The stochastic energy-Casimir methodLa méthode d'énergie-Casimir stochastique

In this paper, we extend the energy-Casimir stability method for deterministic Lie–Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems.     

3d过渡金属掺杂M_2@Si_(20)(M=Sc-Zn)团簇的密度泛函理论研究

利用密度泛函理论(DFT)研究3d过渡金属掺杂硅团簇的几何结构和稳定性,计算了绝热电子亲和能和垂直电离能,内嵌双金属间距,自旋磁矩等.结果表明内嵌的Sc、Ti、V、Mn金属二聚体和十二面体硅笼构成了稳定的富勒烯结构,随着d电子数目的增加其内嵌的富勒烯构型有部分畸变,总体而言Si_(20)团簇掺杂双金属后稳定性得到了提高.     

Existence of solutions for a higher-order semilinear parabolic equation with singular initial data

We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem.     

三维非稳定渗流自由面边界积分项的精确数值计算

利用固定网格法分析三维非稳定渗流问题时,将要面对两项积分难题:以自由面及单元表面为边界的空间积分及以自由面为边界的曲面积分。针对常用的任意8结点6平面三维普通单元,提出采用坐标变换及等参变换技术求取空间积分项的精确数值解;至于曲面积分项,建议改用单元非饱和区部分表面作为积分边界,经过坐标变换及等参变换处理积分边界后,利用高斯数值积分可求出曲面积分项的精确数值解。通过一个普通单元及一项均质半无限边界堤坝的实例分析,表明此方法的精确性和稳定性良好。     

基于噪声误差模型的不规则区域室内定位和锚点分布优化

结合实际工业背景,研究了一类在不规则区域且误差不服从高斯分布的室内无线定位问题.给出了噪声误差模型,在对多个传统定位算法进行性能分析的基础上,研究了待定位区域内锚点阵列的分布,改进了多锚点阵列下的定位方法,并提出基于Delaunay三角剖分锚点分布优化模型和求解方法.     

An investigation of influencing of Sb and Bi contents on surface tensions associated with Pb-free Sn-Zn-Sb-Bi quaternary and sub-quaternary solder alloys

The surface tensions of ternary and quaternary systems of Sn-based Pb-free solder alloys have been calculated using geometric models, such as Muggianu, Kohler, Chou’s general solution model (GSM), Toop, Guggenheim, ideal Butler and Butler models. It is observed from the calculation carried out in the present work that Sb and Bi contents decrease the surface tension of the solder alloys Sn-Zn-Sb-Bi. It is inferred from the statistical analysis that the best agreement between the experimental results and the corresponding calculated values of the surface tensions is generally observed in GSM and Muggianu models among the geometric models. Whereas Muggianu model is the most appropriate. Relatively good agreements have been observed between models considered in this study and experimental data.     

Generation of intense water window X-ray pulses by superposition of an initial state of the helium atom driven by a three-color field

We theoretically study the generation of high-order harmonics and attosecond pulses from the superposition of an initial state in helium atom driven by a three-color laser field. It is shown that when the initial state is chosen to be a single electronic state, due to the rapid depletion of the ground state, the efficiency of the spectral continuum will be decreased as the initial state increases. When the initial state is chosen to be the coherent superposition of the ground state and an arbitrary excited state, the efficiency of the spectral continuum can be enhanced compared to that from the single initial state. Further, with the optimization of the three-color laser beam, not only can the harmonic cutoff be extended to the water window X-ray region but also the spectral continuum is contributed by the single harmonic emission peak with the dominant short quantum path. Consequently, two combinations of the laser parameters can be found to generate the water window spectral continuum. By properly superposing some harmonics on the spectral continuum, a number of intense water window pulses with the duration of sub-35 as can be produced.     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

A survey of surface tension,molar volume and density for Sn–Ag–Cu–Bi–Sb quinary alloys as lead-free solders

ABSTRACT

By applying the geometric models and the theoretical equation, the surface tension, the molar volume and the density were studied. The empirical calculations were carried out in temperature range 623?K?≤?T?≤?1123?K. Only few thermophysical properties were estimated for eight quinary alloys: Sn3.55Ag0.5Cu3Bi3Sb, Sn3.48Ag0.5Cu3Bi5Sb, Sn3.48 Ag0.5Cu5Bi3Sb, Sn3.40 Ag0.5Cu5Bi5Sb, Sn3.53Ag1Cu3Bi3Sb, Sn3.46Ag1Cu3Bi5Sb, Sn3.46Ag1Cu5Bi3Sb, Sn3.38Ag1Cu5Bi5Sb. The results show that surface tension and density have a linear appearance for all temperatures. We have also studied the influence of the composition and temperature in the studied alloys. The obtained theoretical results are compared with the experimental ones and with the conventional Pb–Sn welds.