一种水平变化波导中声传播问题的耦合模态法

针对介质参数及海底边界水平变化波导中的声传播问题,本文基于多模态导纳法提出一种能量守恒且便于数值稳定求解的耦合模态方法.将声压表示为一组正交完备的本地本征函数之和,对声压满足的Helmholtz方程在本地本征函数上作投影,推导出关于声压模态系数的二阶耦合模态方程组.耦合矩阵直观描述水平变化因素对模态耦合的贡献.为避免直接求解二阶耦合模态方程组可能遇到的数值发散问题,将其重构为两个耦合的一阶演化方程组,引入导纳矩阵并使用Magnus数值积分方法获得稳定的声场解.利用该耦合模态方法数值计算水平变化波导中的声场,并与COMSOL参考解比较,结果表明该耦合模态理论能够精确求解水平变化波导中的点源及分布源传播问题.     

Low frequency sound propagation in activated carbon

Activated carbon can adsorb and desorb gas molecules onto and off its surface. Research has examined whether this sorption affects low frequency sound waves, with pressures typical of audible sound, interacting with granular activated carbon. Impedance tube measurements were undertaken examining the resonant frequencies of Helmholtz resonators with different backing materials. It was found that the addition of activated carbon increased the compliance of the backing volume. The effect was observed up to the highest frequency measured (500 Hz), but was most significant at lower frequencies (at higher frequencies another phenomenon can explain the behavior). An apparatus was constructed to measure the effective porosity of the activated carbon as well as the number of moles adsorbed at sound pressures between 104 and 118 dB and low frequencies between 20 and 55 Hz. Whilst the results were consistent with adsorption affecting sound propagation, other phenomena cannot be ruled out. Measurements of sorption isotherms showed that additional energy losses can be caused by water vapor condensing onto and then evaporating from the surface of the material. However, the excess absorption measured for low frequency sound waves is primarily caused by decreases in surface reactance rather than changes in surface resistance.     

Mathematical simulation of sound propagation in a flow channel with impedance walls

The paper considers the specifics of calculating tonal sound propagating in a flow channel with an installed sound-absorbing device. The calculation is performed on the basis of numerical integrating on linearized nonstationary Euler equations using a code developed by the authors based on the so-called discontinuous Galerkin method. Using the linear theory of small perturbations, the effect of the sound-absorbing lining of the channel walls is described with the modified value of acoustic impedance proposed by the authors, for which, under flow channel conditions, the traditional classification of the active and reactive types of lining in terms of the real and imaginary impedance values, respectively, remains valid. To stabilize the computation process, a generalized impedance boundary condition is proposed in which, in addition to the impedance value itself, some additional parameters are introduced characterizing certain fictitious properties of inertia and elasticity of the impedance surface.     

Physical modeling of nonlinear sound wave propagation in oceanic waveguides of variable depth

Results of laboratory experiments aimed at studying the spatial distribution of the difference-frequency acoustic wave field in a shallow-water waveguide with a sloping bottom are presented. It is shown that, in an inhomogeneous waveguide, the direction toward the radiation maximum in the angular spectrum of the low-frequency wave continuously varies as the rib of the wedge is approached, whereas, in a homogeneous waveguide, the angular spectrum is shaped. A spatial filtering of low-frequency modes produced by a parametric radiator and reflected from the coastal wedge is experimentally realized. The results of the experiment are confirmed by numerical modeling. Problems of the physical adequacy of the experimental results obtained under actual and laboratory conditions are discussed.     

High frequency sound propagation in a network of interconnecting streets

We propose a new model for the propagation of acoustic energy from a time-harmonic point source through a network of interconnecting streets in the high frequency regime, in which the wavelength is small compared to typical macro-lengthscales such as street widths/lengths and building heights. Our model, which is based on geometrical acoustics (ray theory), represents the acoustic power flow from the source along any pathway through the network as the integral of a power density over the launch angle of a ray emanating from the source, and takes into account the key phenomena involved in the propagation, namely energy loss by wall absorption, energy redistribution at junctions, and, in 3D, energy loss to the atmosphere. The model predicts strongly anisotropic decay away from the source, with the power flow decaying exponentially in the number of junctions from the source, except along the axial directions of the network, where the decay is algebraic.     

