Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability

We consider concentrated vorticities for the Euler equation on a smooth domain $\mathrm{\Omega }?{\mathbf{R}}^2$ in the form of

$\omega =\sum _{j=1}^N{\omega }_j{\chi }_{{\mathrm{\Omega }}_j},|{\mathrm{\Omega }}_j|=\pi r_j^2,\underset{{\mathrm{\Omega }}_j}{\int }{\omega }_{j}d\mu ={\mu }_j\ne 0,$

supported on well-separated vortical domains ${\mathrm{\Omega }}_j$, $j=1,\dots ,N$, of small diameters $O(r_j)$. A conformal mapping framework is set up to study this free boundary problem with ${\mathrm{\Omega }}_j$ being part of unknowns. For any given vorticities ${\mu }_1,\dots ,{\mu }_N$ and small $r_1,\dots ,r_N\in {\mathbf{R}}^{+}$, through a perturbation approach, we obtain such piecewise constant steady vortex patches as well as piecewise smooth Lipschitz steady vorticities, both concentrated near non-degenerate critical configurations of the Kirchhoff–Routh Hamiltonian function. When vortex patch evolution is considered as the boundary dynamics of $?{\mathrm{\Omega }}_j$, through an invariant subspace decomposition, it is also proved that the spectral/linear stability of such steady vortex patches is largely determined by that of the 2N-dimensional linearized point vortex dynamics, while the motion is highly oscillatory in the 2N-codim directions corresponding to the vortical domain shapes.     

红外动态场景生成装置空间分辨率的测试

建立了一套基于刀口灰度图红外探测的实验装置,对红外场景生成器的空间分辨率进行了测试。首先通过被测红外场景生成器产生带有刀口标志的红外图像,然后利用红外热像仪采集红外场景生成器所成的红外图像,通过对采集到的红外热图的数据处理,实现了对红外场景生成器空间分辨率的测量。测得的红外场景生成器的空间分辨率为5lp/mm,标准误差为0.04。     

透明塑料盒上的显色偏振

依据显色偏振、布鲁斯特角等原理详细解释了透明塑料盒上彩色条纹的形成过程,并进行实验验证,排除了薄膜干涉、色散、散射等其他理论解释.     

新型4-羟色胺类化合物的合成及生物活性

以4-羟基吲哚为原料,经吲哚环4位乙酰基化、3位亲电取代、酰胺化和还原加氢等反应合成目标化合物7.通过核磁共振氢谱及碳谱对化合物进行结构表征,并对目标化合物进行体外抗氧化生物活性测试.初步生物活性测试结果表明,化合物7a,7b,7c和7d对DPPH·均有很强的清除作用(清除率为85.25%~90.73%),7e,7f,7g,7h作用较差;目标化合物与Vc相比,对·OH的清除作用稍差,最高清除率25.66%(Vc的最高清除率为34.67),但各化合物整体水平相当;在清除O-2·能力上化合物7a,7d,7g,7h最大清除率(分别为19.34,35.35,27.93和31.74)均强于同等浓度的Vc(17.58).     

Polypyrrole Shell@3D‐Ni Metal Core Structured Electrodes for High‐Performance Supercapacitors

Three‐dimensional (3D) nanometal films serving as current collectors have attracted much interest recently owing to their promising application in high‐performance supercapacitors. In the process of the electrochemical reaction, the 3D structure can provide a short diffusion path for fast ion transport, and the highly conductive nanometal may serve as a backbone for facile electron transfer. In this work, a novel polypyrrole (PPy) shell@3D‐Ni‐core composite is developed to enhance the electrochemical performance of conventional PPy. With the introduction of a Ni metal core, the as‐prepared material exhibits a high specific capacitance (726 F g^?1 at a charge/discharge rate of 1 A g^?1), good rate capability (a decay of 33 % in C_sp with charge/discharge rates increasing from 1 to 20 A g^?1), and high cycle stability (only a small decrease of 4.2 % in C_sp after 1000 cycles at a scan rate of 100 mV s^?1). Furthermore, an aqueous symmetric supercapacitor device is fabricated by using the as‐prepared composite as electrodes; the device demonstrates a high energy density (≈21.2 Wh kg^?1) and superior long‐term cycle ability (only 4.4 % and 18.6 % loss in C_sp after 2000 and 5000 cycles, respectively).     

