Estimation of the sound pressure field of a baffled uniform elliptically shaped transducer

In this paper an alternative approach to estimate the sound field of an elliptically shaped transducer in an infinite baffle is described. The method is based on a singular value decomposition of a propagating matrix which is computed through a division of the vibrating surface into a finite number of small circular piston sources flush-mounted on the elliptical surface. This decomposition is combined with the volume velocity vector on the discretized surface to obtain the sound pressure field. Numerical examples for both on-axis sound pressure and directivity are presented for the uniform elliptical piston transducer and they are in good agreement with the results given by other methods.     

On the sound field of a resilient disk in free space

Radiation characteristics are calculated for a circular planar sound source in free space with a uniform surface pressure distribution, which can be regarded as a freely suspended membrane with zero mass and stiffness. This idealized dipole source is shown to have closed form solutions for its far-field pressure response and radiation admittance. The latter is found to have a simple mathematical relationship with the radiation impedance of a rigid piston in an infinite baffle. Also, a single expansion is derived for the near-field pressure field, which degenerates to a closed form solution on the axis of symmetry. From the normal gradient of the surface pressure, the surface velocity is calculated. The near-field expression is then generalized to an arbitrary surface pressure distribution. It is shown how this can be used as a simplified solution for a rigid disk in free space or a more realistic sound source such as pre-tensioned membrane in free space with non-zero mass and a clamped rim.     

On the sound fields of infinitely long strips

Exact solutions are derived for sound radiation from four kinds of infinitely-long strips: namely a rigid strip in a baffle of finite width, a resilient strip in free space, and a resilient or rigid strip in an infinite baffle. In one limit, the strip in a finite baffle becomes a rigid strip in free space and in the other, a line source in a finite baffle. Here "rigid" means that the surface velocity is uniform, whereas "resilient" means that the surface pressure is uniform, and the strip is assumed to have zero mass or stiffness, as if a force were driving the acoustic medium directly. According to the Babinet-Bouwkamp principle, radiation from a resilient strip in an infinite baffle is equivalent to diffraction of a plane wave through a slit in the same. Plots are shown for the radiation impedances, far-field directivity patterns, and on-axis pressure responses of the four kinds of strip. A simple relationship between the radiation admittance of the rigid strip in an infinite baffle and the resilient strip in free space is presented. The two-dimensional rectangular wave functions developed in this paper can be applied to related problems.     

Near-field second-harmonic generation induced by local field enhancement

The field near a sharp metal tip can be strongly enhanced if irradiated with an optical field polarized along the tip axis. We demonstrate that the enhanced field gives rise to local second-harmonic (SH) generation at the tip surface thereby creating a highly confined photon source. A theoretical model for the excitation and emission of SH radiation at the tip is developed and it is found that this source can be represented by a single on-axis oscillating dipole. The model is experimentally verified by imaging the spatial field distribution of strongly focused laser modes.     

均匀电场中颗粒簇偶极矩的确定

置于均匀电场中的一簇球形颗粒,由于其内部的相互作用而耦合在一起．这致使簇的感应偶极矩与簇的几何结构,大小以及颗粒的介电常数等参量有关．试图通过已知的链的偶极矩确定任意大小长方结构的簇的偶极矩．假定颗粒链可以被具有同样偶极矩的一个等效介质球代替,并将具有空间结构的颗粒簇处理成面结构簇,再将面结构简化成一个颗粒链,从而确定簇的偶极矩．在这一过程中,通过不断增加等效球的尺寸,将颗粒间的相互作用包含在簇的偶极矩中．数值分析了立方结构簇的偶极矩,结果是可接受的. 关键词：     

Comparison of spheroidal and eigenfunction-expansion trial functions for a membrane in an infinite baffle

The on-axis far-field pressure response of a circular membrane in an infinite baffle when driven by a uniformly distributed electrostatic force is calculated using two different trial functions for the surface velocity distribution. The first is an expansion based upon a solution to the free space wave equation in oblate spheroidal coordinates, which has already been derived in a previous paper [J. Acoust. Soc. Am. 120(5), 2460-2477 (2006)], and the second is a membrane eigenfunction expansion (or Bessel series), which is rigorously derived in this letter. Although the latter can be used as a basis for calculating a number of different radiation characteristics such as the radiation impedance or directivity, etc., only the on-axis far-field sound pressure is considered here. The results are compared and discussed.     

