纳米分辨率的三维形貌检测仪

从光干涉方式，瞳窗关系和光源带宽等基本关系出发，利用空间不变系统理论解析了相移显微干涉检测系统中衍射效应的影响。为了减小横向分辨率对纵向分辨率的影响，利用相关信息提取或数字滤波的方法，获得了纳米分辨率的三维形貌。     

2(1/2)维等离子体粒子模拟分布式并行程序设计

设计了两种粒子模拟的并行算法,并对其进行了比较,基于消息传递环境开发2(1/2)维粒子模拟并行程序,测试并分析了并行性能.粒子模拟算法中,给出了一个初始化粒子三维Maxwell速度分布的算法,并对常用的电磁场的Lindman吸收边界作了推广.最后对激光钻孔问题作了粒子模拟计算,验证了该并行程序.     

Computer Simulation of a 3-D Sensing System with Structured Illumination

A computer simulation system of three-dimensional sensing with structured illumination is presented. It includes the generation of deformed fringe patterns from 3-D shapes and the reconstruction of 3-D shapes, conversely. Some experimental results of the deformed fringe pattern and the reconstructed object shapes are presented. We have also discussed the effect of some major system parameters on the measurement results and considered how to correct these parameters according to the measurement result of the standard plane. Using this simulation system, the major system parameters: environmental conditions, measurement accuracy and algorithm evaluation of the 3-D shape measurement system based on PMP, FTP, SPM, etc., can be researched. © 1997 Elsevier Science Ltd. All rights reserved.     

Simulation of three‐dimensional flows over moving objects by an improved immersed boundary–lattice Boltzmann method

An improved immersed boundary–lattice Boltzmann method (IB–LBM) developed recently [28] was applied in this work to simulate three‐dimensional (3D) flows over moving objects. By enforcing the non‐slip boundary condition, the method could avoid any flow penetration to the wall. In the developed IB–LBM solver, the flow field is obtained on the non‐uniform mesh by the efficient LBM that is based on the second‐order one‐dimensional interpolation. As a consequence, its coefficients could be computed simply. By simulating flows over a stationary sphere and torus [28] accurately and efficiently, the proposed IB–LBM showed its ability to handle 3D flow problems with curved boundaries. In this paper, we further applied this method to simulate 3D flows around moving boundaries. As a first example, the flow over a rotating sphere was simulated. The obtained results agreed very well with the previous data in the literature. Then, simulation of flow over a rotating torus was conducted. The capability of the improved IB–LBM for solving 3D flows over moving objects with complex geometries was demonstrated via the simulations of fish swimming and dragonfly flight. The numerical results displayed quantitative and qualitative agreement with the date in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

(2+1)维Konopelchenko-Dubrovsky方程新的多孤子解

利用齐次平衡方法,将(2+1)维Konopelchenko-Dubrovsky方程转化为两个变量分离的线性偏微分方程,然后采用三种不同的函数假设,得到相应的常系数微分方程,通过求解特征方程,方便地构造出Konopelchenko-Dubrovsky方程新的多孤子解.     

Lower bound for the ratios of eigenvalues of Schrödinger with nonpositive single‐barrier potentials

Horváth and Kiss (Proc. Amer. Math. Soc., 2005) proved the upper bound estimate for Dirichlet eigenvalue ratios of the Schrödinger problem ?y^′′ + q(x)y = λy with nonnegative and single‐well potential q. In this paper, we prove that if q(x) is a nonpositive, continuous, and single‐barrier potential, then for λ_n > λ_m≥ ? 2q^?, where . In particular, if q(x) satisfies the additional condition , then λ₁ > 0 and for n > m ≥ 1. For this result, we develop a new approach to study the monotonicity of the modified Prüfer angle function.     

Concentration on curves for a nonlinear Schrödinger problem with electromagnetic potential

We prove the existence of solutions to the nonlinear Schrödinger equation ${\epsilon }^2{(i\mathrm{?}+\mathit{A})}^{2}u+V(y)u?|u{|}^{p?1}u=0$ in ${\mathbb{R}}^2$ with a magnetic potential $\mathit{A}=(A_1,A_2)$. Here V represents the electric potential, the index p is greater than 1. Along some sequence $\{{\epsilon }_n\}$ tending to zero we exhibit complex-value solutions that concentrate along some closed curves.     

一类特定的AF-代数

讨论了一类特定的AF-代数,其上的恒等同态可以用一列有限维值域的自同态逐点逼近.给出了这类AF-代数的K-理论刻画,并给出了一个不在这一类中的RFD AF-代数的例子.     

Spin–orbit stiffness of the spin‐polarized electron gas

In a spin‐polarized electron gas, Coulomb interaction couples the spin and motion degrees of freedom to build propagating spin waves. The spin wave stiffness S_sw quantifies the energy cost to trigger such excitation by perturbing the kinetic energy of the electron gas (i.e. putting it in motion). Here we introduce the concept of spin–orbit stiffness, S_so, as the energy necessary to excite a spin wave with a spin polarization induced by spin–orbit coupling. This quantity governs the Coulombic enhancement of the spin–orbit field acting of the spin wave. First‐principles calculations and electronic Raman scattering experiments carried out on a model spin‐polarized electron gas, embedded in a CdMnTe quantum well, demonstrate that S_so = S_sw. Through optical gating of the structure, we demonstrate the reproducible tuning of S_so by a factor of 3, highlighting the great potential of spin–orbit control of spin waves in view of spintronics applications. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)