Thec logc contribution to the electrolyte conductance and Onsager's reciprocal relation

The differential equations and the boundary conditions for the nonequilibrium binary distribution function of an unsymmetrical binary electrolyte are derived from the Ebeling-Falkenhagen continuity equation. The connection between the Onsager reciprocal relation and the binary distribution functions is shown. Further, Feistel's result for thec logc contribution to the conductance is extended to unsymmetrical binary electrolytes. The reason for the difference between Feistel's and Chen'sc logc term is explained, and the significance of Onsager's reciprocal relation for the calculation ofc logc and higher-concentration contributions of the conductance is discussed.     

Sm, Pr掺杂CeO2和CeMoO15基固体电解质的结构与性能

采用溶胶凝胶法制备了Sm和Pr掺杂的CeO2和CeMoO15基固体电解质, 通过X射线衍射(XRD)、拉曼光谱(Raman)、场发射扫描电镜(FE-SEM)等手段对氧化物结构进行了分析, 用交流阻抗谱测试了其电性能, 并比较了不同基体及其掺杂体系的结构与电性能. 结果表明, Ce6MoO15基掺杂体系的导电性能高于CeO2基掺杂体系; 元素Mo的加入使Ce6MoO15基材料的晶粒尺寸增大, 晶界相成分减少, 材料的晶界电导率增加, 600 ℃以下材料导电性能明显提高; Pr的掺入减小了材料的晶粒尺寸, 提高了材料的晶界电导率.     

熔体快速冷凝过程的微观结构演化

采用分子动力学模拟技术研究了金属间化合物AuCu3熔体的双体分布函数、键对、多面体、配位数等在快速凝固条件下随温度的变化情况，详细考察了AuCu3中微观组团随温度的演化特点.结果表明，AuCu3熔体降温至700 K时双体分布函数的第二峰已发生劈裂，液态金属中已经产生了非晶态；同时液体中的键对数及多面体数与温度的关系都表明，在上述向非晶转变的过程中，AuCu3熔体的确发生了微观结构组态的变化，其中以液体中的缺陷多面体随温度变化最为剧烈.     

Calculating the energies for Ag(001) twist boundaries utilizing the modified analytical embedded atom method

The unrelaxed energies for Ag(001) twist grain boundaries (GBs) have been calculated using the modified analytical embedded atom method (MAEAM). The results show that, besides zero energy in a perfect crystal (corresponding to the twist angle 0°), the second smallest GB energy corresponds to the twist angle 36.87°. This is consistent with the experimental results. For other twist angles, the GB energies remain nearly constant even for a twist angle as small as 1.94°. Translation parallel to the boundary plane could result in a periodic change in GB energy. Copyright © 2004 John Wiley & Sons, Ltd.     

胶束介质在动力学分析中的应用

评述了胶束介质在动力学分析测定中的作用和应用状况，讨论了胶束催化的动力学特征，胶束对反应物理化学性质的修饰及其在动力学多组份测定和酶催化动力学分析中的应用。     

Reconstructing small perturbations of an obstacle for acoustic waves from boundary measurements on the perturbed shape itself

We derive relationships between the shape deformation of an impenetrable obstacle and boundary measurements of scattering fields on the perturbed shape itself. Our derivation is rigorous by using a systematic way, based on layer potential techniques and the field expansion (FE) method (formal derivation). We extend these techniques to derive asymptotic expansions of the Dirichlet-to-Neumann (DNO) and Neumann-to-Dirichlet (NDO) operators in terms of the small perturbations of the obstacle as well as relationships between the shape deformation of an obstacle and boundary measurements of DNO or NDO on the perturbed shape itself. All relationships lead us to very effective algorithms for determining lower order Fourier coefficients of the shape perturbation of the obstacle.     

曲边区域上的多边形网格间断有限元离散及其多重网格算法

本文利用多边形网格上的间断有限元方法离散二阶椭圆方程,在曲边区域上,采用多条直短边逼近曲边的以直代曲的策略,实现了高阶元在能量范数下的最优收敛.本文还将这一方法用于带曲边界面问题的求解,同样得到高阶元的最优收敛.此外我们还设计并分析了这一方法的\linebreakW-cycle和Variable V-cycle多重网格预条件方法,证明当光滑次数足够多时,多重网格预条件算法一致收敛.最后给出了数值算例,证实该算法的可行性并验证了理论分析的结果.     

Leray–Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress–strain relation

We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba–Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. We prove the existence of global-in-time weak solutions satisfying an energy inequality under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.     

On Two-point Boundary Value Problems for Second-order Difference Equation

In this paper, we aim to investigate the difference equation \begin{align*} \Delta^{2}y(t-1)+|y(t)|=0, \ \ \ \ \ t\in[1,T]_{\mathbb{Z}} \end{align*} with different boundary conditions $y(0)=0$ or $\Delta y(0)=0$ and $y(T+1)=B$ or $\Delta y(T)=B$,\ where\ $T\geq 1$ is an integer and $B\in\mathbb{R}$. We will show that how the values of $T$ and $B$ influence the existence and uniqueness of the solutions to the about problem. In details, for the different problems, the $TB$-plane explicitly divided into different parts according to the number of the solutions to the above problems. These parts of $TB$-plane for the value of $T$ and $B$ guarantee the uniqueness, the existence and the nonexistence of solutions respectively.     

The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family

We here consider testing the hypothesis ofhomogeneity against the alternative of a two-component mixture of densities. The paper focuses on the asymptotic null distribution of 2 log _n , where _n is the likelihood ratio statistic. The main result, obtained by simulation, is that its limiting distribution appears pivotal (in the sense of constant percentiles over the unknown parameter), but model specific (differs if the model is changed from Poisson to normal, say), and is not at all well approximated by the conventional ₍₂₎ ² -distribution obtained by counting parameters. In Section 3, the binomial with sample size parameter 2 is considered. Via a simple geometric characterization the case for which the likelihood ratio is 1 can easily be identified and the corresponding probability is found. Closed form expressions for the likelihood ratio _n are possible and the asymptotic distribution of 2 log _n is shown to be the mixture giving equal weights to the one point distribution with all its mass equal to zero and the ²-distribution with 1 degree of freedom. A similar result is reached in Section 4 for the Poisson with a small parameter value (0.1), although the geometric characterization is different. In Section 5 we consider the Poisson case in full generality. There is still a positive asymptotic probability that the likelihood ratio is 1. The upper precentiles of the null distribution of 2 log _n are found by simulation for various populations and shown to be nearly independent of the population parameter, and approximately equal to the (1–2)100 percentiles of ₍₁₎ ² . In Sections 6 and 7, we close with a study of two continuous densities, theexponential and thenormal with known variance. In these models the asymptotic distribution of 2 log _n is pivotal. Selected (1–) 100 percentiles are presented and shown to differ between the two models.