Scattering of Antiplane SH Waves by Complex Landforms

The multiple scattering of SH waves by isosceles triangular hill, semicircle depression, and isosceles trapezoidal hill in the solid half-space is studied. The complex model is divided into multiple subdomains by using the region matching method, then the wave functions in each subdomain are constructed by using the fractional-order Bessel function, and finally, the infinite algebraic equations for solving the unknown coefficients in the wave function are established by using the multipolar coordinate technique and the complex function method according to the boundary conditions. Fourier series is used to solve the unknown undetermined coefficients. The results show that due to the multiple reflections of the incident wave between complex landforms, surface displacement amplitude is affected by the incident angle, incident frequency, and the distance between the isosceles triangular hill, semicircle depression, and isosceles trapezoidal hill. It is found that when the incident frequency increases, there is a certain amplification effect between the hills and the depression. When the wave is incident horizontally, there is a certain “barrier” effect between hills and depression, and when the distance between the hills and depression reaches a certain level, the “barrier” effect will reach a stable value.

Fourier-Bessel beams of finite energy

In this paper, we consider a new type of Bessel beams having Fourier-invariance property and, therefore, called Fourier-Bessel beams. In contrast to the known Bessel beams, these beams have weak side lobes. Analytical expressions for the complex amplitude of the proposed field in the initial plane of the source and in the far field region have been obtained. It is shown that the proposed Fourier-Bessel beams have a finite energy, although they do not have a Gaussian envelope. Their complex amplitude is proportional to a fractional-order Bessel function (an odd integer divided by 6) in the initial plane and in the Fraunhofer zone. The Fourier-Bessel modes have a smaller internal dark spot compared to the Laguerre-Gauss modes with a zero radial index. The proposed beams can be generated with a spatial light modulator and may find uses in telecommunications, interferometry, and the capture of metal microparticles.

Heterodyne light rangefinder

In this paper, we consider the possibilities and ways to improve the accuracy of linear measurements and reduce modulation power, as well as their implementation in the construction of a new high-precision laser rangefinder. To do this, it is necessary to implement the transition to a new method of the modulation method that occurs when the operating point of the light modem goes over to the average linear portion of the modulation characteristic of light (MHS). In this case, the dependence of the amplitude-modulated reception light on the distance is characterized by a first-order Bessel function J1 (x) instead of J0 (x), which takes place at the compensation method of the extremum. In addition, such a transition leads not only to a decrease in modulation power, but also to nonlinear distortions and spreads of the modulation phase. All this leads to the fact that there is an increase in the accuracy of linear measurements by almost an order of magnitude. The phase error m? of linear measurements is estimated at hundredths of a millimeter, 0,015–0,02 mm. However, for the implementation of this method, there are difficulties associated with the process of phase detection of the receiving modulated light. There are no photoelectric multipliers operating at a frequency of 600–1200 MHz. The proposed work provides a schematic diagram of the heterodyne laser range finder, which makes it possible to realize the operation of a light-range meter with circular polarization of light by using an auxiliary generator-heterodyne.

A Diatomic Chain with A Mass Impurity

A classic diatomic chain with one mass impurity is studied using the recurrence relations method. The momentum autocorrelation function of the impurity results from contributions of two pairs of resonant poles and three branch cuts. The pole contribution is given by cosine function(s) and the cut contribution is the acoustic and optical branches. The acoustic and optical branches are given by expansions of even-order Bessel function. The expansion coefficients are integrals of elliptic functions in the real axis in a complex plane for the acoustic branch and along a contour parallel to the imaginary axis for the optical branch, respectively. An integral 22 22 1 2 0 d / ( r sin )( r sin ) 1 1 ϕ θ − θ− θ ∫ (r2 2 >r1 2 >1) is evaluated.

Interpretation of MUSIC for Location Detecting of Small Inhomogeneities Surrounded by Random Scatterers

We consider the MUltiple SIgnal Classification (MUSIC) algorithm for identifying the locations of small electromagnetic inhomogeneities surrounded by random scatterers. For this purpose, we rigorously analyze the structure of MUSIC-type imaging function by establishing a relationship with zero-order Bessel function of the first kind. This relationship shows certain properties of the MUSIC algorithm, explains some unexplained phenomena, and provides a method for improvements.

Performance Research on Anti-Noise AM Spot Jamming of PRBC-SFM Combined Fuze

This paper gives the research on the anti-noise AM spot jamming performance of pseudo-random binary code phase modulation and sine FM combined fuze based on the criterion of signal to jamming ratio gain. First, the overall signal to jamming ratio gain of its receiver is reduced in detail under the noise AM spot jamming, then, the factors affecting anti-jamming performance are analyzed. The results show that the PRBC-SFM combined fuze has stronger performance of anti-noise AM spot jamming, and its anti-jamming performance can be improved effectively by choosing the parameters of the n-th order Bessel function, and along with decreasing periods and narrowing code width, Doppler frequencys influence on the anti-noise AM spot jamming performance of the PRBC-SFM combined fuze is debased.