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.
Mechanical stress in tissue is important but hard to measure. The angled shear wave identity (ASWI) estimates stress from shear-wave speeds without needing a constitutive model. This work extends ASWI to viscous and anisotropic tissues, deriving the relevant dispersion relations and showing that stress recovery in viscous media requires measuring both wave speed and attenuation. The extension to materials with memory is also discussed.