Multiple monopole scattering of sound waves from spherical particles in liquid and elastic media

A solution to the problem of the mean sound field in liquid and elastic media with spherical particles causing monopole scattering of sound is proposed. The integral equation obtained for the field allows passage to the Helmholtz equation with an effective wave number. The characteristic features of the solution are the absence of radiation loss in the mean field wave and the absence of limitations on the particle concentration. The integral equation is used as the basis for solving the problem of the incidence of a plain sound wave at an arbitrary angle on a plane layer of a medium with particles.     

Multiple ion scattering

The energy spectra and the angular distributions of noble gas ions, reflected from a metal surface, yield information about a number of important properties of this surface. A large number of investigations have been carried out in the past decades, not only to get insight into the interaction mechanism but also to develop methods for applying of the knowledge gained. To obtain information about the outermost surface layer, it appears necessary to use noble gas ions as primary particles, and to detect the scattered particles in the charged state only; the fraction of noble gas ions reaching the detector, after reflection from target atoms in the second layer, is very small because of the high probability of neutralization. However, this is only valid if the initial energy of the incoming ions is relatively low, namely ? 10 KeV. Under certain experimental circumstances it appears justifiable, down to a lower limit of about 20 eV, to conceive the interaction of these ions with the target atoms as single collisions. The relation between the initial energy and the post-collision energy is then very simple if the collision is an elastic one; it depends upon the scattering angle and upon the ratio of the two given masses only and not upon the interaction potential. The shift of the peaks in an energy spectrum is caused by inelastic collisions and is relatively small in the considered energy region. The causes of this shift will be discussed. As opposed to single collisions, the post-collision energies after a multiple collision depend largely upon the interaction potential. Attention will be paid to the search for these potentials. Utilization of the multiple collision phenomenon in the study of surface geometry is hampered by the vibrational motion of the surface atoms. As a result, the energy spectra are blurred and a shift of the so-called quasi-single and quasi-double peaks can occur. Under certain conditions a third peak emerges which can give additional information about the surface vibrations. The intensity of the scattered ions depends upon the cross section for scattering. Recently it has been shown that the relation between this cross section and the initial energy has an oscillating character for certain combinations of incident ions and target atoms. This phenomenon has very important consequences, e.g. in the use of single ion scattering as an analytical tool. To investigate surface structures it appears that single and multiple ion scattering, combined with LEED and AES, can provide valuable information.     

Quasi-wavelet calculations of sound scattering behind barriers

Quasi-wavelets (QWs) are a representation of turbulence consisting of self-similar, eddy-like structures with random orientations and positions in space. They are used in this paper to calculate the scattering, due to turbulent velocity fluctuations, of sound behind noise barriers as a function of the size and spatial location of the eddies. The sound scattering cross-section for QWs of an individual size class (eddy size) is derived and shown to reproduce results for the von Kármán spectrum when the scattered energies from a continuous distribution of QW sizes are combined. A Bragg resonance condition is derived for the eddy size that scatters most strongly for a given acoustic wavenumber and scattering angle. Results for scattering over barriers show that, for typical barrier conditions, most of the scattered energy originates from eddies in the size range of approximately one-half to twice the size of the eddies responsible for maximum scattering. The results also suggest that scattering over the barrier due to eddies with a line of sight to both the source and receiver is generally significant only for frequencies above several kilohertz, for sources and receivers no more than a few meters below the top of the barrier, and for very turbulent atmospheric conditions.     

水下涡流场前向声散射特性分析

研究水下涡声散射特性,在目标探测和流场声成像领域具有重要意义。针对水下低马赫数涡流场前向声散射建立了数值计算方法,探究了其形态函数和指向性。首先,基于摄动声学理论给出了考虑流声耦合作用的涡声散射模型,采用时域有限差分结合完美匹配层构建了数值求解方法;随后,在算法验证的基础上,预报分析了高斯涡涡核尺寸在1~10 m,同时入射平面波无量纲波数在1~10范围内,涡流场强度对前向声散射特性的影响。结果表明,低马赫数下,声散射场具有对称性,且有明显的主瓣和指向性。其前向散射形态函数随入射波波数、涡核尺寸、涡流场强度增加而增大;主瓣方位角随波数增加而趋近入射波传播方向。     

Multiple nuclear Bragg scattering

Multiple nuclear resonant scattering from an ⁵⁷FeBO₃ single crystal has been observed in the three-beam case. A change of the lifetime and a modulation of the quantum beat were observed in our study. The high brilliance of synchrotron radiation and the high perfection of the synthetic ⁵⁷FeBO₃ single crystal enabled us to observe such an effect. This revised version was published online in August 2006 with corrections to the Cover Date.     

