Axisymmetric acoustic scattering by vortices

2002 ◽  
Vol 473 ◽  
pp. 275-294 ◽  
Author(s):  
Y. HATTORI ◽  
STEFAN G. LLEWELLYN SMITH
Keyword(s):  
Mach Number ◽  
Born Approximation ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Order Effects ◽  
Incoming Wave ◽  
Spherical Vortex ◽  
The Difference ◽  
Higher Order Effects

The scattering of acoustic waves by compact three-dimensional axisymmetric vortices is studied using direct numerical simulation in the case where the incoming wave is aligned with the symmetry axis and the direction of propagation of the vortices. The cases of scattering by Hill’s spherical vortex and Gaussian vortex rings are examined, and results are compared with predictions obtained by matched asymptotic expansions and the Born approximation. Good agreement is obtained for long waves, with the Born approximation usually giving better predictions, especially as the difference in scale between vortex and incoming waves decreases and as the Mach number of the flow increases. An improved version of the Born approximation which takes into account higher-order effects in Mach number gives the best agreement.

INVERSE ACOUSTIC SCATTERING PROBLEMS IN OCEAN ENVIRONMENTS

1999 ◽  
Vol 07 (02) ◽  
pp. 111-132 ◽  
Author(s):  
YONGZHI XU
Keyword(s):  
Acoustic Waves ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Stratified Medium ◽  
Computational Results ◽  
Scattering Problems ◽  
Numerical Examples ◽  
Layered Waveguide ◽  
Shape Determination

This paper presents theoretical and computational results from our research on inverse scattering problems for acoustic waves in ocean environments. In particular, we discuss the determination of a three-dimensional (3-D) distributed inhomogeneity in a two-layered waveguide from scattered sound and the shape determination of an object in a stratified medium. Numerical examples are presented.

scholarly journals Three-dimensional acoustic scattering by layered media: a novel surface formulation with operator expansions implementation

2011 ◽  
Vol 468 (2139) ◽  
pp. 731-758 ◽  
Author(s):  
David P. Nicholls
Keyword(s):  
Acoustic Waves ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Boundary Integral ◽  
Helmholtz Equations ◽  
Irregular Structures ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Boundary Integral Operators ◽  
Operator Expansions

The scattering of acoustic waves by irregular structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses on the rapid and highly accurate numerical approximation of solutions of Helmholtz equations coupled across irregular periodic interfaces meant to model acoustic waves incident upon a multi-layered medium. We describe not only a novel surface formulation for the problem in terms of boundary integral operators (Dirichlet–Neumann operators), but also a Boundary Perturbation methodology (the Method of Operator Expansions) for its numerical simulation. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than volumetric approaches), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of Boundary Integral/Element Methods. The approach is a generalization to multiple layers of Malcolm & Nicholls' Operator Expansions algorithm for dielectric structures with two layers. As with this precursor, this approach is efficient and spectrally accurate.

Mechanics Framework for Micron-Scale Planar Structures

2005 ◽  
Vol 9 ◽  
pp. 173-182
Author(s):  
A.C.M. Chong ◽  
Fan Yang ◽  
David C.C. Lam ◽  
Pin Tong
Keyword(s):  
Three Dimensional ◽  
Order Theory ◽  
Higher Order ◽  
Order Effects ◽  
Three Dimensional Objects ◽  
Deformation Behaviors ◽  
Scale Structures ◽  
The Difference ◽  
Higher Order Theory ◽  
Elastic And Plastic Deformation

Structures are assemblies of planar and three-dimensional objects. Planar components and parts are commonly because the deformation behaviors of plates and beams can be analyzed within the plane problem framework. For micron-scale structures, patterning processes in microfabrications are intrinsically planar and the resulting fabricated structures are also planar. These planar micron-scale structures have been designed and analyzed using conventional mechanics, but increasingly as the sizes of these structures become smaller, higher order effects become significant. In nanometer-scale, surfaces were recognized to play significant roles in affecting the physical behavior. Size dependent elastic and plastic deformation behaviors in micron-scale structures were also observed. Size dependence is an intrinsic part of higher order theory of mechanics and has been used successfully to explain scale dependent behavior in threedimensional structures. In this paper, two-dimensional higher order elastic relations in plane stress and plane strain for compressible solids are developed. The difference between the higher order and conventional elasticity theories is compared

scholarly journals Unique Determination of the Shape of a Scattering Screen from a Passive Measurement

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1156
Author(s):  
Emilia Blåsten ◽  
Lassi Päivärinta ◽  
Sadia Sadique
Keyword(s):  
Plane Wave ◽  
Incident Wave ◽  
Acoustic Waves ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Field Pattern ◽  
Unique Determination ◽  
Passive Measurement ◽  
Simply Connected

We consider the problem of fixed frequency acoustic scattering from a sound-soft flat screen. More precisely, the obstacle is restricted to a two-dimensional plane and interacting with an arbitrary incident wave, it scatters acoustic waves to three-dimensional space. The model is particularly relevant in the study and design of reflecting sonars and antennas, cases where one cannot assume that the incident wave is a plane wave. Our main result is that given the plane where the screen is located, the far-field pattern produced by any single arbitrary incident wave determines the exact shape of the screen, as long as it is not antisymmetric with respect to the plane. This holds even for screens whose shape is an arbitrary simply connected smooth domain. This is in contrast to earlier work where the incident wave had to be a plane wave, or more recent work where only polygonal scatterers are determined.

