Multiple scattering by random configurations of circular cylinders: second-order corrections for the effective wavenumber.

A formula for the effective wavenumber in a dilute random array of identical scatterers in two dimensions is derived, based on Lax's quasicrystalline approximation. This formula replaces a widely-used expression due to Twersky, which is shown to be based on an inappropriate choice of pair-correlation function.

• Publication year

  2005

• Venue

  Journal of the Acoustical Society of America

• Publication date

  2005-05-31

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1121/1.1904270PMID 16018445
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Effective medium method in the problem of axial elastic shear wave propagation through fiber composites

  2003cited by this paper
• Antiplane shear wave propagation in fiber-reinforced composites.

  2003cited by this paper
• Sound propagation close to the ground

  2002cited by this paper
• New results for isotropic point scatterers: Foldy revisited

  2002cited by this paper
• Wave dispersion and attenuation in fiber composites

  2001cited by this paper
• Attenuation of sound in concentrated suspensions: theory and experiments

  2001cited by this paper
• Acoustic and electroacoustic spectroscopy for characterizing concentrated dispersions and emulsions.

  2001cited by this paper
• Handbook of Mathematical Techniques for Wave/Structure Interactions

  2001cited by this paper
• Self-Consistent Methods in the Problem of Wave Propagation through Heterogeneous Media

  2000cited by this paper
• On multiple-particle effects in the acoustic characterization of colloidal dispersions

  1999influential reference
• Ultrasonic Techniques for Fluids Characterization

  1997influential reference
• Wave propagation and scattering in random media

  1997cited by this paper
• Method of moments evaluation of the two-dimensional quasi-crystalline approximation

  1996influential reference
• ULTRASONIC PLANE SH WAVE REFLECTION FROM A UNI-DIRECTIONAL FIBROUS COMPOSITE SLAB

  1996cited by this paper
• Attenuation, dispersion, and anisotropy by multiple scattering of transmitted waves through distributions of scatterers

  1995cited by this paper
• Dispersion of elastic waves in random particulate composites

  1995cited by this paper
• Numerical simulation of scatterer positions in a very dense medium with an application to the two‐dimensional Born approximation

  1995cited by this paper
• Self-consistent analysis of elastic wave propagation in two-dimensional matrix-inclusion composites

  1995cited by this paper
• Tables of Integrals, Series, and Products

  1995cited by this paper
• Multiple scattering of elastic waves in a fiber-reinforced composite

  1994cited by this paper
• Comparison of effective medium and multiple‐scattering theories of predicting the ultrasonic properties of dispersions

  1990cited by this paper
• Sound attenuation through trees: measurements and models

  1988cited by this paper
• Multiple scattering of compressional and shear waves by fiber‐reinforced composite materials

  1986cited by this paper
• Acoustic bulk parameters in distributions of pair‐correlated scatterers

  1978cited by this paper
• Multiple scattering of elastic waves by cylinders of arbitrary cross section. I. SH waves

  1978cited by this paper
• Longitudinal shear waves in a fiber-reinforced composite

  1973cited by this paper
• Elastic Wave Velocities in Two-component Systems

  1967cited by this paper
• Wave propagation through an assembly of spheres: IV. Relations between different multiple scattering theories

  1967cited by this paper
• Table of Integrals, Series, and Products

  1966cited by this paper
• Scattering by an Array of Cylinders as a Function of Surface Impedance

  1966cited by this paper
• Multiple scattering from inhomogeneous media

  1966cited by this paper
• Multiple Scattering of Waves. II. ``Hole Corrections'' in the Scalar Case

  1964cited by this paper
• On Scattering of Waves by Random Distributions. I. Free‐Space Scatterer Formalism

  1962cited by this paper
• MULTIPLE SCATTERING OF WAVES

  1961cited by this paper
• MULTIPLE SCATTERING OF WAVES. II. THE EFFECTIVE FIELD IN DENSE SYSTEMS

  1952cited by this paper
• The Multiple Scattering of Waves. I. General Theory of Isotropic Scattering by Randomly Distributed Scatterers

  1945cited by this paper

• Numerical simulation of elastic wave propagation in three-dimensional multiple scattering media

  2026cites this paper
• Designing band gaps with randomly distributed sub-wavelength Helmholtz resonators

  2025cites this paper
• Homogenization model for a dense elastic medium of cylindrical scatterers and based on a realistic pair correlation function

  2025cites this paper
• Reflection of Wind Turbine Noise from Rough Ground Using 3D Multiple Scattering Theory

  2025cites this paper
• Effective bulk and mass densities of randomly distributed coated cylinders in fluid.

  2025cites this paper
• Oblique Multiple Scattering by Gyrotropic Cylinders

  2025cites this paper
• Modeling of ultrasonic velocity and attenuation for concrete inspection: a review.

