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.

Acoustic scattering by a finite nonlinear elastic plate. I Primary, secondary and combination resonances

1987 ◽  
Vol 414 (1846) ◽  
pp. 237-253 ◽  
Keyword(s):  
Incident Wave ◽  
Elastic Plate ◽  
Scattered Field ◽  
Acoustic Waves ◽  
Multiple Scales ◽  
Acoustic Scattering ◽  
Scattered Wave ◽  
Thin Elastic Plate ◽  
Finite Width ◽  
Wave Angle

A thin elastic plate of finite width is irradiated by time-harmonic acoustic waves. The fluid is assumed light compared with the plate mass, and the forcing term is of sufficient amplitude to necessitate the inclusion of a nonlinear term (due to mid-plane stretching) in the plate equation. The order-one scattered field is determined by the method of multiple scales when the forcing frequency approaches a free oscillation frequency (eigenfrequency) of the plate. This solution is shown to agree with previous work, for the linear problem, and can be multivalued for particular values of the plate-fluid parameters. The scattered wave may also exhibit jumps in its amplitude and phase angle as it varies with frequency, incident-wave angle or incident-wave amplitude. The non-linear term further allows the possibility of secondary and combination resonances. These are investigated and the scattered field is shown to contain terms of different frequencies to those of the incident waves. Multivalued solutions and the associated jump phenomenon are again found for these resonant cases.

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 Harmonic morphisms and conformal foliations by geodesics of three-dimensional space forms

1991 ◽  
Vol 51 (1) ◽  
pp. 118-153 ◽  
Author(s):  
Paul Baird ◽  
John C. Wood
Keyword(s):  
Space Form ◽  
Holomorphic Mapping ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Classification ◽  
Harmonic Morphisms ◽  
Connected Space ◽  
Space Forms ◽  
Simply Connected ◽  
Three Dimensional Space

AbstractA complete classification is given of harmonic morphisms to a surface and conformal foliations by geodesics, with or without isolated singularities, of a simply-connected space form. The method is to associate to any such a holomorphic map from a Riemann surface into the space of geodesics of the space form. Properties such as nonintersecting fibres (or leaves) are translated into conditions on the holomorphic mapping which show it must have a simple form corresponding to a standard example.

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.

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.

scholarly journals Above-threshold ionization of hydrogen and hydrogen-like ions by X-ray pulses

Open Physics ◽  
2013 ◽  
Vol 11 (9) ◽  
Author(s):  
Henri Bachau ◽  
Olimpia Budriga ◽  
Mihai Dondera ◽  
Viorica Florescu
Keyword(s):  
Plane Wave ◽  
Cross Sections ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Relativistic Effects ◽  
Electron Interaction ◽  
Radial Coordinate ◽  
Threshold Ionization ◽  
X Ray ◽  
Above Threshold Ionization

AbstractThis paper adresses the problem of above-threshold ionization (ATI) of hydrogen interacting with an intense X-ray electromagnetic field. Two approaches have been used. In the first approach, we calculate generalized differential and total cross sections based on second-order perturbation theory for the electron interaction with a monochromatic plane wave, with the A 2 and A · P contributions from the nonrelativistic Hamiltonian (including retardation) treated exactly. In the second approach, we solve the time-dependent Schrödinger equation (TDSE) for a pulsed plane wave using a spectral approach with a basis of oneelectron orbitals, calculated with L 2-integrable B-spline functions for the radial coordinate and spherical harmonics Y lm for the angular part. Retardation effects are included up to O(1/c), they induce extra terms forcing the resolution of the TDSE in a three dimensional space. Relativistic effects [of O (1/c 2)] are fully neglected. The isoelectronic series of hydrogen is explored in the range Z = 1 − 5 in both TDSE and perturbative approaches. Photoelectron angular distributions are obtained for photon energies of 1 keV and 3 keV for hydrogen, and photon energy of 25 keV for the hydrogenic ion B4+. Perturbative and TDSE calculations are compared.

