Optimal reconstruction of the solution of the wave equation from inaccurate initial data

In the present paper, we consider the problem of the optimal reconstruction of the solution of the wave equation from the approximate values of the Fourier coefficients of the function specifying the initial form of the string. For an operator defined on the weight space of vectors from l ₂, we present the solution of the more general problem of reconstruction from the approximate values of the coordinates of these vectors.     

<Emphasis Type="Italic">Comment on</Emphasis>¶Low temperature specific heat of blue bronze K <Emphasis Type="Bold">0.30</Emphasis>MoO <Emphasis Type="Bold">3</Emphasis>, by J. Odin,J.C. Lasjaunias,K. Biljaković, K. Hasselbach,and P. Monceau

Eur. Phys. J. B 24, 315 (2001) Here we comment on a recently published paper on the presence of a phason contribution in the low temperature heat capacity data of the charge-density-wave compounds K_0.3MoO₃ and (TaSe₄)₂I. We have shown that the anomaly in the C _P / T ³ data reported by Odin et al. is straightforwardly interpreted in terms of low energy phonon modes resulting from the peculiar topology of these compounds. Received 21 February 2002 Published online 19 July 2002     

数学物理方程中的通解问题

通过例证说明,通解法对于偏微分方程而言,其适用范围要比通常认为的大.并表明,只要适当变通,行波法就可用于有界情况.     

透镜初级球差的横向剪切干涉条纹研究

利用玻璃平行平板构成简单的横向剪切干涉仪可以观察到单薄透镜形成的准直光束的剪切干涉条纹,由干涉条纹分布求出对应的几何像差和离焦量.用焦距为190 mm的单薄透镜做实验,实验结果与计算机模拟结果符合,说明可以从剪切干涉条纹的分布求出透镜的轴向调整误差和初级球差.     

计算全息图产生的锥面波在激光准直中的应用

本文提出了用计算全息图产生锥面波的方法.将全息图置于激光光路中,它的衍射图样中心在空间形成了一条准直线.文中对锥面波的传播、准直精度及准直距离作了理论分析,给出了实验结果.     

利用驻波实验研究混沌现象

利用驻波实验演示了混沌现象,并对其进行了理论分析和计算机仿真研究.仿真结果与实验结果都表明:当连接点接近驻波波节处时,振动系统处于混沌运动状态;而当连接点接近驻波波腹处时,系统处于稳定驻波运动状态.     

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.     

An Alternative Approach to Obtain the Exact Wave Functions of Time-Dependent Hamiltonian Systems Involving Quadratic, Inverse Quadratic, and (1/x)p+p(1/x) Terms

By using the Lewis-Riesenfeld theory and algebraic method, we present an alternative approach to obtain the exact solution of time-dependent Hamiltonian systems involving quadratic, inverse quadratic and (1/x)p+p(1/x) terms. This solution is discussed and compared with that obtained by Choi, J. R. (2003). International Journal of Theoretical Physics 42, 853]. PACS: 03.65Ge; 03.65Fd; 03.65Bz     

Multi-cracks problem for piezoelectric materials strip subjected to dynamic loading

This paper analyses and models the dynamic interaction among permeable multi-cracks in a piezoelectric strip under anti-plane shear waves by the Schmidt method. The Fourier transform is applied and then two pairs of triple integral equations can be solved using the Schmidt method. The results show that the stress and the electric displacement intensity factors of cracks depend on not only the crack length and the piezoelectric coefficient, but also the thickness of the piezoelectric strip, the distance between multi-cracks and the frequency of incident wave.