotropic material, we show that the three-dimensional problem Γ-converges to the classical one-dimensional Vlassov model for thin-walled beams.      

Differential–algebraic equations in multibody system modeling

Numerical methods for the efficient integration of both stiff and nonstiff equations of motion of multibody systems having the form of differential-algebraic equations (DAE) of index 3 are discussed. Linear multi-step ABM and BDF methods are considered for the non-iterational integration of nonstiff DAE. The Park method is proposed for integration of stiff equations. This revised version was published online in June 2006 with corrections to the Cover Date.     

Comparison of Two Reformulation-Linearization Technique Based Linear Programming Relaxations for Polynomial Programming Problems

In this paper, we compare two strategies for constructing linear programmingrelaxations for polynomial programming problems using aReformulation-Linearization Technique (RLT). RLT involves an automaticreformulation of the problem via the addition of certain nonlinear impliedconstraints that are generated by using the products of the simple boundingrestrictions (among other products), and a subsequent linearization based onvariable redefinitions. We prove that applying RLT directly to the originalpolynomial program produces a bound that dominates in the sense of being atleast as tight as the value obtained when RLT is applied to the jointcollection of all equivalent quadratic problems that could be constructed byrecursively defining additional variables as suggested by Shor.     

Modification to the Fringe Component of Diffraction Coefficient in TD-EEC Method

A modified formulation for fringe component of diffraction coefficient is implemented to TD-EEC method. An example of diffraction by perfectly conducting plate is used to illustrate our scheme. Comparing with the FDTD results we observe that the improved expression for fringe component is more accurate than that of Michaeli's formulation. This high frequency time domain technique is available for treating the bistatic scattering problems for millimeter waves.     

基于遗传算法的二层线性规划问题的求解算法

本研究了下层以最优解返回上层的二层线性规划问题的遗传算法。在提出可行度概念的基础上，构造了二层线性规划上层规划问题的适应度函数，由此设计了求解二层线性规划问题遗传算法。为了提高遗传算法处理约束的能力，在产生初始种群时将随机产生的初始种群变为满足约束的初始种群，从而避免了使用罚函数处理约束带来的困难，最后用实例验证了本提出的二层线性规划的遗传算法的有效性。     

A discontinuous Galerkin method/HLLC solver for the Euler equations

This paper proposes a fully three‐dimensional non‐linear Euler methodology for solving aerodynamic and acoustic problems in the presence of strong shocks and rarefactions. It uses a discontinuous Galerkin method (DGM) within the element, and a Riemann solver (HLLC) at the boundaries to propagate rarefactions while preserving the entropy condition and capturing shocks with no spurious oscillations. This approach is thought to marry the best aspects of finite element and finite volume methods, achieving conservation while not requiring the solution of a large matrix. Examples in which shock and rarefaction waves are well captured are presented and the propagation of acoustic pulses is well demonstrated. Copyright © 2003 John Wiley & Sons, Ltd.     

The numerical approximation of center manifolds in Hamiltonian systems

In this paper we develop a numerical method for computing higher order local approximations of center manifolds near steady states in Hamiltonian systems. The underlying system is assumed to be large in the sense that a large sparse Jacobian at the equilibrium occurs, for which only a linear solver and a low-dimensional invariant subspace is available. Our method combines this restriction from linear algebra with the requirement that the center manifold is parametrized by a symplectic mapping and that the reduced equation preserves the Hamiltonian form. Our approach can be considered as a special adaptation of a general method from Numer. Math. 80 (1998) 1-38 to the Hamiltonian case such that approximations of the reduced Hamiltonian are obtained simultaneously. As an application we treat a finite difference system for an elliptic problem on an infinite strip.     

<Emphasis FontCategory="NonProportional">L</Emphasis>-Matrices and solvability of linear complementarity problems by a linear program-Matrices and solvability of linear complementarity problems by a linear program

The classes ofL ₁-matrices,L ₂-matrices,L ₃-matrices andW-matrices are introduced to study solvability of a linear complementarity problem via solving a linear program. Three sufficient conditions are presented to guarantee that a linear complementarity problem is solvable via a linear program. The new sufficient conditions are weaker than the ones introduced by Mangasarian. This fact is also illustrated by an example. Partially supported by NSFC. This author is also with College of Business Administration of Human University as a Lotus chair professor.     

一类非线性弹簧振子的周期性振动

本文用数值计算的方法讨论了一类非线性弹簧振子的周期性振动及其特点．     

Dynamics of Random One-Dimensional ±J Systems

Finite chains of a two-state random Potts spin model with periodic boundary conditions are studied within Glauber dynamics. The spin exchange is assumed random with frustration between ferro and antiferromagnetic values (±J). Time-dependent fluctuations are induced by periodic temperature oscillations. Master type differential equations for spin correlation functions are solved within linear response theory. The spectrum of relaxation times are calculated at different temperatures. The ±J Potts glass chains undergo a zero temperature phase transition. The barriers against inversion of the spin chain take only two values; 0 and 2|J|. The temperature behaviour of specific heat is characterized by rounded peaks. The frequency dependence displays two plateaus for the real part of specific heat and two corresponding peaks for the imaginary part. The dynamic specific heat is not affected by the longest relaxing mode like susceptibility. The time separation of the modes is demonstrated by the Cole-Cole plots.