Elastic Theory of Defects in Toroidal Crystals
Abstract
We report a comprehensive analysis of the ground state properties of axisymmetric toroidal crystals based on the elastic theory of defects on curved substrates. The ground state is analyzed as a function of the aspect ratio of the torus, which provides a non-local measure of the underlying Gaussian curvature, and the ratio of the defect core-energy to the Young modulus. Several structural features are discussed,including a spectacular example of curvature-driven amorphization in the limit of the aspect ratio approaching one. The outcome of the elastic theory is then compared with the results of a numerical study of a system of point-like particles constrained on the surface of a torus and interacting via a short range potential.
Cite
@article{arxiv.0807.4538,
title = {Elastic Theory of Defects in Toroidal Crystals},
author = {Luca Giomi and Mark J. Bowick},
journal= {arXiv preprint arXiv:0807.4538},
year = {2008}
}
Comments
24 pages, 24 figures