Atomic to continuum passage for nanotubes. Part II: error estimates

Danny El Kass (1) , Régis Monneau (2)

1 Mathematics Department
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

We consider deformations in $\R^3$ of an infinite general nanotube of atoms where each atom interacts with all the other through a two-body potential. We compute the effect of an external force applied to the nanotube. At the equilibrium, the positions of the atoms satisfy an Euler-Lagrange equation. For large classes of potentials (including Lennard-Jones potential) and under suitable stability assumptions, we prove that every solution is well approximated by the solution of a continuum model involving stretching and twisting, but no bending. We establish an error estimate between the discrete and the continuous solution based on a Saint-Venant principle that the reader can find in the companion paper (part I)

Domaines: Equations aux dérivées partielles [math.AP]

Danny El Kass, Régis Monneau. Atomic to continuum passage for nanotubes. Part II: error estimates. 2012. ⟨hal-00731845⟩