关于声散射声

关于传播方向不同的两有限束的相互作用问题,历年来曾存在着分歧,分歧的焦点是:在公共区之外有没有二阶散射场?Ingard用间断函数ρ={e^j(wt-ky),|x|a 表示有限束(即所谓完全准直束),通过计算求得:在公共区外有二阶散射场。Westervelt讨论了两列平面波的相互作用,却得出否定的结论。实验上也同样出现分歧。AL-Temimi将空间分成内外两部分公共区,分别求解Westervelt方程,将所得到的解在边界上连接。结果表明,公共区之外有二阶散射场。此外,他还认为上述两种相反的结论能够相对地一致。本文讨论两束正交简谐波,将上述间断函数用二个阶跃函数之差表示,代入Westervelt方程求解。结果表明,由这种理想有限束所构成的二阶散射场不是真正的散射场,而是由于按界面分布的δ函数性质的偶极源与平面波相互作用所产生的场,它随着这种界面的消失而熄灭。而这种偶极面源如文献[3,4]所述是人为的,它是由于采用了不满足齐次波动方程的间断函数来表示一阶声场所带来的结果。本文进一步指出,从这种有限束出发求得的解却和文献[6]的结果相同。这就说明,上述两种相反的结论是不能相对地一致的。本文还对文献[6]的连接条件作了分析,并指出这些条件是不恰当的。根据本文的结果,作者认为用上述间断函数来表示有限束从而计算参量发射和接收阵也是有影响的。     

有限声束的二阶积累声场研究

将有限声束分解为一系列平面波,结合声非线性相互作用理论,对有限声束的二阶积累声场进行了分析和计算。结果表明,任意两个平面波相互作用不产生二阶积累波,伴随有限声束传播所发生的二阶积累波仅是各个平面波非线性自作用的结果。此外,本文还得到了具有直观物理意义的有限声束二阶积累声场的表达式。     

复频聚焦超声换能器水中焦区商场特性的研究

本文对新研制的一种复频聚焦超声换能器的辐射声场进行了实验研究,测定了辐射压在轴向上的分布曲线,进而确定了焦区位置,这与理论所得结果符合较好,测定了辐射声压在焦平面上的分布曲线,并对焦区声场进行了定位,最后对换能器在水中焦区辐射声的频谱进行了研究,不仅观测到了两个源波,而且还观测到了和频波,差频波以及倍频波,证实了声散射声效应的存在。     

两层耦合可激发介质中螺旋波转变为平面波

采用Br-Eiswirth模型研究了两层耦合可激发介质中螺旋波的动力学,两层介质通过网络连接,即在每一层介质上,每一列选一个可激发单元作为中心点,在一层介质上同一列的可激发单元只与另一层介质上对应的中心点及其8个邻居有耦合.数值模拟结果表明:通过这种局部耦合,在适当小的耦合强度下两耦合螺旋波可实现同步,增大耦合强度会导致螺旋波漫游和漂移,造成螺旋波不同步,观察到螺旋波与静息态、低频平面波和不规则斑图共存现象.在适当强的耦合强度下,还观察到两螺旋波转变成同步的平面波消失现象.对产生这些现象的物理机理做了讨论.     

有限声波束在Rayleigh角附近从平面液-固界面上散射的新的统一理论

分析有限声波束从平面液-固界面上散射的困难主要发生在平面波反射系数的处理上。本文应用奇异点展开法将反射系数在Rayleigh极点附近展开成一个解析函数(其值为1)和Laurent展开式之和。散射场的计算用波数和界面两个变量的双重积分来进行,常数1产生刚性界面的几何散射波,Rayleigh极点展开项导致Rayleigh泄漏波。本文特别证明,对于大多数液-固界面,极点的留数近似地正比于极点的虚部。因此,根据复极点的值可以确定Rayleigh泄漏波的整个特性,包括激发和再辐射效率。对于反向散射场,既然负Rayleigh极点起作用,自然地出现反向Rayleigh泄漏波。     

反铁磁自旋波对高温超导体的电阻特性的影响

针对含铜氧化物超导体，本引用一个传导电子与局域电子间的自旋耦合来描述Ｃｕ－Ｏ平面上巡游空穴与铜离子上的局域空穴之间的相互作用。采用自旋波近似，使该自旋耦合表现为巡游载流子与自旋波之间的相互作用，其形式与电－声相互作用类似，据此可得到因自旋波对载流子的散射引起的电阻与温度的依赖关系，其性质与电－声散射电阻相同。同时还引入具有自旋波子吸收或发射的层间遂穿散射过程，讨论了垂直方向上的电阻。所得结果与实     

粗糙表面激光散射特性的理论研究

用矢量微扰动方法分析激光束在粗糙表面上散射的分布特性。详细讨论高斯光束的角谱和适用于准直激光束散射问题的波前分割概念认为，当用入射总功率作归一化因子时，准直粗激光束散射可近似地作为平面波处理，而细激光束散射则与平面波存在很大的差异，利用所得结果讨论了一维粗糙表面的激光隐身作用及椭圆偏振光入射时镜反射方向和后向散射场的偏振态。最后介绍两种线偏振光在粗糙表面上散射分布的差异。实验验证了主要结论。     

