电子束敏感材料的原子尺度结构研究

分子筛和金属有机骨架(MOF)材料以其独特的孔道和骨架结构在催化、 储能、 干燥及净化和吸附分离等领域有着广泛应用, 对其结构的原子尺度表征对于深入理解其构效关系具有重要意义. 但其大孔道结构和有机骨架使得它们对电子束辐照极为敏感, 在常规透射电镜成像模式下结构会很快被破坏变为非晶, 从而无法获得孔道和骨架的原子排列信息. 最近发展起来的基于积分差分相位衬度扫描透射电子显微(iDPC-STEM)技术在电子敏感材料和轻元素组分成像方面展现出明显优势, 使得对多孔骨架材料及烃池物种的表征成为了可能. 本文综述了本课题组近期利用该技术对分子筛和MOF材料原子尺度结构方面的研究. 将iDPC-STEM技术应用到ZSM-5分子筛催化剂中, 实现了对该分子筛的原子级骨架结构的成像分析. 在MOF体系中, 利用该技术观察到MIL-101骨架内部有机连接体与金属节点的配位方式, 在此基础上解析了MIL-101结构中有机配体的连接和金属节点的苯环结构, 并观察了MOF的原子级表面、 界面和缺陷等局域结构特征. 最后对iDPC-STEM技术在原子尺度成像方面的应用潜力进行了总结与展望.     

Exceptional Laurent biorthogonal polynomials through spectral transformations of generalized eigenvalue problems

A formulation is given for the spectral transformation of the generalized eigenvalue problem through the decomposition of the second-order differential operators. This allows us to construct some Laurent biorthogonal polynomial systems with gaps in the degree of the polynomial sequence. These correspond to an exceptional-type extension of the orthogonal polynomials, as an extension of the Laurent biorthogonal polynomials. Specifically, we construct the exceptional extension of the Hendriksen–van Rossum polynomials, which are biorthogonal analogs of the classical orthogonal polynomials. Similar to the cases of exceptional extensions of classical orthogonal polynomials, both state-deletion and state-addition occur.     

A multistep collocation method for solving advection equations with delay

Advection equations with delay are appeared in the modeling of the dynamics of structured cell populations. In this article, we construct an efficient two-dimensional multistep collocation method for the numerical solution of a class of advection equations with delay. Equations with aftereffect and equations with both aftereffect and retardation of a state variable are considered. Computability of the algorithm and convergence properties of the proposed numerical method are analyzed for solutions in appropriate Sobolev spaces, and it is shown that the proposed scheme enjoys the spectral accuracy. Numerical examples are given and comparison with other existing methods in the literature is made to demonstrate the efficiency, superiority and high accuracy of the presented method.     

Recent Results on Recurrent Solutions and Limit Distributions of SDEs

The limit distribution for homogeneous Markov processes is studied extensively and well understood, but it is not the case for inhomogeneous Markov processes. In this paper, we review some recent results on inhomogeneous Markov processes generated by non-autonomous stochastic (partial) differential equations (SDE in short). Under some suitable conditions, we show that the distribution of recurrent solutions of SDEs constitutes the limit distribution of the corresponding inhomogeneous Markov processes.     

光纤水听器相位生成载波解调非线性因素的抑制方法

为了消除非线性因素对相位生成载波解调结果的干扰,降低相位生成载波解调过程中低通滤波器的频响特性对相位生成载波解调结果的影响,该文提出了一种基于扩展卡尔曼滤波椭圆参数估计的相位生成载波微分交叉相乘解调方法。该方法在综合考虑各种非线性因素对相位生成载波微分交叉相乘解调结果的影响的基础上,对传统的相位生成载波微分交叉相乘解调过程进行了改进。经过计算机仿真和实验验证,该文所提出的扩展卡尔曼滤波微分交叉相乘方法能够有效地抑制非线性因素对相位生成载波解调结果的干扰,相比传统的相位生成载波微分交叉相乘方法,其信噪比提高了35.0 d B,总谐波失真降低了30.7 dB,信噪谐波比提高了31.0 dB,且扩展卡尔曼滤波微分交叉相乘方法受解调过程中低通滤波器频响特性的影响较小。     

