# Characterization of optimal carbon nanotubes under stretching and validation of the Cauchy-Born rule

## TL;DR

This paper models carbon nanotubes as point configurations, analyzing their optimal structures under stretching and confirming the Cauchy-Born rule through mathematical proofs of periodic local minimizers.

## Contribution

It introduces a rigorous mathematical framework for characterizing optimal nanotube configurations and validates the Cauchy-Born rule under moderate tension conditions.

## Key findings

- Existence of periodic local minimizers under tension
- Validation of the Cauchy-Born rule in this context
- Full geometric characterization of optimal configurations

## Abstract

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.