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得到了不可压缩理想霍尔磁流体方程组的平面波精确解,这些平面波是斜传播的左旋圆极化波或右旋圆极化波,并且涨落速度和涨落磁场通过波数联系起来。讨论了这些平面波解的叠加性质。当波的传播方向平行时,任意两支圆极化平面波都可以叠加;而当波的传播方向不平行时,只有极化方向相同,波数相同,且各自的旋度与自身都是同方向(或都是反方向)的两支圆极化平面波才可以叠加。     

非线性不可压缩霍尔磁流体方程组的精确解

得到了不可压缩理想霍尔磁流体方程组的平面波精确解,这些平面波是斜传播的左旋圆极化波或右旋圆极化波,并且涨落速度和涨落磁场通过波数联系起来。讨论了这些平面波解的叠加性质。当波的传播方向平行时,任意两支圆极化平面波都可以叠加;而当波的传播方向不平行时,只有极化方向相同,波数相同,且各自的旋度与自身都是同方向(或都是反方向)的两支圆极化平面波才可以叠加。     

神经元网络中局部同步引发的各种效应

在大脑皮层中,神经元大范围的同步放电可以引发癫痫,而癫痫发作期间可以自发出现螺旋波,大量神经元的同步放电与螺旋波自发产生之间的关系目前仍不清楚.本文通过增加水平长程连接构造了具有局域长程耦合区的二维神经元网络,采用Morris-Lecar神经元模型研究了具有多个长方形长程耦合区的神经元网络中波的传播,数值模拟结果表明:传播方向与长程耦合朝向平行的平面波和靶波经过长程耦合区会导致长程耦合区内的神经元同步激发,这种同步激发伴随一部分神经元延迟激发,而另一部分提前激发;当长程耦合区宽度超过临界宽度时,长程耦合区所有神经元延迟激发;当长程耦合区宽度超过最大导通宽度时,波将不能通过长程耦合区.当适当选择长方形长程耦合区的尺寸时,神经元同步激发可使网络出现波回传效应和具有波传播方向的选择性,而且这种波传播方向的选择性对神经元是否处于定态和耦合强度变化很敏感,以致高频平面波列可以部分通过宽度超过最大导通宽度的长程耦合区,因此可以通过对长程耦合区内的神经元施加微扰来控制低频波是否可以通过一定宽度的长程耦合区.对于适当选取的神经元网络结构,当平面波或靶波经过长程耦合区时,网络可自发出现自维持平面波、螺旋波和靶波等现象.本文对产生这些现象的物理机制作了分析.     

On long-wave sound scattering by a Rankine vortex: Non-resonant and resonant cases

The well-known two-dimensional problem of sound scattering by a Rankine vortex at small Mach number M is considered. Despite its long history, the solutions obtained by many authors still are not free from serious objections. The common approach to the problem consists in the transformation of governing equations to the d’Alembert equation with right-hand part. It was recently shown [I.V. Belyaev, V.F. Kopiev, On the problem formulation of sound scattering by cylindrical vortex, Acoustical Physics 54(5) (2008) 603-614] that due to the slow decay of the mean velocity field at infinity the convective equation with nonuniform coefficients instead of the d’Alembert equation should be considered, and the incident wave should be excited by a point source placed at a large but finite distance from the vortex instead of specifying an incident plane wave (which is not a solution of the governing equations).Here we use the new formulation of Belyaev and Kopiev to obtain the correct solution for the problem of non-resonant sound scattering, to second order in Mach number M. The partial harmonic expansion approach and the method of matched asymptotic expansions are employed. The scattered field in the region far outside the vortex is determined as the solution of the convective wave equation, and van Dyke's matching principle is used to match the fields inside and outside the vortical region. Finally, resonant scattering is also considered; an O(M²) result is found that unifies earlier solutions in the literature. These problems are considered for the first time.     

Model experiments on acoustic tomography of the nonlinear parameter

It is shown experimentally that the scattering of sound by sound can be observed outside the region of interaction between primary waves and that it carries information on the spatial distribution of the scatterer’s nonlinear characteristics. Based on this effect, a simple method for reconstructing the distribution of the nonlinear parameter by using complex-modulated broadband primary signals and a small number of transmit and receive transducers is implemented. The possibility of reconstructing a two-dimensional distribution of a nonlinear parameter inhomogeneity with the use of only three transducers (two transmitters and one receiver) without additional scanning in the aspect angle is demonstrated. This simple scheme loses information on the low-frequency components of the scatterer’s spatial spectrum and reconstructs the distribution of only the spatial variations of the nonlinear parameter.     

Scattering of two plane electromagnetic waves in the non-linear Born-Infeld electrodynamics

The problem of scattering of two plane waves is exactly solved in the Born-Infeld electrodynamics. The shape and the direction of the plane waves after scattering turn out to be unchanged. There is only change in the wave phase by the value which is the product of its frequency and the momentum of the incident wave. It is shown that in the interaction region the solution becomes a multiple-valued function ofx, t when the electromagnetic field exceeds a certain value which plays the role of an absolute field scale.     

