Sound scattering by rigid oblate spheroids, with implication to pressure gradient microphones

The frequency limit below which sound scattering by a microphone body is sufficiently small to permit accurate pressure gradient measurements was determined. The sound pressure was measured at various points on the surface of a rigid oblate spheroid illuminated by spherical waves generated by a point source at a large distance from the spheroid, insuring an essentially plane sound field. The measurements were made with small pressure microphones flush mounted from the inside of the spheroid model. Numerical solutions were obtained for a variety of spheroid shapes, including that of the experimental model. Very good agreement was achieved between the experimental and theoretical results. It was found that scattering effects are insignificant if the ratio of the major circumference of the spheroid to the wavelength of the incident sound is less than about 0.7, this number being dependent upon the shape of the spheroid. This finding can be utilized in the design of pressure gradient microphones

Understanding Galaxy Formation and Evolution

The old dream of integrating into one the study of micro and macrocosmos is now a reality. Cosmology, astrophysics, and particle physics intersect in a scenario (but still not a theory) of cosmic structure formation and evolution called Lambda Cold Dark Matter (LCDM) model. This scenario emerged mainly to explain the origin of galaxies. In these lecture notes, I first present a review of the main galaxy properties, highlighting the questions that any theory of galaxy formation should explain. Then, the cosmological framework and the main aspects of primordial perturbation generation and evolution are pedagogically detached. Next, I focus on the ``dark side'' of galaxy formation, presenting a review on LCDM halo assembling and properties, and on the main candidates for non-baryonic dark matter. It is shown how the nature of elemental particles can influence on the features of galaxies and their systems. Finally, the complex processes of baryon dissipation inside the non-linearly evolving CDM halos, formation of disks and spheroids, and transformation of gas into stars are briefly described, remarking on the possibility of a few driving factors and parameters able to explain the main body of galaxy properties. A summary and a discussion of some of the issues and open problems of the LCDM paradigm are given in the final part of these notes.Comment: 50 pages, 10 low-resolution figures (for normal-resolution, DOWNLOAD THE PAPER (PDF, 1.9 Mb) FROM http://www.astroscu.unam.mx/~avila/avila.pdf). Lectures given at the IV Mexican School of Astrophysics, July 18-25, 2005 (submitted to the Editors on March 15, 2006

Acoustic scattering by two fluid confocal prolate spheroids

The exact spheroidal-function series solution for the time-harmonic acoustic scattering of a plane wave by two fluid confocal prolate spheroids is developed and a numerical implementation is formulated and validated by independent methods. The two spheroids define three regions in which the acoustic fields are expanded in terms of spheroidal wave functions multiplied by unknown coefficients. These expansions are forced to satisfy the boundary conditions and by using the orthogonality properties of the involved functions an infinite matricial system for the coefficients is obtained. The resulting system is then solved through a truncation procedure. The implementation has no limitations regarding the sound speed and density of the three media involved or in the incidence frequency.Comment: 15 pages, 6 figure

Acoustic scattering by near-surface inhomogeneities in porous media.

A theoretical and experimental investigation into the influence of nearsurface ihhomogeneities on the reflection of air-borne acoustic fields at a porous ground surface is conducted. Two theoretical approaches to the three-dimensional physical problem are presented, both being initially formulated as boundary value problems but with subsequent reformulation as boundary integral equations via Green’s Second Theorem. In the first near-surface inhomogeneity approach, a rigid inhomogeneity is embedded within the porous medium and the boundary value problem is formulated by assuming continuity of pressure and normal velocity at the ground surface, Sommerfeld’s radiation conditions, and the Neumann boundary condition on the surface of the inhomogeneity. In the second surface inhomogeneity approach, the boundary value problem is formulated by assuming an impedance boundary condition on the plane boundary. Any near-surface inhomogeneities are assumed to induce a local variation of surface impedance within the boundary, and analytical expressions for such induced variations in surface impedance are presented. The resultant integral equations require knowledge of the Green’s function for acoustic propagation in the presence of a plane boundary but in the absence of the inhomogeneity, and methods for calculating these Green’s functions are discussed. The numerical solution of the boundary integral equations by a simple , boundary element method is described. The solution, which reduces to a system of linear equations with a block circulant coefficient matrix, is applicable to any inhomogeneity which is axisymmetric about a vertical axis; and for the near-surface inhomogeneity approach, the inhomogeneity must also be smooth. The numerical solutions have shown good agreement with classical results. The experimental measurements, presented in the form of spectra of the difference in sound pressure levels received at vertically separated points above surfaces of different media containing various scatterers, are in good agreement with the theoretical predictions