水下涡流场前向声散射特性分析

研究水下涡声散射特性,在目标探测和流场声成像领域具有重要意义。针对水下低马赫数涡流场前向声散射建立了数值计算方法,探究了其形态函数和指向性。首先,基于摄动声学理论给出了考虑流声耦合作用的涡声散射模型,采用时域有限差分结合完美匹配层构建了数值求解方法;随后,在算法验证的基础上,预报分析了高斯涡涡核尺寸在1～10 m,同时入射平面波无量纲波数在1～10范围内,涡流场强度对前向声散射特性的影响。结果表明,低马赫数下,声散射场具有对称性,且有明显的主瓣和指向性。其前向散射形态函数随入射波波数、涡核尺寸、涡流场强度增加而增大;主瓣方位角随波数增加而趋近入射波传播方向。     

Visualization of the sound scattering by a cylinder

The schlieren method is applied to visualizing the sound scattering ofa cylinder immersed in the liquids.Images of the echoes,caused by normal andoblique incidence from a cylinder,are obtained for two kinds of liquids:(1)theliquid is composed of a transparent liquid;and(2)the liquid is composed of twonon-mixable transparent liquids.It is found experimentally that the echo canbe caused by the discontinaites in the shadow zone.This fact is utilized to dem-onstrate the locus of the helical surface wave creeping along the surface of thecylinder.For such cases the three-dimensional image can be described by thismethod and has not to use the system with special appliances and complexalgorithm.     

Multiple scattering of seismic waves

We present theory and numerical simulations to model seismic wave propagation in the Earth crust. We compare them to observations made in Mexico.     

柱体散射的声场显示

本文应用Schlieren显示方法,对有限长圆柱体在单一液体及有分层界面的两液层中声波垂直入射和斜入射的回波结构以及界面对回波结构的影响作了实验研究,实验用图象显示了影区内不连续处产生的回波,我们利用这一结果,成功地描绘了螺旋表面波的轨迹,从而实现了应用Schlieren法来阐明三维声场的途径,避免了需要用庞大设备和复杂运算的三维显示技术。     

Impedance theory of sound scattering: General relations

The problem of sound scattering by an elastic body of arbitrary geometry in an acoustic medium is solved by the impedance method. It is shown that, for a complete solution, three impedance matrices are necessary: one of them characterizes the scatterer and the other two, the medium. The scattering matrices and other characteristics of the solution are expressed through the incident field and these three impedance matrices. The necessary general relations are presented, and the most important particular cases are considered. Three new representations of the diffraction field are proposed in the form of a sum of two components obtained as solutions to two simpler boundary-value problems. Original Russian Text ￠ Yu.I. Bobrovnitskiĭ, 2006, published in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 5, pp. 601–606.     

Multiple Rayleigh-Gans-Debye scattering in colloidal systems-dynamic light scattering

Equations for (depolarized) intensity auto-correlation functions including second order scattering contributions are derived. The equations obtained are quite similar to those for static light scattering¹). The geometry of the scattering system plays an important role here.An iterative procedure to correct correlation functions for double scattering is presented.Experiments on colloidal solutions containing latex and silica particles are performed, testing the theory and the iterative correction procedure for double scattering. We use cylindrical cuvettes with cylindrical incident and detected beams of radiation. The agreement between experiment and theory is found to be quite good, yielding a routine correction procedure for double scattering.     

Some aspects of the surface scattering of underwater sound

The mechanism of a sound wave reflection by the sea surface in the general context of the theory of time-variant communication channels theory has been studied. It is shown that the surface scattering can be represented by a constant filter in parallel with a random filter. The acoustic equations allow one to calculate the instantaneous transfer function of the equivalent filter. An experimental study conducted with a reduced scale model in an acoustic tank confirms the theoretical results.     

Multiple scattering in random media

The paper is an application of a general microscopic approach to the theory of the average scattering matrix for a particle interacting with random scatterers. We present a detailed treatment for the case of uncorrelated positions of the scatterers. First, the general two-body additive approximation is used to truncate the hierarchy of correlation functions for fluctuations. It is shown that the self-energy is accurate through the fourth power of the individual scattering amplitude. Second, the hierarchy is terminated at the next stage. The self-energy is correct to the sixth power of the scattering amplitude.Work supported in part by the National Science Foundation under Contract No. NSF DMR 79-23213.     

Multiple scattering with three-body forces

The multiple-scattering formalism is generalized to account for simultaneous interactions of a projectile with two target particles. In the cluster expansion of multiple-scattering theory such three-body interactions combine with iterates of two-body interactions. Some comparisons of multiple scattering with the Faddeev theory are given.     

Multiple scattering in dilute systems

Multiple scattering in the limit in which the constituent scatterers are far removed from each other is studied. It is seen how this situation leads, in the Watson multiple-scattering series, to the dominance of on-shell propagation between the constituents. It also yields a version of the Glauber multiple-scattering theory in which no assumption is made to the effect that the individual projectile-constituent scattering amplitudes are eikonal in form. This approach allows for the immediate extraction of Fresnel corrections to the Glauber result and explains several apparent contradictions as to the relationship between the Watson multiple-scattering series approximated with on-shell propagation only and the Glauber theory.     

Radiation and scattering of sound waves in oceanic waveguides

The applicability conditions for the concept of a directivity pattern (a scattering amplitude) in the problems of waveguide propagation are formulated. The consideration is based on the solution of the Sturm-Liouville problem. The results of the comparison between these conditions and the analogous conditions obtained earlier in the ray approximation are discussed. The expression for the scattering matrix of waveguide modes is modified on the basis of the suggested conditions in such a way that it involves only the quantities determined from the solution of the Schrödinger equation. This makes it possible to perform numerical calculations by using the results of numerous studies of the propagation in inhomogeneous waveguides and the diffraction by complex-structured bodies in free space.