Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours

  • Received: 01 February 2017 Revised: 01 November 2017
  • Primary: 74B20; Secondary: 74K10, 74E15, 74G65, 49J45

  • We study continuum limits of discrete models for (possibly heterogeneous) nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown heterostructured nanowires.

    Citation: Roberto Alicandro, Giuliano Lazzaroni, Mariapia Palombaro. 2018: Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours, Networks and Heterogeneous Media, 13(1): 1-26. doi: 10.3934/nhm.2018001

    Related Papers:

  • We study continuum limits of discrete models for (possibly heterogeneous) nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown heterostructured nanowires.



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