Archive for Rational Mechanics and Analysis

, Volume 231, Issue 1, pp 465–517 | Cite as

Characterization of Optimal Carbon Nanotubes Under Stretching and Validation of the Cauchy–Born Rule

  • Manuel FriedrichEmail author
  • Edoardo Mainini
  • Paolo Piovano
  • Ulisse Stefanelli
Open Access


Carbon nanotubes are modeled as point configurations and investigated by minimizing configurational energies including two- and three-body interactions. Optimal configurations are identified with local minima and their fine geometry is fully characterized in terms of lower-dimensional problems. Under moderate tension, we prove the existence of periodic local minimizers, which indeed validates the so-called Cauchy–Born rule in this setting.



Open access funding provided by Austrian Science Fund (FWF). M.F. acknowledges support from the Alexander von Humboldt Stiftung. E.M. acknowledges support from the Austrian Science Fund (FWF) project M 1733-N20. P. P. acknowledges support from the Austrian Science Fund (FWF) project P 29681, and from the Vienna Science and Technology Fund (WWTF), the City of Vienna, and the Berndorf Private Foundation through Project MA16-005. U.S. acknowledges support from the Austrian Science Fund (FWF) projects P 27052, I 2375, and F 65 and from the Vienna Science and Technology Fund (WWTF) through project MA14-009. The authors would like to acknowledge the kind hospitality of the Erwin Schrödinger International Institute for Mathematics and Physics, where part of this research was developed under the frame of the thematic program Nonlinear Flows.

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Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  • Manuel Friedrich
    • 1
    Email author
  • Edoardo Mainini
    • 2
  • Paolo Piovano
    • 3
  • Ulisse Stefanelli
    • 3
    • 4
  1. 1.Applied Mathematics MünsterUniversity of MünsterMünsterGermany
  2. 2.Dipartimento di Ingegneria Meccanica, Energetica, Gestionale e dei Trasporti (DIME)Università degli Studi di GenovaGenovaItaly
  3. 3.Faculty of MathematicsUniversity of ViennaViennaAustria
  4. 4.Istituto di Matematica Applicata e Tecnologie Informatiche “E. Magenes” - CNRPaviaItaly

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