Renormalization of singular potentials and power counting

We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r² potential perturbed by a 1/r⁴ correction. The power-counting rule, an important ingredient of effective theory, is established by seeking the minimum set of short-range counterterms that renormalize the scattering amplitude. We show that leading-order counterterms are needed in all partial waves where the potential overcomes the centrifugal barrier, and that the additional counterterms at next-to-leading order are the ones expected on the basis of dimensional analysis.     

水下多层均匀材料的声特性

本文研究水和空气中由不同厚度的两层弹性板及消声橡胶共同组成的分层介质在斜入射时的声特性,并采用数值方法求解多层结构声场的线性方程组。得到反射,透射系数,当板的厚度远小于波长时,采用弹性薄壳振动模型和弹性波模型进行计算,它们的结果基本相同,但是薄壳振动模型更便于计算和理论分析;对系统反射系数和透射系数的计算结果表明,系统增加消声橡胶层后,极大地改变后射系数和透射系数的频率响应;频率升高,反射系数减小     

水下复合层吸声结构中反向声能与振动能量传输的研究

本文对文献[1，2]所讨论的水下复合层吸声结构中能量的反向传输送行了研究．利用多层结构的传递矩阵求逆．导出声能和振动能的反向传输关系，给出传递损失．数值计算分析了结构的各层参数变化对能量传递损失的影响．     

水下复合层吸声结构中反向声能与振动能量传输的研究

本文对文献「１，２」所讨论了水下复合层吸声结构中能量的反向传输进行了研究。利用多层结构的文献矩阵求逆，导出声能和振动能的反向传输关系，给出传递损失。数值计算分析了结构的各层参数变化对能量传递损失的影响。     

水下均匀材料复合层吸声特性研究

本文对水下阻尼板和其它介质层复合的多层吸声和结构吸声，反声性能进行了研究，利用各层界面压力，振速的四端网络矩阵及层间边界条件导出吸声结构表面阻抗和反射系统数随频率的变化关系，数值计算分析了不同边界条件，多种层以及改变各层参数情况，反声，吸声系数的变化，发现多层结构中厚的水层引起强烈的共振反射峰，并提出了抑制共射的方法。     

Functional integration for Bose fields

The Lagrangian occurring in functional integration of bose fields is shown to be made up of two parts, one pertaining to the Bose commutation and the other to the dynamics.Supported by the U.S. Army Research Office (Durham).     

浅海低频垂直相控阵多模声场聚焦研究*

为了提高低频垂直相控阵声场聚焦的环境适应性,增强环境失配情况下的声场聚焦效果,提出一种多模声场聚焦方法。该方法利用环境失配对低阶模态影响相对较小的特点,只利用前3阶模态进行发射权系数的计算。仿真结果表明,多模声场具有较大的聚焦跨度,在环境失配情况下仍能在期望的聚焦位置实现良好的聚焦效果。进一步地,根据巴斯微扰理论计算分析了多模声场的混响特性。由于多模声场聚焦将能量集中到了掠射角较小的低阶模态中,因此比最优权系数聚焦具有更低的混响平均强度。多模聚焦对聚焦深度进行扫描可以实现目标的深度分辨,这在水下目标探测方面具有较高的应用前景。     

Research on sound radiation from body in free field

I.IntroductionWhenastructurcvibratcs,itsvibratingsurfacewillmakesurroundingmediummovetogethcrwithit.Ifthernotionissofastthatthcmediumroundthestructureproduccaloca1contractionandcxpansionandthcypropagatefaraway,thesoundradiationisformed.Itispossiblctodcscribeanalytica11ytheradiationfic1dofsimplyandregularlyshapcdsourcessuchaspointsoundsourccs,spherica1soundsourccsandinflnite1engthllnearsoundsourccs,butitisa1mostimpossib1ctosolvetheradiationfiledbyanyanalyt-ica1methodforsourcesofvcrycomplicateds…     

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根据反向积分原理编写了流场反演程序,并开展了程序验证计算。在反演区域内,由临界面速度反演出与辐射流体力学程序MULTI计算结果几乎一致的结果;由Saturn加速器上实验测试的单个样品后自由面速度反演出了加载压强历史、多种厚度样品后自由面粒子速度历史等信息,与文献对比发现,反演结果与由加速器工作电流推出结果、WONDY程序计算结果、实验测试结果相吻合。本工作为即将开展的激光驱动准等熵压缩实验奠定了技术基础。     

Measurement of the sound velocity in fluids using the echo signals from scattering particles

With conventional methods the sound velocity c in fluids can be determined using the back wall echo. This paper proposes a novel technique, in which the signals reflected by scattering particles suspended in a fluid are analysed instead. The basic idea is that the particles generate the strongest echo signal when being located in the sound field maximum. Therefore the position of the echo signal maximum is a measure for the propagation time to the sound field maximum. Provided that calibration data or sound field simulations for the ultrasonic transducer are available, this propagation time suffices to determine both sound velocity and the location of the sound field maximum. The feasibility of the new approach is demonstrated by different kinds of experiments: (i) Measurements of the sound velocity c in four fluids covering the wide range between 1116 and 2740 m/s. The results show good agreement with values published elsewhere. (ii) Using the dependence of the sound velocity on temperature, it is possible to vary c over the comparatively small range between 1431 and 1555 m/s with increments of less than 10 m/s. The measured statistical variation of 1.4 m/s corresponds to a relative uncertainty not worse than 0.1%. (iii) The focus position, i.e. the distance of the maximum of the sound field from the transducer, was varied by time-shifted superposition of the receive signals belonging to the different elements of an annular array. The results indicate that the novel method is even capable of measuring profiles of the sound velocity along the ultrasonic beam non-invasively.     