On optimal retreat distance for the equivalent source method-based nearfield acoustical holography

As a basic form of the equivalent source method (ESM) that is used to nearfield acoustical holography (NAH) problems, discrete monopoles are utilized to represent the sound field of interest. When setting up the virtual source distribution, it is vital to maintain a "retreat distance" between the virtual sources and the actual source surface such that reconstruction would not suffer from singularity problems. However, one cannot increase the distance without bound because of the ill-posedness inherent in the reconstruction process with large distance. In prior research, 1-2 times lattice spacing, or the inter-element distance of microphones, is generally recommended as retreat distance in using the ESM-based NAH. While this rule has shown to yield good results in many cases, the optimal choice is a complicated issue that depends on frequency, geometry of the physical source, content of evanescent waves, distribution of sensors and virtual sources, etc. This paper deals about attaining the best compromise between the reconstruction errors induced by the point source singularity; the reconstruction ill-posedness is an interesting problem in its own right. The paper revisits this issue, with the aid of an optimization algorithm based on the golden section search and parabolic interpolation. Numerical simulations were conducted for a baffled planar piston source and a spherically baffled piston source. The results revealed that the retreat distance appropriate for the ESM ranged from 0.4 to 0.5 times the spacing for the planar piston, while from 0.8 to 1.7 times average spacing for the spherical piston. Experiments carried out for a vibrating aluminum plate also revealed that the retreat distance with 0.5 times the spacing yielded better reconstructed velocity than those with 1/20 and 1 times the spacing.     

Effective dielectric constant of dilute polydisperse suspensions of spheres

We study the effective dielectric constant of a dilute, polydisperse suspension of spheres embedded in a uniform background. We consider a frequency region where the dipole polarizability of individual spheres exhibits a resonance. We evaluate the effective dielectric constant to second order in the volume fraction employing the dipole approximation, which in previous work has been shown to be applicable in resonance. We apply our results to suspensions of spheres with identical and uniform dielectric constant, assuming a log-normal distribution of sphere radii.     

Highly efficient second-harmonic nanosource for near-field optics and microscopy

A nanometric source of second-harmonic (SH) light with unprecedented efficiency is demonstrated; it exploits the grazing-incidence illumination of a metal tip, which is conventionally used for atomic force microscopy, by 25-fs laser pulses of a high-energy Ti:sapphire oscillator. Tip scanning around the beam focus shows that the SH generation is strongly localized at its apex. The polarization dependence of the SH light complies with the model of an on-axis nonlinear oscillating dipole.     

An alternative method to measure the on-axis difference-frequency sound in a parametric loudspeaker without using an acoustic filter

The self-demodulation characteristic of finite-amplitude ultrasonic sound waves can be applied with parametric loudspeaker to reproduce audible sound with highly directivity. But measuring the difference-frequency sound is still a problem due to the spurious sound generated as a result of nonlinearity caused by the product of the primary waves at the receiving system. In this paper, based on the phase-cancellation method and the Gaussian beam expansion technique, an alternative method is proposed to measure the on-axis difference-frequency sound accurately without using any traditional acoustic filter, where the spurious sound can be greatly reduced or even eliminated. The proposed method is more suitable for the case where the piston source in the parametric loudspeaker comprises multiple small piezoelectric transducers (PZTs) and each transducer element in the array may have different frequency response. The validity of the proposed method is confirmed both by simulations and experiments.     

