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A proof that multiple waves propagate in ensemble-averaged particulate materials.

Artur L Gower1, I David Abrahams2, William J Parnell3

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Summary
This summary is machine-generated.

This study proves that a unique effective wavenumber does not exist for inhomogeneous materials. Instead, an infinite number of effective wavenumbers are required for accurate wave propagation analysis.

Keywords:
Wiener–Hopfbackscatteringensemble averagingmultiple scatteringrandom mediawave propagation

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Area of Science:

  • Physics
  • Materials Science
  • Acoustics

Background:

  • Effective medium theory simplifies complex materials using macroscopic parameters.
  • The effective wavenumber is crucial for characterizing wave propagation in inhomogeneous media.
  • Existing research focuses on calculating a single effective wavenumber.

Purpose of the Study:

  • To prove the non-existence of a unique effective wavenumber.
  • To demonstrate the necessity of multiple effective wavenumbers for accurate wave propagation.
  • To analyze wave reflection and transmission coefficients in inhomogeneous materials.

Main Methods:

  • Application of the Wiener-Hopf technique.
  • Ensemble averaging over random inhomogeneities.
  • Analysis of scalar (acoustic) waves in a 2D material with cylindrical inclusions.

Main Results:

  • An infinite number of complex effective wavenumbers exist.
  • A small subset of effective wavenumbers significantly contributes to the wave field.
  • Accurate reflection and transmission coefficients require numerous highly attenuating effective waves.

Conclusions:

  • The concept of a single effective wavenumber is insufficient.
  • Wave propagation in inhomogeneous materials is described by a spectrum of effective wavenumbers.
  • The Wiener-Hopf technique offers a robust method for calculating wave phenomena.