LAUSR

Suppose we measure the scattered field from a material with an assortment of randomly placed particles of different sizes. To get a repeatable measurement, we may need to perform the experiment many times and average over time (or space). This talk focuses on how to calculate and understand this average field. For instance, from this average field we could then calculate what effective properties, filling a homogeneous material, would lead to the same scattered field we measured. However, these effective properties are only useful if they can tell us something about the microstructure and the particles. In this talk I will show how these effective properties depend on the geometry of the material, and not just the microstructure. On the other hand, the effective wavenumbers are inherently related to only the material microstructure and not its geometry. This result comes from a framework which was deduced from first principles, using only minimal statistical assumptions. Using this framework we will also show how to calculate the average scattered field, and specialise to a sphere filled with particles. [1] A. L. Gower and G. Kristensson, “Effective waves for random three-dimensional particulate materials.” New J. Phys. (2021).