Phase separation processes in compound materials frequently produce intriguing and complicated microstructures which evolve with time. The geometry of these microstructures can have profound implications for macroscopic material properties, and it is therefore important to develop quantitative metrics for such complex geometries. Associate Professor Thomas Wanner of the Department of Mathematical Sciences uses tools from computational topology to study complex evolving microstructures. These computational techniques have been used to assess the quality of existing mathematical models for a phase separation mechanism called spinodal decomposition. All of these models produce microstructure which qualitatively resemble experimental observations. Yet, the topological characterization reveals significant differences between the simulated geometries, and can therefore detect mismatch between models and experiment.

This research is part of a collaborative project on Multiscale analysis of nonlinear systems using computational homology which is funded by the US Department of Energy. The project is one of only thirteen funded nationally in the Multiscale Mathematics initiative.

For more information we refer to the official press release of the Department of Energy’s Office of Science.