Identification of Whistling Ability of a Single Hole Orifice From an Incompressible Flow Simulation

2011 ◽  
Author(s):  
Romain Lacombe ◽  
Pierre Moussou ◽  
Yves Aure´gan
Keyword(s):  
Mach Number ◽  
Acoustic Waves ◽  
Flow Simulation ◽  
Navier Stokes ◽  
Resonant Condition ◽  
Average Flow Velocity ◽  
Fluid Behavior ◽  
The Difference ◽  
Physical Features ◽  
Lock In

Pure tone noise from orifices in pipe result from vortex shedding with lock-in. Acoustic amplification at the orifice is coupled to resonant condition to create self-sustained oscillations. One key feature of this phenomenon is hence the ability of an orifice to amplify acoustic waves in a given range of frequencies. Here a numerical investigation of the linear response of an orifice is undertaken, with the support of experimental data for validation. The study deals with a sharp edge orifice. Its diameter equals to 0.015 m and its thickness to 0.005 m. The pipe diameter is 0.030 m. An air flow with a Mach number 0.026 and a Reynolds number 18000 in the main pipe is present. At such a low Mach number, the fluid behavior can reasonably be described as locally incompressible. The incompressible Unsteady Reynolds Averaged Navier-Stokes (URANS) equations are solved with the help of a finite volume fluid mechanics software. The orifice is submitted to an average flow velocity, with superimposed small harmonic perturbations. The harmonic response of the orifice is the difference between the upstream and downstream pressures, and a straightforward calculation brings out the acoustic impedance of the orifice. Comparison with experiments shows that the main physical features of the whistling phenomenon are reasonably reproduced.

On the Ordinary, Generalized, and Pseudo-Variational Equations of Motion in Nonlinear Elasticity, Piezoelectricity, and Classical Plate Theories

1995 ◽  
Vol 62 (2) ◽  
pp. 471-478 ◽  
Author(s):  
Yi-Yuan Yu
Keyword(s):  
Nonlinear Elasticity ◽  
Variational Equation ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Classical Type ◽  
Order Effects ◽  
Variational Equations ◽  
Plate Equations ◽  
Higher Order Effects

Ordinary, generalized, and pseudo-variational equations of motion in three-dimensional theories of nonlinear elasticity and piezoelectricity are presented systematically. These are applied to the derivations of plate equations of the classical type. In contrast to the derivations of plate equations that include thickness and higher-order effects, it is shown that the volume and surface integrals in a three-dimensional ordinary variational equation of motion must now be used jointly in a coupled manner. Details are demonstrated by first treating a classical linear plate. Equations of the classical type for large deflections of laminated composite and piezoelectric plates are then derived, with the famous von Ka´rma´n equations of an isotropic homogeneous plate deducible as a special case. Interrelationship among various plate equations is emphasized.

Defocus ramp correction in spot-scan imaging

1992 ◽  
Vol 50 (1) ◽  
pp. 130-131
Author(s):  
Kenneth H. Downing
Keyword(s):  
Computer Control ◽  
Three Dimensional ◽  
Sufficient Accuracy ◽  
Objective Lens ◽  
Electron Crystallography ◽  
Contrast Transfer Function ◽  
Tilt Axis ◽  
Specimen Height ◽  
The Difference ◽  
Envelope Functions

Three-dimensional structures of a number of samples have been determined by electron crystallography. The procedures used in this work include recording images of fairly large areas of a specimen at high tilt angles. There is then a large defocus ramp across the image, and parts of the image are far out of focus. In the regions where the defocus is large, the contrast transfer function (CTF) varies rapidly across the image, especially at high resolution. Not only is the CTF then difficult to determine with sufficient accuracy to correct properly, but the image contrast is reduced by envelope functions which tend toward a low value at high defocus.We have combined computer control of the electron microscope with spot-scan imaging in order to eliminate most of the defocus ramp and its effects in the images of tilted specimens. In recording the spot-scan image, the beam is scanned along rows that are parallel to the tilt axis, so that along each row of spots the focus is constant. Between scan rows, the objective lens current is changed to correct for the difference in specimen height from one scan to the next.

Time after time: support for memory accounts of temporal preparation.

2019 ◽  
Author(s):  
Joe Butler ◽  
Samuel Ngabo ◽  
Marcus Missal
Keyword(s):  
Response Times ◽  
Reaction Times ◽  
Evidence Base ◽  
Higher Order ◽  
Order Effects ◽  
Previous Trial ◽  
Adaptive Responses ◽  
Temporal Preparation ◽  
Subsequent Trial ◽  
Higher Order Effects

Complex biological systems build up temporal expectations to facilitate adaptive responses to environmental events, in order to minimise costs associated with incorrect responses, and maximise the benefits of correct responses. In the lab, this is clearly demonstrated in tasks which show faster response times when the period between warning (S1) and target stimulus (S2) on the previous trial was short and slower when the previous trial foreperiod was long. The mechanisms driving such higher order effects in temporal preparation paradigms are still under debate, with key theories proposing that either i) the foreperiod leads to automatic modulation of the arousal system which influences responses on the subsequent trial, or ii) that exposure to a foreperiod results in the creation of a memory trace which is used to guide responses on the subsequent trial. Here we provide data which extends the evidence base for the memory accounts, by showing that previous foreperiod exposures are cumulative with reaction times shortening after repeated exposures; whilst also demonstrate that the higher order effects associated with a foreperiod remain active for several trials.

Sign in / Sign up

Export Citation Format

Share Document