We resolve the challenge of relating effective wave properties to measurable reflection and transmission coefficients in acoustic measurements of dense particulates by deriving a systematic extension of the quasi-crystalline approximation for halfspace materials with random particulates.
When waves scatter through dense particle arrangements, they bounce multiple times between particles—a process called multiple scattering. This is critical for applications like ultrasound imaging of composites. We solve the wave scattering problem for particles arranged in a cylinder, a case that hasn't been solved before. Using ensemble averaging, we derive an effective T-matrix describing the cylinder's total scattering behavior. For simple scatterers, this reduces to a homogeneous cylinder with an effective wavenumber. Monte Carlo simulations confirm our theoretical predictions are accurate across a wide range of frequencies.
There has not been a satisfying numerical validation of the theory of effective waves in random particulate materials. Validation has been challenging because the theoretical methods for effective waves have been limited to random particulate media in infinite slabs or half-spaces, which require a very large number of particles to perform accurate numerical simulations. This paper offers a solution by providing, from first principles, a method to calculate effective waves for a sphere filled with particles for a spherically symmetric incident wave. We show that this case can excite exactly the same effective wavenumbers, which are the most important feature to validate for effective waves. To check correctness, we also deduce an integral equation method which does not assume the effective wave solution. Our methods are, in principal, valid for any frequency, particle volume fraction and disordered pair-correlation. With the methods we provide, it is now possible to validate, with a heavier Monte Carlo simulation, the predictions from effective wave theory..
[EffectiveWaves.jl](https://github.com/arturgower/EffectiveWaves.jl): a package to calculate the effective waves travelling in materials comprised of randomly distributed particles or inclusions.
Waves (sound, radio, light, and vibrations) in materials with random microstructure.