Investigation of the superionic behaviour of BaF 2 ( x mol% LaF 3 ) by raman and brillouin scattering and molecular dynamics simulations

High temperature Raman and Brillouin light scattering experiments have been combined with molecular dynamics simulations to provide a comprehensive study of the superionic state of BaF 2 ( x v mol% LaF 3 ) over a particularly wide range of LaF 3 dopant concentrations from x =0 to 50. Room temperature Raman spectra for x =0, 5 and 10 show the usual T 2g symmetry mode at 241 v cm m 1 , but for samples with x =20, 30 and 50 the dominant Raman mode is at higher frequencies and of E g symmetry. The temperature dependence of the Raman line-widths show initial near linear increases followed by substantial increases above temperatures ( T c ) at 1200, 850, 800, 975, 950 and 920 v K for x =0, 5, 10, 20, 30 and 50. In the Brillouin scattering experiments, the acoustic modes respectively related to elastic constants C 11 and C 44 initially showed a quasi-linear decrease in frequency with increasing temperature. Above the same characteristic values of T c , where the Raman line-widths show marked increases, there are substantial decreases in the elastic constant C 11 for all samples with x =0 to 50. Only the doped samples showed significant decreases in C 44 at corresponding values of T c . Molecular dynamics (MD) simulations have been carried out on the same systems. From the calculated mean square displacements, the diffusion coefficients ( D ) of the mobile fluorine ions were calculated as a function of temperature for each of the samples. Substantial increases in the values of D occur above the respective values of T c determined in the light scattering experiments. The MD simulations also provide details of the mechanisms of diffusion of the mobile fluorine ions. The results emphasize the role of motional effects as an explanation of the mechanisms responsible and provide a self-consistent explanation of the dominant processes in the superionic phase of doped fluorites.     

Thermodynamic properties of OsB under high temperature and high pressure

The energy-volume curves of OsB have been obtained using the first-principles plane-wave ultrasoft-pseudopotential density functional theory (DFT) within the generalized gradient approximation (GGA) and local density approximation (LDA). Using the quasi-harmonic Debye model we first analyze the specific heat, the coefficients of thermal expansion as well as the thermodynamic Grüneisen parameter of OsB in a wide temperature range at high pressure. At temperature 300 K, the coefficients of thermal expansion α_V by LDA and GGA calculations are 1.67×10⁻⁵ 1/K and 2.01×10⁻⁵ 1/K, respectively. The specific heat of OsB at constant pressure (volume) is also calculated. Meanwhile, we find that the Debye temperature of OsB increases monotonically with increasing pressure. The present study leads to a better understanding of how the OsB materials respond to pressure and temperature.     

Chemistry in Lasers. IX. Reexamination of the Einstein Coefficients and Two Level Population Inversion

From a re-examination of the Einstein coefficients in terms of current theory the common assumption that population inversion cannot be maintained in a two level system by optical pumping is shown to be erroneous. The nonisotropy of the radiative ensemble in an optical resonant cavity, absent from the original derivation by Einstein, is shown to be of decisive importance.     

模糊线性规划在列车运行调整中的应用

利用模糊集理论来处理列车运行调整过程中涉及的不确定因素,通过合理的权重系数来表示不同约束条件和目标函数的相对重要程度,在Werners方法的基础上提出一种基于加法算子带权重系数的对称型模糊线性规划.将该模型用于沪宁段列车运行晚点调整的优化问题,计算得到了优于Werners方法的结果.     

Convex Holes Produce Lower Bounds for Coefficients

Let D denote the open unit disk and $ f:D \to \bar {{\bf C}}$ be meromorphic and injective in D . Especially, we consider such f which have an expansion $$ f(z) = z + \sum \limits_{n=2}^{\infty }a_n(\;f\,)z^n $$ in a neighbourhood of the origin and map D onto a domain whose complement with respect to $\bar {{\bf C}}$ is convex. Let the set of these functions be denoted by Co . We fix | f m 1 ( X )| for f ] Co and determine the inner and outer radius of the ring domain which is the domain of variability of a 2 ( f ) for such f . Further, it is shown that f ] Co implies that $$ \phi (z) = z+2 {f'(z) \over f''(z)}$$ is holomorphic in D and maps D into itself. This implication in turn implies the inequalities | a n ( f )| S 1 for f ] Co and n = 2,3,4. In addition, we show that | a n ( f )| S 1/2 for f ] Co and all n S 2 .     

