多孔功能梯度材料Timoshenko梁的自由振动分析

基于Timoshenko梁理论研究多孔功能梯度材料梁(FGMs)的自由振动问题.首先,考虑多孔功能梯度材料梁的孔隙率模型,建立了两种类型的孔隙分布.其次,基于Timoshenko梁变形理论,给出位移场方程、几何方程和本构方程,利用Hamilton原理推导多孔功能梯度材料梁的自由振动控制微分方程,并进行无量纲化,然后应用微分变换法(DTM)对无量纲控制微分方程及其边界条件进行变换,得到含有固有频率的等价代数特征方程.最后,计算了固定-固定(C-C)、固定-简支(C-S)和简支-简支(S-S)三种不同边界下多孔功能梯度材料梁自由振动的无量纲固有频率.将其退化为均匀材料与已有文献数据结果对照,验证了正确性.讨论了孔隙率、细长比和梯度指数对多孔功能梯度材料梁无量纲固有频率的影响.     

Almost contact Riemannian three-manifolds with Reeb flow symmetry

In this paper we give a complete classification of simply connected homogeneous almost α-Kenmotsu three-manifolds M whose Ricci operator is invariant along the Reeb flow. We get this classification by using the Gaussian and the extrinsic curvature associated with the canonical foliation of M.     

Completion of R2 with a Conformal Metric as a Closed Surface

In this paper,we obtain some asymptotic behavior results for solutions to the prescribed Gaussian curvature equation.Moreover,we prove that under a con-formal metric in R2,if the total Gaussian curvature is 4π,the conformal area of R2 is finite and the Gaussian curvature is bounded,then R2 is a compact C1,α surface after completion at ∞,for any α ∈(0,1).If the Gaussian curvature has a Holder decay at in-finity,then the completed surface is C2.For radial solutions,the same regularity holds if the Gaussian curvature has a limit at infinity.     

Gaussian BV Functions and Gaussian BV Capacity on Stratified Groups

Let $G$ be a stratified Lie group and let $\{X_1, \cdots, X_{n_1}\}$ be a basis of the first layer of the Lie algebra of $G$. The sub-Laplacian $\Delta_G$ is defined by $$\Delta_G= -\sum^{n_1}_{j=1} X^2_j. $$ The operator defined by $$\Delta_G-\sum^{n_1}_{j=1}\frac{X_jp}{p}X_j$$ is called the Ornstein-Uhlenbeck operator on $G$, where $p$ is a heat kernel at time 1 on $G$. In this paper, we investigate Gaussian BV functions and Gaussian BV capacities associated with the Ornstein-Uhlenbeck operator on the stratified Lie group.     

基于高斯回归分析的水稻氮素敏感波段筛选及含量估算

水稻氮素含量的准确监测是稻田精准施肥的重要环节,水稻叶片氮素含量发生变化会引起叶片、冠层的光谱发射率发生变化,高光谱遥感是目前作物氮素无损监测的关键技术之一。以2018年-2019年湖北监利两年水稻氮肥试验为基础,分别获取水稻分蘖期、拔节期、孕穗期、扬花期、灌浆期五个生育期水稻叶片和冠层两个尺度的高光谱反射率数据及对应的叶片氮素含量数据,利用单波段原始光谱和一阶导数光谱的相关性分析、高斯过程回归（GPR）等方法筛选水稻全生育期叶片及冠层尺度氮素敏感波段。针对敏感波段,利用单波段回归分析、随机森林（RF）、支持向量回归（SVR）、高斯过程回归-随机森林（GPR-RF）、高斯过程回归-支持向量回归（GPR-SVR）和GPR构建水稻氮素监测模型,并进行精度对比,以确定水稻叶片在各生育期的氮素估算最佳模型。结果表明：GPR筛选的敏感波段符合水稻氮素含量及光谱变化的规律。相同条件下,叶片模型精度整体高于冠层模型。相关性分析模型中,叶片尺度原始光谱模型更好,冠层尺度刚好相反,冠层一阶导数光谱可以减弱稻田背景噪声的影响。其中,叶片最佳模型建模集R2为0.79,验证集R2为0.84;冠层最佳模型建模集R2为0.80,验证集R2为0.77。与相关性回归分析模型相比,机器学习模型受生育期影响小（R2>0.80,NRMSE<10%）。其中,RF比SVR更适合对GPR敏感波段建模,GPR-RF模型可以用1.5%左右的波段达到RF模型使用全部波段的精度。五种方法中,GPR模型对生育期敏感度最低、叶片及冠层尺度效果都很好(R2>0.94,NRMSE<6%)。且与其他四种机器学习方法相比,GPR模型可有效提高冠层氮素含量估算的精度和稳定性（R2增加0.02,NRMSE降低1.2%）。GPR方法可为筛选作物氮素高光谱敏感波段、反演各生育期叶片及冠层氮素含量提供方法参考。     

Imbert–Fedorov shifts of a Gaussian beam reflected from uniaxially anisotropic chiral media

We study the Imbert–Fedorov (IF) shifts of a reflected Gaussian beam from uniaxially anisotropic chiral media (UACM), where the chirality appears only in one direction and the host medium is a uniaxial crystal or an electric plasma. The numerical results are presented for three kinds of UACM, respectively. It is found that the IF shifts are closely related to the propagation properties of the two eigenwaves in the UACM. In general, when either of the eigenwaves is totally reflected, the IF shifts can change abruptly near the critical angle. The cross-polarized reflection coefficient has a greater effect on the spatial IF (SIF) shift than on the angular IF (AIF) shift, and the sign of the AIF shift depends mainly on that of the difference between the co-polarized reflectivity. By designing artificially the electromagnetic parameters of the UACM, we can control the IF shifts and acquire their more abundant properties.     

Focusing of helico-conical cosh-Gaussian beam

Helico-conical beam is attractive for its phase front is nonseparable helical and conical phase function, which produces a spiral intensity distribution occurs at the focal plane. In this letter, the focal properties of cosh-Gaussian beam with helico-conical wavefront were investigated to show that helico-conical phase front does not always produce spiral intensity distribution. On increasing decentered parameters in cosh parts of the beams, the spiral focal pattern evolves into multiple intensity peaks with center main strongest peak. Under condition of higher decentered parameters, the focal spiral curve disappears. In addition, the topological charge also affects the focal pattern considerably.     

基于偏振无关分束器的两光子部分纠缠态的简化浓缩方案

经由偏振无关的光学分束器实现对未知两光子部分纠缠态的纠缠浓缩,包括利用单光子探测器的线性光学浓缩方案,和利用弱交叉Kerr非线性媒质、零拍探测的浓缩方案。两对部分纠缠的光子对中各一个信号光子同时通过偏振无关分束器后,当探测到分束器输出模中各有一个光子时,剩余的两光子将处于最大纠缠态。与以前的浓缩方案相比较,我们的浓缩方案不需要额外的Hadmard门对信号光子施加作用,所需要的光学器件较少,这增加了方案在实验实现上的可行性。     

180keV O6+离子与锥形玻璃毛细管相互作用研究

实验研究了强流（几个nA/mm2）180 keV O6+离子穿越微米尺度锥形玻璃毛细管的聚焦效应.结果表明,毛细管出口处束流密度比入口处束流密度增加了6~7倍,且出射离子保持原有的电荷态及能量.此外我们发现,当毛细管倾斜一定角度时,离子出射方向偏向毛细管管轴方向.基于自组织充电模型对上述实验结果进行了讨论.