An alternate mathematical model for single-wall carbon nanotubes
Nicolae Cotfas
Abstract
The positions of atoms forming a carbon nanotube are usually described by using a system of generators of the symmetry group. Each atomic position corresponds to an element of the set Z X 0,1,...,n X 0,1, where n is a natural number depending on the considered nanotube. We obtain an alternate rather different description by starting from a description of the honeycomb lattice in terms of Miller indices. In our mathematical model which is a factor space defined by an equivalence relation in the set (v0,v1,v2)∈ Z3 | v0+v1+v2∈ 0,1 the neighbours of an atomic position can be described in a simpler way, and the mathematical objects with geometric or physical significance have a simpler and more symmetric form.
Create a lesson
Related papers
Phase transitions in non-Hermitian spherical integrals
Pierre Bousseyroux, Marc Potters
Factorization method for a clamped obstacle from near-field measurements via a far-field transformation
General Ozochiawaeze, Isaac Harris
Asymmetric phase transitions in random noncommutative geometries
Benedek Bukor, Masoud Khalkhali, Samuel Kováčik et al.
A Cumulative Framework for Solid Deformation
Lev Steinberg
Classification of pairs of second-order Hamiltonian operators and hydrodynamic type systems in six components
Giorgio Gubbiotti, Lambertus Van Geemen, Pierandrea Vergallo
Reconstructability of Inverse Problems under Symmetry: Separating Structural, Effective, and Physical Upper Bounds
Isshin Arai