• Corpus ID: 231719601

Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings

  title={Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings},
  author={Giacomo Del Nin and Mircea Petrache},
We prove discrete-to-continuum convergence of interaction energies defined on lattices in the Euclidean space (with interactions beyond nearest neighbours) to a crystalline perimeter, and we discuss the possible Wulff shapes obtainable in this way. Exploiting the “multigrid construction” of quasiperiodic tilings (which is an extension of De Bruijn’s “pentagrid” construction of Penrose tilings) we adapt the same techniques to also find the macroscopical homogenized perimeter when we… 

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