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.     

An optodynamic method for the real-time determination of the depth of a laser-drilled hole

An experimental method for determining the real-time depth of laser-drilled holes is presented. The proposed method involves detecting the laser-induced optoacoustic waves generated during the interaction of the laser beam with the material. Our optodynamic study involved measuring the propagation times of these waves as they traveled through the material and analyzing their temporal behavior during the drilling process. The experimental observations revealed an exponential relationship between the propagation time of the longitudinal stress wave and the number of consecutive laser pulses. Received: 25 October 2001 / Accepted: 27 October 2001 / Published online: 20 December 2001     

Spin-transfer switching in MgO magnetic tunnel junction nanostructures

Spin-transfer driven switching was observed in MgO based magnetic tunnelling junctions (MTJ) with tunnelling magnetoresistance ratio of up to 160% and the average intrinsic switching current density (J_c0) down to 2 MA/cm², which are the best known results reported in spin-transfer switched MTJ nanostructures. Based on a comparison of results both from MgO and AlO_x MTJs, further switching current decrease via MgO dual structures with two pinned layers is discussed.     

α－萘甲酰呋喃甲酰甲烷的合成及谱学性质的研究

本文用Ｃｌａｉｓｅｎ缩合反应合成了未见文献报道的一种新的β－二酮，α－萘甲酰呋喃甲酰甲烷（α－ＮＦＭ），考察了该化合物的红外光谱、质谱及核磁共振氢谱。确定其存在着互变异构。     

THE ASYMPTOTIC SOLUTION FOR A CLASS OF SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR SINGULAR EQUATION

The singularly perturbed boundary value problem for a class of semilinearsingular equation is considered. Using a simple and special method the asym-ptotic behavior of solution is studied.     

在局部区域上的奇摄动反应扩散方程初始边值问题

本文是讨论一类在局部区域上的奇摄动反应扩散初始边值问题.利用算子理论和 不动点原理,得到了相应问题解的存在性和唯一性.     

WAXS studies on block copolymers of ethylene and propylene

Wide-angle X-ray scattering from presumed block copolymers of polypropylene (PP) and ethylene-propylene copolymer (EPR), i.e., PP-EPR and PP-EPR-PP, synthesized by sequential polymerization with δ-TiCl₃? Et₂AlCl, was examined and compared with WAXS of mechanical blends and chain-transfer mixtures of PP and EPR with comparable compositions. The peak at 2θ = 20° for both the copolymers and the mixtures was attributed to the γ modification of PP in EPR. A strong variation in the ratio of diffraction intensities I₀₄₀/I₁₁₀ of PP in block copolymers and mixtures was explained in terms of crystallite growth in different directions. Analysis of the patterns and calculation of crystallinity, crystallite size, and lattice parameters led to the conclusion that block structure existed in the prepared copolymers.     

毛细管电色谱研究进展

毛细管电色谱是一种新兴的具有高效，高选择性的微分离技术。本文评述了毛细管电色说的发展状况和相关的技术，并对其发展前景进行了展望，引用文献２４篇 。     

毛细管离子交换电色谱的分离行为

在离子交换毛细管色谱柱上实施电色谱，并对其分离行为进行了研究，采用７５μｍ（ｉ．ｄ．）２０ｃｍ的毛细管强阳离子交换柱（３μｍ）以ＮａＨ２ＰＯ４－Ｈ３ＰＯ４缓冲液为淋洗剂，紫外柱上检测（２１４ｎｍ）考察了流动相的ｐＨ值，有机改性剂及分离电压等因素对分离的影响，研究表明，不同的ｐＨ溶质的流出次序发生改变，随着有机改性剂含量增加，溶质的保留时间减小，而电渗流却增大，同时，对分离的柱效和方法的重现性进行了