On the correct writing of the law of conservation of amount of substance at the moving fluid-fluid interface

The reasons for the erroneous writing of the substance conservation law at the moving fluid-fluid interface, which is commonly encountered in related publications, are analyzed. A mathematical statement of this law that is valid for any curved surface that has a nonzero curvature in its equilibrium state is derived in terms of vector analysis. The new writing is independent of the coordinates and can be used for analysis of relaxation phenomena associated with nonlinear wave motions.     

Frequency power law of material damping

The experimental studies often show that the damping in various solid materials increases with frequency over a finite bandwidth, and the increase is weak if the damping is low. A frequency power law is suggested and discussed in this paper to describe this damping behaviour with special respect to the low loss resilient materials used for sound and vibration control. The dynamic modulus as a function of frequency is determined from the loss modulus through the Kramers-Kronig dispersion relations to satisfy the causality requirement. It is proved that the dynamic modulus obeys the frequency power law of the same type as the loss modulus. In addition, it is proved that the weak frequency dependences of damping properties are inevitably associated with the low loss factor. Examples of fitting the frequency power law to experimental data on some materials of acoustical purposes are presented.     

凝聚炸药爆轰波在高声速材料界面上的折射现象分析

凝聚炸药爆轰在边界高声速材料约束下传播时,爆轰波会在约束材料界面上产生复杂的折射现象.本文针对凝聚炸药爆轰波在高声速材料界面上的折射现象展开理论和数值模拟分析.首先通过建立在爆轰ZND模型上的改进爆轰波极曲线理论给出爆轰波折射类型,然后发展一种求解爆轰反应流动方程的基于特征理论的二阶单元中心型Lagrange计算方法来数值模拟典型的爆轰波折射过程.从改进爆轰波极曲线理论和二阶Lagrange方法数值模拟给出的结果看出,凝聚炸药爆轰波在高声速材料界面上的折射类型有四种:反射冲击波的正规折射、带束缚前驱波的非正规折射、带双Mach反射的非正规折射、带λ波结构的非正规折射.     

介质运动时的电磁规律

静止时线性、均匀、各向同性的介质，当它运动时变得不再各向同性，其标志是光线和波法线分离，波面形状由球面变成椭球面．本文给出了非各向同性介质与介质运动速度间的定量关系，导出了电磁波在运动介质表面反射和折射的普遍规律．并且就介质的运动方向与介质表面垂直或平行两种特殊情形进行了较为详细的分析。     

Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces

Abstract

The small-slope approximation (SSA) for wave scattering at the rough interface of two homogeneous half-spaces is developed. This method bridges the gap between two classical approaches to the problem: the method of small perturbations and the Kirchhoff (or quasi-classical) approximation. In contrast to these theories, the SSA is applicable irrespective of the wavelength of radiation, provided that the slopes of roughness are small compared with the angles of incidence and scattering.

The resulting expressions for the SSA are given for the entries of an S-matrix that represents the scattering amplitudes of plane waves of different polarizations interacting with the rough boundary. These formulae are quite general and are valid, in fact, for waves of different origins. Apart from the shape of the boundary, some functions in these formulae are coefficients of the expansion of the S-matrix into a power series in terms of elevations. These roughness independent functions are determined by a specific scattering problem. In this paper they are calculated for the case of electromagnetic scattering at the interface of two dielectric half-spaces. In contrast to an earlier paper by the author, where only the formulae for the reflected field were presented, in this paper both reflected and transmitted fields are considered in detail.

The a priori symmetry relations that this scattering problem should obey (reciprocity and energy conservation) are formulated in terms of the S-matrix.

The statistical moments of scattering amplitudes are directly related to the mean-reflection coefficient and scattering cross sections, which are usually determined experimentally. The corresponding formulae are given here for the case of Gaussian space-homogeneous statistics of roughness.     