空气中快速运动声源水下声场的波数积分模型

本文采用二维波数积分，对空气中高速运动声源激发的水下声场进行建模。针对二维波数积分计算声场时域解计算量大的问题，提出一种快速计算方法。用本文提出的方法，对深海和浅海情况下，空气中高速运动单频点声源激发的水下声场进行了计算和仿真。计算结果表明：在深海，水下接收信号的幅度和瞬时频率随时间发生变化；接收器深度、接收器与声源运动轨迹的最小距离对接收信号的变化快慢有较大影响，而声源高度的影响较小；在浅海中，接收信号呈现快速的幅度起伏，明显的多普勒频移和大的频率展宽效应。与简正波方法相比，本文方法主要适用于近场计算，而简正波方法适用于远场。另外，当声源频率较高时，二维波数积分方法的计算量将迅速增大。     

求解水中加肋板声辐射特性的虚拟声源法*

发展一种利用虚拟声源离散声场的方法求解加肋板在水中的声振耦合问题。由波叠加原理和单元体积速度匹配的原则,根据离散的结构单元满足的动力方程和结构与介质的交界相容性条件,确定虚拟声源强度,计算结构的声辐射功率。本文以简支矩形加肋板为例,在不获得结构表面振速和声压的情况下,计算了结构在水中的声辐射功率,并与解析方法计算的结果进行了比较,表明了该方法具有较好的计算精度。     

Approximation of a general singular vertex coupling in quantum graphs

The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints is joined by an edge carrying a δ potential and a vector potential coupled to the “loose” edges by a δ coupling. It is shown that if the lengths of the connecting edges shrink to zero and the potentials are properly scaled, the limit can yield any prescribed singular vertex coupling, and moreover, that such an approximation converges in the norm-resolvent sense.     

Sound field prediction in long enclosures with branches: A combined method

The propagation of sound in long enclosures with branches has been studied theoretically and experimentally, and an efficient combined method is proposed to predict the sound field in long enclosures with branches. Based on the wave-acoustics theory, the theoretical analysis of the sound field of the long enclosures with branches is performed. This paper also investigated the sound field prediction of long enclosures with branches, by using the acoustic modeling program, ODEON. The results obtained by the theoretical analysis and the numerical simulation ODEON are compared with the experimental measurements, and the characteristics of the two methods for predicting the sound field of long enclosures with branches are analyzed. Compared with the experimental results, it is found that: (1) the results predicted by the theoretical analysis fluctuate relatively large with respect to the source-receiver distance, and the sound pressure level (SPL) attenuation obtained is smaller than that measured; and (2) the results predicted by the numerical simulation is smoother, and the calculated SPL attenuation is larger than that measured. To effectively predict the sound field of long enclosures with branches, a combined numerical method is thus proposed. The effectiveness of the proposed combined method is demonstrated by the scale-model experiments.     

A method for multi-frequency calculation of boundary integral equation in acoustics based on series expansion

The paper presents a method to solve the problem of multi-frequency calculation of Helmholtz boundary integral equation in acoustics. Based on series expansion, system matrices are independent of wavenumber and become the matrix power series of wavenumber. As a result, all matrices in the matrix power series are only dependent on the structure geometry. In addition, an element transform method to calculate the singular integral and Cauchy singular integral is also discussed because the singular integral need to be solved using the method. The convergence of the series expansion method is also proved in this paper. The effectiveness of the method is confirmed by two numerical examples.     

Focusing of a singular beam in the presence of spherical aberration and defocusing

Focusing of a singular beam by a lens in the presence of spherical aberration and defocusing is studied by using Fresnel–Kirchhoff diffraction integral for two different values of topological charge. Results of intensity distribution and encircled energy are plotted for defocused observation planes. Spherical aberration spreads the dark core and reduces the intensity at maxima. The results have been verified by the optical transfer function (OTF) approach.     

Sound transmission in multilayered structures – Introducing finite structural connections in the transfer matrix method

The transfer matrix technique is an efficient tool for calculating sound transmission through multilayered structures. Recent developments, as to the calculation of the sound reduction index, have given better fit to measurement data, e.g. due to the simulation of finite size samples by the spatial windowing technique. In practice, however, finite size structural connections (points or lines) normally do exist between leaves in wall constructions and these are not “natural” elements in the transfer matrix method. The paper describes a simple method to account for the effect of point- and line-connections in double-leaf constructions in a transfer matrix setup. To cover the frequency range above the critical frequency of the constituent plates, some new developments as to the forced radiation from plates were needed. Predicted results compare favorably with measurement results for a number of different cases, also including a heavy wall.     

Solving Maxwell’s equations in singular domains with a Nitsche type method

In this paper, we propose and analyze a method derived from a Nitsche approach for handling boundary conditions in the Maxwell equations. Several years ago, the Nitsche method was introduced to impose weakly essential boundary conditions in the scalar Laplace operator. Then, it has been worked out more generally and transferred to continuity conditions. We propose here an extension to vector div–curl problems. This allows us to solve the Maxwell equations, particularly in domains with reentrant corners, where the solution can be singular. We formulate the method for both the electric and magnetic fields and report some numerical experiments.     

立体声技术近年来的进展

本文总结和评论了立体声技术近年来的进展，包括声像定位理论和实验，传统的双通路立体声系统的改进，环绕产系统，高清晰度电视声系统，假头型立体声系统，数字声频技术在立体声的应用等．文中最后还叙述了对立体声今后发展的展望．