Quench dynamics of ultracold atoms in one-dimensional optical lattices with artificial gauge fields

We study the quench dynamics of noninteracting ultracold atoms loaded in one-dimensional(1D) optical lattices with artificial gauge fields, which are modeled by lattices with complex hopping coefficients. After suddenly changing the hopping coefficient, time evolutions of the density distribution, momentum distribution, and mass current at the center are studied for both finite uniform systems and trapped systems. Effects of filling factor, system size, statistics, harmonic trap, and phase difference in hopping are identified, and some interesting phenomena show up. For example, for a finite uniform fermionic system shock and rarefaction wave plateaus are formed at two ends, whose wave fronts move linearly with speed equaling to the maximal absolute group velocity. While for a finite uniform bosonic system the whole density distribution moves linearly at the group velocity. Only in a finite uniform fermionic system there can be a constant quasisteady-state current, whose amplitude is decided by the phase difference and filling factor. The quench dynamics can be tested in ultracold atoms with minimal modifications of available experimental techniques, and it is a very interesting and fundamental example of the transport phenomena and the nonequilibrium dynamics.     

低频振荡电位的能量和相位稳定性与偶极子电流活动相关性的仿真

能量和相位是分析脑节律的重要物理量, 虽有许多研究, 但其与脑组织电特性和脑节律源的关系尚不完全清楚, 弄清这一问题有助于脑电测量及脑功能和疾病的分析. 为此, 借鉴脑电正问题研究方法, 大脑可看作均匀球, 脑组织电特性用导体各向同性和各向异性电导率来表示, 脑节律源用准静态偶极子电流来模拟, 其活动表达为较低频率的正弦振荡, 在改变该活动的振幅和相位时程时, 用球表面剖分网格的振荡电位仿真脑节律, 提取节律的能量和相位, 计算源和节律的窄带相位稳定性. 结果表明: 仿真节律的能量随电导率增大而减小, 受网格位置、电导率各向异性、偶极子电流幅值和偏心位置影响较大; 但仿真节律的相位稳定性只与自身的相位时程有关. 说明能量与相位稳定性电学意义无交集, 同时用来分析脑节律可提供更多神经信息; 能量的电学意义更复杂, 取决于包括测量条件在内的多种因素; 相位稳定性的优势在于它仅与脑节律相位时程直接相关, 可预测的是脑的非线性导致的相位时程越离散, 则相位稳定性越差.     

Formation of expanded smooth quasi-Bessel beam range due to the transformation of the Gaussian beam in absorbing axicon

The quasi-Bessel beam range produced by an absorbing axicon is investigated. It is shown that when an incident Gaussian beam is used, the absorbing axicon stretches (with respect to transparent axicon case) the uniform on-axis light intensity distribution length, as well as expanding the quasi-Bessel beam range. In addition, the peak of axial light distribution is shifted from the axicon tip. As a result any spatial modulation formed due to the bluntness of the tip is reduced close to the on-axis intensity peak, which becomes more smooth and uniform.     

有限波束作用下掩埋球体的散射声场计算

计算并分析了海底掩埋物体的三维散射声场。采用“等效垂直线列阵”方法来进行有限波束的建模,并将浅海波导中点声源散射声场的波数积分计算方法,推广到有限波束作用下海底掩埋物体的散射场计算,本文导出了物体位于沉积层中的散射声场计算公式。计算结果表明,在波导中垂直面内的散射声场,与沉积层中点源形成的声场非常相似;当距离较远时,散射声波呈柱面波衰减。文章还分析利用海面反射以提高散射能量的可能性,表明波束指向性及波束宽度对散射声场有较大影响。     

Directionality of sperm whale sonar clicks and its relation to piston radiation theory

This paper investigates the applicability to sperm whales of the theory of sound radiating from a piston. The theory is applied to a physical model and to a series of sperm whale clicks. Results show that wave forms of off-axis signals can be reproduced by convolving an on-axis signal with the spatial impulse response of a piston. The angle of a recorded click can be estimated as the angle producing the spatial impulse response that gives the best match with the observation when convolved with the on-axis wave form. It is concluded that piston theory applies to sperm whale sonar click emission.     

基于共焦原理的反射式自聚焦光纤传感技术研究

基于共焦显微成象原理,提出了一种由自聚焦透镜和X型光纤组成的高精度反射式自聚焦光纤传感器.该传感器具有绝对位置跟踪的特殊能力,并有体积小、抗干扰性强、轴向分辨率高等特点.由实验分析得,其轴向分辨率可达30nm.可用于表面微观形貌、外形尺寸、曲面轮廓等测量领域.     