  2025cites this paper
• Acoustic waves in a halfspace material filled with random particulate

  2024influential citation
• 2D Analytical Modelling for Ultrasonic Inspection of Concrete Structures: Effects of Scatterers Position Correlation

  2024cites this paper
• Effective properties of randomly distributed poroelastic cylinders in a poroelastic matrix

  2024cites this paper
• Acoustic waves in random distributions of double porosity cylinders.

  2023cites this paper
• The average transmitted wave in random particulate materials

  2023influential citation
• Effective T-matrix of a cylinder filled with a random two-dimensional particulate

  2023influential citation
• Modélisation semi-analytique avancée de l’inspection ultrasonore de structures en béton

  2023cites this paper
• Numerical and analytical studies of attenuation coefficient in 2D matrix-inclusion composites with randomly distributed circular inclusions

  2023cites this paper
• Impact of the Scatterer Type on Ultrasound Wave Propagation in Microstructure Composites: Calculation and Application

  2022cites this paper
• Effective longitudinal wave in an elastic matrix containing coated or uncoated spheres: Influence of the second order approximation including multiple scattering

  2022cites this paper
• The effective medium for a cylinder with cylindrical inclusions.

  2021cites this paper
• Fast and slow effective waves across dilute random distributions of elastic spheres in a poroelastic medium.

  2021cites this paper
• A Fast Forest Reverberator Using Single Scattering Cylinders

  2021cites this paper
• Propagation of scalar waves in dense disordered media exhibiting short- and long-range correlations.

  2021cites this paper
• Polarimetric Bistatic Scattering From Multiple Parallel Cylinders

  2020cites this paper
• Effective waves for random three-dimensional particulate materials

  2020cites this paper
• Use of a Modal Model in Predicting Propagation from a Point Source Over Grooved Ground

  2020cites this paper
• Influence of the microstructure of two-dimensional random heterogeneous media on propagation of acoustic coherent waves.

  2020cites this paper
• Modelling Of Sound Attenuation By Periodic, Rectangular Structures

  2020cites this paper
• Low frequency propagation through random polydisperse assemblies of cylindrical or spherical poroelastic obstacles.

  2019cites this paper
• Springer Series in Light Scattering: Volume 4: Light Scattering and Radiative Transfer

  2019cites this paper
• Numerical simulation of two-dimensional multiple scattering of sound by a large number of circular cylinders.

  2019cites this paper
• Effective dynamic properties of random complex media with spherical particles.

  2019cites this paper
• A proof that multiple waves propagate in ensemble-averaged particulate materials

  2019influential citation
• Influence of bubble distributions on the propagation of linear waves in polydisperse bubbly liquids.

  2019cites this paper
• Simulations of ultrasonic wave propagation in concrete based on a two‐dimensional numerical model validated analytically and experimentally

  2019cites this paper
• Electromagnetic scattering by discrete random media. I: The dispersion equation and the configuration-averaged exciting field

  2019cites this paper
• Relection from a multi-species material and its transmitted efective wavenumber

  2019cites this paper
• Institutional Repository Reflection of sound from random distributions of semicylinders on a hard plane : models and data

  2019cites this paper
• Incoherent Scattering — a Literature Study

  2019cites this paper
• Anomalous Diffusion of Acoustic Fields in Periodic and Random Scattering Media and Its Application to Remote Sensing

  2019cites this paper
• MULTIPLE WAVES PROPAGATE IN RANDOM PARTICULATE MATERIALS\ast

  2019influential citation
• Acoustic wave propagation through a random dispersion of solid particles in a viscous fluid

  2019cites this paper
• Exploitation de la diffusion multiple et considération de l'interfacial Transition Zone pour la caractérisation ultrasonore du béton

  2019cites this paper
• Image conditions for polar and cylindrical coordinate separation-of-variables acoustic multiple scattering models with perfectly reflecting flat boundaries

  2018cites this paper
• Multiple scattering of an ultrasonic shock wave in bubbly media

  2018cites this paper
• A theoretical approach to multiple scattering of surface waves by shallow cavities in a half-space.

  2018cites this paper
• Multiple Waves Propagate in Random Particulate Materials

  2018cites this paper
• Occurrence of anomalous diffusion and non-local response in highly-scattering acoustic periodic media

  2018cites this paper
• Low frequency approximations for effective wavenumbers and moduli of randomly perforated poroelastic media

  2018cites this paper
• Effective Wavenumber of a Random Polydisperse Assembly of Poroelastic Spheres

  2018cites this paper
• Multiple Scattering of Light in Ordered Particulate Media

  2018cites this paper
• Structures

  2018cites this paper
• Effective wave propagation along a rough thin-elastic beam

  2017cites this paper
• Coherent wave propagation in viscoelastic media with mode conversions and pair-correlated scatterers

  2017cites this paper
• Instructions for use Title Attenuation and dispersion of antiplane shear waves due to scattering by many two-dimensional cavities Author ( s )

  2017cites this paper
• Reflection from a multi-species material and its transmitted effective wavenumber

  2017influential citation
• Effective wavenumbers for sound scattering by trunks, branches, and the canopy in a forest.