Vortex sound generation due to a flow impedance discontinuity on a flat surface

The sound generated by the unsteady motion of a vortex filament moving over a flat boundary with a sharp flow impedance discontinuity is studied theoretically. Theoretical results show that the vortex filament undergoes significant accelerating or decelerating motions and radiates sound at the instant when it moves across the plane of impedance discontinuity. The accelerations and decelerations of the vortex filament are shown to be the major mechanisms of sound generation. The sound so produced has a large low-frequency content such that the change in the flow impedance affects only the sound generation process but not the subsequent sound propagation to the far field.     

多阶声模态分解的改进阻抗管法测量材料的高频吸声系数

为了测量高频材料吸声系数,采用声模态分解的方法,基于阻抗管构建测试设备,在阻抗管内测量超过平面波截止频率的的高频吸声系数。测量过程中,通过在阻抗管的周向和轴向分别布置传声器阵列,分离管道内前3阶周向声模态以及各阶声模态的轴向传播入射波和反射波,从而得到最高频率达10000 Hz的材料吸声系数,并通过对比常规阻抗管测试方法的测量结果,说明采用声模态分解法对高频材料吸声系数的准确性。     

Measurements of sound transmission through panels of locally resonant materials between impedance tubes

We present a method for the measurements of complex transmission coefficient through high transmission loss samples using three-sensors, two impedance tubes, monotonic wave excitation, and phase sensitive detection. Having demonstrated the effectiveness of the method on perforated plates measurements have been made on locally resonant sonic materials (LRSMs). The transmission losses of perforated plates are found to decrease with decreasing frequency down to 120 Hz, following the mass law. For the LRSM’s panels with the same area mass density but different compositions, the local resonance frequency (at which the transmission loss is maximum) is found to vary according to the predesigned value. Transmission losses as high as 96.5 dB at 630 Hz and 87 dB at 250 Hz can be measured with good accuracy, with corresponding phase spectra that match the theoretical prediction of LRSMs, confirming the reliability of the transmission data.     

The complex equivalent source method for sound propagation over an impedance plane

The sound field caused by a monopole source above an impedance plane can be calculated by using a superposition of equivalent point sources located along a line in the mirror space below the plane. Originally, such an approach for representing the half-space Green's function was described by Sommerfeld at the beginning of the last century, in order to treat half-space problems of heat conduction. However, the representation converges only for masslike impedances and cannot be used for the more important case of reflecting planes with springlike surface impedances. The singular part of the line integral can be transformed into a Hankel function, which shows that surface waves are contained in the whole solution. Unfortunately, this representation suffers from the lack of validity at certain receiver points and from restrictions on wave number and impedance range to ensure the necessary convergence. The main idea of the present method is to use also a superposition of equivalent point sources, but to allow that these sources can be located at complex source points. The corresponding form of the half-space Green's function is suitable for both masslike and springlike surface impedances, and can be used as a cornerstone for a boundary element method.     

Time-domain impedance formulation for transmission line matrix modelling of outdoor sound propagation

Outdoor sound propagation modelling has attracted considerable attention in the past and has lead to many analytical and numerical models. More recently, the increase of computational power has led to consider time-domain methods that enable to consider transient phenomena. Among these models, the transmission line matrix (TLM) method has been proposed, but the sound absorption at boundaries appears to be a somewhat underdeveloped aspect of this approach. In this paper, a specific implementation of impedance boundary condition is proposed. The method is based on the approximation of the impedance as a sum of linear systems, which allows the formulation of an equivalent impedance model in the time-domain. The proposed implementation is applied for two common impedance models of porous material. Numerical simulations have been carried out in the case of sound propagation over a flat ground with and without an impedance discontinuity, and for several values of specific airflow resistivity. TLM numerical predictions expressed in terms of excess attenuation relative to free field show a good agreement with analytical solutions.     