An Iterative Method for the Solution of Three-Dimensional Inverse Acoustic Scattering Problems

2002 ◽  
Author(s):  
Charbel Farhat ◽  
Radek Tezaur ◽  
Rabia Djellouli
Keyword(s):  
Domain Decomposition Method ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Field Pattern ◽  
Far Field ◽  
Computationally Efficient ◽  
Scattering Problems ◽  
Multi Stage ◽  
Computational Methodology ◽  
Acoustic Scattering Problems

We present a computational methodology for retrieving the shape of an impenetrable obstacle from the knowledge of some acoustic far-field patterns. This methodology is based on the well-known regularized Newton algorithm, but distinguishes itself from similar optimization procedures by (a) a frequency-aware multi-stage solution strategy, (b) a computationally efficient usage of the exact sensitivities of the far-field pattern to the specified shape parameters, and (c) a numerically scalable domain decomposition method for the fast solution of three-dimensional direct acoustic scattering problems. We illustrate the salient features and highlight the performance characteristics of the proposed computational methodology with the solution on a parallel processor of various inverse mockup submarine problems.

The inverse scattering problem for a cylinder

1979 ◽  
Vol 84 (1-2) ◽  
pp. 135-143 ◽  
Author(s):  
David Colton
Keyword(s):  
Plane Wave ◽  
Moment Problem ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Wave Number ◽  
Field Pattern ◽  
Far Field ◽  
Simply Connected Domain ◽  
Simply Connected ◽  
Far Field Pattern

SynopsisLet D be a bounded simply connected domain in the plane and Ω the unit disk. Let F(Θ;k) be the far field pattern arising from the scattering of an incoming plane wave by the obstacle D and let an(k) denote the nth Fourier coefficient of F. Then if f conformally maps ℝ2\D onto ℝ2\Ω, a “moment” problem is derived which expresses an(k) in terms of f−1 for small values of the wave number k. The solution of this moment problem then gives the Laurent coefficients of f−1 and hence ∂D.

scholarly journals Scattering of Elastic Waves by an Inhomogeneous Boundary in the Acoustic Testing of Permanent Joints

2019 ◽  
Vol 10 (4) ◽  
pp. 360-372
Author(s):  
A. R. Baev ◽  
N. V. Levkovich ◽  
A. L. Mayorov ◽  
M. V. Asadchaya
Keyword(s):  
Elastic Waves ◽  
Dimensional Space ◽  
Ultrasonic Method ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Field Pattern ◽  
Acoustic Beam ◽  
Practical Applications ◽  
Scattering Field ◽  
Scattering Of Elastic Waves

Improving the reliability and testing performance of permanent joints оf different materials made by welding, spraying, gluing, soldering and other methods is an important production task, for which the ultrasonic method is the simplest and most effective. The purpose of this work was to expand the technical possibilities and increase the sensitivity of ultrasonic testing of adhesion defects of materials joints based on the establishment of laws governing the formation of a scattering field of elastic waves from an inhomogeneous boundary in three-dimensional space and issuing recommendations for the development of suggested method.For the first time, in the framework of classical concepts, the scattering fields of elastic waves of an acoustic beam with a circular cross section moving across the boundary of a semi-infinite defect are calculated. It is proposed to use a phase shift between the waves reflected from the indicated surfaces, which varies in the range of π/4–π, as an important parameter of the material joint's defect. It has a significant effect on the field pattern and its angular amplitude extrema — minima and maxima of different orders when the defect boundary is moved relative to the center of the acoustic beam spot.The features of the evolution of the structure of the scattering field are established, which make it possible to identify optimal conditions for the detection of weakly reflective defects in sound. It is shown that it is possible in principle to estimate the defect's area by measuring a change in the amplitude of the primary maximum of the radiation pattern of the scattered waves.Specific examples show the effectiveness of using the proposed method for a number of practical applications.

scholarly journals About the geographic grid of the three-dimensional hypersphere

2020 ◽  
Vol 223 ◽  
pp. 02005
Author(s):  
Pavel Kim
Keyword(s):  
Population Distribution ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The State ◽  
Dimensional Manifold ◽  
State Assignment ◽  
Distribution Process ◽  
Technological Means ◽  
Simply Connected ◽  
Three Dimensional Space

According to the Poincaré conjecture (1904) proved by Grigory Perelman (2002-2003) that any simply connected compact three- dimensional manifold without edges is homeomorphic to a three- dimensional hypersphere [1], to solve the problems of visualizing four- dimensional objects in three-dimensional space [2], it is proposed to choose a suitable manifold, in in this case, a ball, establishing a homeomorphism between objects located in different spaces by technological means of cartography. As a result of this work, it seems possible to build a dynamic video of the population distribution process on a map of the globe, which provides informational four-dimensional data flow, following the ideas embodied in 4D Anatomy [3]. The proposed technology opens up new ways of visualizing four-dimensional space This work was performed within the framework of the state assignment of the ICM MG SB RAS (project 0315-2019-0003).

Sign in / Sign up

Export Citation Format

Share Document