Multiscale homogenization and random matrix theory for sea ice

Sea ice is a multiscale composite displaying complex structure on length scales ranging over many orders of magnitude. Finding the effective properties relevant to large-scale dynamics and thermodynamics is a central challenge in modeling and predicting sea ice behavior, similar to finding macroscopic behavior from microscopic laws in statistical mechanics. Integral representations for the homogenized properties of composites, where the microstructural geometry is encoded into the spectrum of a random operator, have opened up new theoretical and computational approaches to sea ice modeling. We’ll give an overview of how they’re being used to study sea ice electromagnetics, thermal transport, wave-ice interactions, and advection diffusion processes at the floe scale. They also allow us to connect sea ice to random matrix theory, uncertainty quantification, and exotic materials such as twisted bilayer graphene.