Group Representation of Relativistic Quantum Crystal Optics

A group representation of radiation propagation in an anisotropic medium is developed. The system of wave equations for electromagnetic potentials, obtained from the Maxwell equations with account for the constitutive equations, has been factorized. It is shown that the linear differential operator of the factorized system is orthogonal in transparent crystals and unitary in gyrotropic ones and is represented through the momentum operator. On the basis of the commutation relations for the components of this operator, the eigenvalue problem has been solved and the expression for the change in the radiant energy in the crystal in the form of spherical waves has been obtained. The dependences of the ray and phase velocities and the polarization vectors of waves on the birefringence anisotropy and gyrotropy as well as on the angular momentum, displacement current, and bound charge determining them have been analyzed. It has been established that in the general case of gyrotropic crystals where the nonreciprocity phenomenon takes place and in magnetoelectrics Maxwell equations are represented in a form similar to the Dirac equations and the electromagnetic radiation is correctly described by means of bispinors and is quantized as fermions.     

Influence of velocity and surface temperature of alumina particles on the properties of plasma sprayed coatings

In this paper are described the main characteristics of the plasma spraying process of alumina deposits, i.e., the temperature and flow field of the plasma jets obtained with the classical spraying torches, the injection of the particles into the plasma jet, the particle surface temperature and velocities in the plasma (measured for calibrated alumina particles), and the coating generation. The measurements on the alumina particles are compared with the predictions of a mathematical model. The experimental and computed particle velocities are in rather good agreement. However, this is not the case for the particle surface temperature. Possible reasons for the discrepancy are proposed (influence of the carrier gas, thermophoretic forces, and poor penetration of the particles into the plasma core even for an injection velocity twice that of the optimal calculated one, as shown by recent measurements). Finally the correlations between the particle velocities and surface temperature, and the properties of the alumina coating (porosity, crystal structure, mechanical properties) are studied.     

用声透射损失测气一水混相介质中的含气量

本文利用超声检测中的穿透法,用频率为０．５ＭＨｚ、１ＭＨｚ、１．２５ＭＨｚ、２ＭＨｚ、２．５ＭＨｚ的声波,测量了气－水混相介质听声速比值和声透射损失,结果表明,在气泡大小,分布一定的情况下,可能用声透射损失来确定混相介质中的含量量,但不宜用声速比值。     

On the signal degradation induced by the interpolation and the sampling rate reduction in aeroacoustics hybrid methods

Taking place within more extensive work that focuses on hybrid methods in aeroacoustics, the present study is devoted to the data transfer operations that are to be performed between two stages of a hybrid calculation. More precisely, the article focuses on two typical operations that usually accompany such data transfer, which are (i) the sampling rate reduction and (ii) the interpolation of the unsteady perturbations to be transmitted from one stage to the other. First part of the paper analyzes the two main issues of such operations, which are the spuriousing and the aliasing phenomena. For doing so, the usual notions of the interpolation theory are revisited before they are synthesized within an original approach. The here proposed formalism allows to understand better both the spuriousing and the aliasing phenomena, as well as to accurately predict the impact of the latter on the data to be transmitted in terms of signal degradation. Second part of the paper provides an illustration and a validation of these theoretical developments via a direct application to a typical aerodynamic noise problem (aeroacoustic emission by a 2D cylinder cross flow). There, it is further shown how the here proposed formalism can help in improving aeroacoustics hybrid calculations by predicting (and thus possibly minimizing) the bias to be induced on the acoustic extrapolation stage because of the aliasing and/or spuriousing effects inherited from the sampling rate reduction and/or interpolation of CFD data—which is likely to occur in any hybrid scenario. Copyright © 2012 John Wiley & Sons, Ltd.     

Elastic constants of galena down to liquid helium temperatures

The elastic constants of single crystal galena have been determined from the measured ultrasonic velocities down to liquid helium temperature. A cryostat incorporating an arrangement to inject the liquid bonding material at low temperature is described. At 5 K, the values of elastic constants are C₁₁=14.9₀, C₁₂=3.5₁ and C₄₄=2.9₂×10¹⁰ N/m².     

Approximations of spectra of Schrödinger operators with complex potentials on ℝd

We study spectral approximations of Schrödinger operators T = ?Δ+Q with complex potentials on Ω = ?^d, or exterior domains Ω??^d, by domain truncation. Our weak assumptions cover wide classes of potentials Q for which T has discrete spectrum, of approximating domains Ω_n, and of boundary conditions on ?Ω_n such as mixed Dirichlet/Robin type. In particular, Re Q need not be bounded from below and Q may be singular. We prove generalized norm resolvent convergence and spectral exactness, i.e. approximation of all eigenvalues of T by those of the truncated operators T_n without spectral pollution. Moreover, we estimate the eigenvalue convergence rate and prove convergence of pseudospectra. Numerical computations for several examples, such as complex harmonic and cubic oscillators for d = 1,2,3, illustrate our results.     

表面张力-重力短峰波作用的海底边界层速度二阶解

依据最近提出的三阶表面张力-重力短峰波理论,通过求解经典的Prandtl边界层方程,给出海底边界层速度的二阶解析解,为确定海底边界层的质量输运提供了一个必备的先行理论基础.     

用声波速度确定骨组织弹性参数

本文用超声方法确定密质骨的弹性特征,其基本原理是基于弹性波理论中的Christoffel方程。本文应用液浸、声波穿透技术,对牛胫骨样品中一些特殊入射方向的声波速度进行了测试,利用固体中沿任意方向的弹性波传播速度与材料的弹性系数间的关系,通过计算机编程反演出具有六方晶体对称结构的密质骨组织的5个独立弹性常数。结果与相关文献中其它方法所得结果一致。     

The reaction-annihilator distribution and the nonholonomic Noether theorem for lifted actions

We consider nonholonomic systems with linear, time-independent constraints subject to positional conservative active forces. We identify a distribution on the configuration manifold, that we call the reaction-annihilator distribution ℜ°, the fibers of which are the annihilators of the set of all values taken by the reaction forces on the fibers of the constraint distribution. We show that this distribution, which can be effectively computed in specific cases, plays a central role in the study of first integrals linear in the velocities of this class of nonholonomic systems. In particular we prove that, if the Lagrangian is invariant under (the lift of) a group action in the configuration manifold, then an infinitesimal generator of this action has a conserved momentum if and only if it is a section of the distribution ℜ°. Since the fibers of ℜ° contain those of the constraint distribution, this version of the nonholonomic Noether theorem accounts for more conserved momenta than what was known so far. Some examples are given.      

球形Dirac方程的空间格点求解及假态问题

本文在空间格点上利用虚时间步长方法求解了球形Dirac方程, 着重研究了出现的假态问题. 利用三点数值导数公式离散方程中一阶导数项, 可以证明对于量子数为 κ 和 -κ的单粒子能级能量是完全相同的, 其中一个为物理解, 另一个为假态. 通过在径向Dirac方程中引入Wilson 项, 可以解决假态问题, 得到全部物理解. 文章以 Woods-Saxon 势为例, 考虑 Wilson 项后, 得到与打靶法一致的结果.