Low frequency coupled mode sound propagation over a continental shelf

A two-way integral equation coupled mode method is applied to a continental shelf ocean waveguide proposed for a special session devoted to range-dependent acoustic modeling at the 141st meeting of the Acoustical Society of America. The coupled mode solution includes both sediment trapped and continuum modes. The continuum is approximated by a finite number of leaky modes but neglects the branch cut contribution. Mode coupling matrix elements and the range evolution of the modal amplitudes show the nature of the mode coupling. Transmission loss versus range at 100 Hz predicted by the integral equation approach is compared to the transmission loss predicted by a wide angle parabolic equation method. While there is very good agreement, one observes small differences that can be interpreted as backscattering predicted by the integral equation solution.     

Three-dimensional cytoplasmic calcium propagation with boundaries

Ca²⁺plays an important role in cell signal transduction.Its intracellular propagation is the most basic process of Ca²⁺signaling,such as calcium wave and double messenger system.In this work,with both numerical simulation and mean field ansatz,the three-dimensional probability distribution of Ca²⁺,which is read out by phosphorylation,is studied in two scenarios with boundaries.The coverage of distribution of Ca²⁺is found at an order of magnitude ofμm,which is consistent with experimental observed calcium spike and wave.Our results suggest that the double messenger system may occur in the ER-PM junction to acquire great efficiency.The buffer effect of kinase is also discussed by calculating the average position of phosphorylations and free Ca²⁺.The results are helpful to understand the mechanism of Ca²⁺signaling.     

Methods of measuring frequency shifts in the interference structure of the sound field in oceanic waveguides

The efficiency of the correlation method is considered as applied to measuring frequency shifts of maxima in the interference structure of the sound speed under the influence of distortions of the sound-speed profile. The method is based on tracing the position of the maximum of the cross-correlation function corresponding to the spectrum of the transmitted signal in the frequency domain. The distortion is modeled by seasonal variations of the hydrological environment. The noise immunity of the method is analyzed. The correlation method is compared with other known methods of tracing frequency shifts of the interference maxima.     

Advanced impedance matching in photonic crystal waveguides

We demonstrate that the dispersion of guided propagating modes in certain Photonic Crystal Waveguides (PCWGs) can be kept constant when the waveguide’s structure changes along the propagation direction. This suggests that the principle of constant group velocity matching may be utilized to improve impedance matching between different types of PCWGs while at the same time providing significant design flexibility. We illustrate this principle through the design of several efficient coupling structures between two different PCWGs via a local density of states and Fourier transform analysis of the associate electromagnetic fields. The couplers consist of heterostructures whose individual sections exhibit rather distinct structural parameters. Furthermore, we compare these structures to an adiabatic coupler.     

Wave propagation in deep-subwavelength mode waveguides

This Letter proposes a dielectric waveguide with deep-subwavelength mode sizes. Results of both frequency domain and time domain analysis show that the effective mode area is below λ(0)(2)/400 and can even reach λ(0)(2)/1000 (λ(0) is the wavelength in vacuum). The effective electrical mode area can be comparable to that of a hybrid plasmonic subwavelength confinement waveguide, with reduced optical absorption. In contrast to slot waveguides, which guide light in low-index materials, the proposed structure guides light in high-index materials. Results obtained in this Letter show that the losses are sensitive to the surface roughness on the tens of nanometers scale. The structure can be used to design ring resonators with a quality factor comparable to that of a diffraction-limited dielectric ring resonator with the same standing wave numbers. The property can be applied in nonlinear effect enhancement or laser design with ultralow threshold.     

Localization properties of eigenstates in waveguides and cavities with corrugated boundaries

In this paper, we investigate the localization properties of eigenstates for the infinite periodic and closed versions of the generalized ripple billiard (exemplifying corrugated waveguides and corrugated cavities, respectively) having Dirichlet and Neumann boundary conditions. In particular, we demonstrate the existence of strongly energy-localized eigenstates that suffer repulsion, in configuration space, from highly corrugated billiard boundaries. Thus, exhibiting the repulsion effect as a universal property present in billiards with corrugated boundaries. We also characterize this repulsion effect (both, in energy and in configuration space) and provide heuristic expressions for the repelled eigenstate profiles in configuration representation.