On a fast direct elliptic solver by a modified Fourier method

We describe high order numerical algorithms for the solution of second order elliptic equations in rectangular domains. These algorithms are based on the Fourier method in combination with a subtraction procedure. The singularities at the corner points, arising due to non-smoothness of the boundaries, are treated explicitly using properly constructed singular corner functions. The present algorithm is a generalization of the Fast Poisson Solver developed in our previous paper. This revised version was published online in August 2006 with corrections to the Cover Date.     

q-positive definiteness and related operators

We are in progress of extending the family of ‘q-deformed operators’ considered in the previous papers by joining to them q-subnormal as well as q-formally subnormal ones. It turns out that q-positive definiteness, a notion generalizing Halmos' standard positive definiteness of bounded subnormal operators, is likewise central for our new scheme.     

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

离化团簇束法制备c轴取向的ZnO薄膜

为了探索低温可调控ZnO薄膜沉积技术,提出了一种新的ZnO薄膜制备方法,即离化团簇束（ICB）法,并自行设计研制了应用该方法制备ZnO薄膜的专门装置.采用超音速喷嘴获得高速锌原子团簇束,用Hall等离子体源产生氧离子束离化锌原子团簇,获得了较高的离化率.在沉积过程中,可以通过调节衬底偏压、氩氧比、衬底加热温度等参数,来控制成膜的质量;应用这个装置成功地在硅衬底上制备的ZnO薄膜,经XRD和EDS检测,薄膜的c轴取向一致,Zn、O原子百分比接近于1：1,成膜质量好.     

57Fe Mössbauer spectroscopic study of (25−x)MnO–xZnO–15Fe2O3–60B2O3 glasses

The ⁵⁷Fe Mössbauer technique has been used to investigate the effect of zinc oxide substitution in (25???x)MnO–xZnO–15Fe₂O₃–60B₂O₃ glass system (x?=?0, 5, 10, 15 and 20 mol% of ZnO ). Mössbauer absorption spectra for all the samples recorded at room temperature suggest the existence of the two paramagnetic quadrupole doublets. The observed variations in hyperfine parameters have been explained on the basis of cations distribution and exchange interaction at the lattice sites and it is concluded that B–B interaction increases while the metal–metal interaction decreases due to replacement of manganese oxide by zinc oxide. These results suggest that the present glass system exhibits a paramagnetic behaviour that changes towards the weak paramagnetic when manganese oxide was replaced with zinc oxide.     

光刻机硅片表面不平度原位检测技术

随着光刻特征尺寸的不断减小,硅片表面不平度对光刻性能的影响越来越显著.该文提出了一种新的硅片表面不平度的原位检测技术本文在分析特殊测试标记成像规律的基础上,讨论了测试标记的对准位置偏移量与硅片表面起伏高度的变化规律,提出了一种新的硅片表面不平度原位检测技术.实验表明,该技术可实现硅片表面不平度及硅片表面形貌的高准确度原位测量.该技术考虑了光刻机承片台吸附力的非均匀性对硅片表面不平度的影响,更真实反映曝光工作状态下的硅片表面不平度大小.与现有的原位检测方法相比,硅片表面不平度的测量空间分辨率提高了1.67%倍,可实现硅片表面形貌的原位检测.     

Simultaneous Measurement of Particle Size and Particle Velocity by the Spatial Filtering Technique

The objective of this study was to compare the measuring results of a fiber‐optical probe based on a modified spatial filtering technique with given size distributions of different test powders and also with particle velocity values of laser Doppler measurements. Fiber‐optical spatial filtering velocimetry was modified by fiber‐optical spot scanning in order to determine simultaneously the size and the velocity of particles. The fiber‐optical probe system can be used as an in‐line measuring device for sizing of particles in different technical applications. Spherical test particles were narrow‐sized glass beads in the range 30–100 μm and irregularly shaped test particles were limestone particles in the range 10–600 μm. Particles were dispersed by a brush disperser and the measurements were carried out at a fixed position in a free particle‐laden air stream. Owing to the measurement of chord lengths and to the influence of diffraction and divergent angle, the probe results show differences from the given test particle sizes. Owing to the particle‐probe collisions, the mean velocity determined by the probe is smaller than the laser Doppler mean velocity.     

Flow in a waterfall with large Froude number

An approximate method is developed to solve the full nonlinear equations governing two-dimensional irrotational flow in a free waterfall, falling under the influence of gravity, at high Froude number based on conditions far upstream. Schwarz—Christoffel transformation is used to map the region, in the complex potential-plane, onto the upper half-plane. The Hilbert transformation as well as the perturbation technique, for large Froude number, are used as a basis for the approximate solution of the problem. A complete solution, up to second-order approximation, for the downstream free-surfaces profiles, for different Froude number, is discussed and illustrated. The obtained approximate solutions are compared with those of other authors. Favourable agreement with other results suggests that this method is effective in dealing with flow problems strongly influenced by gravity and high Froude number. The results obtained by this method are sufficiently accurate for practical purposes.