第一性原理方法研究He掺杂Al晶界力学性质

基于密度泛函理论方法,本文开展了氦掺杂AlΣ3((111)/180°)晶界数值模拟拉伸试验.计算结果表明,He在晶界中最低杂质形成能为2.942 eV,偏析到晶界的偏析能为0.085 eV;在拉伸条件下,清洁Σ3晶界的理论拉伸强度为9.65 GPa,拉伸断裂从晶界界面开始;而He掺杂后,晶界的理论拉伸强度下降到7.14 GPa,在断裂发生前应力曲线中出现平台效应,拉伸断裂从包含He杂质的界面开始.通过对比键长和电荷密度分布,本文认为He的满壳层电子结构一方面导致了He与Al之间 关键词： He 晶界 第一性原理计算 力学性质     

Compact block boundary value methods for semi-linear delay-reaction–diffusion equations with algebraic constraints

In the present paper, we study a class of linear approximation methods for solving semi-linear delay-reaction–diffusion equations with algebraic constraint (SDEACs). By combining a fourth-order compact difference scheme with block boundary value methods (BBVMs), a class of compact block boundary value methods (CBBVMs) for SDEACs are suggested. It is proved under some suitable conditions that the CBBVMs are convergent of order 4 in space and order p in time, where p is the local order of the used BBVMs, and are globally stable. With several numerical experiments for Fisher equation with delay and algebraic constraint, the computational effectiveness and theoretical results of CBBVMs are further illustrated.     

周期性边界条件下多孔介质方腔内自然对流换热数值研究

对充满多孔介质的倾斜方腔,在其上下壁面绝热、右侧壁面维持恒温To及左侧壁面温度基于To随时间按正弦规律变化的情况下,采用Brinkman扩展达西模型和SIMPLER算法对方腔内的自然对流与换热进行了非稳态数值模拟,方腔倾角α的范围为0°～90°,Pr数为1,Ra数为106.计算研究不同的振荡频率和方腔倾角对方腔内对流换热的影响.数值模拟结果表明:振荡频率f为60π,方腔倾角为43°时,方腔内的换热最强.     

Instability of two-phase flows: A lower bound on the dimension of the global attractor of the Cahn-Hilliard-Navier-Stokes system

We consider a model for the flow of a mixture of two viscous and incompressible fluids in a two or three dimensional channel-like domain. The model consists of the Navier-Stokes equations governing the fluid velocity coupled with a convective Cahn-Hilliard equation for the relative density of atoms of one of the fluids. We prove the instability of certain stationary solutions for such a system endowed with periodic boundary conditions on elongated domains (0,2π/α₀)×(0,2π) or (0,2π/α₀)×(0,2π)×(0,2π/β₀) for a special class of periodic body forces, provided that α₀ and β₀ are small enough. As a consequence, we deduce a lower bound for the Hausdorff dimension of the global attractor.     

Asymptotic behavior of solutions for the 1-D isentropic Navier–Stokes–Korteweg equations with free boundary

In this paper, we consider the problem with a gas–gas free boundary for the one dimensional isentropic compressible Navier–Stokes–Korteweg system. For shock wave, asymptotic profile of the problem is shown to be a shifted viscous shock profile, which is suitably away from the boundary, and prove that if the initial data around the shifted viscous shock profile and its strength are sufficiently small, then the problem has a unique global strong solution, which tends to the shifted viscous shock profile as time goes to infinity. Also, we show the asymptotic stability toward rarefaction wave without the smallness on the strength if the initial data around the rarefaction wave are sufficiently small.     

开边界条件下一类新Hubbard模型的精确解

用坐标Bethe ansatz方法详细研究了开边界条件下一类新Hubbard模型的可积性问题. 得到了系统的能谱、可积边界条件和Bethe ansatz方程.     

格林公式的教学探究

首先通过一个热点问题和两个计算题引出学习格林公式的目的和必要性,迅速抓住学生的兴趣点,从第二型曲线积分入手,通过逐步分析操作给出前提条件,并最终得到公式,打破了书上的传统推导模式.     

The influence of temperature gradients on the kinetic boundary layer problem for a condensing droplet

We extend an earlier method for solving kinetic boundary layer problems to the case of particles moving in aspatially inhomogeneous background. The method is developed for a gas mixture containing a supersaturated vapor and a light carrier gas from which a small droplet condenses. The release of heat of condensation causes a temperature difference between droplet and gas in the quasistationary state; the kinetic equation describing the vapor is the stationary Klein-Kramers equation for Brownian particles diffusing in a temperature gradient. By means of an expansion in Burnett functions, this equation is transformed into a set of coupled algebrodifferential equations. By numerical integration we construct fundamental solutions of this equation that are subsequently combined linearly to fulfill appropriate mesoscopic boundary conditions for particles leaving the droplet surface. In view of the intrinsic numerical instability of the system of equations, a novel procedure is developed to remove the admixture of fast growing solutions to the solutions of interest. The procedure is tested for a few model problems and then applied to a slightly simplified condensation problem with parameters corresponding to the condensation of mercury in a background of neon. The effects of thermal gradients and thermodiffusion on the growth rate of the droplet are small (of the order of 1%), but well outside of the margin of error of the method.     

维数连续可变康托尔集分层介质中波的反射透射特性

本文研究了波通过一类可连续控制分维的广义Cantor集合介质层的反射透射频谱特性。利用自相似性,给出了任意分维情况的一般计算方法,从而使我们能研究反射透射频谱随分维的变化特点,并认识到,在一般分维下,谱具有广义自相似性和“混沌”周期性,这是一种新的物理现象,必定蕴藏着一定的实用价值。     

A boundary only procedure for time-dependent diffusion equations

In the recent literature, the boundary element method (BEM) is extensively used to solve time-dependent partial differential equations. However, most of these formulations yield algorithms where one has to include all interior points in the computation process if finite difference procedures are used to approximate the temporal derivative. This obviously restricts the advantages of the BEM, which is mainly considered to be a boundary only algorithm for time-independent problems. A new algorithm is demonstrated here, which extends the boundary only nature of the method to time-dependent partial differential equations. Using this procedure, one can reduce the finite difference time integration algorithm, generated in a standard manner, to a boundary only process. The proposed method is demonstrated with considerable success for diffusion problems. Results obtained in these applications are presented comparatively with analytical and other boundary element time integration procedures. The algorithm proposed may utilize several coordinate functions in the secondary reduction phase of the formulation. A summary of such functions is described here and performances of these functions are tested and compared in three applications. It is shown that some coordinate functions perform better than others under certain conditions. Using these results, we propose a general coordinate function, which may be used with satisfactory results in all parabolic partial differential equation applications.