maximize
[1] P. W. Dondl, B. Heeren, and M. Rumpf. Optimization of the branching pattern in coherent phase transitions. C. R. Math. Acad. Sci. Paris, 354(6):639-644, 2016.
bib | arXiv ]
Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and Müller studied a branching pattern with optimal scaling of the energy with respect to its parameters. Here, we present finite element simulations that suggest a topologically different class of branching patterns and derive a novel, low dimensional family of patterns. After a geometric optimization within this family, the resulting pattern bears a striking resemblance to our simulation. The novel microstructure admits the same scaling exponents but results in a significantly lowered upper energy bound.