Stability of Objective Structures: General Criteria and Applications

TL;DR

This paper presents a comprehensive stability analysis framework for objective structures, extending crystal lattice concepts to more general particle systems, with practical algorithms and applications to carbon nanotubes.

Contribution

It introduces general stability criteria and computational methods for objective structures, broadening the scope beyond traditional crystal lattices.

Findings

Developed stability criteria based on symmetry group representations.

Provided a computational algorithm for stability testing.

Applied method to verify stability of carbon nanotubes with chirality.

Abstract

We develop a general stability analysis for objective structures, which constitute a far reaching generalization of crystal lattice systems. We show that these particle systems, although in general neither periodic nor space filling, allow for the identification of stability constants in terms of representations of the underlying symmetry group and interaction potentials. Our main results provide general stability criteria and second order energy bounds for equilibrium configurations. In particular, a general computational algorithm to test objective structures for their stability is derived. By way of example we show that our method can be applied to verify the stability of carbon nanotubes with chirality.