Effect of fluorination on the phase sequence,dielectric and electro-optical properties of ferroelectric and antiferroelectric mixtures

Four multicomponent room temperature mixtures were formulated using a pyrimidine-based achiral matrix as host and four terphenyl-based ester chiral compounds as dopants. Among the four mixtures, two exhibit antiferroelectric and two other exhibit ferroelectric phases at room temperature. Dopant molecules differ from each other by position and number of fluorine atom substitution at the benzoate group of the molecular rigid core. Number and location of fluorine atoms in the dopant structure show significant effect on the phase sequences as well as on different physical properties. All the mixtures found to have moderate spontaneous polarisation, high tilt angle, very fast switching time and low viscosity which are important for liquid crystal-based display applications.     

拉曼光谱子空间重合识别修正液中氯代烃

利用拉曼光谱子空间重合对修正液中氯代烃成分进行识别分析。通过计算混合卤代烃组分与标准样品数据库拉曼光谱之间的子间空夹角,依据夹角变化排列筛选出含有最少标准样品数目的子空间,该子空间所含的标准样品组成为待定性混合氯代烃组成,从而实现对混合氯代烃组分的定性分析。将该方法用于修正液中氯代烃的成分定性分析,准确率达100%。该方法操作简单,检测时间短,准确率高,适用于多组分混合体系中的物质定性分析。     

An inverse backward problem for degenerate parabolic equations

This work studies the inverse problem of reconstructing an initial value function in the degenerate parabolic equation using the final measurement data. Problems of this type have important applications in the field of financial engineering. Being different from other inverse backward parabolic problems, the mathematical model in our article may be allowed to degenerate at some part of boundaries, which may lead to the corresponding boundary conditions missing. The conditional stability of the solution is obtained using the logarithmic convexity method. A finite difference scheme is constructed to solve the direct problem and the corresponding stability and convergence are proved. The Landweber iteration algorithm is applied to the inverse problem and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown initial value is recovered very well.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1900–1923, 2017     

Self–gravitating fluid flows with Gowdy symmetry near cosmological singularities

We consider self-gravitating fluids in cosmological spacetimes with Gowdy symmetry on the torus T³ and, in this class, we solve the singular initial value problem for the Einstein–Euler system of general relativity, when an initial data set is prescribed on the hypersurface of singularity. We specify initial conditions for the geometric and matter variables and identify the asymptotic behavior of these variables near the cosmological singularity. Our analysis of this class of nonlinear and singular partial differential equations exhibits a condition on the sound speed, which leads us to the notion of sub-critical, critical, and super-critical regimes. Solutions to the Einstein–Euler systems when the fluid is governed by a linear equation of state are constructed in the first two regimes, while additional difficulties arise in the latter one. All previous studies on inhomogeneous spacetimes concerned vacuum cosmological spacetimes only.     

一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题

依据一维六方准晶压电材料反平面问题的基本方程,利用复变函数方法,通过引入适当的保角映射,研究了一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题,并利用Cauchy积分理论,得到电不可通和电可通边界条件下的应力场和位移场的复表示以及裂纹尖端场强度因子的解析表达式.     

灰色GM(1,1)模型研究综述

GM(1,1)是灰色预测理论的核心模型和基础模型.从累加生成方法、初值优化、背景值优化、参数估计方法、模型性质和模型拓展的视角,梳理了GM(1,1)模型的研究进展.明确了有待进一步研究的问题,对GM(1,1)模型的未来研究方向提出了建议.     

Formation of abnormal dual‐peak profiles in large tilt angle boron implantation

Large tilt angle (LTA) implantation has been employed in Si manufacturing processes in many applications, such as lightly doped drain and halo implant. The depth profile of boron ions usually consists of only single peak at incident angle of 0° with respect to the perpendicular of the silicon surface. However, an abnormal dual‐peak profile was observed at LTA (>40°) with incident energy of 160 keV. By using a Monte Carlo method to simulate the ion implant process, it was found that the projected range of boron ions agrees completely with the formation of the first peak position that is shallower in depth, while the cause for the second peak that corresponds with a depth much deeper in the Si substrate was unknown. During the simulation, it was also found that when the tilt angle was increased, the sputtering yields and Si displacements increased significantly, and this phenomenon indicates that during LTA implantation, Si damage may not be negligible anymore. The Si damage effect that was as due to either low Si density or transient Si displacement in the simulation could have led to partial incident boron ions penetrating much deeper into the Si substrate and thus, caused the emergence of the second peak. Copyright © 2016 John Wiley & Sons, Ltd.     

Characterization of high‐aspect‐ratio periodic structures by X‐ray photoelectron spectroscopy

X‐ray photoelectron spectroscopy (XPS) is a powerful surface characterization technique often relied on for quantification of surface species and coverages. Investigation of silicon microrods, considered a model for high‐aspect‐ratio structures, at different angles with respect to substrate normal was determined to have a significant impact on the relative sensitivity of surface‐bound species on rods relative to the base substrate. Comparison between planar silicon and microrod arrays demonstrates that the angular dependence is complicated and that careful studies must optimize conditions to differentiate between surfaces. In addition, the use of reverse angle resolved XPS, where the substrate is turned away from the X‐ray source, is shown to assist in simplifying the spectrum by removing underlying signal from the substrate near the base. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical solution of a singular integral equation arising in a cruciform crack problem

A singular integral equation arising in a cruciform crack problem is investigated in the present paper. Based on the convex technique, the piecewise Taylor-series expansion method is extended by introducing a weight parameter. An approximate solution of the singular integral equation is constructed and its convergence and error estimate are made. The variations of the approximate solutions associating with stress intensity factors are analyzed by considering internal pressures of power and sine functions, respectively. By comparing with the known methods, the observations reveal that a good approximation can be achieved using less derivative times, less discretization points, and a suitable weight parameter. The obtained results show that the crack growth is dependent on applied mechanical loadings.     

A nonhomogeneous boundary value problem for the Kuramoto–Sivashinsky equation in a quarter plane

We study the initial boundary value problem for the one‐dimensional Kuramoto–Sivashinsky equation posed in a half line with nonhomogeneous boundary conditions. Through the analysis of the boundary integral operator, and applying the known results of the Cauchy problem of the Kuramoto–Sivashinsky equation posed on the whole line , the initial boundary value problem of the Kuramoto–Sivashinsky equation is shown to be globally well‐posed in Sobolev space for any s >?2. Copyright © 2017 John Wiley & Sons, Ltd.