A SIMPLE MODEL TO ESTIMATE THE IMPACT FORCE INDUCED BY PISTON SLAP

The dynamics of piston's secondary motion (lateral and rotational motion) across the clearance between piston and cylinder inner wall of reciprocating machines are analyzed. This paper presents an analytical model, which can predict the impact forces and vibratory response of engine block surface induced by the piston slap of an internal combustion engine. A piston is modelled on a three-degree-of-freedom system to represent its planar motion. When slap occurs, the impact point between piston skirt and cylinder inner wall is modelled on a two-degree-of-freedom vibratory system. The equivalent parameters such as mass, spring constant, and damping constant of piston and cylinder inner wall are estimated by using measured (driving) point mobility. Those parameters are used to calculate the impact force and for estimating the vibration level of engine block surfaces. The predicted results are compared with experimental results to verify the model.     

Three-dimensional analysis of scattering by pressure-release plane surfaces and the validity of the image solution

Because of the complexity of the scattering integrals in three dimensions, numerous approximations are used to obtain closed-form solutions. By considering the scattering by an infinite, pressure-release plane surface, the effects of various phase approximations and source directivity approximations can be examined independently of the surface roughness. Calculations are carried out using the Fraunhofer and Fresnel phase approximations, and two directivity approximations. It has been shown experimentally that the image solution is valid for the reflection of an acoustic beam by an infinite, pressure-release plane surface if the plane is in the farfield of the source. Consequently, the image solution is used to compare analytical solutions obtained using various phase and directivity approximations, and it is found that both the Fresnel phase approximation and a realistic directivity approximation are required to achieve a good fit. The solution produced by the Fraunhofer phase approximation is obtained as an asymptotic limit of the modified Fresnel solution. Criteria for the validity of the Fraunhofer and Fresnel phase approximations are developed. The Fresnel phase approximation is valid under fairly broad conditions, but the Fraunhofer phase approximation is never valid for an infinite plane surface that must be in the farfield of the source.     

氢负离子在电介质球面附近的光剥离研究

利用镜像法结合半经典闭合轨道理论,对氢负离子在电介质球面附近的光剥离进行了研究.首先利用镜像法分析了剥离电子在电介质球内的镜像电荷分布情况,然后给出了体系的哈密顿量.通过求解哈密顿正则方程,找到了剥离电子在电介质球面附近运动时的闭合轨道.借助于半经典闭合轨道理论,推导出了体系的光剥离截面,并且对光剥离截面进行了计算和分析.计算结果表明,氢负离子在电介质球面附近的光剥离截面不仅与入射光子的能量有关,而且还与电介质球面的介电常数有关.对于给定的电介质球面,随着入射光子的能量增加,光剥离截面的振荡振幅减小、振荡频率增加.当入射光子的能量增加到某一临界值时,光剥离截面的振荡结构消失.除此之外,随着电介质球面介电常数的增大,光剥离截面的振荡结构变得更加复杂.当电介质常数增大到无穷大时,体系的光剥离截面和氢负离子在金属球面附近的光剥离截面一致.因此,可以通过改变入射光子的能量及电介质球面的介电常数对氢负离子在电介质球面附近的光剥离截面进行调控研究.研究结果对负离子体系在电介质球面附近的光剥离的实验研究可以提供一定的理论指导和参考价值.     

Analyses of surface temperatures on patterned sapphire substrate for the growth of GaN with metal organic chemical vapor deposition

The surface temperature of cone-shaped patterned sapphire substrate (PSS) in GaN epitaxial growth by MOCVD and its relation to forced convection conditions and substrate surface topography were systematically investigated. Calculations using finite element method (FEM) exhibited that increase of substrate thickness would reduce surface temperature variation on PSS in typical growth condition. A hydrodynamics model under different chamber conditions is established, suggesting that carrier gas's velocity V_∞ plays a significant role on surface temperature of PSS in comparison with planar substrate. Also, carrier gas's pressure P_carrier is found to be another important factor on surface thermal distribution. Results of temperatures of surface with different pattern topographies suggested that an ideal PSS structure can confine the in-cell temperature discrepancy on surface into less than 0.4 K. Pattern scales of PSS and their influence on surface temperature variation were also discussed.