NUMERICAL LOCALIZATION OF ELECTROMAGNETIC IMPERFECTIONS FROM A PERTURBATION FORMULA IN THREE DIMENSIONS

This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms： the Current Projection method, the MUltiple Signal Classification （MUSIC） algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings.     

A POSTERIORI ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF THE CAHN-HILLIARD EQUATION AND THE HELE-SHAW FLOW

This paper develops a posteriori error estimates of residual type for conforming and mixed finite element approximations of the fourth order Cahn-Hilliard equation ut ＋ △（ε△Au-ε^-1f（u）） = 0. It is shown that the a posteriori error bounds depends on ε^-1 only in some low polynomial order, instead of exponential order. Using these a posteriori error estimates, we construct at2 adaptive algorithm for computing the solution of the Cahn- Hilliard equation and its sharp interface limit, the Hele-Shaw flow. Numerical experiments are presented to show the robustness and effectiveness of the new error estimators and the proposed adaptive algorithm.     

On the Elliptic Equation △u ＋ K（x）e^2u -0 with K（x） Positive Somewhere

This paper considers the existence problem of an elliptic equation.which is equivalent to the prescribing conformal Gaussian curvature problem on R2.An existence result is pried.In particular,K(x)is allowed to be unbounded above.     

消常数化齐次

<正>一条直线与圆锥曲线交于A、B两点,对于与OA、OB夹角相关的问题,用消元法处理,运算量较大,很容易出错.若设法将直线方程与圆锥曲线方程中的常数项消去,化为二次齐次方程来处理,则简洁明快.     

类比法求解抽象函数问题

类比是根据两类不同事物之间具有某些类似性，推测其中一类事物具有与另一类事物类似（或相同）的性质的思维方法．类比思想是中学数学学习的逻辑思维方式。它既是一种推理方法，同时也是一种学习方法．抽象函数是一类没有给出具体解析式的函数。在探讨抽象函数的有关性质时。由于函数的不具体性。往往显得很盲目，无从下手。因而思维受阻，经常会出现盲点，     

均匀棒纯纵向运动方程初边值问题的有限体积法

提出了均匀棒纯纵向运动方程初边值问题的有限体积格式,给出了有限体积解的误差分析,得到了有限体积解的最优阶L2和H1误差估计及超收敛H1误差估计,提供了一个数值算例.     

非均匀介质GL型热弹性问题解的存在唯一性

We study a new model named the Green-Lindsay type therm-elastic model for nonhomogeneous media that consists of a system of dynamic thermoelasticity equations of displacement and dynamic heat conduction equation. We construct the model based on the classical GL-model for homogeneous material. This system is coupled dynamic problem and the displacement field and heat field must be solved at the same time. By using Fadeo-Galerkin method, we proved that the problem we proposed exist unique weak solution under some regular assumption.     

中国科学技术大学物理50年

在中国科学技术大学建校50周年之际,回顾其物理学教学和科研发展的风雨历程是一件有意义的事情.中国科学技术大学物理学50年来的发展变迁跌宕起伏,难于全面叙述, 我们编写了<中国科大物理50年>一书,本文根据该书压缩而成.下面仅以现在的中国科学技术大学理学院物理系及与其有历史渊源的院系单位作为介绍对象进行介绍.     

A MIXED FINITE ELEMENT METHOD ON A STAGGERED MESH FOR NAVIER-STOKES EQUATIONS

In this paper, we introduce a mixed finite element method on a staggered mesh for the numerical solution of the steady state Navier-Stokes equations in which the two components of the velocity and the pressure are defined on three different meshes. This method is a conforming quadrilateral Q1 × Q1 - P0 element approximation for the Navier-Stokes equations. First-order error estimates are obtained for both the velocity and the pressure. Numerical examples are presented to illustrate the effectiveness of the proposed method.