Some New Results for McKean’s Graphs with Applications to Kac’s Equation

The main goal of the present paper is to sharpen some results about the error made when the Wild sums, used to represent the solution of the Kac analog of Boltzmann’s equation, are truncated at the n-th stage. More precisely, in Carlen, Carvalho and Gabetta (J. Funct. Anal. 220: 362–387 (2005)), one finds a bound for the above-mentioned error which depends on (an ^Λ+ε). On the one hand, it is shown that Λ, the least negative eigenvalue of the linearized collision operator, is the best possible exponent. On the other hand, ε is an extra strictly positive number and a a positive coefficient which depends on ε too. Thus, it is interesting to check whether ε can be removed from the above bound. According to the aforesaid reference, this problem is studied here by means of the probability distribution of the depth of a leaf in a McKean random tree. In fact, an accurate study of the probability generating function of such a depth leads to conclude that the above bound can be replaced with (a′ n ^Λ).     

MgB2超导薄膜的微波测量

报道了利用蓝宝石介质谐振器技术测量MgB2超导薄膜的微波表面电阻Rs、OK时的穿透深度λ(O)和超导能隙△(O)．λ(O)和△(O)的值是通过先测量样品穿透深度λ(T)的变化量△λ(T)，然后由BCS理论模型拟合△λ（T)的实验数据得到的．测试样品是利用化学气相沉积技术在MgO(111)基片上制备的c轴织构的MgB2超导薄膜，薄膜的超导转变温度和转变宽度分别为38K和0．1K．微波测试结果表明在10K，18GHz下MgB2薄膜的Rs约为100μΩ，可以和高质量的YBCO薄膜的Rs值相比拟；BCS理论拟合得到的MgB2超导薄膜的λ(0)=102nm，△(0)：1．13kTc．     

超导体磁场穿透深度测量中的数据分析问题

讨论了目前在超导体磁场穿透深度λ测量中常用的几种数据分析方法.着重指出对于那些只能测量λ随温度的变化值Δλ(T),而无法测量其绝对值的实验而言,一种合适的数据分析方法对于我们从实验中得出正确的结论尤其重要.而微分归一法将有效地克服目前此类实验中常用数据处理方法的不足,从而实现理论与实验间的无参量比较. 关键词： 超导体 磁场穿透深度     

具有几乎最大深度的滤链的Hilbert 系数

设${\cal F}$是Cohen-Macaulay R-模的一个Hilbert滤链. 当$G({\cal F},M)$和$F_K({\cal F},M)$有几乎最大深度时,我们证明长度$\lambda(KI_nM/JI_{n-1}M)$和约化数$r^K_J({\cal F},M)$与$J$无关,并且给出了第一和第二个Hilbert 系数的下界.     

A New Method to Examine Interfacial Reactions of a Multilayered System NiAl–Hf–hBN on a Sapphire Fibre

Fibre reinforced NiAl offers new possibilities for the development of high strength structural materials of low density applicable in gas turbines at high operating temperatures. The properties of composite materials are strongly influenced by the strength of the fibre–matrix interface. In addition, if fibre and matrix differ in their thermal expansion coefficients, a well controlled interface reaction at high temperature changes is demanded. Therefore, two layers consisting of BN and Hf were embedded between a sapphire fibre and NiAl and heated at 1350 °C to find a compromise between adhesion and ductility. The control and characterization of the reaction zone is essential for the development of these new materials. Especially, the characterization of the fibre-coating interface is a challenge. The different hardness of fibre and coating makes it nearly impossible to use a conventional cross-section preparation. Further, the small dimension of the reaction zone requires the use of analytical techniques providing high lateral resolution. In order to accomplish these requirements, a newly developed technique FIB (Focused Ion Beam)-EPMA (Electron Probe Microanalysis) was combined with XRD (X-ray diffraction). XRD was performed for the identification of the phases. The reaction zone was exposed by a special FIB preparation technique and examined by surface-sensitive EPMA. This allowed to determine the spatial distribution of the different phases.     

Combined EPMA and AES depth profiling of a multilayer Ti-Al-O-N coating

In order to compare thin-film electron probe microanalysis (EPMA) and Auger electron spectroscopy (AES) regarding reliability in quantifying chemical compositions of Ti-Al-O-N coatings with depth, a multilayer was prepared on a silicon wafer by using reactive ionized cluster beam deposition technique. Within a total thickness of about 25 nm the composition of the multilayer varied step by step from Ti-Al-O-N at the bottom to Al-O at the top. AES and, as an innovation, EPMA crater edge profiling was applied to measure the composition with depth. For quantification special thin-film EPMA techniques based on Monte Carlo simulations were applied. The chemical binding states of Al and Ti with depth were analysed using a high resolution energy analyser (MAC 3) for the AES investigations working in the direct mode. According to the deposition procedure the concentration profiles of the components varied with depth for both AES and EPMA measurements. AES provided a better depth resolution than EPMA. To get a true calibration of the depth scale an in-situ measurement method like an optical interferometry will be required. Assuming that the relative sensitivity factors are available AES depth profiling delivers concentration profiles with good accuracy. The new EPMA application provided quantitative depth profiles concerning concentration and coverage. For EPMA crater edge profiling the coating needs to be deposited on a foreign substrate because depth distributions of elements being present in both the layer and the substrate cannot be resolved.The combination of AES-depth profiling with EPMA crater edge profiling techniques is a powerful tool to analyse heterostructures quantitatively.     

二元光学元件制作误差分析与模拟

从标量衍射理论出发，首先从理论上计算出多台阶二元化学元件发生深度误差时衍射效率的解析式，然后以４台阶和８台阶闪耀光栅为例，对二元光学元件套刻制作中的主要误差及其这些误差之间的相互影响进行了系统的分析和计算机模拟研究，模拟结果给实际制作提供了重要理论指导和实验参数。     

Experimental investigation of supersonic radiation propagation in low-density plastic and copper-doped foams

1 Introduction The investigation of supersonic radiation wave transporting in low density foam pro-duced by thermal radiation is of crucial importance in inertial confinement fusion (ICF) research[1]. When the intense radiation flux is incident in the media, first, a supersonic heat wave is formed which propagates into the undisturbed material. In time, due to the increasing mass of heated material, it slows down and is overtaken by a shock wave,thus becoming of the ablative type. Normally, …     

1:1分步亚微米光刻镜头

本文介绍一个数值孔径0.4、视场10×10mm~2可用于1:1分步投影光刻机的镜头的光学设计及其模型实验结果.光学设计在Wynne-Dyson的1:1折反式系统的基础上,对该系统作了某些改变.实验结果表明,该镜头具有亚微米的光刻分辨率.     

The superconducting penetration depth from the semiclassical model

The semiclassical approach of Onsager and Pippard has been very successful in relating the electronic properties of a normal metal to its band structure and fermi surface. This paper extends the method to a superconductor. A generalized London equation relating the supercurrent density to the vector potential is obtained, in terms of band and fermi surface parameters and an energy gap which may be anisotropic. The results allow an interpretation of measured penetration depths directly in terms of the electronic and gap structures of the superconductor. They lead to easy physical visualization of the origin of anisotropies and other features of measured penetration depths.