| Abstract: |
| Polar sea ice is a critical component of Earth`s climate system. As a material it displays composite structure over a vast range of length scales. In fact, fractals appear naturally throughout the sea ice system, from brine inclusions inside the ice and labyrinthine melt ponds on its surface, to the ice pack itself on the scale of the Arctic Ocean. We explore how the fractal dimension of these structures depends on the parameters characterizing their dynamical evolution. These investigations lead us into percolation theory, statistical physics, and topological data analysis. In related work, we consider a dynamical systems model of algae living in the brine inclusions, with model parameters treated as random variables. Uncertainty quantification methods are used to study bloom dynamics. |
|