Fast and Accurate Boundary Element Methods in Three Dimensions

The Laplace and Helmholtz equations are two of the most important partial differential equations (PDEs) in science, and govern problems in electromagnetism, acoustics, astrophysics, and aerodynamics. The boundary element method (BEM) is a powerful method for solving these PDEs. The BEM reduces the dimensionality of the problem by one, and treats complex boundary shapes and multi-domain problems well. The BEM also suffers from a few problems. The entries in the system matrices require computing boundary integrals, which can be difficult to do accurately, especially in the Galerkin formulation. These matrices are also dense, requiring O(N^2) to store and O(N^3) to solve using direct matrix decompositions, where N is the number of unknowns. This can effectively restrict the size of a problem. Methods are presented for computing the boundary integrals that arise in the Galerkin formulation to any accuracy. Integrals involving geometrically separated triangles are non-singular, and are computed using a technique based on spherical harmonics and multipole expansions and translations. Integrals involving triangles that have common vertices, edges, or are coincident are treated via scaling and symmetry arguments, combined with recursive geometric decomposition of the integrals. The fast multipole method (FMM) is used to accelerate the BEM. The FMM is usually designed around point sources, not the integral expressions in the BEM. To apply the FMM to these expressions, the internal logic of the FMM must be changed, but this can be difficult. The correction factor matrix method is presented, which approximates the integrals using a quadrature. The quadrature points are treated as point sources, which are plugged directly into current FMM codes. Any inaccuracies are corrected during a correction factor step. This method reduces the quadratic and cubic scalings of the BEM to linear. Software is developed for computing the solutions to acoustic scattering problems involving spheroids and disks. This software uses spheroidal wave functions to analytically build the solutions to these problems. This software is used to verify the accuracy of the BEM for the Helmholtz equation. The product of these contributions is a fast and accurate BEM solver for the Laplace and Helmholtz equations

Effects of a finite size reflecting disk in sound power measurements

© 2018 Elsevier Ltd In practical sound power measurements in an anechoic room, a baffle sometimes has to be used to support the sound source under test so that the anechoic room can be used as a hemi-anechoic room by laying a reflecting plane. To understand the effects of a finite size reflecting plane on measurements quantitatively, this paper investigates the effects of a disk on sound power measurements by formulating an exact solution to the problem based on the spheroidal wave functions. Three practical measurement cases are considered and the correction terms for the cases are presented based on numerical simulations. Experiments are conducted to validate the analytical solutions and numerical results

The Fast Scattering Code (FSC): Validation Studies and Program Guidelines

The Fast Scattering Code (FSC) is a frequency domain noise prediction program developed at the NASA Langley Research Center (LaRC) to simulate the acoustic field produced by the interaction of known, time harmonic incident sound with bodies of arbitrary shape and surface impedance immersed in a potential flow. The code uses the equivalent source method (ESM) to solve an exterior 3-D Helmholtz boundary value problem (BVP) by expanding the scattered acoustic pressure field into a series of point sources distributed on a fictitious surface placed inside the actual scatterer. This work provides additional code validation studies and illustrates the range of code parameters that produce accurate results with minimal computational costs. Systematic noise prediction studies are presented in which monopole generated incident sound is scattered by simple geometric shapes - spheres (acoustically hard and soft surfaces), oblate spheroids, flat disk, and flat plates with various edge topologies. Comparisons between FSC simulations and analytical results and experimental data are presented

Dispersion Relations in Scattering and Antenna Problems

This dissertation deals with physical bounds on scattering and absorption of acoustic and electromagnetic waves. A general dispersion relation or sum rule for the extinction cross section of such waves is derived from the holomorphic properties of the scattering amplitude in the forward direction. The derivation is based on the forward scattering theorem via certain Herglotz functions and their asymptotic expansions in the low-frequency and high-frequency regimes. The result states that, for a given interacting target, there is only a limited amount of scattering and absorption available in the entire frequency range. The forward dispersion relation is shown to be valuable for a broad range of frequency domain problems involving acoustic and electromagnetic interaction with matter on a macroscopic scale. In the modeling of a metamaterial, i.e., an engineered composite material that gains its properties by its structure rather than its composition, it is demonstrated that for a narrow frequency band, such a material may possess extraordinary characteristics, but that tradeoffs are necessary to increase its usefulness over a larger bandwidth. The dispersion relation for electromagnetic waves is also applied to a large class of causal and reciprocal antennas to establish a priori estimates on the input impedance, partial realized gain, and bandwidth of electrically small and wideband antennas. The results are compared to the classical antenna bounds based on eigenfunction expansions, and it is demonstrated that the estimates presented in this dissertation offer sharper inequalities, and, more importantly, a new understanding of antenna dynamics in terms of low-frequency considerations. The dissertation consists of 11 scientific papers of which several have been published in peer-reviewed international journals. Both experimental results and numerical illustrations are included. The General Introduction addresses closely related subjects in theoretical physics and classical dispersion theory, e.g., the origin of the Kramers-Kronig relations, the mathematical foundations of Herglotz functions, the extinction paradox for scattering of waves and particles, and non-forward dispersion relations with application to the prediction of bistatic radar cross sections