Optimization of the branching pattern in coherent phase transitions

@article{Dondl2015OptimizationOT,
  title={Optimization of the branching pattern in coherent phase transitions},
  author={P. Dondl and Behrend Heeren and M. Rumpf},
  journal={arXiv: Numerical Analysis},
  year={2015}
}
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… Expand

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