@ARTICLE{DoHe15, author = {Dondl, Patrick W. and Heeren, Behrend and Rumpf, Martin}, title = {Optimization of the branching pattern in coherent phase transitions}, journal = {C. R. Math. Acad. Sci. Paris}, year = {2016}, volume = {354}, pages = {639--644}, number = {6}, abstract = {Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and M\"uller 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.}, eprint = {1512.06620}, fjournal = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris}, owner = {rumpf}, doi = {10.1016/j.crma.2016.03.013} }