平面屏系统中标量光波传播的矩阵理论(柱坐标)

本文在文献[8]的基础上,提出了一个平面屏系统中标量光波传播的矩阵理论。由于采用的是柱坐标系,所以它主要适宜于具有理想轴对称性的系统。它的主要优点,是较便于处理上述系统中某些用已有理论实际上较难处理的光传播问题。本文中未考虑散射屏。这个理论的适用范围是:系统中所有平面屏都垂直光传播轴;可对每一屏的衍射应用本文的衍射公式和近似条件;在反射、吸收和增益屏上的入射光锥角较小等。作为应用的例子,本文得出和讨论了无源光学谐振腔中振荡模的矩阵方程。把它和已有的Fox和Li的积分方程作了比较,表明了矩阵方程具有某些重要的实际优点。 关键词：     

On the statement of the problem of sound scattering by a cylindrical vortex

The well-known problem of sound wave scattering by a Rankine vortex is investigated. Although the problem has been studied for years, none of the solutions reported in the literature can be considered completely correct. It is demonstrated that the main difficulty consists in the absence of a mathematically well-posed statement of the problem for a plane wave (which is used in most of the approaches) because of the slow decrease in the mean flow velocity at infinity. This gives rise to multiple solutions, including those singular on a line behind the vortex, and each of them claims to be correct. It is shown that, in spite of the decrease in the mean flow velocity, the problem does not possess any remote region at infinity, tending to which it is possible to preset the plane wave condition for the incident field. Therefore, for the external field, the remote point source condition is proposed. This approach makes it possible to state a mathematically well-posed problem, to reveal the origin of the aforementioned ambiguity, and to compare previous approaches used for solving the problem under consideration.     

Double stimulated mandelstam-brillouin scattering of electromagnetic waves of arbitrary polarization in an isotropic plasma

We study the nonlinear interaction of a system of incident and reflected electromagnetic waves of arbitrary polarization, propagating in a quasihomogeneous plane layer of isotropic plasma obliquely to the boundary, with scattered electromagnetic waves. These waves are coupled in the double stimulated Mandelstam-Brillouin scattering by a common sound wave that is parallel to the layer boundary. We examine the influence of the wave polarization on the threshold intensity, instability growth rate, and characteristics of the stationary solution. It is found that the nonlinear interaction scales are different for waves of different polarization. In particular, this leads to a change of the wave polarization in the course of the interaction. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 7, pp. 851–859, July, 1997.     

球形粒子之间的声相互作用

本文讨论某种介质(其中包括许多球形粒子,例如浓悬浮体)对平面波的散射问题,计算了粒子之间的声相互作用场,从而得到了粒子的等效散射截面。当粒子大小比声波波长小很多时,可有如下的结论:(1)由于声相互作用,一个粒子的散射截面只有原来的Q倍,从几何上看,这是由于粒子的互相遮蔽的结果,其遮蔽因子为Q= |1-(γ₀A₀⁽¹⁾+γ₁A₁⁽¹⁾|²;(2)考虑到相互作用之后,散射系数与浓度不再是线性关系;(3)当粒子的尺度比声波波长小很多但比粘滞波波长大很多时,相互作用之后粒子的散射系数与频率的关系仍服从瑞利散射。但当粒子半径接近或小于粘滞波波长时,散射系数与频率的关系比四次方要高。 关键词：     

Reflection of sound at area expansions in a flow duct

An analytical model for scattering at area discontinuities and sharp edges in flow ducts and pipes is presented. The application we have in mind is large industrial duct systems, where sound attenuation by reactive and absorptive baffle silencers is of great importance. Such devices commonly have a rectangular cross-section, so the model is chosen as two-dimensional. Earlier solutions to this problem are reviewed in the paper. The modelling of the flow conditions downstream of the area expansion, with and without extended edges, and its implications for the resulting acoustic modes are discussed. Here, the scattering problem is solved with the Wiener-Hopf technique, and a Kutta condition is applied at the edge. The solution of the wave equation downstream of the expansion includes hydrodynamic waves, of which one is a growing wave. Theoretical results are compared with experimental data for the reflection coefficient for the plane wave, at frequencies below the cut-on for higher order modes. Influence of the interaction between the sound field and the flow field is discussed. A region where the reflection coefficient is strongly Strouhal number dependent is found.     

Scattering of a plane sound wave by spherical particles performing monopole oscillations and positioned at the sites of an infinite plane lattice with identical cells

The problem of plane wave scattering by an infinite regular lattice whose sites are occupied by spherical particles performing monopole oscillations is solved. Expressions are derived for the particle oscillation amplitudes and the coefficients of sound reflection from the lattice and sound transmission through it; the expressions are valid up to the case where the particles come in contact with each other. It is shown that, for a dense lattice with a distance between neighboring sites being much smaller than the sound wavelength, the coefficient of sound reflection from the lattice is close to unity in a wide frequency range. In the limiting case of an incompressible medium, the particle oscillation amplitude is zero, in contrast to the case of particles distributed in the volume or the case of a single particle.