Analysis of rippling in incommensurate one-dimensional coupled chains

Paul Cazeaux, Mitchell Luskin, Ellad B. Tadmor

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Graphene and other recently developed two-dimensional materials exhibit exceptionally strong in-plane stiffness. Relaxation of few-layer structures, either freestanding or on slightly mismatched substrates, occurs mostly through out-of-plane bending and the creation of large-scale ripples. In this work, we present a novel double chain model, where we allow relaxation to occur by bending of the incommensurate coupled system of chains. As we will see, this model can be seen as a new application of the well-known Frenkel-Kontorova model for a one-dimensional atomic chain lying in a periodic potential. We focus in particular on modeling and analyzing ripples occurring in ground state configurations, as well as their numerical simulation.

Original languageEnglish (US)
Pages (from-to)56-73
Number of pages18
JournalMultiscale Modeling and Simulation
Issue number1
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 Society for Industrial and Applied Mathematics.


  • Atomistic relaxation
  • Frenkel-Kontorova
  • Heterostructures
  • Incommensurability
  • Ripples
  • Two-dimensional materials


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