激光能量对反钙钛矿GaCMn_3薄膜结构与物性的影响

本文采用脉冲激光沉积方法在LaAlO3(001)单晶衬底上制备了反钙钛矿GaCMn3薄膜,通过控制制备过程中脉冲激光的能量,研究了不同激光能量条件对GaCMn3薄膜结构与物理性能的影响.分别利用X射线衍射仪、原子力显微镜、超导量子干涉仪和物理性能测试系统,对所制备的薄膜的晶体结构、表面形貌和磁性、电输运性质进行了研究.结果表明,制备的样品均为具有多个晶面取向的反钙钛矿薄膜,且薄膜结构和物性明显随制备激光能量的变化而变化.当激光能量为450mJ时,制备的薄膜多晶面取向性最弱,结晶性和表面形貌最优良.实验所得的薄膜均表现出顺磁-铁磁-反铁磁相转变,然而转变过程比块材较平缓,同时薄膜的电阻率并未表现出块材中的突变特征,我们推测该现象很可能是由衬底的应力及衬底的晶格膨胀对薄膜反常晶格变化的抑制作用造成的.     

锡苯和铅苯二聚反应的理论研究

采用密度泛函理论B3LYP方法,研究了锡苯和铅苯的[2+2],[4+2]及[4+4]二聚反应的微观机理和势能剖面,考察了Sn(Pb)原子上的2,4,6-三甲基苯基(Mes)取代基对反应势能剖面的影响.研究结果表明,所有反应均为协同过程,且大多数情况下,2个C—Sn(Pb)键同步形成.[2+2]和[4+2]反应在热力学和动力学上均比相应的[4+4]反应容易进行,而[4+2]反应在动力学上比相应的[2+2]反应有利.Sn(Pb)原子上的Mes取代基在热力学和动力学上均不利于反应的进行.铅苯的动力学稳定性与锡苯相当,但其热力学稳定性高于锡苯.     

基于DIS数字信息化系统对透光物质透光性能的研究

采用DIS数字信息化系统,对不同浓度的蓝墨水溶液在激光光源照射下的透射平均照度及照度分布图像进行实验研究,得到了平均照度值随溶液浓度变化的规律。对不同颜色塑料膜片对白炽灯光源透过照度值及照度分布图像进行实验研究得到及其相关之规律。     

Synthesis,Crystal Structure,and Magnetic Properties of a New Dinuclear Iron Complex with Schiff Base Ligand

A new dinuclear iron(Ⅲ) complex has been synthesized and structurally characterized by X-ray crystallography: [FeⅢ2(L)(C6H5COO)(SO4)(CH3OH)2]·CH3CN·CH3OH(1, H3 L = N,N'-bis(salicylidene)-1,3-diamino-2-propanol). Complex 1 belongs to orthorhombic space group Pna21 with a = 11.4400(8), b = 22.9705(2), c = 12.5712(9) , V = 3303.5(4) 3, Z = 4, F(000) = 1576, Dc = 1.531 g·cm–3, Mr = 761.36, μ = 1.007 mm–1, S = 1.014, the final R = 0.0505 and wR = 0.1018. The crystal packing is stabilized by intermolecular O–H···O hydrogen bonds, forming an extended one-dimensional chain structure. The temperature dependence of magnetic susceptibility measurement shows that antiferromagnetic interaction is propagated between the metal centers. Fit as dinuclear arrangement gave parameters of J = 19.7 cm-1, g = 1.89 and R2 = 0.9999.