Evolution of pattern complexity in the Cahn-Hilliard theory of phase separation

33. Marcio Gameiro, Konstantin Mischaikow, Thomas Wanner:
    Evolution of pattern complexity in the Cahn-Hilliard theory of phase separation
    Acta Materialia 53(3), pp. 693-704, 2005.

Abstract

Phase separation processes in compound materials can produce intriguing and complicated patterns. Yet, characterizing the geometry of these patterns quantitatively can be quite challenging. In this paper we propose the use of computational algebraic topology to obtain such a characterization. Our method is illustrated for the complex microstructures observed during spinodal decomposition and early coarsening in both the deterministic Cahn-Hilliard theory, as well as in the stochastic Cahn-Hilliard-Cook model. While both models produce microstructures that are qualitatively similar to the ones observed experimentally, our topological characterization points to significant differences. One particular aspect of our method is its ability to quantify boundary effects in finite size systems.

Links

The published version of the paper can be found at https://doi.org/10.1016/j.actamat.2004.10.022.

Bibtex

@article{gameiro:etal:05a,
   author = {Marcio Gameiro and Konstantin Mischaikow and Thomas Wanner},
   title = {Evolution of pattern complexity in the {C}ahn-{H}illiard
            theory of phase separation},
   journal = {Acta Materialia},
   year = 2005,
   volume = 53,
   number = 3,
   pages = {693--704},
   doi = {10.1016/j.actamat.2004.10.022}
   }