The coefficients of reflection and refraction on interface of the crystals in the Savart polariscope

According to the boundary conditions of the electromagnetic field, the coefficients of reflection and refraction on the interface of crystal in the Savart polariscope are obtained for ordinary ray (o-ray) and extraordinary ray (e-ray).The coefficients of reflection and refraction are different from an isotropic medium and have more complicated forms than isotropic medium.     

An analysis of the solution set to a homotopy equation between polynomials with real coefficients

We investigate the structure of the solution setS to a homotopy equationH(Z,t)=0 between two polynomialsF andG with real coefficients in one complex variableZ. The mapH is represented asH(x+iy, t)=h ₁(x, y, t)+ih ₂(x, y, t), whereh ₁ andh ₂ are polynomials from ℝ² × [0,1] into ℝ and i is the imaginary unit. Since all the coefficients ofF andG are real, there is a polynomialh ₃ such thath ₂(x, y, t)=yh₃(x, y, t). Then the solution setS is divided into two sets {(x, t)∶h ₁(x, 0, t)=0} and {(x+iy, t)∶h ₁(x, y, t)=0,h ₃(x, y, t)=0}. Using this division, we make the structure ofS clear. Finally we briefly explain the structure of the solution set to a homotopy equation between polynomial systems with real coefficients in several variables.     

纳米二氧化锆改性聚醚砜的研究

互联网的高速发展对通讯速度和通讯容量提出了越来越高的要求,也对基础性的材料科学提出同样的挑战。目前的信息高速传输网络主干线主要采用石英玻璃光纤,由于其光纤芯极细（8～62μm）,因而对光纤连接器的性能要求极高,而光纤连接器性能的好坏又直接影响到通讯的速度及容量。     

Stabilities and Transfer Activity Coefficients from Water to Polar Nonaqueous Solvents of Benzo-15-Crown-5- and 15-Crown-5-Alkali Metal Ion Complexes

Stability constants (K_ML) of 1 : 1 benzo-15-crown-5 (B15C5) complexes with alkali metal ions were conductometrically measured in water at 25°C. Transfer activity coefficients of B15C5 and 15-crown-5 (15C5) from water to polar nonaqueous solvents were determined at 25°C. By using these data and the literature values, transfer activity coefficients of the B15C5 and 15C5 complexes with alkali metal ions from water to the polar nonaqueous solvents were calculated to study the solute-solvent interaction of the crown ether complexes. The stability of the B15C5 complex is lower in water than in any other nonaqueous solvent. The K_ML value for B15C5 is always smaller than the corresponding K ML value for 15C5. The interaction of the B15C5 or the 15C5 complex with the solvents depends on the alkali metal ion in the crown cavity. All the B15C5 and 15C5 complexes undergo hydrophobic hydration, which is particularly stronger for the B15C5 complexes with Na⁺ and K⁺. The unexpectedly lowest stability of the B15C5- or the 15C5-alkali metal ion complex in water among all the solvents is caused by the hydrogen bonding between ether oxygen atoms of uncomplexed B15C5 or 15C5 and water.     

A remark on the Cauchy problem of 1D compressible Navier-Stokes equations with density-dependent viscosity coefficients

This paper is concerned with the Cauchy problems of one-dimensional compressible Navier-Stokes equations with density-dependent viscosity coefcients.By assumingρ0∈L1（R）,we will prove the existence of weak solutions to the Cauchy problems forθ〉0.This will improve results in Jiu and Xin’s paper（Kinet.Relat.Models,1（2）：313–330（2008））in whichθ〉12is required.In addition,We will study the large time asymptotic behavior of such weak solutions.