  In this work, a Landauer approach enabled by the Frequency Domain Perfectly
Matched Layer Method (FDPML) is used to study phonon transport in a series of
large 2D domains with randomly embedded nanoparticles over a wide range of
nanoparticle loadings and wavelengths. The effect of nanoparticle packing
density on the mean free path and localization length is characterized. We
observe that in the Mie scattering regime, the independent scattering
approximation is valid up to volume fractions exceeding 10% and often higher
depending on scattering parameter, indicating the mean free path can usually be
calculated much less expensively using the number density and the scattering
cross-section of a single scatterer. We also study localization lengths and
their dependence on particle loading. In the case of heavy particles in a
lighter matrix, we have been able to observe localization only at volume
fractions >30% using the Landauer approach and only for high frequency modes,
exceeding the vibration frequencies of the embedded nanoparticles. Using modal
analysis we show that localization in nanoparticle laden materials is primarily
due to energetic confinement rather than Anderson localization. Subsequently,
we show that by using light particles in a heavy matrix the fraction of
confined modes can be substantially increased.