  2017cites this paper
• Acoustique des milieux bulleux

  2016cites this paper
• Surface/interface effects on the effective propagation constants of coherent waves in composites with random parallel nanofibers.

  2016cites this paper
• Multiple scattering by infinitely long cylindrical glass inclusions in a saturated Biot porous medium of glass beads.

  2016cites this paper
• Random acoustic metamaterial with a subwavelength dipolar resonance.

  2016cites this paper
• Acoustic propagation over periodic and quasi-periodic rough surfaces

  2016cites this paper
• Acoustique des milieux bulleux : applications à la conception de métamatériaux et à la manipulation de bulles

  2016cites this paper
• Influence of multiple scattering in heterogeneous concrete on results of the surface wave inverse problem

  2016cites this paper
• Rayleigh limits for effective wavenumbers of randomly distributed porous cylinders. Comparison of explicit and implicit methods

  2016cites this paper
• Disorder persistent transparency within the bandgap of a periodic array of acoustic Helmholtz resonators

  2015cites this paper
• Acoustic metamaterials and phononic crystals Directional source of water waves by a crystal of surface-piercing cylinders Source directive de vagues dans un cristal de cylindres émergeant en surface

  2015cites this paper
• Surface effects on the wave propagation in composites with random dispersive parallel cylindrical nanofibers

  2015influential citation
• Directional source of water waves by a crystal of surface-piercing cylinders

  2015cites this paper
• Evolution of Directional Wave Spectra Through Finite Regular and Randomly Perturbed Arrays of Scatterers

  2015influential citation
• Rayleigh limits for effective wavenumbers of randomly distributed porous cylinders in a fluid

  2015cites this paper
• An explicit formula for the coherent SH waves' attenuation coefficient in random porous materials with low porosities.

  2015cites this paper
• Sound propagation in dilute suspensions of spheres: Analytical comparison between coupled phase model and multiple scattering theory.

  2015cites this paper
• Metamaterials: supra-classical dynamic homogenization

  2015cites this paper
• Application of an effective medium theory for modeling ultrasound wave propagation in healing long bones.

  2014cites this paper
• Generalization of the Waterman & Truell formula for an elastic medium containing random configurations of cylindrical scatterers

  2014cites this paper
• Scattering mean free path in continuous complex media: beyond the Helmholtz equation.

  2014cites this paper
• Scattering by a semi-infinite lattice and the excitation of Bloch waves

  2014cites this paper
• Multiple scattering in porous media: comparison with water saturated double porosity media.

  2014cites this paper
• Analytical model of optical fluence inside multiple cylindrical inhomogeneities embedded in an otherwise homogeneous turbid medium for quantitative photoacoustic imaging.

  2014cites this paper
• Modeling of sound propagation in forests using the Transmission Line Matrix method

  2014cites this paper
• Improved characterisation and modelling of microbubbles in biomedical applications

  2013cites this paper
• Numerical simulation of effective phase velocity and attenuation of shear elastic wave propagation in unidirectional composite materials.

  2013cites this paper
• Multiple scattering of acoustic waves by small sound-soft obstacles in two dimensions: Mathematical justification of the Foldy–Lax model

  2013cites this paper
• Diffraction assisted rough ground effect: models and data.

  2013cites this paper
• Waves in discrete and continuous heterogeneous media : propagation, scattering, cloaking

  2013influential citation
• Modélisation de la propagation des ondes élastiques dans un milieu composite à microstructure 3D

  2013cites this paper
• Dynamic homogenization for the elastic properties of periodic and random composites

  2013cites this paper
• Analytical approximations for low frequency band gaps in periodic arrays of elastic shells.

  2012cites this paper
• Time-domain numerical simulations of multiple scattering to extract elastic effective wavenumbers

  2012cites this paper
• Discussion on various model of multiple scattering in acoustics and elastic heterogeneous media

  2012cites this paper
• Effective wave numbers for media sustaining the propagation of three types of bulk waves and hosting a random configuration of scatterers

  2012influential citation
• Coherent acoustic wave propagation in media with pair-correlated spheres.

  2012cites this paper
• RESEARCH ARTICLE Multiple scattering of elastic waves: a numerical method for computing the effective wavenumbers

  2012influential citation
• Homogenization Methods to Approximate theEffective Response of RandomFibre-reinforced Composites

  2012cites this paper
• Comparison of phase velocity in trabecular bone mimicking-phantoms by time domain numerical (EFIT) and analytical multiple scattering approaches.

  2012cites this paper
• On the estimation of dynamic mass density of random composites.

  2012cites this paper
• Multiple scattering of flexural waves by random configurations of inclusions in thin plates

  2011influential citation
• Multiple scattering by cylinders randomly located in a fluid: Effective properties

  2011cites this paper
• Coherent acoustic response of a screen containing a random distribution of scatterers: Comparison between different approaches

  2011cites this paper
• The effective wavenumber of a pre-stressed nonlinear microvoided composite

  2011cites this paper
• Investigation of Ultrasonic Wave Scattering Effects using Computational Methods

  2011cites this paper