The consistent Mindlin’s thermopiezoelectric equations and the principle of virtual work

The thermal field vector, an overlooked concept of importance, is introduced for the consistency in Mindlin’s thermopiezoelectric equations. The gradient of the temperature increment is defined as the thermal field vector; an analogous to the electric and magnetic field vectors (i.e., the gradients of the electric and magnetic potentials). The thermal field vector is used to state the universal gradient equations, and then, the principle of virtual work.     

An adaptation of Page’s CUSUM test for change detection

Summary Page’s CUSUM test for detecting change in a sequence of independent observations is extended to the general parametric model involving nuisance parameters. The test statistic is the standardized efficient score vector. The model of nested random effects is analyzed in detail.     

MgS晶体结构性质的密度泛函研究

采用基于密度泛函理论(DFT)基础上的第一性原理赝势平面波方法对MgS晶体四种构型(B1，B2，B3，B4)的体相性质进行了系统研究.计算结果表明，B1构型的晶体是间接带隙型半导体，而B2，B3和B4构型的晶体则是直接带隙型材料，其中B2构型的带隙宽度最窄，其值为0.42eV.在压力不超过200.3GPa时，B1构型的MgS 晶胞是最稳定的，当压力大于该值时，会发生B1构型到B2构型的转化. 关键词： MgS 第一性原理赝势平面波方法 电子结构 转化压力     

First-principles pair potentials across the metal-ceramic interface

Systematic approaches are presented to invert the first-principle binding energy to obtain the pair potentials across the metal/ceramic interfaces. The conformation characteristics of two virtual interface models suitable for the inversion are summarized: (1) the positions of one kind of ceramic ions stay unchanged, but those of the other change; or, (2) there is no change in the relative positions of the ceramic ions to the metal atoms but the positions of two kinds of ceramic ions are all exchanged each other. As an example, we derive the pair potentials of Ni-Zr(4+) and Ni-O(2-) across the Ni/ZrO(2) interface with this method, which exhibit comparable accuracy to the first-principle results. This provides direct evidence that the interfacial potentials obtained from this method can reasonably describe the general features of bondings across the metal-ceramic interface. The limitation of this method is also discussed.     

Maximum Principles and Singular Elliptic Inequalities

In this paper, we present a version of the Omori-Yau maximum principle, a Liouville-type result, and a Phragmen-Lindelöff-type theorem for a class of singular elliptic operators on a Riemannian manifold, which include the p-Laplacian and the mean curvature operator. Some applications of the results obtained are discussed.     

具非线性边界条件的拟线性抛物型方程解的Blow-up

本文考虑一类具非线性边界条件的拟线性抛物方程初边值问题解的整体性态 .通过构造与解有关的适当积分 ,利用“凸性方法”及非线性抛物型方程的极大值原理 ,证明了在某些条件下 ,问题的光滑解u(x ,t)只能在一个有界区间 (0 ,T0 )中存在 ,即有 :limt→T-0sup‖u(· ,t)‖ ∞ =+∞ .     

单相多铁性体CaMn7O12的理论研究与固相合成

在理论研究方面,采用基于密度泛函理论(DFT)的第一性原理方法对CaMn_7O_(12)的晶体结构进行了计算和表征,对螺旋桨型磁序的电子结构及相变机制进行了理论分析和研究;在实验方面以TG-DSC为指导,采用固相反应法制备了单相多铁性体CaMn_7O_(12),并检测表征其磁、电学性能。磁学方面验证了CaMn_7O_(12)的2个磁相转变温度(T_(N1)=90 K和T_(N2)=45 K),测得其在10 K温度下存在磁滞回线(Mr=0.02 emu·g~(-1),Hc≈1 000 Oe);电学方面在室温条件下表征其在10 MHz频率时ε_r=280,tanδ=1.69。     

立方KCaF_3电子、弹性和光学性质的第一性原理研究

基于密度泛函理论和赝势平面波近似法计算研究了立方钙钛矿KCaF_3的弹性、电子和光学性质.基态时,KCaF_3平衡晶格常数、体积弹性模量和实验及其他计算值一致.根据Hooke定律和Christoffel方程,研究了KCaF_3弹性常数Cij、体积弹性模量B、各向同性波速和弹性各向性异性因子随压力的变化关系.从电子能带理论出发,计算得到了KCaF_3电子能带、态密度和Milliken电荷布居数,并对其电子性质进行了详细分析.结果显示:立方钙钛矿KCaF_3为直接带隙绝缘体材料,其禁带宽度为6.22 e V;电荷主要从Ca和K原子向F原子转移;立方钙钛矿KCaF_3属于纯粹的共价型化合物.同时,本文还计算研究了KCaF_3的光学介电函数、吸收系数、复折射率、能量损失谱和反射系数等光学性质.     

Exclusion Principles as Restricted Permutation Symmetries

We give a derivation of exclusion principles for the elementary particles of the standard model, using simple mathematical principles arising from a set theory of identical particles. We apply the theory of permutation group actions, stating some theorems which are proven elsewhere, and interpreting the results as a heuristic derivation of Pauli's Exclusion Principle (PEP) which dictates the formation of elements in the periodic table and the stability of matter, and also a derivation of quark confinement. We arrive at these properties by using a symmetry property of collections of the particles themselves as compared for example to the symmetry property of their wave function under interchange of two particles.     

Ag,Au,K吸附在W(001)表面上的功函数随外加电场的变化

基于局域密度泛函理论和第一性原理赝势法,计算了Ag,Au,K在W(001)表面上吸附时的功函数随外加电场的变化关系.从计算结果可以看到,所有吸附系统的功函数变化与外加电场强度变化之间呈线性关系.通过比较系统功函数随外加电场强度变化的斜率的不同,可以推断Ag—W(001)的键合作用与Au—W(001)键合作用之间的细致差别,表明了Au—W(001)键合作用会略强于Ag—W(001)间的键 关键词： 功函数变化 外加电场 第一性原理计算