Influence of Differential Diffusion on Super-Equilibrium Temperature in Turbulent Non-Premixed Hydrogen/Air Flames

In this paper we wish to investigate the occurrence of super-equilibrium temperature values, observed in many experimental configurations. We would like to understand the origin of this phenomenon. Previous authors have already shown that differential diffusion can lead to considerable changes in the temperature field and we would like to build on top of this observation. We investigate numerically super-equilibrium combustion by considering both laminar counter-flow and turbulent diluted hydrogen/air diffusion flames. These turbulent flames are computed using direct numerical simulations (DNS). A detailed reaction mechanism is employed and the transport properties are modeled using multicomponent diffusion velocities, including the Soret effect. Analyzing these results we introduce three complementary parameters (dilution-free mixture fraction, dilution excess and local enthalpy) to describe the local combustion conditions. Introducing a measure of dilution separately from the mixture fraction is necessary for a proper analysis. Using this set of parameters it becomes possible to explain super-equilibrium temperature levels as a consequence of differential diffusion.     

On a Model of a Currency Exchange Rate – Local Stability and Periodic Solutions

A delay differential equation is presented which models how the behavior of traders influences the short time price movements of an asset. Sensitivity to price changes is measured by a parameter a. There is a single equilibrium solution, which is non-hyperbolic for all a>0. We prove that for a< 1 the equilibrium is asymptotically stable, and that for a>1 a 2-dimensional global center-unstable manifold connects the equilibrium to a periodic orbit. Its birth at a=1 is not of Hopf type and seems part of a Takens–Bogdanov scenario.     

Milling Bifurcations from Structural Asymmetry and Nonlinear Regeneration

This paper investigates multiple modeling choices for analyzing the rich and complex dynamics of high-speed milling processes. Various models are introduced to capture the effects of asymmetric structural modes and the influence of nonlinear regeneration in a discontinuous cutting force model. Stability is determined from the development of a dynamic map for the resulting variational system. The general case of asymmetric structural elements is investigated with a fixed frame and rotating frame model to show differences in the predicted unstable regions due to parametric excitation. Analytical and numerical investigations are confirmed through a series of experimental cutting tests. The principal results are additional unstable regions, hysteresis in the bifurcation diagrams, and the presence of coexisting periodic and quasiperiodic attractors which is confirmed through experimentation.     

Dichotomy Spectrum for Nonautonomous Differential Equations

For nonautonomous linear differential equations x=A(t) x with locally integrable A: RR ^N×N the so-called dichotomy spectrum is investigated in this paper. As the closely related dichotomy spectrum for skew product flows with compact base (Sacker–Sell spectrum) our dichotomy spectrum for nonautonomous differential equations consists of at most N closed intervals, which in contrast to the Sacker–Sell spectrum may be unbounded. In the constant coefficients case these intervals reduce to the real parts of the eigenvalues of A. In any case the spectral intervals are associated with spectral manifolds comprising solutions with a common exponential growth rate. The main result of this paper is a spectral theorem which describes all possible forms of the dichotomy spectrum.     

微分求积方法对于桩基大变形分析的应用

本文基于大变形的理论,采用弧坐标首先建立了具有初始位移的桩基的非线性数学模型,一组强非线性的微分-积分方程,其中,地基的抗力采用了Winkeler模型;其次,引入变数变换将微分-积分方程转化为一组非线性微分方程,并用微分求积方法离散了方程组,得到一组离散化的非线性代数方程;最后用Newton-Raphson迭代方法对离散化方程进行了求解,得到了桩基变形前后的构形、弯矩和剪力.计算中选取了两种不同类型的初始位移,并考察了它们对桩基大变形力学行为的影响.