基于应变梯度理论的微尺度蜂窝等效模量计算方法

本文提出了一种新的能够计及尺度效应的微纳米蜂窝等效模量的计算方法。将一种单参数应变梯度理论引入到本构方程当中,并基于能量等效原理推导了蜂窝面内等效模量地计算公式。算例分析表明,本文方法能够有效地计及尺度效应对蜂窝等效模量的影响。尺度效应与胞壁厚度和长度的值都有关,当胞壁厚度较小时,尺度效应显著,本文方法预测的模量会明显高于传统方法;而当胞壁厚度较大时,尺度效应变得微弱乃至可以忽略不计。但如果胞壁的长度/厚度比很大,则面内等效模量会趋近于0,此时是否考虑尺度效应意义不大。     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

有机张力半导体及其光电特性

分子张力作为空间设计的重要组成部分正成为调控有机半导体的重要手段。由于分子内产生的拉伸张力、扭曲/弯曲张力以及空间张力而导致p轨道排布重组和构型构象结构发生变化,最近各种几何与拓扑结构的高张力有机半导体材料相继被报道,这使得高张力有机半导体材料成为有机电子领域研究的焦点。为了进一步梳理分子张力在有机半导体材料中扮演的角色与价值,该综述从分子张力的类型、实验与理论量化以及可视化出发,总结了高张力共轭芳烃的分子设计策略、与其光电性能分子张力之间的关系,以及这类新兴材料在光电领域的应用。最后,对高张力共轭芳烃的研究前景进行了展望,阐述了该类材料所面临的机遇与挑战。     

Skyrmion transport driven by pure voltage generated strain gradient

The magnetic skyrmion transport driven by pure voltage-induced strain gradient is proposed and studied via micromagnetic simulation. Through combining the skyrmion with multiferroic heterojunction, a voltage-induced uniaxial strain gradient is adjusted to move skyrmions. In the system, a pair of short-circuited trapezoidal top electrodes can generate the symmetric strain. Due to the symmetry of strain, the magnetic skyrmion can be driven with a linear motion in the middle of the nanostrip without deviation. We calculate the strain distribution generated by the trapezoidal top electrodes pair, and further investigate the influence of the strain intensity as well as the strain gradient on the skyrmion velocity. Our findings provide a stable and low-energy regulation method for skyrmion transport.     

Effect of biaxial strain and hydrostatic pressure on the magnetic properties of bilayer CrI3

Two-dimensional van der Waals magnetic materials are intriguing for applications in the future spintronics devices, so it is crucial to explore strategy to control the magnetic properties. Here, we carried out first-principles calculations and Monte Carlo simulations to investigate the effect of biaxial strain and hydrostatic pressure on the magnetic properties of the bilayer CrI₃. We found that the magnetic anisotropy, intralayer and interlayer exchange interactions, and Curie temperature can be tuned by biaxial strain and hydrostatic pressure. Large compressive biaxial strain may induce a ferromagneticto-antiferromagnetic transition of both CrI₃ layers. The hydrostatic pressure could enhance the intralayer exchange interaction significantly and hence largely boost the Curie temperature. The effect of the biaxial strain and hydrostatic pressure revealed in the bilayer CrI₃ may be generalized to other two-dimensional magnetic materials.     

Second moment of error term of mean value for binary Egyptian fractions

We study the mean square of the error term of the mean value for binary Egyptian fractions.We get an asymptotic formula under the Riemann Hypothesis.     

More efficient time integration for Fourier pseudospectral DNS of incompressible turbulence

Time integration of Fourier pseudospectral DNS is usually performed using the classical fourth-order accurate Runge-Kutta method or other second- or third-order methods, with a fixed step size. We investigate the use of higher-order Runge-Kutta pairs and automatic step size control based on local error estimation. We find that the fifth-order accurate Runge-Kutta pair of Bogacki and Shampine gives much greater accuracy at a significantly reduced computational cost. Specifically, we demonstrate speedups of 2× to 10× for the same accuracy. Numerical tests (including the Taylor-Green vortex, Rayleigh-Taylor instability, and homogeneous isotropic turbulence) confirm the reliability and efficiency of the method. We also show that adaptive time stepping provides a significant computational advantage for some problems (like the development of a Rayleigh-Taylor instability) without compromising accuracy.     

一种非正交对称条带束流位置监测器设计

介绍了一种条带束流位置监测器(BPM)的设计与仿真方法。在国家同步辐射实验室"太赫兹近场高通量材料物性测试系统"工程项目中,针对波荡器出口处真空室非正交对称性的问题,设计了矩形真空室和跑道形真空室下的两种非正交对称性条带BPM,并与传统的圆形真空室下条带BPM进行对比。基于边界元法,利用MATLAB软件分别对三种真空室下的条带BPM进行建模和仿真。仿真结果表明:相对于传统的圆形真空室下条带BPM,矩形和跑道形真空室下条带BPM灵敏度提高了30%,阻抗匹配误差相对降低了20%,束流位置拟合误差降低了80%。考虑加工精度,矩形真空室下的条带BPM更适用于该工程。     

砂岩方梁断裂过程区范围的实验确定方法

裂纹前端的断裂过程区是引起岩石非线性断裂及尺寸效应的主要原因。利用数字图像相关技术对砂岩开展了三点弯曲梁实验,获得观测区域高精度的全场位移和应变数据,根据断裂韧带区域水平位移和水平应变的分布特征,结合裂尖岩石颗粒变化的微观分析,提出采用裂纹尖端水平位移波动性和水平应变突变性所得到的波动系数和水平应变突变值,确定断裂过程区形状和临界尺寸的方法。结果表明:砂岩断裂过程区的形状为不规则的狭长带状区域,断裂过程区的临界长度为11~13mm,临界宽度为1.58~2.36mm。断裂过程区区域内形变在趋向裂尖时呈指数增加,但其单位区域内的形变增量呈波动状态。该方法能够更加准确判断岩石断裂过程区的范围,有助于分析岩石的非线性断裂特性。