Frequency shift of Rayleigh waves excited by a source moving perpendicularly to the interface between two media

Characteristic features of the Doppler frequency shift of Rayleigh and bulk waves excited in an elastic halfspace by a source vertically moving in a contacting gaseous halfspace (atmosphere) are studied.     

Reflection and refraction of elastic wave at VTI-TTI media interface

We explore the physical phenomenon of acoustic waves induced at the interface between two different anisotropic rock media.Specifically,one medium is a transversely isotropic medium with a vertical axis of symmetry(VTI medium)and the other one is a transversely isotropic medium with a tilt axis of symmetry(TTI medium).By solving the Kelvin-Christoffel equation,an eighth-order polynomial is established for reflection and refraction angles,which is confirmed from SnelFs law.Three types of analytical expressions of the polarization coefficients of the induced waves are obtained corresponding to different incident angle regions.An effective algorithm has been developed for numerical analysis of the polarization coefficients.Applying characteristic anisotropic parameters reported in the literature,the influencing factors on reflection and refraction coefficients are analyzed,e.g.,the anisotropy,the tilt-angle of rock-layer,and the incident-angle.The calculated reflection and refraction coefficients have been rechecked for energy conservation.     

Surface-plasmon wave at the planar interface of a metal film and a structurally chiral medium

The solution of a boundary-value problem formulated for a modified Kretschmann configuration shows that a surface-plasmon wave can be excited at the planar interface of a sufficiently thin metal film and a nondissipative structurally chiral medium, provided the exciting plane wave is p-polarized. An estimate of the wavenumber of the surface-plasmon wave also emerges thereby.     

Frequency modulation in the transmittivity of wave guides in elastic-wave band-gap materials

It is shown, for the first time, that the transmittivity of wave guides created as rectilinear defects in periodic elastic band-gap materials oscillates as a function of frequency. The results are obtained using the finite difference time domain method for elastic waves propagating in two-dimensional inhomogeneous media. The oscillations of the transmittivity are due to the richness of modes in the elastic systems and, mainly, due to the periodicity of the potential in the direction of the wave propagation. Results are presented for a periodic array of Pb and Ag cylinders inserted in an epoxy host, as well as for Hg cylinders in an Al host.     

Frequency characteristics of the dark and bright surface solitons at a nonlinear metamaterial interface

We investigate the generation and properties of dark and bright surface waves at the interface of a conventional medium and a metamaterial. It is shown that the stable dark and bright surface solitons can coexist even when the nonlinear Kerr coefficients of the two media are negative, completely different from those at the interface between two conventional media. Most importantly, both the dark and bright surface solitons exist only within a certain range of the effective refractive index of the metamaterial, greatly depending on the frequency of the electromagnetic wave propagating in it. Therefore, the generation conditions for surface solitons, and the properties of the generated surface solitons such as the peak positions and the intensity of the dark and bright surface solitons, can be controlled by adjusting the structure parameters of the metamaterial and/or the frequency of the electromagnetic wave.     

Surface self-induced transparency solitons at an interface of gallium arsenide and a left-handed material

The theory of surface solitons in a system composed of gallium arsenide and a left-handed metamaterial that has semiconductor quantum dots at the interface between the media is constructed. The formation of surface solitons under the conditions of self-induced transparency upon the excitation of exciton and biexciton transitions in quantum dots is considered. Explicit analytical expressions for solitons (2π-pulses) of surface TM modes in experimentally feasible conditions are obtained. It is shown that the parameters of the surface optical soliton depend on the negative magnetic permeability of the left-handed metamaterial.     

Frequency modulation of a gas laser

A theoretical analysis of a s ingle-frequency gas laser is presented, together with some experimental results. The experimental results are in qualitative agreement with theory.Translated from Izvestiya VUZ. Fizika, No. 6, pp. 111–115, June, 1973.     

Diffraction of an electromagnetic wave at an arbitrarily moving surface

Radiophysics and Quantum Electronics -